url
stringlengths 6
1.61k
| fetch_time
int64 1,368,856,904B
1,726,893,854B
| content_mime_type
stringclasses 3
values | warc_filename
stringlengths 108
138
| warc_record_offset
int32 9.6k
1.74B
| warc_record_length
int32 664
793k
| text
stringlengths 45
1.04M
| token_count
int32 22
711k
| char_count
int32 45
1.04M
| metadata
stringlengths 439
443
| score
float64 2.52
5.09
| int_score
int64 3
5
| crawl
stringclasses 93
values | snapshot_type
stringclasses 2
values | language
stringclasses 1
value | language_score
float64 0.06
1
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
http://math.furman.edu/~jpoole/euclidselements/Translation/prop23/prop23~1.htm
| 1,542,128,432,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-47/segments/1542039741324.15/warc/CC-MAIN-20181113153141-20181113175141-00145.warc.gz
| 220,863,533
| 1,342
|
THE ELEMENTS Book I Proposition 23 Let AB be the given straight line, A be the given point on it, and the angle DCE be the given rectilineal angle; thus it is necessary to construct a rectilineal angle equal to the rectilineal angle DCE on the straight line AB at the point A. Return to Propositions Next Page
| 78
| 314
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.734375
| 3
|
CC-MAIN-2018-47
|
longest
|
en
| 0.629665
|
https://answers.yahoo.com/question/index?qid=20110907133328AA73vFc
| 1,571,307,374,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-43/segments/1570986673538.21/warc/CC-MAIN-20191017095726-20191017123226-00527.warc.gz
| 363,215,623
| 20,425
|
# Help with math cubic feet problem?
This is the problem and I honestly don't know what to do. The cubit is an ancient unit. Its length equals six palms. (A palm varies from 2.5 to 3.5 inches depending on the individual.) We are told Noah's ark was 300 cubits long, 50 cubits wide, and 30 cubits high. Estimate the volume of the ark (in cubic... show more This is the problem and I honestly don't know what to do.
The cubit is an ancient unit. Its length equals six palms. (A palm varies from 2.5 to 3.5 inches depending on the individual.) We are told Noah's ark was 300 cubits long, 50 cubits wide, and 30 cubits high. Estimate the volume of the ark (in cubic feet). Assume the ark has a shoe-box shape and that 1 palm = 3.50 inch.
| 200
| 735
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.546875
| 4
|
CC-MAIN-2019-43
|
latest
|
en
| 0.942722
|
https://istopdeath.com/solve-by-factoring-6-x7-x3/
| 1,670,443,951,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-49/segments/1669446711218.21/warc/CC-MAIN-20221207185519-20221207215519-00780.warc.gz
| 357,442,925
| 17,861
|
# Solve by Factoring 6/x=7/(x+3)
Move to the left side of the equation by subtracting it from both sides.
Simplify .
To write as a fraction with a common denominator, multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Multiply and .
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify the numerator.
Apply the distributive property.
Multiply by .
Subtract from .
Simplify with factoring out.
Factor out of .
Rewrite as .
Factor out of .
Simplify the expression.
Rewrite as .
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Multiply and .
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify the numerator.
Apply the distributive property.
Multiply by .
Subtract from .
Simplify with factoring out.
Factor out of .
Rewrite as .
Factor out of .
Simplify the expression.
Rewrite as .
Move the negative in front of the fraction.
Find the LCD of the terms in the equation.
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Since contain both numbers and variables, there are four steps to find the LCM. Find LCM for the numeric, variable, and compound variable parts. Then, multiply them all together.
Steps to find the LCM for are:
1. Find the LCM for the numeric part .
2. Find the LCM for the variable part .
3. Find the LCM for the compound variable part .
4. Multiply each LCM together.
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
The factor for is itself.
occurs time.
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
The factor for is itself.
occurs time.
The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
The Least Common Multiple of some numbers is the smallest number that the numbers are factors of.
Multiply each term by and simplify.
Multiply each term in by in order to remove all the denominators from the equation.
Simplify .
Cancel the common factor of .
Move the leading negative in into the numerator.
Cancel the common factor.
Rewrite the expression.
Apply the distributive property.
Multiply by .
Simplify .
Apply the distributive property.
Simplify the expression.
Multiply by .
Move to the left of .
Multiply by .
Solve the equation.
Subtract from both sides of the equation.
Multiply each term in by
Multiply each term in by .
Multiply .
Multiply by .
Multiply by .
Multiply by .
Solve by Factoring 6/x=7/(x+3)
| 708
| 3,241
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.4375
| 4
|
CC-MAIN-2022-49
|
latest
|
en
| 0.921033
|
http://cboard.cprogramming.com/c-programming/111204-linked-list-tutorial-sample-code-question-printable-thread.html
| 1,475,266,941,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2016-40/segments/1474738662336.11/warc/CC-MAIN-20160924173742-00279-ip-10-143-35-109.ec2.internal.warc.gz
| 43,116,577
| 3,652
|
# Linked List Tutorial sample code question
• 01-16-2009
Kalleos
Linked List Tutorial sample code question
Hello everybody,
http://www.cprogramming.com/tutorial/c/lesson15.html
in the sample code of that Tutorial, which shows how one can traverse a linked list, there are some things I don't understand. Here is the part of the code. I've added a comment to the line I don't understand:
Code:
```/*...*/ struct node { int x; struct node *next; }; int main() { /* This won't change, or we would lose the list in memory */ struct node *root; /* This will point to each node as it traverses the list */ struct node *conductor; root = malloc( sizeof(struct node) ); root->next = 0; /* QUESTION: Why giving root->next a null pointer? */ root->x = 12; conductor = root; if ( conductor != 0 ) { while ( conductor->next != 0) { conductor = conductor->next; } } /*...*/ }```
Why is root->next set to a null pointer? Isn't root->next a null pointer by default?
Furthermore, there are 2 things I don't understand:
1. What is the use for "if ( conductor != 0 )" when they just wrote conductor = root before?
2. What is the goal of "while ( conductor->next != 0)"? If you just wrote "root->next = 0; conductor = root;" then is "conductor->next" in any case also 0! So the checking "while ( conductor->next != 0)" doesn't make any sense, because it's always 0.
• 01-16-2009
yougene
1.
if ( conductor != 0 )
is a roundabout way of checking if malloc was able to allocate memory to root. If no memory was allocated malloc returns a NULL pointer address.
2.
The code at hand is going to be part of a more complete linked list agorithm. The conditional will check if the loop has reached the end of a linked list. As it stands now, it doesn't do anything.
• 01-16-2009
matsp
Quote:
Originally Posted by yougene
1.
if ( conductor != 0 )
is a roundabout way of checking if malloc was able to allocate memory to root. If no memory was allocated malloc returns a NULL pointer address.
I agree with that - however the code is then broken, as it accesses root->next and root->x before checking that the pointer is non-null. Bad coding.
Edit: thinking about it, it probably makes more sense with Yougene's comment #2: This comes from a bigger project, and that check is essentially "Is the list completely empty".
--
Mats
| 612
| 2,400
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.59375
| 3
|
CC-MAIN-2016-40
|
latest
|
en
| 0.880264
|
http://forums.wolfram.com/mathgroup/archive/1999/Jul/msg00139.html
| 1,582,434,617,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-10/segments/1581875145746.24/warc/CC-MAIN-20200223032129-20200223062129-00414.warc.gz
| 59,864,880
| 7,592
|
RE: Simplifying constants
• To: mathgroup at smc.vnet.net
• Subject: [mg18544] RE: [mg18489] Simplifying constants
• From: hanssen at zeiss.de
• Date: Sat, 10 Jul 1999 02:18:44 -0400
• Sender: owner-wri-mathgroup at wolfram.com
```> Hi,
>
> I am working with some annoyingly long equations that I want to simplify
> by including one set of parameters in a constant (or function) A, and
> another in B and so on.
>
> You can easily do:
>
> A = b+c+d+e
>
> but what I want to do is the reverse:
>
> b+c+d+e = A
>
> and use this information to reduce the equations. Does anybody know how
> to do this?
>
Hi, Morten
Use pattern matching like this
(b+c+d+e+f)*(1+a^2) /. b+c+d+f-> A
which gives you
(1 + a^2)*(A + e)
The other way around:
%/. A -> b+c+d+e
gives you
(1 + a^2)*(b + c + d + 2*e)
Another question is, how to find common subexpressions in lengthy expressions.
Here you might use Optimize.m, which is available from MathSource (in two flavours).
Some hand work still has to be done after this, but it gives you good hints.
Regards
| 327
| 1,051
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.734375
| 3
|
CC-MAIN-2020-10
|
longest
|
en
| 0.88713
|
https://www.quizzes.cc/metric/percentof.php?percent=4340&of=474
| 1,600,780,982,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-40/segments/1600400206133.46/warc/CC-MAIN-20200922125920-20200922155920-00083.warc.gz
| 978,369,350
| 4,389
|
#### What is 4340 percent of 474?
How much is 4340 percent of 474? Use the calculator below to calculate a percentage, either as a percentage of a number, such as 4340% of 474 or the percentage of 2 numbers. Change the numbers to calculate different amounts. Simply type into the input boxes and the answer will update.
## 4340% of 474 = 20571.6
Calculate another percentage below. Type into inputs
Find number based on percentage
percent of
Find percentage based on 2 numbers
divided by
Calculating four thousand, three hundred and fourty of four hundred and seventy-four How to calculate 4340% of 474? Simply divide the percent by 100 and multiply by the number. For example, 4340 /100 x 474 = 20571.6 or 43.4 x 474 = 20571.6
#### How much is 4340 percent of the following numbers?
4340% of 474.01 = 2057203.4 4340% of 474.02 = 2057246.8 4340% of 474.03 = 2057290.2 4340% of 474.04 = 2057333.6 4340% of 474.05 = 2057377 4340% of 474.06 = 2057420.4 4340% of 474.07 = 2057463.8 4340% of 474.08 = 2057507.2 4340% of 474.09 = 2057550.6 4340% of 474.1 = 2057594 4340% of 474.11 = 2057637.4 4340% of 474.12 = 2057680.8 4340% of 474.13 = 2057724.2 4340% of 474.14 = 2057767.6 4340% of 474.15 = 2057811 4340% of 474.16 = 2057854.4 4340% of 474.17 = 2057897.8 4340% of 474.18 = 2057941.2 4340% of 474.19 = 2057984.6 4340% of 474.2 = 2058028 4340% of 474.21 = 2058071.4 4340% of 474.22 = 2058114.8 4340% of 474.23 = 2058158.2 4340% of 474.24 = 2058201.6 4340% of 474.25 = 2058245
4340% of 474.26 = 2058288.4 4340% of 474.27 = 2058331.8 4340% of 474.28 = 2058375.2 4340% of 474.29 = 2058418.6 4340% of 474.3 = 2058462 4340% of 474.31 = 2058505.4 4340% of 474.32 = 2058548.8 4340% of 474.33 = 2058592.2 4340% of 474.34 = 2058635.6 4340% of 474.35 = 2058679 4340% of 474.36 = 2058722.4 4340% of 474.37 = 2058765.8 4340% of 474.38 = 2058809.2 4340% of 474.39 = 2058852.6 4340% of 474.4 = 2058896 4340% of 474.41 = 2058939.4 4340% of 474.42 = 2058982.8 4340% of 474.43 = 2059026.2 4340% of 474.44 = 2059069.6 4340% of 474.45 = 2059113 4340% of 474.46 = 2059156.4 4340% of 474.47 = 2059199.8 4340% of 474.48 = 2059243.2 4340% of 474.49 = 2059286.6 4340% of 474.5 = 2059330
4340% of 474.51 = 2059373.4 4340% of 474.52 = 2059416.8 4340% of 474.53 = 2059460.2 4340% of 474.54 = 2059503.6 4340% of 474.55 = 2059547 4340% of 474.56 = 2059590.4 4340% of 474.57 = 2059633.8 4340% of 474.58 = 2059677.2 4340% of 474.59 = 2059720.6 4340% of 474.6 = 2059764 4340% of 474.61 = 2059807.4 4340% of 474.62 = 2059850.8 4340% of 474.63 = 2059894.2 4340% of 474.64 = 2059937.6 4340% of 474.65 = 2059981 4340% of 474.66 = 2060024.4 4340% of 474.67 = 2060067.8 4340% of 474.68 = 2060111.2 4340% of 474.69 = 2060154.6 4340% of 474.7 = 2060198 4340% of 474.71 = 2060241.4 4340% of 474.72 = 2060284.8 4340% of 474.73 = 2060328.2 4340% of 474.74 = 2060371.6 4340% of 474.75 = 2060415
4340% of 474.76 = 2060458.4 4340% of 474.77 = 2060501.8 4340% of 474.78 = 2060545.2 4340% of 474.79 = 2060588.6 4340% of 474.8 = 2060632 4340% of 474.81 = 2060675.4 4340% of 474.82 = 2060718.8 4340% of 474.83 = 2060762.2 4340% of 474.84 = 2060805.6 4340% of 474.85 = 2060849 4340% of 474.86 = 2060892.4 4340% of 474.87 = 2060935.8 4340% of 474.88 = 2060979.2 4340% of 474.89 = 2061022.6 4340% of 474.9 = 2061066 4340% of 474.91 = 2061109.4 4340% of 474.92 = 2061152.8 4340% of 474.93 = 2061196.2 4340% of 474.94 = 2061239.6 4340% of 474.95 = 2061283 4340% of 474.96 = 2061326.4 4340% of 474.97 = 2061369.8 4340% of 474.98 = 2061413.2 4340% of 474.99 = 2061456.6 4340% of 475 = 2061500
1% of 474 = 4.74 2% of 474 = 9.48 3% of 474 = 14.22 4% of 474 = 18.96 5% of 474 = 23.7 6% of 474 = 28.44 7% of 474 = 33.18 8% of 474 = 37.92 9% of 474 = 42.66 10% of 474 = 47.4 11% of 474 = 52.14 12% of 474 = 56.88 13% of 474 = 61.62 14% of 474 = 66.36 15% of 474 = 71.1 16% of 474 = 75.84 17% of 474 = 80.58 18% of 474 = 85.32 19% of 474 = 90.06 20% of 474 = 94.8 21% of 474 = 99.54 22% of 474 = 104.28 23% of 474 = 109.02 24% of 474 = 113.76 25% of 474 = 118.5
26% of 474 = 123.24 27% of 474 = 127.98 28% of 474 = 132.72 29% of 474 = 137.46 30% of 474 = 142.2 31% of 474 = 146.94 32% of 474 = 151.68 33% of 474 = 156.42 34% of 474 = 161.16 35% of 474 = 165.9 36% of 474 = 170.64 37% of 474 = 175.38 38% of 474 = 180.12 39% of 474 = 184.86 40% of 474 = 189.6 41% of 474 = 194.34 42% of 474 = 199.08 43% of 474 = 203.82 44% of 474 = 208.56 45% of 474 = 213.3 46% of 474 = 218.04 47% of 474 = 222.78 48% of 474 = 227.52 49% of 474 = 232.26 50% of 474 = 237
51% of 474 = 241.74 52% of 474 = 246.48 53% of 474 = 251.22 54% of 474 = 255.96 55% of 474 = 260.7 56% of 474 = 265.44 57% of 474 = 270.18 58% of 474 = 274.92 59% of 474 = 279.66 60% of 474 = 284.4 61% of 474 = 289.14 62% of 474 = 293.88 63% of 474 = 298.62 64% of 474 = 303.36 65% of 474 = 308.1 66% of 474 = 312.84 67% of 474 = 317.58 68% of 474 = 322.32 69% of 474 = 327.06 70% of 474 = 331.8 71% of 474 = 336.54 72% of 474 = 341.28 73% of 474 = 346.02 74% of 474 = 350.76 75% of 474 = 355.5
76% of 474 = 360.24 77% of 474 = 364.98 78% of 474 = 369.72 79% of 474 = 374.46 80% of 474 = 379.2 81% of 474 = 383.94 82% of 474 = 388.68 83% of 474 = 393.42 84% of 474 = 398.16 85% of 474 = 402.9 86% of 474 = 407.64 87% of 474 = 412.38 88% of 474 = 417.12 89% of 474 = 421.86 90% of 474 = 426.6 91% of 474 = 431.34 92% of 474 = 436.08 93% of 474 = 440.82 94% of 474 = 445.56 95% of 474 = 450.3 96% of 474 = 455.04 97% of 474 = 459.78 98% of 474 = 464.52 99% of 474 = 469.26 100% of 474 = 474
| 2,868
| 5,489
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.96875
| 4
|
CC-MAIN-2020-40
|
latest
|
en
| 0.829979
|
https://codebase64.org/doku.php?id=base:8bit_logarithm_table_generator_routine&rev=1429237808&do=diff
| 1,571,833,448,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-43/segments/1570987833766.94/warc/CC-MAIN-20191023122219-20191023145719-00168.warc.gz
| 436,564,604
| 4,733
|
### Site Tools
base:8bit_logarithm_table_generator_routine
# Differences
This shows you the differences between two versions of the page.
— base:8bit_logarithm_table_generator_routine [2015-04-17 04:30] (current) Line 1: Line 1: + ====== 8bit log table generator ====== + Logarithm tables are often used in C64 and for much the same reason they were originally invented, that is exploiting the same identities your old slide rule uses for transforming multiplication and division into addition and subtraction:<code>lg(x*y) = lg(x) + lg(y) + lg(x/y) = lg(x) - lg(y)Typically they'd be used together with an exponentiation table (to get the approximate result), with the exponent built-in to another table (such as in my atan routine), or on their own for comparison purposes (as for dot products and the like.) + + Yet they're also poorly compressible so a generator routine comes in handy. This version is an eight-bit implementation of the classic shift-add algorithm where you repeatedly try to factorize (x²-1)/x² factors out of a normalized number, with the factors' logarithms stored in a pre-calculated table. An alternative would be to use BASIC to get a much smaller, more precise, and frustratingly slow generator. But this seems like a fair tradeoff between size, speed and precision (saving some 145 bytes or so after compression.) + + Note that the result is scaled to fit in eight-bits. This can most naturally be viewed a base-two logarithm in 3:5 fixed-point. + <code>table = \$c000 ;page aligned + + seed .byte \$00,\$00 + .byte \$02,\$05 + .byte \$0c,\$1f + + reduce pla + adc seed,y + sec + next pha + ldy #5 + txa + sta shift+4 + + shift ror shift+4 + sbx #\$00 + bcs reduce + tax + dey + bpl shift + + pla + store sbc #\$1f + sta table + lsr store+3 + bcc store + + enter dec *+4 + lda #\$00 + sta store+3 + asl a + tax + lda #\$00 + bcs next + + ; sta table ;do whatever makes most sense for log(0) + rts
| 523
| 1,939
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.890625
| 3
|
CC-MAIN-2019-43
|
longest
|
en
| 0.854476
|
https://www.learningoutofthebox.org/product/p4-problem-sums-guide-for-parents-vol-1-2-starter-kit/
| 1,643,265,477,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-05/segments/1642320305141.20/warc/CC-MAIN-20220127042833-20220127072833-00206.warc.gz
| 907,883,792
| 48,781
|
Select Page
Sale!
# P4. Problem Sums Guide for Parents Volume 1 & 2 (Quick Starter Kit for CA1, SA1, CA2 & SA2)
\$55.10
Here are 17 Must-know problem sums types for your P4 child. Does your child know all of these before sitting for his next exam? Help him to master them now.
Purchase this product now and earn 110 Points!
SKU: P4V1V2 Categories: , ,
## Description
Here is our new volume for – “Problem Sums Guide for Parents – P4 Special Edition“.
Why do we create this?
There are so many math books out there.
So what makes this different?
As you know, most assessment books just provide your child with the questions in a topical format. But he is tested problem sums types in tests/ exams. (Something that 8 out of 10 parents we asked are unaware.)
While children can make out these solutions on the spot, 8 to 9 out of 10 children won’t understand the type of problem sum that is being tested.
As a result, they just solve the questions as individual questions.
Then, they move on to the next one, treating it as a new question again.
This old method of solving is too slow. (Lots of precious time wasted, resulting in not being able to complete the paper)
The good news is there is a faster and more effective way.
While the way the questions always changes, the types of problem sums are fixed.
So we specially designed this book just for our P4 children and parents.
This proven study method has worked for hundreds of our students. Even our parents, who used to find teaching math hard, told us that they finally understood how to solve the problem sums the easy way.
Here are the 17 Types of Problem Sums with more Advanced levels (your child should know all these by P4)
1. Part whole ( 2 or 3 identities)
2. More than / less than
3. More than / less than (make part to whole)
4. Multiply / Divide (1 – step problem)
5. Fractions problem (part – whole)’
6. Intervals
7. Guess and Check
8. Matchstick method
9. Simultaneous
10. Guess A Number
11. Listing
12. Same One
13. Same Total
14. Same Difference
15. Equal After Change
16. Working Backwards
17. 2 ifs
How can you get hold of this book?
If you know your child can start benefiting by learning math in a smarter way, you can order this math resource book from us.
All you need to do now is click on the “Add to Cart” button below.
Purchase this product now and earn 110 Points!
| 594
| 2,370
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.84375
| 4
|
CC-MAIN-2022-05
|
latest
|
en
| 0.906084
|
https://oeis.org/A212028/internal
| 1,638,857,353,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-49/segments/1637964363336.93/warc/CC-MAIN-20211207045002-20211207075002-00337.warc.gz
| 512,962,922
| 3,354
|
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.
Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A212028 G.f. satisfies: A(x) = 1 + x*A(x*A(x)^3)^2. 1
%I
%S 1,1,2,11,74,635,6296,70268,864106,11546531,165996792,2548556963,
%T 41546769324,715850868468,12986529841038,247255748839532,
%U 4926870211273246,102495266879754087,2221254395951869988,50049980203162990978,1170440788530570387644
%N G.f. satisfies: A(x) = 1 + x*A(x*A(x)^3)^2.
%e G.f.: A(x) = 1 + x + 2*x^2 + 11*x^3 + 74*x^4 + 635*x^5 + 6296*x^6 +...
%e Related expansions:
%e A(x)^2 = 1 + 2*x + 5*x^2 + 26*x^3 + 174*x^4 + 1462*x^5 + 14279*x^6 +...
%e A(x)^3 = 1 + 3*x + 9*x^2 + 46*x^3 + 306*x^4 + 2526*x^5 + 24311*x^6 +...
%e A(x*A(x)^3) = 1 + x + 5*x^2 + 32*x^3 + 273*x^4 + 2715*x^5 + 30542*x^6 + 379200*x^7 + 5117211*x^8 + 74266646*x^9 + 1150267802*x^10 +...
%o (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A^3, x, x*A^3)); polcoeff(A, n)}
%o for(n=0,30,print1(a(n),", "))
%Y Cf. A143501, A143508, A212029.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Apr 27 2012
Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.
Last modified December 6 22:42 EST 2021. Contains 349567 sequences. (Running on oeis4.)
| 689
| 1,741
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.71875
| 4
|
CC-MAIN-2021-49
|
latest
|
en
| 0.58379
|
https://www.sarthaks.com/1051400/find-the-particular-solution-of-the-differential-equation-dy-dx-1-x-y-xy-given-that-y-0-when-x
| 1,669,574,808,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-49/segments/1669446710417.25/warc/CC-MAIN-20221127173917-20221127203917-00837.warc.gz
| 1,061,319,845
| 14,471
|
# Find the particular solution of the differential equation dy/dx = 1 + x + y + xy given that y = 0 when x = 1.
965 views
closed
Find the particular solution of the differential equation $\frac{dy}{dx}$ = 1 + x + y + xy given that y = 0 when x = 1.
+1 vote
by (35.4k points)
selected by
Given differential equation is $\frac{dy}{dx}$ = 1 + x + y + xy
| 114
| 357
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.09375
| 3
|
CC-MAIN-2022-49
|
latest
|
en
| 0.860833
|
https://www.physicsforums.com/threads/geometry-problem-calculating-curve-coordinates-from-versines.718163/
| 1,508,630,728,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-43/segments/1508187824899.75/warc/CC-MAIN-20171021224608-20171022004608-00660.warc.gz
| 1,010,545,679
| 18,581
|
# Geometry problem - calculating curve coordinates from versines
1. Oct 22, 2013
### banksie
Hi,
I was wondering if anyone can help me. I don’t have a homework problem, but a problem I have encountered at work. I am a mechanical engineer working in the railway industry and I am struggling with a problem of reconstructing the vertical geometry of a rail in terms of height and distance along the rail.
The rail is measured using a chord measuring system, with versines taken at two points along the chord:- a point halfway along the chord and a point between the mid-point and the end. The measuring chord is moved along the rail at equally spaced intervals and the versine pairs measured at each point. The chord length is an integer multiple of the measuring interval.
Currently the process used to obtain the original rail position from the versine information uses the centre versine only. However this means that wavelengths equal to half the chord length cannot be reconstructed, hence the requirement to somehow incorporate the information encoded in the second versine measurement. The current method uses a simple geometric relationship to calculate the height of the rail at one end of the chord, given initial starting values of zero (i.e. the other end of the chord is at zero). I don't see how I can use this method and incorporate the second versine though, and i am struggling on how to approach this problem. Can anyone help point me in the right direction?!
I hope that I have defined the problem clearly enough, if not please do ask if there is any more information I can provide.
Many thanks
2. Oct 22, 2013
### Staff: Mentor
Welcome to PF!
Can you draw a picture of what you're describing and what you want to compute?
http://en.wikipedia.org/wiki/Versine
3. Oct 22, 2013
### banksie
OK,
So the first picture hopefully describes what's going on. We have a profile P on which we lay our chord AB at two points, we then measure the offset from the chord to the profile at two points C and D. These offsets are termed the versines, which I've labelled u and v. This process is repeated along the profile - the chord is advanced along the profile by some distance and the versines are measured again. The second picture tries to illustrate this for the first three points. Note that this process would continue along the profile beyond the point where A is at B
So, we know the chord length AB, the sub chord lengths, AC, CD and DB, and the versines u and v. Given a number of these versine measurements collected along the length of the profile, how can we reconstruct the profile P from this information? In particular we need to utilize both u and v, as I mentioned in my first post...
Many thanks
Banksie
#### Attached Files:
File size:
7.9 KB
Views:
239
• ###### screenshot.586.jpeg
File size:
8.4 KB
Views:
147
4. Oct 22, 2013
### Staff: Mentor
I dont have an answer as it seems that there's not enough info yet.
You mentioned that the profile is advanced some distance each time. Do you know this distance?
Also shouldn't the versines be perpendicular to the chord?
Lastly, do you know the angle of the profile at each measurement?
Last edited: Oct 22, 2013
5. Oct 22, 2013
### banksie
yes you're right the versines are measured perpendicular to the chord. I sketched that up in Word and just couldn't get the lines in the right place!
The chord is advanced along the profile at regular intervals. Lets say that the interval is 1m and the chord length is 20m, the distance AC is 7m and distance AD is 10m. The angle is unknown.
You would assume that the profile starts at zero and the remainder of the profile would be relative to that.
6. Oct 22, 2013
### banksie
Also, as we are talking about railway track geometry, the versine measurements are small compared to the radius of the curve so I think we can neglect the angle of the versine measurements relative to the chord.
7. Oct 23, 2013
| 890
| 3,952
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.671875
| 4
|
CC-MAIN-2017-43
|
longest
|
en
| 0.936038
|
https://resources.wolframcloud.com/FormulaRepository/resources/Damped-Driven-Spring-Harmonic-Oscillator
| 1,721,482,113,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-30/segments/1720763515164.46/warc/CC-MAIN-20240720113754-20240720143754-00790.warc.gz
| 427,876,590
| 12,509
|
# Damped Driven Spring Harmonic Oscillator
A spring harmonic oscillator is a spring that, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement. A damped driven spring harmonic oscillator experiences a frictional force (damping) proportional to the velocity, as well as an external time-dependent force driving the system.
The angular frequency for a damped driven harmonic oscillator equals the driving angular frequency as well as 2\[Pi] times the frequency. The frequency equals the reciprocal of the period. The amplitude is directly proportional to the driving amplitude, and maximizes when the natural angular frequency equals the driving frequency. The damping ratio decreases the amplitude. The phase depends on the difference between the natural angular frequency and driving frequency, adjusted by the damping ratio. The natural angular frequency equals the square root of the ratio between the spring constant and the mass.
## Formula
symbol description physical quantity
ω angular frequency "AngularFrequency"
ωd driving angular frequency "AngularFrequency"
ω0 natural angular frequency "AngularFrequency"
k spring constant "SpringConstant"
m mass "Mass"
f frequency "Frequency"
T period "Period"
A amplitude "Unitless"
ζ damping ratio "Unitless"
ϕ phase "Angle"
## Examples
Get the resource:
In[1]:=
Out[1]=
Get the formula:
In[2]:=
Out[2]=
Use some values:
In[3]:=
Out[3]=
| 294
| 1,458
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.796875
| 3
|
CC-MAIN-2024-30
|
latest
|
en
| 0.848965
|
https://physics.stackexchange.com/questions/461952/derivation-of-the-dynamical-matrix
| 1,580,299,108,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-05/segments/1579251796127.92/warc/CC-MAIN-20200129102701-20200129132701-00414.warc.gz
| 590,401,944
| 29,417
|
# Derivation of the dynamical matrix
I am following a derivation of the dynamical matrix given at http://physik.uni-graz.at/~pep/Lehre/PP/DynMat.pdf. Here T and W are kinetic and potential energies.
$$T=\sum_{n\alpha i}\frac{M_{\alpha}}{2}\dot{s}_{n\alpha i}^{2}$$
$$W = \frac{1}{2}\sum_{n\alpha i}\sum_{n'\alpha' i'} \Phi_{n\alpha i}^{n'\alpha' i'} s_{n\alpha i} s_{n'\alpha' i'}$$
What I get after plugging T and W to the Euler-Lagrange equation ( $$\frac{d}{dt}\frac{\partial L}{\partial \dot{s}_{n\alpha i}} -\frac{\partial L}{\partial s_{n\alpha i}} = 0$$ ) is,
$$\sum_{n\alpha i}M_{\alpha}\ddot{s}_{n\alpha i} = -\sum_{n'\alpha' i'} \Phi_{n\alpha i}^{n'\alpha' i'} s_{n\alpha i}$$
But in the derivation, he has got, $$M_{\alpha}\ddot{s}_{n\alpha i} = -\sum_{n'\alpha' i'} \Phi_{n\alpha i}^{n'\alpha' i'} s_{n\alpha i}$$.
I don't understand how he got rid of the summation sign on the left hand side.
$$\frac{\partial}{\partial \dot{s}_{n'\alpha 'i'}} \sum_{n\alpha i}\frac{M_{\alpha}}{2}\dot{s}_{n\alpha i}^{2} = M_{\alpha '}\dot{s}_{n'\alpha 'i'}$$
| 408
| 1,063
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 6, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.28125
| 3
|
CC-MAIN-2020-05
|
latest
|
en
| 0.493567
|
https://splessons.com/lesson/average-practice-set-2/
| 1,726,226,843,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-38/segments/1725700651513.89/warc/CC-MAIN-20240913101949-20240913131949-00261.warc.gz
| 503,025,962
| 15,552
|
Average Practice Set 2
Home > > Tutorial
5 Steps - 3 Clicks
Average Practice Set 2
Introduction
Average is a straight- forward concept and it can be solved easily by equal distribution method. Average is the sum of all the elements in a given data set divided by the total number of elements in the data set. The most commonly denoted term for average is Arithmetic Mean, simply termed as mean. The article Average Practice Set 2 very useful for for different competitive examinations like RRB ALP/Technical Exams/Junior Engineer Recruitment Exams, SSC, IBPS PO Exams and etc.
The Average (arithmetic mean) of a group or set of N numbers is defined as the sum of those numbers divided by N. Here N is the number of values or observations in a set
Average = $\frac {Sum of Numbers / Values}{Numbers of Values / Observation}$
A = $\frac {Sum}{N}$ Or Sum = N * Average
Quiz
Q1. The average age of a family of 6 members is 22 years. If the age of the youngest member be 7 years, then what was the average age of the family at the birth of the youngest member?
A. 15 B. 18 C. 28 D. 24
Explanation: Total age of all members = $6 \times 22$= 132 years
7 years ago, total sum of ages = 132 – $(6 \times 7)$ = 90 years
But at that time there were 5 members in the family
Average at that time = $\frac {90} {5}$ = 18 years
Q2. A batsman in his 17th innings makes a score of 85 and thereby increases his average by 3. What is his average after 17 innings?
A. 30 B. 37 C. 40 D. 45
Explanation: Let the average after 16th innings be a
then total score after 17th innings $\Rightarrow$ 16a + 85 = 17 (a + 3)
a = 85 - 51 = 34
Average after 17 innings = a + 3 = 34 + 3 = 37
Q3. There were 35 students in a hostel. If the number of students increases by 7, the expenses of the mess increase by Rs 42 per day while the average expenditure per head diminishes by Rs 1. Find the original expenditure of the mess?
A. 450 B. 420 C. 430 D. 410
Explanation: Suppose the average expenditure was Rs a.
Then total expenditure = 35 a
When 7 more students join the mess, total expenditure = 35a + 42
Now, the average expenditure= $\frac {(35a + 42)}{(35 + 7)}$
Now, we have $\frac {(35a + 42)}{42}$ = (a – 1)
or, 35a + 42 = 42a – 42
7a = 84
a = 12
Q4. The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of the remaining 55% is:
A. 51.4 B. 52.6 C. 56.1 D. 55.3
Explanation: Let the required mean score be a
Then, $20 \times 80 + 25 \times 31 + 55 \times a = 52 \times 100$
1600 + 775 + 55a = 5200
55a = 2825
a = 51.4
Q5. The average of a non-zero number and its square is 5 times the number. The number is:
A. 0 , 7 B. 0 , 6 C. 5 , 7 D. 0 , 9
Explanation: Let the number be x.
Then, $\frac {(x + {x}^{2})}{2} = 5x$
${x}^{2} – 9x$ = 0
$x (x – 9)$ = 0
$x = 0 or x$ = 9.
Q1. If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of ${a}^{2}, {b}^{2}, {c}^{2}$is:
A. 3 M x M B. 3 M C. 9 M D. 9 M x M
Explanation: We have :
$\frac {(a + b + c)}{3}$ = M or (a + b + c) = 3 M.
Now, ${(a + b + c)}^{2}$ = ${(3 M)}^{2} = {9 M}^{2}$
${a}^{2} + {b}^{2} + {c}^{2} + 2 (ab + bc + ca) = {9 M}^{2}$
${a}^{2} + {b}^{2} + {c}^{2} = {9 M}^{2}$
Required mean = $\frac {({a}^{2} + {b}^{2} + {c}^{2})} {3}$ = $\frac {{9 M}^{2}} {3} = {3 M}^ {2}$
Q2. The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one them weighing 65 kg. What might be the weight of the new person?
A. 65 kg B. 70 kg C. 85 kg D. 92 kg
Explanation: Total weight increased = $(8 \times 2.5) kg = 20 kg$
Weight of new person = $(65 + 20) kg = 85 kg$
Q3. The average age of the boys in a class is 16 years and that of the girls is 15 years. The average age for the whole class is:
A. 15 B. 16 C. 17 D. Data inadequate
Explanation: Clearly, to find the average, we ought to know the number of boys, girls or students in the class, neither of which has been given
So, the data provided is inadequate
Q4. A cricketer has completed 10 innings and his average is 21.5 runs. How many runs must he make in his next innings so as to raise his average to 24?
A. 44 B. 45 C. 49 D. 48
Explanation: Total of 10 innings = $21.5 \times 10$ = 215
Suppose he needs a score of a in ${11}^{th}$ innings; then average in 11 innings = $\frac {(215 + a)}{11}$= 24
or, a = 264 - 215 = 49
Q5. Find the average of 13 + 26 + 39 + …….. + 260
A. 136.5 B. 136 C. 137 D. 135
Explanation: $\frac {13 (1 + 2 + 3 + ..... + 20)}{20 \times 2}$
$\frac {13 \times 20 \times 21}{40}$
$\frac {5460}{40}$ = 136. 5
Q1. The average of six numbers is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers?
A. 4.2 B. 4.6 C. 5.1 D. 5.6
Explanation: Sum of the remaining two numbers = $(3.95 \times 6) – [(3.4 \times 2) + (3.85 \times 2)]$
= 23.70 – (6.8 + 7.7)
= 23.70 – 14.5 = 9.20
Average = $\frac {9.2}{2}$ = 4.6
Q2. The average salary of the entire staff in an office is Rs 120 per month. The average salary of officers is Rs 460 and that of non-officer is Rs 110. If the number of officers is 15, then find the number of non-officer in the office?
A. 450 B. 550 C. 510 D. 520
Explanation: Let the required number of non-officers = a
Then, $110a + 460 \times 15$ = 120 (15 + a)
or, 120a – 110a = $450 \times 15 – 120 \times 15$ = 15 (460 – 120)
or, 10a = $15 \times 340$
a = $15 \times 34$ = 510
Q3. Find the average of first 20 multiple of 7?
A. 71.5 B. 73.5 C. 75.2 D. 76.6
Explanation: Average = $\frac { 7 (1 + 2 + 3 + ……. + 20)}{20} = 7 \times 20 \times \frac {21} {20 \times 2} = 73.5$
Q4. The average of four consecutive ODD number is 28.Find the largest number.
A. 25 B. 31 C. 13 D. 27
Explanation: $\frac {x + (x + 2) + (x + 4) + (x + 6)}{4}$ = 28
4x +12 = $28 \times 4 = > 112$
$x = \frac {(112 - 12)}{4} = \frac {100}{4}$ 24
Largest number $x + 6 = 25 + 6 = 31$
Q5. Find the average of first 60 natural numbers
A. 30.5 B. 31 C. 31.5 D. 32
Explanation: Sum of First 60 Natural numbers = $\frac { n (n + 1)}{2}$
$\frac {60 \times 61}{2}$ = 1830
Average = $\frac {1830}{60}$ = 30. 5
Exams
Competitive Exams - College Entrance Exams
Diploma NITC New Delhi
PG GATE 2020
Competitive Exams - Recent Job Notifications
Category
Banking SSC Railway
Defence Police Insurance
SP Quiz
Competitive Exams - Practice Sets
Category Quiz
Quant Aptitude Permutation and Combination
Spotting Errors
Profit and Loss
Reasoning Ability Puzzles
Insurance Awareness Insurance Awareness
GK
General Knowledge for Competitive Examinations
Topic Name of the Article
| 2,353
| 6,595
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.6875
| 5
|
CC-MAIN-2024-38
|
latest
|
en
| 0.941804
|
https://howtomechatronics.com/how-it-works/electrical-engineering/transistor-schmitt-trigger/
| 1,708,895,746,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-10/segments/1707947474643.29/warc/CC-MAIN-20240225203035-20240225233035-00364.warc.gz
| 314,939,777
| 29,844
|
# Transistor Schmitt Trigger Working Principle
In the previous tutorial we explained what is Schmitt Trigger and how it works using Operational Amplifiers. Now in this tutorial we will explain the Transistor based Schmitt Trigger.
You can watch the following video or read the written tutorial below.
## How It Works
The Schmitt Trigger is a logic input type that provides hysteresis or two different threshold voltage levels for rising and falling edge. This is useful because it can avoid the errors when we have noisy input signals from which we want to get square wave signals. The Transistor Schmitt Triger circuit contains two transistors and five resistors. For better explanation I will assign values to the components, and later I will make demonstration and build this circuit on a protoboard to see how it really works.
We will start like this. Let’s suppose that the Vin input is 0 V. That means that transistor T1 is cut off and not conducting. On the other hand the Transistor T2 is conducting because we have a voltage of about 1.98 V at the B node as we can consider this part of the circuit as a voltage divider and calculate the voltage using this expressions.
So because the Transistor T2 is conducting the output voltage will be low and the voltage at the emitter will be about 0.7 V lower than the voltage at the base of the transistor, or that’s about 1.28 V.
The emitter of the transistor T1 is connected with the emitter of the transistor T2 so they are at the same voltage level of 1.28 V which means that the transistor T1 will turn on when the voltage Vin at its base will be 0.7 V above this value of 1.28 V, or about 1.98 V.
So as we increase the Vin input and we cross this value of 1.98 the transistor T1 will start conducting. This will cause the voltage at the base of the transistor T2 to drop and will cut the transistor off. As the transistor T2 is no longer conducting the output voltage will go high.
Next, the voltage Vin at the base of the transistor T1 will start declining and it will turn the transistor off when the base voltage will be 0.7 V above the voltage of its emitter. This will happen as the current in the emitter will decline to a point where the transistor will get into forward-active mode.
In this mode the collector voltage will increase, which will also increase the voltage at the base of the transistor T2. This will cause small amount of current to flow through the transistor T2 which will further drop the voltage at the emitters and will cause the transistor T1 to turn off. In our case the Vin input needs to drop to about 1.3 V to turn off the transistor T1.
That’s it. Now the cycle repeats over and over again. So we got two thresholds, the high threshold at about 1.9 V and the low threshold at about 1.3 V.
There is a demonstration of this circuit on a protoboard and it can be found at the end of the video attached above.
| 646
| 2,907
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.15625
| 3
|
CC-MAIN-2024-10
|
longest
|
en
| 0.910134
|
https://nrich.maths.org/public/topic.php?code=47&cl=3&cldcmpid=5955
| 1,571,765,645,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-43/segments/1570987822458.91/warc/CC-MAIN-20191022155241-20191022182741-00465.warc.gz
| 628,142,373
| 9,856
|
# Search by Topic
#### Resources tagged with Creating and manipulating expressions and formulae similar to Unusual Long Division - Square Roots Before Calculators:
Filter by: Content type:
Age range:
Challenge level:
### There are 126 results
Broad Topics > Algebraic expressions, equations and formulae > Creating and manipulating expressions and formulae
### Unusual Long Division - Square Roots Before Calculators
##### Age 14 to 16 Challenge Level:
However did we manage before calculators? Is there an efficient way to do a square root if you have to do the work yourself?
### Magic W
##### Age 14 to 16 Challenge Level:
Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
### Plum Tree
##### Age 14 to 18 Challenge Level:
Label this plum tree graph to make it totally magic!
### Enriching Experience
##### Age 14 to 16 Challenge Level:
Find the five distinct digits N, R, I, C and H in the following nomogram
### Consecutive Squares
##### Age 14 to 16 Challenge Level:
The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?
### Dating Made Easier
##### Age 14 to 16 Challenge Level:
If a sum invested gains 10% each year how long before it has doubled its value?
### Training Schedule
##### Age 14 to 16 Challenge Level:
The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?
### Always Two
##### Age 14 to 18 Challenge Level:
Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.
### Odd Differences
##### Age 14 to 16 Challenge Level:
The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.
### Interactive Number Patterns
##### Age 14 to 16 Challenge Level:
How good are you at finding the formula for a number pattern ?
### Gutter
##### Age 14 to 16 Challenge Level:
Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?
### Pick's Theorem
##### Age 14 to 16 Challenge Level:
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
### Terminology
##### Age 14 to 16 Challenge Level:
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
### Really Mr. Bond
##### Age 14 to 16 Challenge Level:
115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?
### 2-digit Square
##### Age 14 to 16 Challenge Level:
A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?
### There and Back
##### Age 14 to 16 Challenge Level:
Brian swims at twice the speed that a river is flowing, downstream from one moored boat to another and back again, taking 12 minutes altogether. How long would it have taken him in still water?
### Magic Squares for Special Occasions
##### Age 11 to 16
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
### Inside Outside
##### Age 14 to 16 Challenge Level:
Balance the bar with the three weight on the inside.
### Square Pizza
##### Age 14 to 16 Challenge Level:
Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?
### Hand Swap
##### Age 14 to 16 Challenge Level:
My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the. . . .
### Pair Products
##### Age 14 to 16 Challenge Level:
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
### One and Three
##### Age 14 to 16 Challenge Level:
Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .
### Lower Bound
##### Age 14 to 16 Challenge Level:
What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =
### ' Tis Whole
##### Age 14 to 18 Challenge Level:
Take a few whole numbers away from a triangle number. If you know the mean of the remaining numbers can you find the triangle number and which numbers were removed?
### Triangles Within Triangles
##### Age 14 to 16 Challenge Level:
Can you find a rule which connects consecutive triangular numbers?
### Triangles Within Pentagons
##### Age 14 to 16 Challenge Level:
Show that all pentagonal numbers are one third of a triangular number.
### Screen Shot
##### Age 14 to 16 Challenge Level:
A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees. . . .
### Magic Sums and Products
##### Age 11 to 16
How to build your own magic squares.
### Balance Point
##### Age 14 to 16 Challenge Level:
Attach weights of 1, 2, 4, and 8 units to the four attachment points on the bar. Move the bar from side to side until you find a balance point. Is it possible to predict that position?
### Reasonable Algebra
##### Age 14 to 16 Challenge Level:
Use algebra to reason why 16 and 32 are impossible to create as the sum of consecutive numbers.
### Algebra Match
##### Age 11 to 16 Challenge Level:
A task which depends on members of the group noticing the needs of others and responding.
### Simplifying Doughnut
##### Age 14 to 18 Challenge Level:
An algebra task which depends on members of the group noticing the needs of others and responding.
### Robert's Spreadsheet
##### Age 14 to 16 Challenge Level:
Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?
### Generating Triples
##### Age 14 to 16 Challenge Level:
Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
### Steel Cables
##### Age 14 to 16 Challenge Level:
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
### Semi-square
##### Age 14 to 16 Challenge Level:
What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?
### Algebra from Geometry
##### Age 11 to 16 Challenge Level:
Account of an investigation which starts from the area of an annulus and leads to the formula for the difference of two squares.
### What's Possible?
##### Age 14 to 16 Challenge Level:
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
### Hike and Hitch
##### Age 14 to 16 Challenge Level:
Fifteen students had to travel 60 miles. They could use a car, which could only carry 5 students. As the car left with the first 5 (at 40 miles per hour), the remaining 10 commenced hiking along the. . . .
### Sums of Pairs
##### Age 11 to 16 Challenge Level:
Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”
### Pinned Squares
##### Age 14 to 16 Challenge Level:
What is the total number of squares that can be made on a 5 by 5 geoboard?
### Pareq Calc
##### Age 14 to 16 Challenge Level:
Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel. . . .
### Matchless
##### Age 14 to 16 Challenge Level:
There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?
### Back to Basics
##### Age 14 to 16 Challenge Level:
Find b where 3723(base 10) = 123(base b).
### Fair Shares?
##### Age 14 to 16 Challenge Level:
A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?
### Series Sums
##### Age 14 to 16 Challenge Level:
Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.
### Salinon
##### Age 14 to 16 Challenge Level:
This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
### DOTS Division
##### Age 14 to 16 Challenge Level:
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.
### Number Rules - OK
##### Age 14 to 16 Challenge Level:
Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...
### Painted Cube
##### Age 14 to 16 Challenge Level:
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
| 2,365
| 9,857
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.90625
| 4
|
CC-MAIN-2019-43
|
longest
|
en
| 0.838365
|
http://tutorialsources.com/excel/tutorials/auto-sequence-number-based-on-another-column.htm
| 1,394,481,869,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2014-10/segments/1394010995802/warc/CC-MAIN-20140305091635-00086-ip-10-183-142-35.ec2.internal.warc.gz
| 192,854,215
| 6,552
|
You are here: HomeExcelTutorials
# auto- sequence number based on another column?
## auto- sequence number based on another column?
Price: FREE
my problem:
column A contains a unique ID # for a well, in other columns are events for that well. Multiple events occur for each well (multiple rows with same unique ID #)
now I need to put into column B, a sequential number counting each event for each well.
I know I did not describe this well so let me try to show
A B
how to auto-generate column B?
Visit publisher's web-site: auto- sequence number based on another column?
Category and Tags: ExcelTutorials :
## Related Tutorials
### Unique Sequence Number Based On The 1st Column
Free: Yes
Tags: Excel ›
I have a spreadsheet with in the first column names and I want to create an unique sequence number per record name , hope somebody can help with a macro.
So I have this:
Name(A)
2AA
2AA
BB
BB
BB
CC
DD
DD
DD
DD
And it should be like this:
Name(A), Unique Seqno(B)
2AA, 1
2AA, 2
BB, 1
BB, 2
BB, 3
CC, 1
DD, 1
DD, 2
DD, 3
DD, 4
### auto numbering rows based on changing values in another column
Free: Yes
Tags: Excel ›
I have a list of items for multiple people (territories). I would like an Excel formula that would restart a row numbering sequence every time the territory number changes. The simple spreadsheet attached illustrates the results I would like to obtain.
### [solved]Auto Sequence Date of of previous entry
Free: Yes
Tags: Excel ›
im developing a spreadsheet for end users that will assign the day of the week based off of the date and give feedback based on that. what im looking for is a way to foolproof the spreadsheet so they enter day 0, and excel will auto fill the dates after that to reduce chances of them screwing up (31 days in November, forgetting leap year, etc)
so my sheet looks like this:
a1 = 11/15/2011
a2 = 11/16/2011
a3 = 11/17/2011
what im looking for is a simple statement that will look at cell a3, and apply 11/18/2011 in a4. does something like this exist? non-vba preferred if possible
### auto sequence
Free: Yes
Tags: Excel › Functions
how to make a cell advance numerically
### Auto fill column with sequential numbers with decimals
Free: Yes
Tags: Excel ›
Want to auto fill as follows: 3, 3.1, 3.2, 3.3, 3.4
What method works? Can only seem to get sequence on primary number, example:
I want the number to the right of the decimal to change.
## Related Applications & Scripts
### Manual Slideshow
Free: No
Tags: JavaScript › Excel Slide Shows
A collection of images can be viewed in any ordered sequence using manual/auto slide show script.
Features:
- You can switch to any slide using the manual slider options provided.
- You can also set the size and duration of the image show.
- It supports JPEG, TIFF, BMP and PNG formats.
- Try the manual slide show given below.
### No-nonsense sequencer
Free: No
Tags: Flash › Excel Image Galleries
Tired of getting complicated banner rotators and image sequence items implemented properly in your works?
No-nonsense sequencer is a very basic image/swf rotator. It generates a number of pictures or SWF files in sequence, fading in and out. It's bare bone default setup will work in any template, file or website. Simple as that.
All you need to adjust if you want in the XML file is the time to fade in, time to fade out, the path to where the images/swf folders are, and the size of your canvas.
But if you need a few simple extras, you can add a few basic masking transitions, basic reveal movements and ken burns effect, to each item in the sequence individually
### BANNER ROTATOR with Auto Delay Time
Free: No
Tags: Flash › Excel Banner Rotation
This is an XML banner rotator with automatic delay time depending on the number of words used in caption. There are more features, around 35 settings parameters available in the xml file.
Features:
- Can load JPEG , PNG, GIF images and SWF files
- Resizable to any extent
- Auto Time delay according to number of words (length of caption)
- Fixed time delay also can be added
- 5 Different Transition Effects
### XML Based BannerRotator
Free: No
Tags: Flash › Excel Banner Rotation
Flash version: 9, ActionScript 3.0. A simple Banner Rotator based on xml files
* auto resize images
* timer for every image
* pause timer
* auto rotate images
* well commented source
* drag and drop
* xml configuration file
* TweenLite engine used
### Auto Image Gallery Class
Free: No
Tags: PHP › Excel Image Galleries
Simple Gallery is a class based auto image gallery creator. The idea for this is to allow the user to instantly insert a photo gallery into their site with absolute ease. The goal for this class is to make it easy for any one to achieve an attractive image gallery with out having to know PHP or tediously setting up the gallery by hand coding html . Simple gallery works by taking a folder of images, you supply, and based off that folder a gallery will be created for you. All you have to do is select the options you want, insert two lines of code and style your gallery with css. Its that simple! All the code has been written for you and simple gallery comes pre-built with prettyPhoto, a JQUERY photo lightbox. Theres no need for a mySQL database or an admin panel, just input your folder location on your server and your good-to-go.
Features:
Class based, for full customization
Auto Thumbnail generation, for quick page load.
Implement JQUERY prettyPhoto lightbox with ease
| 1,318
| 5,466
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.609375
| 3
|
CC-MAIN-2014-10
|
longest
|
en
| 0.868813
|
http://www.societyofrobots.com/member_tutorials/node/315
| 1,484,586,813,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-04/segments/1484560279224.13/warc/CC-MAIN-20170116095119-00099-ip-10-171-10-70.ec2.internal.warc.gz
| 693,775,347
| 9,118
|
## 1 Basic Control Methods
Basic Control Methods
First of all it is easier to define the pins you will be using to control your stepper motor:
#define mout1 PORTDbits.RD0
#define mout2 PORTDbits.RD1
#define mout3 PORTDbits.RD2
#define mout4 PORTDbits.RD3
If you have read the other tutorials, you will no doubt have seen the different methods of control. Wave, Full Step and Half Step, I like to implement these as a 3 dimensional array:-
//phaseArray[phasetype][phaseposition][outputnumber]
//phasetype:- 0 = wave ; 1 = full step ; 2 = half step
char phaseArray[3][8][4]={
{{1,0,0,0},{1,0,0,0},
{0,0,1,0},{0,0,1,0},
{0,1,0,0},{0,1,0,0},
{0,0,0,1},{0,0,0,1}},
{{1,0,1,0},{1,0,1,0},
{0,1,1,0},{0,1,1,0},
{0,1,0,1},{0,1,0,1},
{1,0,0,1},{1,0,0,1}},
{
{1,0,0,0},
{1,0,1,0},
{0,0,1,0},
{0,1,1,0},
{0,1,0,0},
{0,1,0,1},
{0,0,0,1},
{1,0,0,1}
}
};
For wave and full step mode, we should only need to supply 4 elements for the 2nd array list but to integrate half step mode into the array we need to double the sequences up for wave and full step modes. This means that we need to increment these two modes by 2 for each step.
so in order to use the array you will need to do something like this:
mout1 = phaseArray[*phasetype*][*phaseposition*][0];
mout2 = phaseArray[*phasetype*][*phaseposition*][1];
mout3 = phaseArray[*phasetype*][*phaseposition*][2];
mout4 = phaseArray[*phasetype*][*phaseposition*][3];
mout refers to the pins we have defined earlier
*phasetype* refers to the 1st array dimension, if we set this as 1 then we will be operarting with full step mode
*phaseposition* refers to what step cycle we are currently on. Incrementing this by 2 will send us to the next step cycle in the array.
the number in the 3rd array dimension just refers to the port state for the current cycle.
so looking at the array defined above:
mout1 = phaseArray[1][0][0];
mout2 = phaseArray[1][0][1];
mout3 = phaseArray[1][0][2];
mout4 = phaseArray[1][0][3];
would produce the following:
mout1 = 1
mout2 = 0
mout3 = 1
mout4 = 0
Here is a full program that uses the array above to control a stepper motor with continuous forward motion
The program controls the steps at 5000us Lets try it out
Its working, but its a bit slow. Lets try with a 1500us step delay intead
Its better but still a bit slow. Lets try it with a 500us step delay
Whoops, it stalls. It wont move at all at 500us. Is 1500us the fastest we can go then?
Well the answer is no. We can move a lot faster.
Stepper motors have to start slow in order for the coils to catch. Once its spinning, you can slowly ramp up the speed.
Notice in the videos how the motors are moving bit they are really jittery, they are suffering from mechanical resonance at a slow speed.(more on this later).
Follow to the next page to see how to drive your motor faster.
| 912
| 2,855
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.9375
| 3
|
CC-MAIN-2017-04
|
latest
|
en
| 0.733421
|
http://mcs.open.ac.uk/pp2464/ALLIGATOR/alligator1.0_manual.txt
| 1,556,167,253,000,000,000
|
text/plain
|
crawl-data/CC-MAIN-2019-18/segments/1555578681624.79/warc/CC-MAIN-20190425034241-20190425060241-00383.warc.gz
| 121,581,538
| 4,935
|
-------------------------------------------------------- ALLIGATOR 1.0 MANUAL Paul Piwek Centre for Research in Computing The Open University, UK April, 2006; Updated May 3, 2006 -------------------------------------------------------- Contents -------- - License - Documentation URL - Abstract - Main Predicate - Parameters - Running Alligator and Examples of queries - Exception Handling License ------- ALLIGATOR is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 2.0 England & Wales License. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA. Documentation ------------- Further documentation on ALLIGATOR is available at http://mcs.open.ac.uk/pp2464/alligator Abstract -------- ALLIGATOR is an experimental prototype of a theorem prover for Pure Type Systems extended with Sigma Types. It also deals with a restricted form of definitions. It has been implemented in Sicstus Prolog and been tested with version 3.12.2 of Sicstus. There is also a version of ALLIGATOR available for (the freely available) SWI Prolog (http://www.swi-prolog.org/). Main Predicate -------------- The main predicate is: prove(+Pseudo_Context,-Term:+Goal) Term is a Prolog variable which the system will instantiate with a proof term for Goal, if such a term exists (given a certain maximum search depth and search time, see below). Otherwise, the call fails. Formally, Goal is a pseudo term. Pseudo-terms (PT) are defined as follows: PT ::= S | V | A | PT-PT | pair(PT,PT) | pi1(PT) | pi2(PT) | lambda(V:PT,PT) | pi(V:PT,PT) | sigma(V:PT,PT) V ::= Prolog Variable A ::= Prolog Atom S ::= type_prop | type_set | prop | set The constructors -, pair(x,y), pi1, pi2, lambda, pi and sigma stand, respectively, for function application (left associative), pairs (i.e., (x,y)), left and right projection, lambda abstraction, (dependent) function types and (dependent) product types. In order to facilitate manual input of pseudo terms we allow for the following abbreviations: Shorthand Notation: [V1:PT1,..,Vn:PTn]=>PT = pi(V1:PT1,..(pi(Vn:PTn,PT)..) [V1:PT1,..,Vn:PTn]/\PT = sigma(V1:PT1,..(sigma(Vn:PTn,PT)..) PT -> PT = pi(V1:PT1,PT), provided V1 does not occur in PT. PT & PT = sigma(V1:PT1,PT), provided V1 does not occur in PT. ~ PT = pi(V1:PT,false) PT1\/PT2 = pi(V1:(pi(V2:A,false)),PT2) Pseudo contexts are Prolog lists containing introductions which are of the form A:PT or def(A,PT1):PT2. Here, A is a Prolog atom. In general, we represent bound PTS variables (bound by lambda, pi or sigma) with Prolog variables. All other PTS variables (unbound) are represented using Prolog atoms. This allows us to use the build-in Prolog unification for comparing pseudo-terms. Parameters ---------- Before the user calls the predicate prove, it is possible to set a number of parameters, using setval(+Param,+Value). The parameters and respective values in question are: 1. feedback with values on/off: for error report and status reports of the proof process (search depth); 2. base_context with values classic/falsum/...: for setting the base contexts that should be loaded. classic consists of dn_pr:([P:prop]=>(((P->false)->false)->P)) and falsum consists of false:prop; 3. maxtime with number of seconds as value: maximum time that the proof search should continue; 4. maxdepth with integer as value: maximum search depth at which the system should search for a proof. The proof search always proceeds using the consecutive-bounded depth-first strategy; 5. startdepth with integer as value: the depth at which the consecutive-bounded depth-first strategy starts searching for proofs. Finally, there are two parameters for determining how long reduction should continue and what proportion of memory reduction is allowed to use (to avoid looping and memory overflow for terms that do not normalize: 6. reduce_time_out with value in milliseconds 7. reduce_space_out with value a number in [0..1] When alligator is consulted or compiled, the default settings of all the aforementioned parameters are printed to the screen (default values can be modified by changing the corresponding val(Param,Val) clauses in the source code): - feedback on; - maximum search time: 3600 seconds; - start search depth: 1; - maximum search depth: 50; - maximum time for reduce: 2500 milliseconds; - maximal proportion of global stack for reduce: 0.9. ALLIGATOR implements Pure Type Systems. Pure Type Systems are highly flexible in terms of the dependent type systems that can be implemented in them. The following clauses in the source code specificy the system that ALLIGATOR uses by default (it can be modified manually in the source code): %%% TYPE SYSTEM: LambdaPREDomega extended with Sigma Types % The type system that we use here is LambdaPREDomega % which can be used for higher order predicate logic. % Sigma's can be added without losing consistency % for Sigma(X:A:,B) with A:Set. %%% SORTS sorts([set,type_set,prop,type_prop]). %%% AXIOMS axioms([(set,type_set), (prop,type_prop)]). %%% TYPE SYSTEM RULES pi_rules([ (set,set), (set,type_prop), % Can be used to make A->prop % and A->(A->prop). % The domains of unary preds and % binary relations. (type_prop,type_prop), % (A->prop)->prop:type_prop; % ((A->prop)->prop->)prop:type_prop % Quantification over type_prop % covering % all higher order domains. (prop,prop), % For forming implications. (set,prop), % For universal quantification over % set types. (type_prop,prop)]). % Quantification over domains of type % type_prop such % as A->prop and A->(A->prop). sigma_rules([(set,prop), % Existential quantification over set % types. (prop,prop)]). % Conjunction. % Note that we cannot have the lambda % cube's (box,star) % which is here (type_set/type_prop, % set/prop). % Addition of the latter rules makes % the system lose % strong normalization and consequently % consistency (see Geuvers, 1994). Running Alligator and Examples of queries ----------------------------------------- To run ALLIGATOR follow these steps: 1. Start Sicstus Prolog. 2. Compile or consult the file alligator1.0.pl. 3. The following message will appear: Alligator 1.0, January 2006. Author: Paul Piwek. - feedback on; - maximum search time: 3600 seconds; - start search depth: 1; - maximum search depth: 50; - maximum time for reduce: 2500 milliseconds; - maximal proportion of global stack for reduce: 0.9. 4. Type your query for alligator (or change the values of parameters using setval as described above). EXAMPLE 1: In the following example we have two sets, a and b and an inhabitant x of a. There is also a function f from set a to set b. In this context we ask for an inhabitant of set b. | ?- prove([a:set,b:set,f:a->b,x:a],X:b). ...context normalized to standard notation and reduced. ...checked context. ...context normalized to arrow notation. ...forward inferences completed. The following Context will be used to construct a proof: false:prop a:set b:set f:[_160:a]=>b x:a dn_pr:[_586:prop,_590:[_598:[_606:_586]=>false]=>false]=>_586 ...searching at depth: 1 2 ...proof found after 0.030 seconds. ...the goal in input notation: b ...the goal in arrow notation: b ...the reduced goal in standard notation: b ...the unreduced proof with atoms and arrows: f-x ...the unreduced proof: f-x ...the reduced proof: f-x ...type checking of the proof succeeded ...the type of b is set X = f-x ? EXAMPLE 2: p or q implies that it is not the case that not p and not q. | ?- prove([p:prop,q:prop],_E: ( p \/ q) -> ~ ( ~ p & ~q)). ...context normalized to standard notation and reduced. ...checked context. ...context normalized to arrow notation. ...forward inferences completed. The following Context will be used to construct a proof: false:prop p:prop q:prop dn_pr:[_729:prop,_733:[_741:[_749:_729]=>false]=>false]=>_729 ...searching at depth: 1 2 3 4 5 ...proof found after 0.030 seconds. ...the goal in input notation: p\/q-> ~ (~p& ~q) ...the goal in arrow notation: [_272:[_278:[_284:p]=>false]=>q]=>[_251:sigma (_263:[_269:p]=>false,[_260:q]=>false)]=>false ...the reduced goal in standard notation: pi(_272:pi(_278:pi(_284:p,false),q), pi(_251:sigma(_263:pi(_269:p,false),pi(_260:q,false)),false)) ...the unreduced proof with atoms and arrows: lambda(v_42:[_2522:[_2530:p]=> false]=>q,lambda(v_43:sigma(_2688:[_2696:p]=>false,[_2685:q]=>false),def (v_44,pi2(v_43))-(v_42-def(v_45,pi1(v_43))))) ...the unreduced proof: lambda(_5699:pi(_2522:pi(_2530:p,false),q),lambda(_5722: sigma(_2688:pi(_2696:p,false),pi(_2685:q,false)),def(v_44,pi2(_5722))-(_5699-def (v_45,pi1(_5722))))) ...the reduced proof: lambda(_583:pi(_623:pi(_629:p,false),q),lambda(_589:sigma (_608:pi(_614:p,false),pi(_605:q,false)),pi2(_589)-(_583-pi1(_589)))) ...type checking of the proof succeeded ...the type of pi(_1330:pi(_1364:pi(_1370:p,false),q),pi(_1525:sigma (_1541:pi(_1547:p,false),pi(_1538:q,false)),false)) is prop yes EXAMPLE 3: b is a set, a is an inhabitant of b and c is predicate over set b. f is a proof that every b has the property c. The goal is to prove that there is a b which is a c. | ?- prove([b:set,a:b,c:[X:b]=>prop,f:pi(X:b,c-X)],_A:[S:b]/\c-S). ...context normalized to standard notation and reduced. ...checked context. ...context normalized to arrow notation. ...forward inferences completed. The following Context will be used to construct a proof: false:prop b:set a:b c:[_217:b]=>prop f:[_200:b]=>c-_200 dn_pr:[_676:prop,_680:[_688:[_696:_676]=>false]=>false]=>_676 ...searching at depth: 1 2 3 ...proof found after 0.030 seconds. ...the goal in input notation: [_43:b]/\c-_43 ...the goal in arrow notation: sigma(_306:b,c-_306) ...the reduced goal in standard notation: sigma(_306:b,c-_306) ...the unreduced proof with atoms and arrows: pair(a,f-a) ...the unreduced proof: pair(a,f-a) ...the reduced proof: pair(a,f-a) ...type checking of the proof succeeded ...the type of sigma(_798:b,c-_798) is prop true ? Exception Handling ------------------ Malformed input (terms, contexts) are handled as exceptions. We use the predicate throw/1 to report such exceptions (see SWI or Sicstus manual; they can be caught with catch/3). We have the following exceptions (note that in verbose mode feedback also writes a brief description of the exception to the screen): error_variable_not_fresh error_cyclic_type error_has_no_type error_unbound_variable error_context_not_existing error_syntax_var_incorrect error_synt_incorrect_var_in_context error_reduction_failed([TimeOut,SpaceOut,Cyclic,FreeVars,SafeTerm]) with TimeOut :== time_out | success with SpaceOut :== space_out | success with Cyclic :== cyclic | not_cyclic with FreeVars :== free_vars | no_free_vars with SafeTerm :== safe | not_safe
| 2,848
| 10,769
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.796875
| 3
|
CC-MAIN-2019-18
|
latest
|
en
| 0.721084
|
https://it.mathworks.com/matlabcentral/cody/problems/74-balanced-number/solutions/1379945
| 1,582,669,397,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-10/segments/1581875146160.21/warc/CC-MAIN-20200225202625-20200225232625-00185.warc.gz
| 416,068,204
| 15,669
|
Cody
# Problem 74. Balanced number
Solution 1379945
Submitted on 14 Dec 2017 by Toolman Thoolen
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
n = 13722; assert(isequal(isBalanced(n),true))
2 Pass
n = 23567414; assert(isequal(isBalanced(n),true))
3 Pass
n = 20567410; assert(isequal(isBalanced(n),false))
4 Pass
n = 1; assert(isequal(isBalanced(n),true))
5 Pass
n = 11111111; assert(isequal(isBalanced(n),true))
6 Pass
n = 12345678; assert(isequal(isBalanced(n),false))
7 Pass
n = 12333; assert(isequal(isBalanced(n),false))
8 Pass
n = 9898; assert(isequal(isBalanced(n),true))
9 Pass
n = 469200; assert(isequal(isBalanced(n),false))
10 Pass
n = 57666; assert(isequal(isBalanced(n),true))
| 280
| 839
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.84375
| 3
|
CC-MAIN-2020-10
|
latest
|
en
| 0.485169
|
https://www.edupil.com/question/percentage-marks-third-subject/
| 1,550,748,195,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-09/segments/1550247504594.59/warc/CC-MAIN-20190221111943-20190221133943-00530.warc.gz
| 855,024,448
| 14,778
|
# What will be His Percentage of Marks in the Third Subject? If
In an Examination there are three subject of 100 marks each. A student scores 60% in the 1st subject and 80% in the second subject. He scored 70% in aggregate. His percentage of marks in the third subject is:
1. 70
2. 80
3. 60
4. 65
Monis Rasool Professor Asked on 28th June 2015 in
1 Answer(s)
Answer: (1) 70%
Explanation:-
Let be the score of third subject = X
A student of score in first subject = 60% = 60 x 100/100 = 60
A student of score in second subject = 80% = 80 x 100/100 = 80
70% of 300 = 300 x 70/100 = 210
score of third subject = 210 – ( 60 + 80)
= 210 – 140 = 70
Percentage of score in third subject = 70 x 100/100 = 70%
Hence, the answer is (1) 70%
Anurag Mishra Professor Answered on 28th June 2015.
### Your Answer
By posting your answer, you agree to the privacy policy and terms of service.
| 284
| 881
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.21875
| 4
|
CC-MAIN-2019-09
|
latest
|
en
| 0.936751
|
https://www.gradesaver.com/textbooks/math/other-math/thinking-mathematically-6th-edition/chapter-10-geometry-10-4-area-and-circumference-exercise-set-10-4-page-646/13
| 1,545,043,295,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-51/segments/1544376828501.85/warc/CC-MAIN-20181217091227-20181217113227-00027.warc.gz
| 917,182,183
| 12,112
|
## Thinking Mathematically (6th Edition)
567 $m^{2}$
Given h = 18 m, a = 26 m, and b = 37m: The formula for area of a trapezoid is: A = $\frac{1}{2}$h(a+b). =$\frac{1}{2}$x18 x (26 + 37) =$\frac{1}{2}$x18 x 63 = 567 $m^{2}$
| 101
| 224
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.0625
| 4
|
CC-MAIN-2018-51
|
latest
|
en
| 0.591138
|
https://easierwithpractice.com/what-does-it-mean-to-outstrip-something/
| 1,701,840,229,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-50/segments/1700679100583.13/warc/CC-MAIN-20231206031946-20231206061946-00419.warc.gz
| 268,426,584
| 40,534
|
# What does it mean to outstrip something?
## What does it mean to outstrip something?
transitive verb. 1 : to go faster or farther than.
## How do you use example in a sentence?
You use for example to introduce and emphasize something which shows that something is true.
1. Take, for example, the simple sentence: ‘The man climbed up the hill’.
2. A few simple precautions can be taken, for example ensuring that desks are the right height.
How do you use written in a sentence?
Using Written in a Sentence
1. I had written an amazing paper, but I lost it.
2. They had written our paper in 10 minutes, and it showed.
3. He had written an amazing agenda, but it was changed.
4. There were so many poems that he had written.
5. How he had written all those works, I’ll never know.
### What is a good sentence for motion?
Examples of motion in a Sentence He made hand motions to get our attention. She made a motion calling for the repeal of the law. Her motion was voted on.
### What is the motion answer in one sentence?
Answer: In physics, motion is a change in position of an object with respect to time. Motion is typically described in terms of displacement, distance (scalar), velocity, acceleration, time and speed.
What is the formula for motion?
Newton’s second law, which states that the force F acting on a body is equal to the mass m of the body multiplied by the acceleration a of its centre of mass, F = ma, is the basic equation of motion in classical mechanics.
#### What are the 5 equations of motion?
In circumstances of constant acceleration, these simpler equations of motion are usually referred to as the “SUVAT” equations, arising from the definitions of kinematic quantities: displacement (S), initial velocity (u), final velocity (v), acceleration (a), and time (t).
#### What are the 3 kinematic equations?
Our goal in this section then, is to derive new equations that can be used to describe the motion of an object in terms of its three kinematic variables: velocity (v), position (s), and time (t). There are three ways to pair them up: velocity-time, position-time, and velocity-position.
What are the five equations of motion?
Equations of Motion
Variable Equation
Velocity v, equals, u, plus, a, t,v=u+at
Displacement with positive acceleration s, equals, u, t, plus, one half, a, t, squared,s=ut+21at2
Displacement with negative acceleration s, equals, v, t, minus, one half, a, t, squared,s=vt−21at2
## Where is the equation of motion used?
The equations of motion of kinematics describe the most fundamental concepts of motion of an object. These equations govern the motion of an object in 1D, 2D and 3D. They can easily be used to calculate expressions such as the position, velocity, or acceleration of an object at various times.
## Who gives the equation of motion?
Galileo and the Equations of Motion. The first of the three laws of motion formulated by Newton (1642-1726) says that every object in a state of uniform motion remains in that state unless an external force is applied. This is essentially a reformulation of Galileo’s inertia concept.
What is value of G?
The acceleration due to gravity on Earth or the value of g on Earth is 9.8 m/s2. This acceleration is due to the Earth’s gravity.
### Is value of G actually constant?
The measured value of the constant is known with some certainty to four significant digits. In SI units, its value is approximately 6.674×10−11 m3⋅kg−1⋅s−2….Gravitational constant.
Values of G Units
6.67430(15)×10−11 m3⋅kg–1⋅s–2
4.30091(25)×10−3 pc⋅M⊙–1⋅(km/s)2
### What is G called?
G is called Universal Gravitation Constant because its value i.e. 6.67 x 10-11 Nm2kg-2 is constant thought the universe.
Why value of g is constant?
The force of attraction between any two unit masses separated by a unit distance is called universal gravitational constant denoted by G measured in Nm2/kg2. The value of the gravitational constant is the same throughout the universe. The value of G is different from g, which denotes the acceleration due to gravity.
poles
#### Where is the value of g 0?
Since, mass m of an object can never be 0. Therefore, when F=0, then g has to be 0. Thus, the value of g is zero at the centre of Earth.
Where is the value of g is maximum and minimum?
Value of g is maximum at the poles, thats why we may weigh more than we are in the equators. Value of g is minimum at the equator and hence we will weigh less.
## What is the value of g in minimum?
The value of ‘g’ is minimum at the equator because earth is not a perfect sphere. Its radius is maximum at the equator. Hence, according to the equation g = GM/R2, the equator is the place where g will be minimum….Thank you.
What Does Flora Mean The Central Oxygen Atom In Ether Is
## Why value of g is greater at pole?
It is frequently stated that the value of the acceleration due to gravity at the pole is larger than at the equator because the poles are closer to the center of the earth due to the earth’s oblateness. The measured value is larger because the earth’s density is not uniform but increases toward the center.
What is the value of G at Pole?
### What is the value of G on moon?
approximately 1.625 m/s2
### Can you jump off the moon?
No, you can’t escape the Moon’s gravity by jumping. The Moon’s gravity extends to infinity; it does not end or go to zero. And no one can just up with enough energy to achieve Escape Velocity: 2400 m/s (2 miles/sec).
Is Gravity present on moon?
The Moon’s surface gravity is about 1/6th as powerful or about 1.6 meters per second per second. The Moon’s surface gravity is weaker because it is far less massive than Earth. A body’s surface gravity is proportional to its mass, but inversely proportional to the square of its radius.
274 m/s²
| 1,399
| 5,794
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.546875
| 4
|
CC-MAIN-2023-50
|
latest
|
en
| 0.967831
|
http://www.800score.com/forum/viewtopic.php?f=3&t=15329&view=previous
| 1,540,036,747,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-43/segments/1539583512693.40/warc/CC-MAIN-20181020101001-20181020122501-00009.warc.gz
| 415,812,599
| 5,562
|
It is currently Sat Oct 20, 2018 7:59 am
All times are UTC - 5 hours [ DST ]
Page 1 of 1 [ 2 posts ]
Print view Previous topic | Next topic
Author Message
Post subject: GMAT Coordinate GeometryPosted: Wed Apr 17, 2013 2:46 am
Joined: Sun May 30, 2010 3:15 am
Posts: 424
In a rectangular coordinate system, which of the following points is intersected by the line connected by the coordinates (5, 6) and (21, 18)?
A. (9, 9)
B. (12, 12)
C. (13, 13)
D. (12, 13)
E. (16, 15)
(A) To solve this problem, we first need to determine the slope of the line by substituting values into the slope equation.
Slope = change in y / change in x = (y2 – y1)/(x2 – x1)
Therefore, slope = (18 – 6)/(21 – 5) = 12/16 = 3/4 .
Now that we have the slope, we can determine the equation of the line. The equation for a line is y = mx + b, where m is the slope and b is the y-intercept.
Since m = 3/4, we can solve for b by plugging in the point (5, 6) for the values of x and y:
y = mx + b
6 = (3/4)(5) + b
6 = 15/4 + b
6 – 15/4 = b
9/4 = b
So the equation for the line is:
y = (3/4)x + 9/4
Only the (x, y) pair that makes the equation true will be a point on the line described by the equation above. When we substitute the values of x and y from the coordinates in the answer choices, only choice (A) makes the equation true:
9 = (3/4)(9) + 9/4
9 = 27/4 + 9/4 = 36/4 = 9.
The correct answer is choice (A). This question is also easy to solve by simply back-solving the answer choices.
----------
12 and 13 also works:
12 = (3/4) × 13 + 9/4
12 = 39/4 + 9/4
12 = 48/4
12 = 12
Top
Post subject: Re: GMAT Coordinate GeometryPosted: Wed Apr 17, 2013 2:47 am
Joined: Sun May 30, 2010 2:23 am
Posts: 498
Quote:
12 = (3/4) × 13 + 9/4
Here y = 12 and x = 13. You have used point (13, 12), NOT (12, 13), which would be
13 ?= (3/4) × 12 + 9/4
This does not fit.
Top
Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
Page 1 of 1 [ 2 posts ]
All times are UTC - 5 hours [ DST ]
#### Who is online
Users browsing this forum: Exabot [Bot] and 5 guests
You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum
Search for:
Jump to: Select a forum ------------------ GMAT GMAT: Quantitative Section (Math) GMAT: Verbal Section GMAT: Integrated Reasoning GMAT: General Questions GRE GRE: Quantitative Reasoning (Math) GRE: Verbal Reasoning GRE: General Questions General questions Other questions
| 858
| 2,646
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.40625
| 4
|
CC-MAIN-2018-43
|
latest
|
en
| 0.913703
|
http://www.mathisfunforum.com/post.php?tid=19732
| 1,398,404,194,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2014-15/segments/1398223210034.18/warc/CC-MAIN-20140423032010-00635-ip-10-147-4-33.ec2.internal.warc.gz
| 701,259,048
| 5,682
|
Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
You are not logged in.
|
Options
anonimnystefy
2013-07-07 02:52:18
The thing I dislike about those kinds of ideas are that they can be tough to get. It does come down to luck and experience a lot.
bob bundy
2013-07-07 02:45:27
hi Stefy,
That is a brilliant way to do it. Short and no complicated trig stuff. I am in awe. ( no dazzled-smiley-face available)
Bob
anonimnystefy
2013-07-07 01:44:24
I do not have an exact definition. Roughly, it means that some times you will think of it, sometimes you won't, and it mostly depends on luck, not unlike many other geometry problems.
My solution extends the line AB and names E the foot of the perpendicular from C to that line. Then I used The basic trig equations to get the result.
bob bundy
2013-07-07 01:05:22
hi Stefy,
What does 'quite a bit of inspection' mean exactly.
Bob
anonimnystefy
2013-07-06 23:33:08
Well, I have a solution that takes 2 or 3 lines to write up, but requires quite a bit of inspection.
bob bundy
2013-07-06 23:25:05
hi mukesh,
Here's an outline of a way to prove this. see diagram below.
There's no right angle to get tanA easily so I used the sine and cosine rules:
and
Put these together to get tanA and simplify.
work on this expression for tanA, making use of the following:
After much simplification you can get this equal to -2tanB, from which the required result follows.
It's a tough one so expect it to take 2 or 3 pages. If you get stuck post back where you've got to, and I'll compare your answer with mine.
Bob
mukesh
2013-07-06 04:07:32
if the median 'AD' of a triangle 'ABC' is perpendicular to side AB then prove that 'tanA+2tanB=0'
| 532
| 1,773
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.4375
| 3
|
CC-MAIN-2014-15
|
latest
|
en
| 0.865419
|
https://questions.examside.com/past-years/jee/question/if-a--0-b--0-then-the-maximum-area-of-the-parallelogram-w-wb-jee-mathematics-trigonometric-functions-and-equations-1w2pfarlmnvvgszg
| 1,723,405,038,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-33/segments/1722641008125.69/warc/CC-MAIN-20240811172916-20240811202916-00111.warc.gz
| 383,102,744
| 35,358
|
1
WB JEE 2021
+1
-0.25
If a > 0, b > 0 then the maximum area of the parallelogram whose three vertices are O(0, 0), A(a cos$$\theta$$, b sin$$\theta$$) and B(a cos$$\theta$$, $$-$$ b sin$$\theta$$) is
A
ab when $$\theta$$ = $${\pi \over 4}$$
B
3ab when $$\theta$$ = $${\pi \over 4}$$
C
ab when $$\theta$$ = $$-$$ $${\pi \over 2}$$
D
2ab
2
WB JEE 2021
+1
-0.25
Let A be the fixed point (0, 4) and B be a moving point on X-axis. Let M be the midpoint of AB and let the perpendicular bisector of AB meets the Y-axis at R. The locus of the midpoint P of MR is
A
y + x2 = 2
B
$${x^2} + {(y - 2)^2} = {1 \over 4}$$
C
$${(y - 2)^2} - {x^2} = {1 \over 4}$$
D
$${x^2} + {y^2} = 16$$
3
WB JEE 2021
+1
-0.25
A moving line intersects the lines x + y = 0 and x $$-$$ y = 0 at the points A, B respectively such that the area of the triangle with vertices (0, 0), A and B has a constant area C. The locus of the mid-point AB is given by the equation
A
$${({x^2} + {y^2})^2} = {C^2}$$
B
$${({x^2} - {y^2})^2} = {C^2}$$
C
$${(x + y)^2} = {C^2}$$
D
$${(x - y)^2} = {C^2}$$
4
WB JEE 2021
+1
-0.25
A ray of light along $$x + \sqrt 3 y = \sqrt 3$$ gets reflected upon reaching X-axis, the equation of the reflected ray is
A
$$y = x + \sqrt 3$$
B
$$\sqrt 3 y = x - \sqrt 3$$
C
$$y = \sqrt 3 x - \sqrt 3$$
D
$$\sqrt 3 y = x - 1$$
EXAM MAP
Medical
NEET
| 601
| 1,328
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.234375
| 3
|
CC-MAIN-2024-33
|
latest
|
en
| 0.713125
|
http://www.wolfram.com/books/profile.cgi?id=6649
| 1,477,010,061,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2016-44/segments/1476988717959.91/warc/CC-MAIN-20161020183837-00244-ip-10-142-188-19.ec2.internal.warc.gz
| 669,816,354
| 8,780
|
SEARCH Advanced Search Topic All Topics Algebra Applied Mathematics Calculus and Analysis Chemistry Computer Science Courseware Differential Equations Discrete Mathematics Earth Sciences Economics and Finance Engineering Geometry Graphics Life Sciences Modeling and Simulation Number Theory Physics Probability and Statistics Programming Recreational Social Sciences Tutorial and Reference Language All Languages English Bulgarian Catalan Chinese Dutch Finnish French German Greek Hungarian Italian Japanese Korean Lithuanian Norwegian Polish Portuguese Russian Spanish Swedish
BROWSE TOPICS Algebra» Applied Mathematics» Calculus and Analysis» Chemistry» Computer Science» Courseware» Differential Equations» Discrete Mathematics» Earth Sciences» Economics and Finance» Engineering» Geometry» Graphics» Life Sciences» Modeling and Simulation» Number Theory» Physics» Probability and Statistics» Programming» Recreational» Social Sciences» Tutorial and Reference»
Some Concepts of Functional Analysis using Mathematica
by Gyorgy Popper
• Year: 2006
• 94 pp
Description
This textbook contains the course of lectures about some concepts in functional analysis for Ph.D. students of engineering. Functional analysis is a study of abstract linear spaces resulting from a synthesis of geometry, linear algebra and mathematical analysis. Some of the calculations of this textbook were made using symbolic-numeric computer algebra system Mathematica. The author found this system very useful for presenting these concepts because it does algebra and calculus computations quickly in an exact, symbolic manner.
The book also contains an easy introduction into the Lebesque measure and integration theory. Contents
Vector spaces, subspaces, linear manifolds | Dimension, spanning sets and (algebraic) basis | Linear operator | Normed spaces | Convergence, complete spaces | Continuous and bounded linear operator | Dense sets, separable spaces | Inner product, Hilbert space | Sets of measure zero, measurable functions | The space L2 | Generalized derivatives, distributions, Sobolev spaces | Weak (or generalized) solutions | Orthogonal systems, Fourier series | The projection theorem, the best approximation Related Topics
Applied Mathematics, Engineering
The Mathematica Journal
Articles on all aspects of Mathematica usage
Can't find what you're looking for or don't see your title listed? Contact us.
| 432
| 2,400
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.671875
| 3
|
CC-MAIN-2016-44
|
longest
|
en
| 0.756531
|
http://ilcasarosf.com/verbs-worksheet-for-kindergarten/action-words-worksheets-for-kindergarten-pdf-kidz-activities/
| 1,531,903,184,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-30/segments/1531676590074.12/warc/CC-MAIN-20180718080513-20180718100513-00537.warc.gz
| 171,795,825
| 11,740
|
Categories
Recent Files
Archives
# Worksheets Verbs Worksheet Forrten Free Printable Verb Linking Action Activity
By Christy B. Racette on July 12 2018 03:04:50
The addition worksheets on this page introduce addition math facts, multiple digit addition without regrouping, regrouping, decimals and other concepts designed to foster a mastery of all things addition. All of the worksheets include answer keys, and there are four versions of each worksheet with different problems.
Skip counting is counting at intervals of whichever number you choose. For example, if I was to skip count by 7 I would count, 7, 14, 21… and so on. Using this method you can do single digit multiplication with ease. Say the teacher asks you to multiply 4 x 7 = __. You simply skip count 7’s, 4 times, 7, 14, 21, 28. The answer to 4 x 7 = 28.
That still leaves the problem of memorizing a string of numbers, and here’s where the magic is. Teach children to skip count to the tune of a simple song. Have you ever wondered why children can learn the lyrics to songs so easily? It is because music can be used as a Mnemonic device, that is a strategy to assist with memorization. If you can associate the numbers with the sounds in a song, the children will not only learn them faster, but retain them much longer than they would memorizing them exclusively through repetition.
| 316
| 1,360
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.859375
| 3
|
CC-MAIN-2018-30
|
latest
|
en
| 0.936283
|
http://cboard.cprogramming.com/c-programming/65527-sin-cos-use-degrees.html
| 1,405,207,805,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2014-23/segments/1404776435471.2/warc/CC-MAIN-20140707234035-00053-ip-10-180-212-248.ec2.internal.warc.gz
| 22,333,567
| 11,449
|
# sin() and cos() that use degrees
This is a discussion on sin() and cos() that use degrees within the C Programming forums, part of the General Programming Boards category; Hi all, I was wondering if anyone knew of versions of sin() and cos() that use degrees. RHIDE's sin() and ...
1. ## sin() and cos() that use degrees
Hi all,
I was wondering if anyone knew of versions of sin() and cos() that use degrees. RHIDE's sin() and cos() use radians. I know how to convert between radians and degrees, but it doesn't work.
When I display a bitmap at the equivalent of 90 degrees, it's slightly off, because (I assume) of inaccuracies in converting between radians and degrees. Or is it inaccuracies with floating point numbers? Either way, could someone point me to a degrees version if cos() and sin()? I already tried using google but didn't get too much information.
DWK
2. You tried this? Make sure you're using doubles they have double precision.
Code:
double sind(double angle)
{
double angleradians = angle * M_PI / 180.0f;
return sin(angleradians) * M_PI / 180.0f;
}
salem knows best
3. Well it's down to inaccuracies for sure. Besides, any degree version will simply call the radian version behind your back without you realising it, so it doesn't save anything.
Or you could define
Code:
double sintable[90];
Making sure the cardinal points are set correctly, and using a loop calling sin() to initialise the rest.
4. Okay, thanks. I'll try that.
| 350
| 1,464
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.578125
| 3
|
CC-MAIN-2014-23
|
longest
|
en
| 0.928582
|
http://jabsto.com/Tutorial/topic-54/Microsoft-Office-2010-448.html
| 1,555,715,924,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-18/segments/1555578528430.9/warc/CC-MAIN-20190419220958-20190420002958-00184.warc.gz
| 94,672,501
| 6,181
|
Microsoft Office Tutorials and References
In Depth Information
Working with Worksheets
Problem Solving: Writing Effective Formulas
You can use formulas to quickly perform calculations and solve problems. First, identify the
problem you need to solve. Then, gather the data needed to solve the problem. Finally,
create accurate and effective formulas that use the data to answer or resolve the problem.
Keep formulas simple. Use functions in place of long, complex formulas whenever
possible. For example, use the SUM function instead of entering a formula that adds individual
cells, which makes it easier to confirm that the formula is making an accurate calculation
as it provides answers needed to evaluate the problem.
Do not hide data values within formulas. The worksheet displays formula results, not the
actual formula. For example, to calculate a 5% interest rate on a currency value in cell A5,
you could enter the formula =0.05*A5. However, this doesn’t show how the value is
calculated. A better approach places the value 0.05 in a cell accompanied by a descriptive label
and uses the cell reference in the formula. If you place 0.05 in cell A6, the formula =A6*A5
would calculate the interest value. Other people can then easily see the interest rate as
well as the resulting interest, ensuring that the formula is solving the right problem.
Break up formulas to show intermediate results. When a worksheet contains complex
computations, other people can more easily comprehend how the formula results are
calculated when different parts of the formula are distinguished. For example, the formula
=SUM(A1:A10)/SUM(B1:B10) calculates the ratio of two sums, but hides the two sum
values. Instead, enter each SUM function in a separate cell, such as cells A11 and B11, and
use the formula =A11/B11 to calculate the ratio. Other people can see both sums and the
value of their ratio in the worksheet and better understand the final result, which makes
it more likely that the best problem resolution will be selected.
Finding a solution to a problem requires accurate data and analysis. With workbooks,
this means using formulas that are easy to understand, clearly show the data being used
in the calculations, and demonstrate how the results are calculated. Only then can you be
confident that you are choosing the best problem resolution.
Working with Worksheets
You’ve seen that new workbooks are created with three initial worksheets labeled Sheet1,
Sheet2, and Sheet3. If needed, you can add new worksheets to a workbook and remove
unused sheets. You can also give worksheets more descriptive and meaningful names.
Inserting or Deleting a Worksheet
When you insert a new worksheet in a workbook, the new sheet is named based on the
number and names of the other sheets in the workbook. For example, if a workbook
has four worksheets named Sheet1 through Sheet4, the next inserted worksheet is named
Sheet5. You’ll add a new, blank worksheet to the RipCity Digital Orders workbook.
To insert a new worksheet
to the left of the active
sheet, right-click a sheet
tab, click Insert on the
sheet type, and then click
the OK button.
To insert a new worksheet:
1. Locate the three sheet tabs in the lower-left corner of the worksheet window.
2. To the right of the Sheet3 sheet tab, click the Insert Worksheet tab . A new
worksheet named Sheet4 appears at the end of the workbook and is active.
The workbook now includes two empty worksheets: Sheet3 and Sheet4. Because you
don’t plan to use these sheets, it’s a good idea to remove them.
Search JabSto ::
Custom Search
| 769
| 3,578
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.890625
| 4
|
CC-MAIN-2019-18
|
latest
|
en
| 0.890683
|
http://archives.math.utk.edu/visual.calculus/2/tangents.2/mpp.html
| 1,540,258,649,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-43/segments/1539583515564.94/warc/CC-MAIN-20181023002817-20181023024317-00352.warc.gz
| 23,942,590
| 1,581
|
Problem:
Graphically, find the tangent line to the graph of the function
f(x) = sin(2x)
at the point x = 0.7 as the limit of secant lines.
Visualization:
Using MPP:
1. At the main menu, either enter 4 or use the arrow keys to move to 4. Slopes and press
2. At the prompt, f(x) =, type sin(2x)
3. At the prompt, x0 = type 0.7
4. Press to draw the graph.
5. At this point, you will see the graph.
6. The program chooses intially h = ?0.5 and draws the corresponding secant lines. Slopes are shown at the left of the screen. This process, with h divided by 2 each time, is repeated several times automatically. What is interesting about this program is that when the h is too small to be seen on the screen, the scale is automatically changed and the process is repeated:
7. Eventually you will see the tangent line as a very good approximation to the function:
8. Pressing of any key will stop the drawing and the pressing of will return you to the previous screen where you can either change the function or the intial point x0.
| 265
| 1,034
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.53125
| 3
|
CC-MAIN-2018-43
|
latest
|
en
| 0.911361
|
https://www.yaclass.in/p/science-cbse/class-7/electric-current-and-its-effects-4324/re-e3542125-b0aa-409f-a83c-8682a1f4f2a9
| 1,632,094,870,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-39/segments/1631780056902.22/warc/CC-MAIN-20210919220343-20210920010343-00133.warc.gz
| 1,088,256,809
| 9,218
|
### Theory:
Circuit diagram:
A simple circuit is constructed where the bulb glows when the switch is turned 'ON', and when the switch is turned 'OFF', the bulb stops glowing.
(CBSE Class 7 chapter 14 'Electric current and its effects')
This circuit arrangement can be drawn using the symbols of electric components. An electric circuit is generally represented by a circuit diagram to make it simple.
Circuit diagram showing the switch in ON state
Circuit diagram showing the switch in OFF state
(CBSE Class 7 chapter 14 'Electric current and its effects')
The symbols of the cell, switch, and a lamp or bulb can be drawn anywhere in the circuit.
Electricity inside a bulb:
The bulb is made up of a glass that is fixed on a metallic base. Filament is made of thin tungsten wire that gives light when electricity flows through it. It is placed between two thick connecting wires which act as a support to the filament.
Parts of a light bulb
When the tip of the base of the bulb is in contact with the positive terminal of the cell, the bulb glows. When the bulb is taken away from the terminal of the electric cell, the bulb does not glow. A bulb becomes fused if there is a break in the filament of an electric bulb. Due to the break in the path of the current, the fused bulb does not glow.
Important!
One should never experiment with the electric mains or the power supply as it leads to shock. Carelessness while handling electric circuit may create accident and could be dangerous.
NOTE:Thomas Alva Edison invented electric bulbs. He has invented around $$1300$$ products which includes gramophone, the motion picture camera and the carbon transmitter.
Heating effect in the bulb:
An electric circuit can made using a single cell and a bulb. The bulb does not glow when the switch is kept in the 'OFF' state, and hence no heat is produced. When the switch is turned 'ON', the bulb glows.
Switch in ON and OFF state
After a minute of glowing, some amount of heat is felt when the bulb is touched. Again when the switch is turned 'OFF', heat is not sensed in the bulb. Due to the continuous flow of electric supply, the bulb becomes very hot. That is why one should never touch an electric bulb when it is lighted.
Never touch a lighted bulb
| 510
| 2,254
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.15625
| 3
|
CC-MAIN-2021-39
|
latest
|
en
| 0.898042
|
https://mackys.livejournal.com/399090.html?thread=1225202
| 1,582,421,251,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-10/segments/1581875145742.20/warc/CC-MAIN-20200223001555-20200223031555-00464.warc.gz
| 467,075,772
| 74,421
|
• Mood:
• Music:
# In which Ben does the math on a hoverboard.
The equation for the magnetic force on a wire is:
F = BLI
B is the magnetic field, in Teslas
L is the length of the wire, in meters
I is the current, in amps
The earth's magnetic field is about .3-.6 Gauss. There are 10,000 Gauss in a Tesla. Let's be optimistic and call it .5 Gauss. Converting to Teslas, B = .00005
Let's say the wire is one meter long, because it makes the math easier. L = 1.
How much force do we need? Let's say a 200 lb person, call it 90 kg. Gravity pulls them down with an acceleration of 9.8 m/s^2. F = ma, so F = 90 * 9.8, or 882 Newtons.
882 = I * 1 * .00005
I = 882 / .00005
I = 17,640,000 amps
A little more than seventeen and a half million amps.
To get some sense of scale, most circuit breakers for houses are about 200 amps. Your whole house, everything in it, all the lights going full blast, stereo, fridge, washer/dryer, everything, takes less than 200 amps. (And requires a cable about 3/4 of an inch across.) Doing the math, we see that this is the electrical equivalent of 88,200 houses going full bore.
In terms of energy, P = I^2V, so this comes to 3.7 x 10^16 Joules per second. In more familiar terms, this about the same energy as you would produce if you exploded 40 million tons of TNT. Per second.
| 380
| 1,320
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.953125
| 4
|
CC-MAIN-2020-10
|
latest
|
en
| 0.90729
|
https://www.chiefdelphi.com/t/cargo-actual-diameter-at-pressure/402473
| 1,726,814,311,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-38/segments/1725700652138.47/warc/CC-MAIN-20240920054402-20240920084402-00327.warc.gz
| 641,923,439
| 8,519
|
# Cargo Actual Diameter at Pressure
We were wondering what other teams cargo diameter is at correct pressure. Ours is measuring about 9 1/4". Currently we’re still waiting for our pressure gauge to come in, but have filled the cargo up until it’s definitely over pressurized and it doesn’t seem to be growing any larger.
I thought it’s weird that the manual says the cargo is 9 1/2" instead of ~ 9 1/2".
Section 5.7
CARGO is 9½ in. (~24 cm) in diameter, weighs 9½ oz. (~270 g), and has a fuzz surface.
CARGO is inflated to 3½ psi. ±½ psi.
What diameter are you guys getting with your cargo?
All the cargo I have measured has been 9.25ish. Granted we only have 2 currently. Waiting on more.
yup, 9.25" diameter, and it doesn’t change appreciably with pressure, past about 2psi
1 Like
Have you seen any expansion of similar inflated game pieces in previous years as they get used throughout competition?
1 Like
I can’t recall any similar game pieces. The closest might be 2010. The rubber balls with very elastic skin, as used in 2019, and the large balls with a cloth bag around an elastic bladder in 2008-2014, are not really the same as the 2022 game piece.
As I’ve been told many times after learning the hard way in 2020. Design around the variations (different psi and worn out game pieces). I dont have much confidence in the pressure gauge regulation at events, and I’ll bet it’ll vary from event to event.
6 Likes
Stupid question I should know the answer to, but don’t have a complex enough mental model.
Would atmospheric pressure at different alititudes come into play here?
Or, maybe asked differently… does the spec’ed inflation PSI refer to some absolute measurement that won’t vary as altitude/weather changes, or is it relative to outside atmospheric pressure?
I really feel like I should know this answer, but I’m drawing a blank on how to even think about it.
good question…I can take a wild guess.
If the ball is elastic, then it will expand when going to a higher elevation (lower atmospheric pressure). The gauge pressure may not change much.
If the ball is inelastic, then the absolute pressure in the ball will stay the same, but atmospheric pressure will drop with increased elevation, so the gauge should read higher. The spec’d pressure is a relative pressure reading. So when you bring a ball from your home in San Diego, to play in Denver, you’ll need to let some air out. And reinflate it when you get back home.
But that’s only my wild guess, from watching thin plastic water bottles as I drive to lower elevations all the time.
2 Likes
Going off what the user in this post explained, it sounds like it most certainly would/will.
Definitely the rule means gauge pressure, that is, the pressure in excess of local atmospheric pressure. 3½ psi absolute pressure would cause the CARGO to collapse into a bowl shape at sea level.
We are just trying to figure out how much variation to account for. At this point I would think cargo would mostly be shrinking due to lowering pressure. If it doesn’t grow much past 2 psi, then I would think they won’t over expand much throughout the competition.
We’re getting +/- 0.25"
Also, we intentionally inflated one to 10 psi for over a week now. Still only ~0.25" larger than the normal ball. It does have a noticeable firmness to it and it bounces about 6-8" higher with the test drop.
1 Like
Are you saying yours are 9.5" +/- .25"?
Understandable. Based on my observations so far, the variation in the ball due to change in psi, isnt remotely close to what happened to the yellow balls in 2020 as it got damaged and shrunk over time.
1 Like
I just measured a ball that we purchased from AndyMark that is inflated to about 3.5 psi and bounces within the prescribed parameters. It’s almost exactly 9.5". I’m at 200 feet above sea level.
1 Like
We got our pressure gauge today and filled one of the cargo balls to pressure. I noticed when measuring it this time that it’s not perfectly round. Not that I’m surprised by this, but just thought it would be good to mention. This could be why some people are getting different diameters. To measure ours I set it on a table and used a height gauge. I was getting heights from 9.20" to 9.40".
Also FYI, in the manual for the digital gauge we got, it has you zero the pressure first so that it’s set for you altitude.
1 Like
We aired some up today and a significant portion weren’t round. 1/3 to 1/2 I think.
This topic was automatically closed 365 days after the last reply. New replies are no longer allowed.
| 1,072
| 4,554
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.875
| 3
|
CC-MAIN-2024-38
|
latest
|
en
| 0.957966
|
https://fdocument.org/document/lecture-8-distortion-niknejadee142fa05lectspdflect8pdf-fractional-harmonic.html
| 1,632,790,141,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-39/segments/1631780058589.72/warc/CC-MAIN-20210928002254-20210928032254-00387.warc.gz
| 292,956,800
| 20,826
|
of 26
• date post
06-Sep-2019
• Category
## Documents
• view
13
2
Embed Size (px)
### Transcript of Lecture 8: Distortion niknejad/ee142_fa05lects/pdf/lect8.pdfآ Fractional Harmonic Distortion The...
• EECS 142
Lecture 8: Distortion Metrics
University of California, Berkeley
A. M. Niknejad University of California, Berkeley EECS 142 Lecture 8 p. 1/26 – p. 1/26
• Output Waveform
In general, then, the output waveform is a Fourier series
vo = V̂o1 cos ω1t + V̂o2 cos 2ω1t + V̂o3 cos 3ω1t + . . .
V̂o
V̂i
V̂o2
V̂o3
100mV
10mV1mV100µV10µV1µV
10mV
1mV
100µV
10µV
1µV
Gain Compression
Higher Order
Distortion Products
A. M. Niknejad University of California, Berkeley EECS 142 Lecture 8 p. 2/26 – p. 2/26
• Fractional Harmonic Distortion
The fractional second-harmonic distortion is a commonly cited metric
HD2 = ampl of second harmonic
ampl of fund
If we assume that the square power dominates the second-harmonic
HD2 = a2
S21 2
a1S1
or HD2 =
1
2
a2
a1 S1
A. M. Niknejad University of California, Berkeley EECS 142 Lecture 8 p. 3/26 – p. 3/26
• Third Harmonic Distortion
The fractional third harmonic distortion is given by
HD3 = ampl of third harmonic
ampl of fund
If we assume that the cubic power dominates the third harmonic
HD3 = a3
S21 4
a1S1
or
HD3 = 1
4
a3
a1 S21
A. M. Niknejad University of California, Berkeley EECS 142 Lecture 8 p. 4/26 – p. 4/26
• Output Referred Harmonic Distortion
In terms of the output signal Som, if we again neglect gain expansion/compression, we have Som = a1S1
HD2 = 1
2
a2
a2 1
Som
HD3 = 1
4
a3
a3 1
S2om
On a dB scale, the second harmonic increases linearly with a slope of one in terms of the output power whereas the thrid harmonic increases with a slope of 2.
A. M. Niknejad University of California, Berkeley EECS 142 Lecture 8 p. 5/26 – p. 5/26
• Signal Power
Recall that a general memoryless non-linear system will produce an output that can be written in the following form
vo(t) = V̂o1 cos ω1t + V̂o2 cos 2ω1t + V̂o3 cos 3ω1t + . . .
By Parseval’s theorem, we know the total power in the signal is related to the power in the harmonics
T v2(t)dt =
T
j
V̂oj cos(jω1t) ∑
k
V̂ok cos(kω1t)dt
= ∑
j
k
T V̂oj cos(jω1t)V̂ok cos(kω1t)dt
A. M. Niknejad University of California, Berkeley EECS 142 Lecture 8 p. 6/26 – p. 6/26
• Power in Distortion
By the orthogonality of the harmonics, we obtain Parseval’s Them
T v2(t)dt =
j
k
1
2 δjkV̂ojV̂ok =
1
2
j
V̂ 2oj
The power in the distortion relative to the fundamental power is therefore given by
Power in Distortion Power in Fundamental
= V 2o2 V 2o1
+ V 2o3 V 2o1
+ · · ·
= HD22 + HD 2
3 + HD 2
4 + · · ·
A. M. Niknejad University of California, Berkeley EECS 142 Lecture 8 p. 7/26 – p. 7/26
• Total Harmonic Distortion
We define the Total Harmonic Distortion (THD) by the following expression
THD = √
HD2 2
+ HD2 3
+ · · ·
Based on the particular application, we specify the maximum tolerable THD
Telephone audio can be pretty distorted (THD < 10%)
High quality audio is very sensitive (THD < 1% to THD < .001%)
Video is also pretty forgiving, THD < 5% for most applications
Analog Repeaters < .001%. RF Amplifiers < 0.1%
A. M. Niknejad University of California, Berkeley EECS 142 Lecture 8 p. 8/26 – p. 8/26
• Intermodulation Distortion
So far we have characterized a non-linear system for a single tone. What if we apply two tones
Si = S1 cos ω1t + S2 cos ω2t
So = a1Si + a2S 2
i + a3S 3
i + · · ·
= a1S1 cos ω1t + a1S2 cos ω2t + a3(Si) 3 + · · ·
The second power term gives
a2S 2
1 cos 2 ω1t + a2S
2
2 cos 2 ω2t + 2a2S1S2 cos ω1t cos ω2t
= a2 S2
1
2 (cos 2ω1t + 1) + a2
S2 2
2 (cos 2ω2t + 1) +
a2S1S2 (cos(ω1 + ω2)t − cos(ω1 − ω2)t) A. M. Niknejad University of California, Berkeley EECS 142 Lecture 8 p. 9/26 – p. 9/26
• Second Order Intermodulation
The last term cos(ω1 ± ω2)t is the second-order intermodulation term
The intermodulation distortion IM2 is defined when the two input signals have equal amplitude Si = S1 = S2
IM2 = Amp of Intermod
Amp of Fund =
a2
a1 Si
Note the relation between IM2 and HD2
IM2 = 2HD2 = HD2 + 6dB
A. M. Niknejad University of California, Berkeley EECS 142 Lecture 8 p. 10/26 – p. 10/26
• Practical Effects of IM2
This term produces distortion at a lower frequency ω1 − ω2 and at a higher frequency ω1 + ω2 Example: Say the receiver bandwidth is from 800MHz − 2.4GHz and two unwanted interfering signals appear at 800MHz and 900MHz.
Then we see that the second-order distortion will produce distortion at 100MHz and 1.7GHz. Since 1.7GHz is in the receiver band, signals at this frequency will be corrupted by the distortion.
A weak signal in this band can be “swamped” by the distortion.
Apparently, a “narrowband” system does not suffer from IM2? Or does it ?
A. M. Niknejad University of California, Berkeley EECS 142 Lecture 8 p. 11/26 – p. 11/26
In a low-IF or direct conversion receiver, the signal is down-converted to a low intermediate frequency fIF Since ω1 − ω2 can potentially produce distortion at low frequency, IM2 is very important in such systems
Example: A narrowband system has a receiver bandwidth of 1.9GHz - 2.0GHz. A sharp input filter eliminates any interference outside of this band. The IF frequency is 1MHz
Imagine two interfering signals appear at f1 = 1.910GHz and f2 = 1.911GHz. Notice that f2 − f1 = fIF Thus the output of the amplifier/mixer generate distortion at the IF frequency, potentially disrupting the communication.
A. M. Niknejad University of California, Berkeley EECS 142 Lecture 8 p. 12/26 – p. 12/26
• Cubic IM
Now let’s consider the output of the cubic term
a3s 3
i = a3(S1 cos ω1t + S2 cos ω2t) 3
Let’s first notice that the first and last term in the expansion are the same as the cubic distortion with a single input
a3S 3 1,2
4 (cos 3ω1,2t + 3 cos ω1,2t)
The cross terms look like (
3
2
)
a3S1S 2
2 cos ω1t cos 2 ω2t
A. M. Niknejad University of California, Berkeley EECS 142 Lecture 8 p. 13/26 – p. 13/26
• Third Order IM
Which can be simplified to
3 cos ω1t cos 2 ω2t =
3
2 cos ω1t(1 + cos 2ω2t) =
= 3
2 cos ω1t +
3
4 cos(2ω2 ± ω1)
The interesting term is the intermodulation at 2ω2 ± ω1 By symmetry, then, we also generate a term like
a3S 2
1S2 3
4 cos(2ω1 ± ω2)
Notice that if ω1 ≈ ω2, then the intermodulation 2ω2 − ω1 ≈ ω1
A. M. Niknejad University of California, Berkeley EECS 142 Lecture 8 p. 14/26 – p. 14/26
• Inband IM3 Distortion
ω1 ω2ω3
2ω2 ω12ω1 ω2
S(ω)
ω
Interfering Signals
wanted distortion product
Now we see that even if the system is narrowband, the output of an amplifier can contain in band intermodulation due to IM3.
This is in contrast to IM2 where the frequency of the intermodulation was at a lower and higher frequency. The IM3 frequency can fall in-band for two in-band interferer
A. M. Niknejad University of California, Berkeley EECS 142 Lecture 8 p. 15/26 – p. 15/26
• Definition of IM3
We define IM3 in a similar manner for Si = S1 = S2
IM3 = Amp of Third Intermod
Amp of Fund =
3
4
a3
a1 S2i
Note the relation between IM3 and HD3
IM3 = 3HD3 = HD3 + 10dB
A. M. Niknejad University of California, Berkeley EECS 142 Lecture 8 p. 16/26 – p. 16/26
• Complete Two-Tone Response
ω1 ω2
2ω2 − ω12ω1 − ω2
S(ω)
ω
3ω2 − 2ω13ω1 − 2ω2 2ω1 2ω2
ω1 + ω2ω2
− ω1 3ω2 − ω13ω1 − ω2 3ω13ω22ω1 + ω2 2ω2 + ω1
2ω2 − 2ω1 ω2 − ω1
We have so far identified the harmonics and IM2 and IM3 products
A more detailed analysis shows that an order n non-linearity can produce intermodulation at frequencies jω1 ± kω2 where j + k = n
All tones are spaced by the difference ω2 − ω1 A. M. Niknejad University of California, Berkeley EECS 142 Lecture 8 p. 17/26 – p. 17/26
• Distortion of AM Signals
Consider a simple AM signal (modulated by a single tone)
s(t) = S2(1 + m cos ωmt) cos ω2t
where the modulation index m ≤ 1. This can be written as
s(t) = S2 co
| 2,727
| 7,953
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.890625
| 3
|
CC-MAIN-2021-39
|
latest
|
en
| 0.680875
|
https://www.physicsforums.com/threads/work-done-per-unit-charge-by-electric-field-on-charge.948129/
| 1,618,377,142,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-17/segments/1618038076819.36/warc/CC-MAIN-20210414034544-20210414064544-00540.warc.gz
| 1,052,583,726
| 18,089
|
# Work done per unit charge by electric field on charge
## The Attempt at a Solution
I know the units for V is J/C so #3 and #4 are wrong. But how do I determine the signs?
#### Attachments
• Screen Shot 2018-05-25 at 2.37.17 pm.png
27.1 KB · Views: 2,418
kuruman
Homework Helper
Gold Member
Is the work done by the electric field positive or negative? What do you need to ascertain in order to answer this question? Hint: When is the work done by a force positive and when is it negative?
Is the work done by the electric field positive or negative? What do you need to ascertain in order to answer this question? Hint: When is the work done by a force positive and when is it negative?
Work is positive when force is in same direction as displacement. So here the direction is X to Y and the force is also from X to Y because Vx>Vy?
kuruman
| 213
| 849
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.796875
| 3
|
CC-MAIN-2021-17
|
longest
|
en
| 0.948252
|
http://www.science.gov/topicpages/m/markov+chain+monte.html
| 1,481,227,400,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2016-50/segments/1480698542655.88/warc/CC-MAIN-20161202170902-00148-ip-10-31-129-80.ec2.internal.warc.gz
| 677,866,090
| 258,775
|
#### Sample records for markov chain monte
1. Markov Chain Monte Carlo and Irreversibility
Ottobre, Michela
2016-06-01
Markov Chain Monte Carlo (MCMC) methods are statistical methods designed to sample from a given measure π by constructing a Markov chain that has π as invariant measure and that converges to π. Most MCMC algorithms make use of chains that satisfy the detailed balance condition with respect to π; such chains are therefore reversible. On the other hand, recent work [18, 21, 28, 29] has stressed several advantages of using irreversible processes for sampling. Roughly speaking, irreversible diffusions converge to equilibrium faster (and lead to smaller asymptotic variance as well). In this paper we discuss some of the recent progress in the study of nonreversible MCMC methods. In particular: i) we explain some of the difficulties that arise in the analysis of nonreversible processes and we discuss some analytical methods to approach the study of continuous-time irreversible diffusions; ii) most of the rigorous results on irreversible diffusions are available for continuous-time processes; however, for computational purposes one needs to discretize such dynamics. It is well known that the resulting discretized chain will not, in general, retain all the good properties of the process that it is obtained from. In particular, if we want to preserve the invariance of the target measure, the chain might no longer be reversible. Therefore iii) we conclude by presenting an MCMC algorithm, the SOL-HMC algorithm [23], which results from a nonreversible discretization of a nonreversible dynamics.
2. Exploring Mass Perception with Markov Chain Monte Carlo
ERIC Educational Resources Information Center
Cohen, Andrew L.; Ross, Michael G.
2009-01-01
Several previous studies have examined the ability to judge the relative mass of objects in idealized collisions. With a newly developed technique of psychological Markov chain Monte Carlo sampling (A. N. Sanborn & T. L. Griffiths, 2008), this work explores participants; perceptions of different collision mass ratios. The results reveal…
3. Regenerative Markov Chain Monte Carlo for any distribution.
SciTech Connect
Minh, D.
2012-01-01
While Markov chain Monte Carlo (MCMC) methods are frequently used for difficult calculations in a wide range of scientific disciplines, they suffer from a serious limitation: their samples are not independent and identically distributed. Consequently, estimates of expectations are biased if the initial value of the chain is not drawn from the target distribution. Regenerative simulation provides an elegant solution to this problem. In this article, we propose a simple regenerative MCMC algorithm to generate variates for any distribution
4. Markov Chain Monte Carlo Bayesian Learning for Neural Networks
NASA Technical Reports Server (NTRS)
Goodrich, Michael S.
2011-01-01
Conventional training methods for neural networks involve starting al a random location in the solution space of the network weights, navigating an error hyper surface to reach a minimum, and sometime stochastic based techniques (e.g., genetic algorithms) to avoid entrapment in a local minimum. It is further typically necessary to preprocess the data (e.g., normalization) to keep the training algorithm on course. Conversely, Bayesian based learning is an epistemological approach concerned with formally updating the plausibility of competing candidate hypotheses thereby obtaining a posterior distribution for the network weights conditioned on the available data and a prior distribution. In this paper, we developed a powerful methodology for estimating the full residual uncertainty in network weights and therefore network predictions by using a modified Jeffery's prior combined with a Metropolis Markov Chain Monte Carlo method.
5. Accelerating Monte Carlo Markov chains with proxy and error models
Josset, Laureline; Demyanov, Vasily; Elsheikh, Ahmed H.; Lunati, Ivan
2015-12-01
In groundwater modeling, Monte Carlo Markov Chain (MCMC) simulations are often used to calibrate aquifer parameters and propagate the uncertainty to the quantity of interest (e.g., pollutant concentration). However, this approach requires a large number of flow simulations and incurs high computational cost, which prevents a systematic evaluation of the uncertainty in the presence of complex physical processes. To avoid this computational bottleneck, we propose to use an approximate model (proxy) to predict the response of the exact model. Here, we use a proxy that entails a very simplified description of the physics with respect to the detailed physics described by the "exact" model. The error model accounts for the simplification of the physical process; and it is trained on a learning set of realizations, for which both the proxy and exact responses are computed. First, the key features of the set of curves are extracted using functional principal component analysis; then, a regression model is built to characterize the relationship between the curves. The performance of the proposed approach is evaluated on the Imperial College Fault model. We show that the joint use of the proxy and the error model to infer the model parameters in a two-stage MCMC set-up allows longer chains at a comparable computational cost. Unnecessary evaluations of the exact responses are avoided through a preliminary evaluation of the proposal made on the basis of the corrected proxy response. The error model trained on the learning set is crucial to provide a sufficiently accurate prediction of the exact response and guide the chains to the low misfit regions. The proposed methodology can be extended to multiple-chain algorithms or other Bayesian inference methods. Moreover, FPCA is not limited to the specific presented application and offers a general framework to build error models.
6. MARKOV CHAIN MONTE CARLO POSTERIOR SAMPLING WITH THE HAMILTONIAN METHOD
SciTech Connect
K. HANSON
2001-02-01
The Markov Chain Monte Carlo technique provides a means for drawing random samples from a target probability density function (pdf). MCMC allows one to assess the uncertainties in a Bayesian analysis described by a numerically calculated posterior distribution. This paper describes the Hamiltonian MCMC technique in which a momentum variable is introduced for each parameter of the target pdf. In analogy to a physical system, a Hamiltonian H is defined as a kinetic energy involving the momenta plus a potential energy {var_phi}, where {var_phi} is minus the logarithm of the target pdf. Hamiltonian dynamics allows one to move along trajectories of constant H, taking large jumps in the parameter space with relatively few evaluations of {var_phi} and its gradient. The Hamiltonian algorithm alternates between picking a new momentum vector and following such trajectories. The efficiency of the Hamiltonian method for multidimensional isotropic Gaussian pdfs is shown to remain constant at around 7% for up to several hundred dimensions. The Hamiltonian method handles correlations among the variables much better than the standard Metropolis algorithm. A new test, based on the gradient of {var_phi}, is proposed to measure the convergence of the MCMC sequence.
7. Ensemble bayesian model averaging using markov chain Monte Carlo sampling
SciTech Connect
Vrugt, Jasper A; Diks, Cees G H; Clark, Martyn P
2008-01-01
Bayesian model averaging (BMA) has recently been proposed as a statistical method to calibrate forecast ensembles from numerical weather models. Successful implementation of BMA however, requires accurate estimates of the weights and variances of the individual competing models in the ensemble. In their seminal paper (Raftery etal. Mon Weather Rev 133: 1155-1174, 2(05)) has recommended the Expectation-Maximization (EM) algorithm for BMA model training, even though global convergence of this algorithm cannot be guaranteed. In this paper, we compare the performance of the EM algorithm and the recently developed Differential Evolution Adaptive Metropolis (DREAM) Markov Chain Monte Carlo (MCMC) algorithm for estimating the BMA weights and variances. Simulation experiments using 48-hour ensemble data of surface temperature and multi-model stream-flow forecasts show that both methods produce similar results, and that their performance is unaffected by the length of the training data set. However, MCMC simulation with DREAM is capable of efficiently handling a wide variety of BMA predictive distributions, and provides useful information about the uncertainty associated with the estimated BMA weights and variances.
8. Markov chain Monte Carlo methods: an introductory example
Klauenberg, Katy; Elster, Clemens
2016-02-01
When the Guide to the Expression of Uncertainty in Measurement (GUM) and methods from its supplements are not applicable, the Bayesian approach may be a valid and welcome alternative. Evaluating the posterior distribution, estimates or uncertainties involved in Bayesian inferences often requires numerical methods to avoid high-dimensional integrations. Markov chain Monte Carlo (MCMC) sampling is such a method—powerful, flexible and widely applied. Here, a concise introduction is given, illustrated by a simple, typical example from metrology. The Metropolis-Hastings algorithm is the most basic and yet flexible MCMC method. Its underlying concepts are explained and the algorithm is given step by step. The few lines of software code required for its implementation invite interested readers to get started. Diagnostics to evaluate the performance and common algorithmic choices are illustrated to calibrate the Metropolis-Hastings algorithm for efficiency. Routine application of MCMC algorithms may be hindered currently by the difficulty to assess the convergence of MCMC output and thus to assure the validity of results. An example points to the importance of convergence and initiates discussion about advantages as well as areas of research. Available software tools are mentioned throughout.
9. Cool walking: a new Markov chain Monte Carlo sampling method.
PubMed
2003-01-15
Effective relaxation processes for difficult systems like proteins or spin glasses require special simulation techniques that permit barrier crossing to ensure ergodic sampling. Numerous adaptations of the venerable Metropolis Monte Carlo (MMC) algorithm have been proposed to improve its sampling efficiency, including various hybrid Monte Carlo (HMC) schemes, and methods designed specifically for overcoming quasi-ergodicity problems such as Jump Walking (J-Walking), Smart Walking (S-Walking), Smart Darting, and Parallel Tempering. We present an alternative to these approaches that we call Cool Walking, or C-Walking. In C-Walking two Markov chains are propagated in tandem, one at a high (ergodic) temperature and the other at a low temperature. Nonlocal trial moves for the low temperature walker are generated by first sampling from the high-temperature distribution, then performing a statistical quenching process on the sampled configuration to generate a C-Walking jump move. C-Walking needs only one high-temperature walker, satisfies detailed balance, and offers the important practical advantage that the high and low-temperature walkers can be run in tandem with minimal degradation of sampling due to the presence of correlations. To make the C-Walking approach more suitable to real problems we decrease the required number of cooling steps by attempting to jump at intermediate temperatures during cooling. We further reduce the number of cooling steps by utilizing "windows" of states when jumping, which improves acceptance ratios and lowers the average number of cooling steps. We present C-Walking results with comparisons to J-Walking, S-Walking, Smart Darting, and Parallel Tempering on a one-dimensional rugged potential energy surface in which the exact normalized probability distribution is known. C-Walking shows superior sampling as judged by two ergodic measures. PMID:12483676
10. Markov Chain Monte-Carlo Orbit Computation for Binary Asteroids
Oszkiewicz, D.; Hestroffer, D.; Pedro, David C.
2013-11-01
We present a novel method of orbit computation for resolved binary asteroids. The method combines the Thiele, Innes, van den Bos method with a Markov chain Monte Carlo technique (MCMC). The classical Thiele-van den Bos method has been commonly used in multiple applications before, including orbits of binary stars and asteroids; conversely this novel method can be used for the analysis of binary stars, and of other gravitationally bound binaries. The method requires a minimum of three observations (observing times and relative positions - Cartesian or polar) made at the same tangent plane - or close enough for enabling a first approximation. Further, the use of the MCMC technique for statistical inversion yields the whole bundle of possible orbits, including the one that is most probable. In this new method, we make use of the Metropolis-Hastings algorithm to sample the parameters of the Thiele-van den Bos method, that is the orbital period (or equivalently the double areal constant) together with three randomly selected observations from the same tangent plane. The observations are sampled within their observational errors (with an assumed distribution) and the orbital period is the only parameter that has to be tuned during the sampling procedure. We run multiple chains to ensure that the parameter phase space is well sampled and that the solutions have converged. After the sampling is completed we perform convergence diagnostics. The main advantage of the novel approach is that the orbital period does not need to be known in advance and the entire region of possible orbital solutions is sampled resulting in a maximum likelihood solution and the confidence regions. We have tested the new method on several known binary asteroids and conclude a good agreement with the results obtained with other methods. The new method has been implemented into the Gaia DPAC data reduction pipeline and can be used to confirm the binary nature of a suspected system, and for deriving
11. Regeneration and Fixed-Width Analysis of Markov Chain Monte Carlo Algorithms
Latuszynski, Krzysztof
2009-07-01
In the thesis we take the split chain approach to analyzing Markov chains and use it to establish fixed-width results for estimators obtained via Markov chain Monte Carlo procedures (MCMC). Theoretical results include necessary and sufficient conditions in terms of regeneration for central limit theorems for ergodic Markov chains and a regenerative proof of a CLT version for uniformly ergodic Markov chains with E_{π}f^2< infty. To obtain asymptotic confidence intervals for MCMC estimators, strongly consistent estimators of the asymptotic variance are essential. We relax assumptions required to obtain such estimators. Moreover, under a drift condition, nonasymptotic fixed-width results for MCMC estimators for a general state space setting (not necessarily compact) and not necessarily bounded target function f are obtained. The last chapter is devoted to the idea of adaptive Monte Carlo simulation and provides convergence results and law of large numbers for adaptive procedures under path-stability condition for transition kernels.
12. Experiences with Markov Chain Monte Carlo Convergence Assessment in Two Psychometric Examples
ERIC Educational Resources Information Center
Sinharay, Sandip
2004-01-01
There is an increasing use of Markov chain Monte Carlo (MCMC) algorithms for fitting statistical models in psychometrics, especially in situations where the traditional estimation techniques are very difficult to apply. One of the disadvantages of using an MCMC algorithm is that it is not straightforward to determine the convergence of the…
13. A Markov Chain Monte Carlo Approach to Confirmatory Item Factor Analysis
ERIC Educational Resources Information Center
Edwards, Michael C.
2010-01-01
Item factor analysis has a rich tradition in both the structural equation modeling and item response theory frameworks. The goal of this paper is to demonstrate a novel combination of various Markov chain Monte Carlo (MCMC) estimation routines to estimate parameters of a wide variety of confirmatory item factor analysis models. Further, I show…
14. An Evaluation of a Markov Chain Monte Carlo Method for the Rasch Model.
ERIC Educational Resources Information Center
Kim, Seock-Ho
2001-01-01
Examined the accuracy of the Gibbs sampling Markov chain Monte Carlo procedure for estimating item and person (theta) parameters in the one-parameter logistic model. Analyzed four empirical datasets using the Gibbs sampling, conditional maximum likelihood, marginal maximum likelihood, and joint maximum likelihood methods. Discusses the conditions…
15. Markov Chain Monte Carlo Estimation of Item Parameters for the Generalized Graded Unfolding Model
ERIC Educational Resources Information Center
de la Torre, Jimmy; Stark, Stephen; Chernyshenko, Oleksandr S.
2006-01-01
The authors present a Markov Chain Monte Carlo (MCMC) parameter estimation procedure for the generalized graded unfolding model (GGUM) and compare it to the marginal maximum likelihood (MML) approach implemented in the GGUM2000 computer program, using simulated and real personality data. In the simulation study, test length, number of response…
16. An NCME Instructional Module on Estimating Item Response Theory Models Using Markov Chain Monte Carlo Methods
ERIC Educational Resources Information Center
Kim, Jee-Seon; Bolt, Daniel M.
2007-01-01
The purpose of this ITEMS module is to provide an introduction to Markov chain Monte Carlo (MCMC) estimation for item response models. A brief description of Bayesian inference is followed by an overview of the various facets of MCMC algorithms, including discussion of prior specification, sampling procedures, and methods for evaluating chain…
17. Teaching Markov Chain Monte Carlo: Revealing the Basic Ideas behind the Algorithm
ERIC Educational Resources Information Center
Stewart, Wayne; Stewart, Sepideh
2014-01-01
For many scientists, researchers and students Markov chain Monte Carlo (MCMC) simulation is an important and necessary tool to perform Bayesian analyses. The simulation is often presented as a mathematical algorithm and then translated into an appropriate computer program. However, this can result in overlooking the fundamental and deeper…
18. Marathon: An Open Source Software Library for the Analysis of Markov-Chain Monte Carlo Algorithms.
PubMed
Rechner, Steffen; Berger, Annabell
2016-01-01
We present the software library marathon, which is designed to support the analysis of sampling algorithms that are based on the Markov-Chain Monte Carlo principle. The main application of this library is the computation of properties of so-called state graphs, which represent the structure of Markov chains. We demonstrate applications and the usefulness of marathon by investigating the quality of several bounding methods on four well-known Markov chains for sampling perfect matchings and bipartite graphs. In a set of experiments, we compute the total mixing time and several of its bounds for a large number of input instances. We find that the upper bound gained by the famous canonical path method is often several magnitudes larger than the total mixing time and deteriorates with growing input size. In contrast, the spectral bound is found to be a precise approximation of the total mixing time. PMID:26824442
19. Marathon: An Open Source Software Library for the Analysis of Markov-Chain Monte Carlo Algorithms
PubMed Central
Rechner, Steffen; Berger, Annabell
2016-01-01
We present the software library marathon, which is designed to support the analysis of sampling algorithms that are based on the Markov-Chain Monte Carlo principle. The main application of this library is the computation of properties of so-called state graphs, which represent the structure of Markov chains. We demonstrate applications and the usefulness of marathon by investigating the quality of several bounding methods on four well-known Markov chains for sampling perfect matchings and bipartite graphs. In a set of experiments, we compute the total mixing time and several of its bounds for a large number of input instances. We find that the upper bound gained by the famous canonical path method is often several magnitudes larger than the total mixing time and deteriorates with growing input size. In contrast, the spectral bound is found to be a precise approximation of the total mixing time. PMID:26824442
20. Finding noncommunicating sets for Markov chain Monte Carlo estimations on pedigrees.
PubMed Central
Lin, S.; Thompson, E.; Wijsman, E.
1994-01-01
Markov chain Monte Carlo (MCMC) has recently gained use as a method of estimating required probability and likelihood functions in pedigree analysis, when exact computation is impractical. However, when a multiallelic locus is involved, irreducibility of the constructed Markov chain, an essential requirement of the MCMC method, may fail. Solutions proposed by several researchers, which do not identify all the noncommunicating sets of genotypic configurations, are inefficient with highly polymorphic loci. This is a particularly serious problem in linkage analysis, because highly polymorphic markers are much more informative and thus are preferred. In the present paper, we describe an algorithm that finds all the noncommunicating classes of genotypic configurations on any pedigree. This leads to a more efficient method of defining an irreducible Markov chain. Examples, including a pedigree from a genetic study of familial Alzheimer disease, are used to illustrate how the algorithm works and how penetrances are modified for specific individuals to ensure irreducibility. PMID:8128968
1. Finding noncommunicating sets for Markov chain Monte Carlo estimations on pedigrees
SciTech Connect
Lin, S. ); Thompson, E.; Wijsman, E. )
1994-04-01
Markov chain Monte Carlo (MCMC) has recently gained use as a method of estimating required probability and likelihood functions in pedigree analysis, when exact computation is impractical. However, when a multiallelic locus is involved, irreducibility of the constructed Markov chain, an essential requirement of the MCMC method, may fail. Solutions proposed by several researchers, which do not identify all the noncommunicating sets of genotypic configurations, are inefficient with highly polymorphic loci. This is a particularly serious problem in linkage analysis, because highly polymorphic markers are much more informative and thus are preferred. In the present paper, the authors describe an algorithm that finds all the noncommunicating classes of genotypic configurations on any pedigree. This leads to a more efficient method of defining an irreducible Markov chain. Examples, including a pedigree from a genetic study of familial Alzheimer disease, are used to illustrate how the algorithm works and how penetrances are modified for specific individuals to ensure irreducibility. 20 refs., 7 figs., 6 tabs.
2. Integration within the Felsenstein equation for improved Markov chain Monte Carlo methods in population genetics
PubMed Central
Hey, Jody; Nielsen, Rasmus
2007-01-01
In 1988, Felsenstein described a framework for assessing the likelihood of a genetic data set in which all of the possible genealogical histories of the data are considered, each in proportion to their probability. Although not analytically solvable, several approaches, including Markov chain Monte Carlo methods, have been developed to find approximate solutions. Here, we describe an approach in which Markov chain Monte Carlo simulations are used to integrate over the space of genealogies, whereas other parameters are integrated out analytically. The result is an approximation to the full joint posterior density of the model parameters. For many purposes, this function can be treated as a likelihood, thereby permitting likelihood-based analyses, including likelihood ratio tests of nested models. Several examples, including an application to the divergence of chimpanzee subspecies, are provided. PMID:17301231
3. Integration within the Felsenstein equation for improved Markov chain Monte Carlo methods in population genetics.
PubMed
Hey, Jody; Nielsen, Rasmus
2007-02-20
In 1988, Felsenstein described a framework for assessing the likelihood of a genetic data set in which all of the possible genealogical histories of the data are considered, each in proportion to their probability. Although not analytically solvable, several approaches, including Markov chain Monte Carlo methods, have been developed to find approximate solutions. Here, we describe an approach in which Markov chain Monte Carlo simulations are used to integrate over the space of genealogies, whereas other parameters are integrated out analytically. The result is an approximation to the full joint posterior density of the model parameters. For many purposes, this function can be treated as a likelihood, thereby permitting likelihood-based analyses, including likelihood ratio tests of nested models. Several examples, including an application to the divergence of chimpanzee subspecies, are provided. PMID:17301231
4. Adaptive Markov chain Monte Carlo forward projection for statistical analysis in epidemic modelling of human papillomavirus.
PubMed
Korostil, Igor A; Peters, Gareth W; Cornebise, Julien; Regan, David G
2013-05-20
A Bayesian statistical model and estimation methodology based on forward projection adaptive Markov chain Monte Carlo is developed in order to perform the calibration of a high-dimensional nonlinear system of ordinary differential equations representing an epidemic model for human papillomavirus types 6 and 11 (HPV-6, HPV-11). The model is compartmental and involves stratification by age, gender and sexual-activity group. Developing this model and a means to calibrate it efficiently is relevant because HPV is a very multi-typed and common sexually transmitted infection with more than 100 types currently known. The two types studied in this paper, types 6 and 11, are causing about 90% of anogenital warts. We extend the development of a sexual mixing matrix on the basis of a formulation first suggested by Garnett and Anderson, frequently used to model sexually transmitted infections. In particular, we consider a stochastic mixing matrix framework that allows us to jointly estimate unknown attributes and parameters of the mixing matrix along with the parameters involved in the calibration of the HPV epidemic model. This matrix describes the sexual interactions between members of the population under study and relies on several quantities that are a priori unknown. The Bayesian model developed allows one to estimate jointly the HPV-6 and HPV-11 epidemic model parameters as well as unknown sexual mixing matrix parameters related to assortativity. Finally, we explore the ability of an extension to the class of adaptive Markov chain Monte Carlo algorithms to incorporate a forward projection strategy for the ordinary differential equation state trajectories. Efficient exploration of the Bayesian posterior distribution developed for the ordinary differential equation parameters provides a challenge for any Markov chain sampling methodology, hence the interest in adaptive Markov chain methods. We conclude with simulation studies on synthetic and recent actual data. PMID
5. Exact Likelihood-free Markov Chain Monte Carlo for Elliptically Contoured Distributions
PubMed Central
Marjoram, Paul
2015-01-01
Recent results in Markov chain Monte Carlo (MCMC) show that a chain based on an unbiased estimator of the likelihood can have a stationary distribution identical to that of a chain based on exact likelihood calculations. In this paper we develop such an estimator for elliptically contoured distributions, a large family of distributions that includes and generalizes the multivariate normal. We then show how this estimator, combined with pseudorandom realizations of an elliptically contoured distribution, can be used to run MCMC in a way that replicates the stationary distribution of a likelihood based chain, but does not require explicit likelihood calculations. Because many elliptically contoured distributions do not have closed form densities, our simulation based approach enables exact MCMC based inference in a range of cases where previously it was impossible. PMID:26167984
6. Markov chain Monte Carlo methods for statistical analysis of RF photonic devices.
PubMed
Piels, Molly; Zibar, Darko
2016-02-01
The microwave reflection coefficient is commonly used to characterize the impedance of high-speed optoelectronic devices. Error and uncertainty in equivalent circuit parameters measured using this data are systematically evaluated. The commonly used nonlinear least-squares method for estimating uncertainty is shown to give unsatisfactory and incorrect results due to the nonlinear relationship between the circuit parameters and the measured data. Markov chain Monte Carlo methods are shown to provide superior results, both for individual devices and for assessing within-die variation. PMID:26906783
7. Bayesian Modeling of Time Trends in Component Reliability Data via Markov Chain Monte Carlo Simulation
SciTech Connect
D. L. Kelly
2007-06-01
Markov chain Monte Carlo (MCMC) techniques represent an extremely flexible and powerful approach to Bayesian modeling. This work illustrates the application of such techniques to time-dependent reliability of components with repair. The WinBUGS package is used to illustrate, via examples, how Bayesian techniques can be used for parametric statistical modeling of time-dependent component reliability. Additionally, the crucial, but often overlooked subject of model validation is discussed, and summary statistics for judging the model’s ability to replicate the observed data are developed, based on the posterior predictive distribution for the parameters of interest.
8. Observational constraints on G-corrected holographic dark energy using a Markov chain Monte Carlo method
2014-02-01
We constrain holographic dark energy (HDE) with time varying gravitational coupling constant in the framework of the modified Friedmann equations using cosmological data from type Ia supernovae, baryon acoustic oscillations, cosmic microwave background radiation and X-ray gas mass fraction. Applying a Markov Chain Monte Carlo (MCMC) simulation, we obtain the best fit values of the model and cosmological parameters within 1 σ confidence level (CL) in a flat universe as: , , and the HDE constant . Using the best fit values, the equation of state of the dark component at the present time w d0 at 1 σ CL can cross the phantom boundary w=-1.
9. Bayesian and Markov chain Monte Carlo methods for identifying nonlinear systems in the presence of uncertainty
PubMed Central
Green, P. L.; Worden, K.
2015-01-01
In this paper, the authors outline the general principles behind an approach to Bayesian system identification and highlight the benefits of adopting a Bayesian framework when attempting to identify models of nonlinear dynamical systems in the presence of uncertainty. It is then described how, through a summary of some key algorithms, many of the potential difficulties associated with a Bayesian approach can be overcome through the use of Markov chain Monte Carlo (MCMC) methods. The paper concludes with a case study, where an MCMC algorithm is used to facilitate the Bayesian system identification of a nonlinear dynamical system from experimentally observed acceleration time histories. PMID:26303916
10. Markov chain Monte Carlo linkage analysis of a complex qualitative phenotype.
PubMed
Hinrichs, A; Lin, J H; Reich, T; Bierut, L; Suarez, B K
1999-01-01
We tested a new computer program, LOKI, that implements a reversible jump Markov chain Monte Carlo (MCMC) technique for segregation and linkage analysis. Our objective was to determine whether this software, designed for use with continuously distributed phenotypes, has any efficacy when applied to the discrete disease states of the simulated data from the Mordor data from GAW Problem 1. Although we were able to identify the genomic location for two of the three quantitative trait loci by repeated application of the software, the MCMC sampler experienced significant mixing problems indicating that the method, as currently formulated in LOKI, was not suitable for the discrete phenotypes in this data set. PMID:10597502
11. An efficient interpolation technique for jump proposals in reversible-jump Markov chain Monte Carlo calculations.
PubMed
Farr, W M; Mandel, I; Stevens, D
2015-06-01
Selection among alternative theoretical models given an observed dataset is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing Bayesian model selection, but it suffers from a fundamental difficulty and it requires jumps between model parameter spaces, but cannot efficiently explore both parameter spaces at once. Thus, a naive jump between parameter spaces is unlikely to be accepted in the Markov chain Monte Carlo (MCMC) algorithm and convergence is correspondingly slow. Here, we demonstrate an interpolation technique that uses samples from single-model MCMCs to propose intermodel jumps from an approximation to the single-model posterior of the target parameter space. The interpolation technique, based on a kD-tree data structure, is adaptive and efficient in modest dimensionality. We show that our technique leads to improved convergence over naive jumps in an RJMCMC, and compare it to other proposals in the literature to improve the convergence of RJMCMCs. We also demonstrate the use of the same interpolation technique as a way to construct efficient 'global' proposal distributions for single-model MCMCs without prior knowledge of the structure of the posterior distribution, and discuss improvements that permit the method to be used in higher dimensional spaces efficiently. PMID:26543580
12. Population synthesis of radio and gamma-ray millisecond pulsars using Markov Chain Monte Carlo techniques
Gonthier, Peter L.; Koh, Yew-Meng; Kust Harding, Alice
2016-04-01
We present preliminary results of a new population synthesis of millisecond pulsars (MSP) from the Galactic disk using Markov Chain Monte Carlo techniques to better understand the model parameter space. We include empirical radio and gamma-ray luminosity models that are dependent on the pulsar period and period derivative with freely varying exponents. The magnitudes of the model luminosities are adjusted to reproduce the number of MSPs detected by a group of thirteen radio surveys as well as the MSP birth rate in the Galaxy and the number of MSPs detected by Fermi. We explore various high-energy emission geometries like the slot gap, outer gap, two pole caustic and pair starved polar cap models. The parameters associated with the birth distributions for the mass accretion rate, magnetic field, and period distributions are well constrained. With the set of four free parameters, we employ Markov Chain Monte Carlo simulations to explore the model parameter space. We present preliminary comparisons of the simulated and detected distributions of radio and gamma-ray pulsar characteristics. We estimate the contribution of MSPs to the diffuse gamma-ray background with a special focus on the Galactic Center.We express our gratitude for the generous support of the National Science Foundation (RUI: AST-1009731), Fermi Guest Investigator Program and the NASA Astrophysics Theory and Fundamental Program (NNX09AQ71G).
13. An efficient interpolation technique for jump proposals in reversible-jump Markov chain Monte Carlo calculations
PubMed Central
Farr, W. M.; Mandel, I.; Stevens, D.
2015-01-01
Selection among alternative theoretical models given an observed dataset is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing Bayesian model selection, but it suffers from a fundamental difficulty and it requires jumps between model parameter spaces, but cannot efficiently explore both parameter spaces at once. Thus, a naive jump between parameter spaces is unlikely to be accepted in the Markov chain Monte Carlo (MCMC) algorithm and convergence is correspondingly slow. Here, we demonstrate an interpolation technique that uses samples from single-model MCMCs to propose intermodel jumps from an approximation to the single-model posterior of the target parameter space. The interpolation technique, based on a kD-tree data structure, is adaptive and efficient in modest dimensionality. We show that our technique leads to improved convergence over naive jumps in an RJMCMC, and compare it to other proposals in the literature to improve the convergence of RJMCMCs. We also demonstrate the use of the same interpolation technique as a way to construct efficient ‘global’ proposal distributions for single-model MCMCs without prior knowledge of the structure of the posterior distribution, and discuss improvements that permit the method to be used in higher dimensional spaces efficiently. PMID:26543580
14. Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling
SciTech Connect
Vrugt, Jasper A; Hyman, James M; Robinson, Bruce A; Higdon, Dave; Ter Braak, Cajo J F; Diks, Cees G H
2008-01-01
Markov chain Monte Carlo (MCMC) methods have found widespread use in many fields of study to estimate the average properties of complex systems, and for posterior inference in a Bayesian framework. Existing theory and experiments prove convergence of well constructed MCMC schemes to the appropriate limiting distribution under a variety of different conditions. In practice, however this convergence is often observed to be disturbingly slow. This is frequently caused by an inappropriate selection of the proposal distribution used to generate trial moves in the Markov Chain. Here we show that significant improvements to the efficiency of MCMC simulation can be made by using a self-adaptive Differential Evolution learning strategy within a population-based evolutionary framework. This scheme, entitled DiffeRential Evolution Adaptive Metropolis or DREAM, runs multiple different chains simultaneously for global exploration, and automatically tunes the scale and orientation of the proposal distribution in randomized subspaces during the search. Ergodicity of the algorithm is proved, and various examples involving nonlinearity, high-dimensionality, and multimodality show that DREAM is generally superior to other adaptive MCMC sampling approaches. The DREAM scheme significantly enhances the applicability of MCMC simulation to complex, multi-modal search problems.
15. Markov chain Monte Carlo based analysis of post-translationally modified VDAC gating kinetics
PubMed Central
Tewari, Shivendra G.; Zhou, Yifan; Otto, Bradley J.; Dash, Ranjan K.; Kwok, Wai-Meng; Beard, Daniel A.
2015-01-01
The voltage-dependent anion channel (VDAC) is the main conduit for permeation of solutes (including nucleotides and metabolites) of up to 5 kDa across the mitochondrial outer membrane (MOM). Recent studies suggest that VDAC activity is regulated via post-translational modifications (PTMs). Yet the nature and effect of these modifications is not understood. Herein, single channel currents of wild-type, nitrosated, and phosphorylated VDAC are analyzed using a generalized continuous-time Markov chain Monte Carlo (MCMC) method. This developed method describes three distinct conducting states (open, half-open, and closed) of VDAC activity. Lipid bilayer experiments are also performed to record single VDAC activity under un-phosphorylated and phosphorylated conditions, and are analyzed using the developed stochastic search method. Experimental data show significant alteration in VDAC gating kinetics and conductance as a result of PTMs. The effect of PTMs on VDAC kinetics is captured in the parameters associated with the identified Markov model. Stationary distributions of the Markov model suggest that nitrosation of VDAC not only decreased its conductance but also significantly locked VDAC in a closed state. On the other hand, stationary distributions of the model associated with un-phosphorylated and phosphorylated VDAC suggest a reversal in channel conformation from relatively closed state to an open state. Model analyses of the nitrosated data suggest that faster reaction of nitric oxide with Cys-127 thiol group might be responsible for the biphasic effect of nitric oxide on basal VDAC conductance. PMID:25628567
16. Accelerating Markov chain Monte Carlo simulation through sequential updating and parallel computing
Ren, Ruichao
Monte Carlo simulation is a statistical sampling method used in studies of physical systems with properties that cannot be easily obtained analytically. The phase behavior of the Restricted Primitive Model of electrolyte solutions on the simple cubic lattice is studied using grand canonical Monte Carlo simulations and finite-size scaling techniques. The transition between disordered and ordered, NaCl-like structures is continuous, second-order at high temperatures and discrete, first-order at low temperatures. The line of continuous transitions meets the line of first-order transitions at a tricritical point. A new algorithm-Random Skipping Sequential (RSS) Monte Carl---is proposed, justified and shown analytically to have better mobility over the phase space than the conventional Metropolis algorithm satisfying strict detailed balance. The new algorithm employs sequential updating, and yields greatly enhanced sampling statistics than the Metropolis algorithm with random updating. A parallel version of Markov chain theory is introduced and applied in accelerating Monte Carlo simulation via cluster computing. It is shown that sequential updating is the key to reduce the inter-processor communication or synchronization which slows down parallel simulation with increasing number of processors. Parallel simulation results for the two-dimensional lattice gas model show substantial reduction of simulation time by the new method for systems of large and moderate sizes.
17. A new method for RGB to CIELAB color space transformation based on Markov chain Monte Carlo
Chen, Yajun; Liu, Ding; Liang, Junli
2013-10-01
During printing quality inspection, the inspection of color error is an important content. However, the RGB color space is device-dependent, usually RGB color captured from CCD camera must be transformed into CIELAB color space, which is perceptually uniform and device-independent. To cope with the problem, a Markov chain Monte Carlo (MCMC) based algorithms for the RGB to the CIELAB color space transformation is proposed in this paper. Firstly, the modeling color targets and testing color targets is established, respectively used in modeling and performance testing process. Secondly, we derive a Bayesian model for estimation the coefficients of a polynomial, which can be used to describe the relation between RGB and CIELAB color space. Thirdly, a Markov chain is set up base on Gibbs sampling algorithm (one of the MCMC algorithm) to estimate the coefficients of polynomial. Finally, the color difference of testing color targets is computed for evaluating the performance of the proposed method. The experimental results showed that the nonlinear polynomial regression based on MCMC algorithm is effective, whose performance is similar to the least square approach and can accurately model the RGB to the CIELAB color space conversion and guarantee the color error evaluation for printing quality inspection system.
18. A Markov-Chain Monte-Carlo Based Method for Flaw Detection in Beams
SciTech Connect
Glaser, R E; Lee, C L; Nitao, J J; Hickling, T L; Hanley, W G
2006-09-28
A Bayesian inference methodology using a Markov Chain Monte Carlo (MCMC) sampling procedure is presented for estimating the parameters of computational structural models. This methodology combines prior information, measured data, and forward models to produce a posterior distribution for the system parameters of structural models that is most consistent with all available data. The MCMC procedure is based upon a Metropolis-Hastings algorithm that is shown to function effectively with noisy data, incomplete data sets, and mismatched computational nodes/measurement points. A series of numerical test cases based upon a cantilever beam is presented. The results demonstrate that the algorithm is able to estimate model parameters utilizing experimental data for the nodal displacements resulting from specified forces.
19. Markov Chain Monte Carlo Sampling Methods for 1D Seismic and EM Data Inversion
Energy Science and Technology Software Center (ESTSC)
2008-09-22
This software provides several Markov chain Monte Carlo sampling methods for the Bayesian model developed for inverting 1D marine seismic and controlled source electromagnetic (CSEM) data. The current software can be used for individual inversion of seismic AVO and CSEM data and for joint inversion of both seismic and EM data sets. The structure of the software is very general and flexible, and it allows users to incorporate their own forward simulation codes and rockmore » physics model codes easily into this software. Although the softwae was developed using C and C++ computer languages, the user-supplied codes can be written in C, C++, or various versions of Fortran languages. The software provides clear interfaces for users to plug in their own codes. The output of this software is in the format that the R free software CODA can directly read to build MCMC objects.« less
20. Of bugs and birds: Markov Chain Monte Carlo for hierarchical modeling in wildlife research
USGS Publications Warehouse
Link, W.A.; Cam, E.; Nichols, J.D.; Cooch, E.G.
2002-01-01
Markov chain Monte Carlo (MCMC) is a statistical innovation that allows researchers to fit far more complex models to data than is feasible using conventional methods. Despite its widespread use in a variety of scientific fields, MCMC appears to be underutilized in wildlife applications. This may be due to a misconception that MCMC requires the adoption of a subjective Bayesian analysis, or perhaps simply to its lack of familiarity among wildlife researchers. We introduce the basic ideas of MCMC and software BUGS (Bayesian inference using Gibbs sampling), stressing that a simple and satisfactory intuition for MCMC does not require extraordinary mathematical sophistication. We illustrate the use of MCMC with an analysis of the association between latent factors governing individual heterogeneity in breeding and survival rates of kittiwakes (Rissa tridactyla). We conclude with a discussion of the importance of individual heterogeneity for understanding population dynamics and designing management plans.
1. Reconciling data using Markov Chain Monte Carlo: An application to the Yellow Sea - Korean Peninsula region
SciTech Connect
Pasyanos, M E; Franz, G A; Ramirez, A L
2004-08-30
In an effort to build seismic models that are most consistent with multiple data sets, we have applied a new probabilistic inverse technique. This method uses a Markov Chain Monte Carlo (MCMC) algorithm to sample models from a prior distribution and test them against multiple data types to generate a posterior distribution. While computationally expensive, this approach has several advantages over a single deterministic model, notably the reconciliation of different data types that constrain the model, the proper handling of uncertainties, and the ability to include prior information. We also benefit from the advantage of forward modeling rather than inverting the data. Here, we use this method to determine the crust and upper mantle structure of the Yellow Sea and Korean Peninsula (YSKP) region. We discuss the data sets, parameterization and starting model, outline the technique and its implementation, observe the behavior of the inversion, and demonstrate some of the advantages of this approach.
2. Markov Chain Monte Carlo methods applied to measuring the fine structure constant from quasar spectroscopy .
King, J. A.; Mortlock, D. J.; Webb, J. K.; Murphy, M. T.
Recent attempts to constrain cosmological variation in the fine structure constant, alpha , using quasar absorption lines have yielded two statistical samples which initially appear to be inconsistent. One of these samples was subsequently demonstrated to not pass consistency tests; it appears that the optimisation algorithm used to fit the model to the spectra failed. Nevertheless, the results of the other hinge on the robustness of the spectral fitting program VPFIT, which has been tested through simulation but not through direct exploration of the likelihood function. We present the application of Markov Chain Monte Carlo (MCMC) methods to this problem, and demonstrate that VPFIT produces similar values and uncertainties for Delta alpha /alpha , the fractional change in the fine structure constant, as our MCMC algorithm, and thus that VPFIT is reliable.
3. Markov Chain Monte Carlo methods applied to measuring the fine structure constant from quasar spectroscopy
King, Julian; Mortlock, Daniel; Webb, John; Murphy, Michael
2010-11-01
Recent attempts to constrain cosmological variation in the fine structure constant, α, using quasar absorption lines have yielded two statistical samples which initially appear to be inconsistent. One of these samples was subsequently demonstrated to not pass consistency tests; it appears that the optimisation algorithm used to fit the model to the spectra failed. Nevertheless, the results of the other hinge on the robustness of the spectral fitting program VPFIT, which has been tested through simulation but not through direct exploration of the likelihood function. We present the application of Markov Chain Monte Carlo (MCMC) methods to this problem, and demonstrate that VPFIT produces similar values and uncertainties for Δα/α, the fractional change in the fine structure constant, as our MCMC algorithm, and thus that VPFIT is reliable.
4. Analysis of aerial survey data on Florida manatee using Markov chain Monte Carlo.
PubMed
Craig, B A; Newton, M A; Garrott, R A; Reynolds, J E; Wilcox, J R
1997-06-01
We assess population trends of the Atlantic coast population of Florida manatee, Trichechus manatus latirostris, by reanalyzing aerial survey data collected between 1982 and 1992. To do so, we develop an explicit biological model that accounts for the method by which the manatees are counted, the mammals' movement between surveys, and the behavior of the population total over time. Bayesian inference, enabled by Markov chain Monte Carlo, is used to combine the survey data with the biological model. We compute marginal posterior distributions for all model parameters and predictive distributions for future counts. Several conclusions, such as a decreasing population growth rate and low sighting probabilities, are consistent across different prior specifications. PMID:9192449
5. Recovery of Graded Response Model Parameters: A Comparison of Marginal Maximum Likelihood and Markov Chain Monte Carlo Estimation
ERIC Educational Resources Information Center
Kieftenbeld, Vincent; Natesan, Prathiba
2012-01-01
Markov chain Monte Carlo (MCMC) methods enable a fully Bayesian approach to parameter estimation of item response models. In this simulation study, the authors compared the recovery of graded response model parameters using marginal maximum likelihood (MML) and Gibbs sampling (MCMC) under various latent trait distributions, test lengths, and…
6. Multi-Physics Markov Chain Monte Carlo Methods for Subsurface Flows
Rigelo, J.; Ginting, V.; Rahunanthan, A.; Pereira, F.
2014-12-01
For CO2 sequestration in deep saline aquifers, contaminant transport in subsurface, and oil or gas recovery, we often need to forecast flow patterns. Subsurface characterization is a critical and challenging step in flow forecasting. To characterize subsurface properties we establish a statistical description of the subsurface properties that are conditioned to existing dynamic and static data. A Markov Chain Monte Carlo (MCMC) algorithm is used in a Bayesian statistical description to reconstruct the spatial distribution of rock permeability and porosity. The MCMC algorithm requires repeatedly solving a set of nonlinear partial differential equations describing displacement of fluids in porous media for different values of permeability and porosity. The time needed for the generation of a reliable MCMC chain using the algorithm can be too long to be practical for flow forecasting. In this work we develop fast and effective computational methods for generating MCMC chains in the Bayesian framework for the subsurface characterization. Our strategy consists of constructing a family of computationally inexpensive preconditioners based on simpler physics as well as on surrogate models such that the number of fine-grid simulations is drastically reduced in the generated MCMC chains. In particular, we introduce a huff-puff technique as screening step in a three-stage multi-physics MCMC algorithm to reduce the number of expensive final stage simulations. The huff-puff technique in the algorithm enables a better characterization of subsurface near wells. We assess the quality of the proposed multi-physics MCMC methods by considering Monte Carlo simulations for forecasting oil production in an oil reservoir.
7. Mapping systematic errors in helium abundance determinations using Markov Chain Monte Carlo
SciTech Connect
Aver, Erik; Olive, Keith A.; Skillman, Evan D. E-mail: olive@umn.edu
2011-03-01
Monte Carlo techniques have been used to evaluate the statistical and systematic uncertainties in the helium abundances derived from extragalactic H II regions. The helium abundance is sensitive to several physical parameters associated with the H II region. In this work, we introduce Markov Chain Monte Carlo (MCMC) methods to efficiently explore the parameter space and determine the helium abundance, the physical parameters, and the uncertainties derived from observations of metal poor nebulae. Experiments with synthetic data show that the MCMC method is superior to previous implementations (based on flux perturbation) in that it is not affected by biases due to non-physical parameter space. The MCMC analysis allows a detailed exploration of degeneracies, and, in particular, a false minimum that occurs at large values of optical depth in the He I emission lines. We demonstrate that introducing the electron temperature derived from the [O III] emission lines as a prior, in a very conservative manner, produces negligible bias and effectively eliminates the false minima occurring at large optical depth. We perform a frequentist analysis on data from several ''high quality'' systems. Likelihood plots illustrate degeneracies, asymmetries, and limits of the determination. In agreement with previous work, we find relatively large systematic errors, limiting the precision of the primordial helium abundance for currently available spectra.
8. Geometrically Constructed Markov Chain Monte Carlo Study of Quantum Spin-phonon Complex Systems
Suwa, Hidemaro
2013-03-01
We have developed novel Monte Carlo methods for precisely calculating quantum spin-boson models and investigated the critical phenomena of the spin-Peierls systems. Three significant methods are presented. The first is a new optimization algorithm of the Markov chain transition kernel based on the geometric weight allocation. This algorithm, for the first time, satisfies the total balance generally without imposing the detailed balance and always minimizes the average rejection rate, being better than the Metropolis algorithm. The second is the extension of the worm (directed-loop) algorithm to non-conserved particles, which cannot be treated efficiently by the conventional methods. The third is the combination with the level spectroscopy. Proposing a new gap estimator, we are successful in eliminating the systematic error of the conventional moment method. Then we have elucidated the phase diagram and the universality class of the one-dimensional XXZ spin-Peierls system. The criticality is totally consistent with the J1 -J2 model, an effective model in the antiadiabatic limit. Through this research, we have succeeded in investigating the critical phenomena of the effectively frustrated quantum spin system by the quantum Monte Carlo method without the negative sign. JSPS Postdoctoral Fellow for Research Abroad
9. Improving Bayesian analysis for LISA Pathfinder using an efficient Markov Chain Monte Carlo method
Ferraioli, Luigi; Porter, Edward K.; Armano, Michele; Audley, Heather; Congedo, Giuseppe; Diepholz, Ingo; Gibert, Ferran; Hewitson, Martin; Hueller, Mauro; Karnesis, Nikolaos; Korsakova, Natalia; Nofrarias, Miquel; Plagnol, Eric; Vitale, Stefano
2014-02-01
We present a parameter estimation procedure based on a Bayesian framework by applying a Markov Chain Monte Carlo algorithm to the calibration of the dynamical parameters of the LISA Pathfinder satellite. The method is based on the Metropolis-Hastings algorithm and a two-stage annealing treatment in order to ensure an effective exploration of the parameter space at the beginning of the chain. We compare two versions of the algorithm with an application to a LISA Pathfinder data analysis problem. The two algorithms share the same heating strategy but with one moving in coordinate directions using proposals from a multivariate Gaussian distribution, while the other uses the natural logarithm of some parameters and proposes jumps in the eigen-space of the Fisher Information matrix. The algorithm proposing jumps in the eigen-space of the Fisher Information matrix demonstrates a higher acceptance rate and a slightly better convergence towards the equilibrium parameter distributions in the application to LISA Pathfinder data. For this experiment, we return parameter values that are all within ˜1 σ of the injected values. When we analyse the accuracy of our parameter estimation in terms of the effect they have on the force-per-unit of mass noise, we find that the induced errors are three orders of magnitude less than the expected experimental uncertainty in the power spectral density.
10. A Scalable Multi-chain Markov Chain Monte Carlo Method for Inverting Subsurface Hydraulic and Geological Properties
Bao, J.; Ren, H.; Hou, Z.; Ray, J.; Swiler, L.; Huang, M.
2015-12-01
We developed a novel scalable multi-chain Markov chain Monte Carlo (MCMC) method for high-dimensional inverse problems. The method is scalable in terms of number of chains and processors, and is useful for Bayesian calibration of computationally expensive simulators typically used for scientific and engineering calculations. In this study, we demonstrate two applications of this method for hydraulic and geological inverse problems. The first one is monitoring soil moisture variations using tomographic ground penetrating radar (GPR) travel time data, where challenges exist in the inversion of GPR tomographic data for handling non-uniqueness and nonlinearity and high-dimensionality of unknowns. We integrated the multi-chain MCMC framework with the pilot point concept, a curved-ray GPR forward model, and a sequential Gaussian simulation (SGSIM) algorithm for estimating the dielectric permittivity at pilot point locations distributed within the tomogram, as well as its spatial correlation range, which are used to construct the whole field of dielectric permittivity using SGSIM. The second application is reservoir porosity and saturation estimation using the multi-chain MCMC approach to jointly invert marine seismic amplitude versus angle (AVA) and controlled-source electro-magnetic (CSEM) data for a layered reservoir model, where the unknowns to be estimated include the porosity and fluid saturation in each reservoir layer and the electrical conductivity of the overburden and bedrock. The computational efficiency, accuracy, and convergence behaviors of the inversion approach are systematically evaluated.
11. CIGALEMC: GALAXY PARAMETER ESTIMATION USING A MARKOV CHAIN MONTE CARLO APPROACH WITH CIGALE
SciTech Connect
Serra, Paolo; Amblard, Alexandre; Temi, Pasquale; Im, Stephen; Noll, Stefan
2011-10-10
We introduce a fast Markov Chain Monte Carlo (MCMC) exploration of the astrophysical parameter space using a modified version of the publicly available code Code Investigating GALaxy Emission (CIGALE). The original CIGALE builds a grid of theoretical spectral energy distribution (SED) models and fits to photometric fluxes from ultraviolet to infrared to put constraints on parameters related to both formation and evolution of galaxies. Such a grid-based method can lead to a long and challenging parameter extraction since the computation time increases exponentially with the number of parameters considered and results can be dependent on the density of sampling points, which must be chosen in advance for each parameter. MCMC methods, on the other hand, scale approximately linearly with the number of parameters, allowing a faster and more accurate exploration of the parameter space by using a smaller number of efficiently chosen samples. We test our MCMC version of the code CIGALE (called CIGALEMC) with simulated data. After checking the ability of the code to retrieve the input parameters used to build the mock sample, we fit theoretical SEDs to real data from the well-known and -studied Spitzer Infrared Nearby Galaxy Survey sample. We discuss constraints on the parameters and show the advantages of our MCMC sampling method in terms of accuracy of the results and optimization of CPU time.
12. Fitting complex population models by combining particle filters with Markov chain Monte Carlo.
PubMed
Knape, Jonas; de Valpine, Perry
2012-02-01
We show how a recent framework combining Markov chain Monte Carlo (MCMC) with particle filters (PFMCMC) may be used to estimate population state-space models. With the purpose of utilizing the strengths of each method, PFMCMC explores hidden states by particle filters, while process and observation parameters are estimated using an MCMC algorithm. PFMCMC is exemplified by analyzing time series data on a red kangaroo (Macropus rufus) population in New South Wales, Australia, using MCMC over model parameters based on an adaptive Metropolis-Hastings algorithm. We fit three population models to these data; a density-dependent logistic diffusion model with environmental variance, an unregulated stochastic exponential growth model, and a random-walk model. Bayes factors and posterior model probabilities show that there is little support for density dependence and that the random-walk model is the most parsimonious model. The particle filter Metropolis-Hastings algorithm is a brute-force method that may be used to fit a range of complex population models. Implementation is straightforward and less involved than standard MCMC for many models, and marginal densities for model selection can be obtained with little additional effort. The cost is mainly computational, resulting in long running times that may be improved by parallelizing the algorithm. PMID:22624307
13. Improving Hydrologic Data Assimilation by a Multivariate Particle Filter-Markov Chain Monte Carlo
Yan, H.; DeChant, C. M.; Moradkhani, H.
2014-12-01
Data assimilation (DA) is a popular method for merging information from multiple sources (i.e. models and remotely sensing), leading to improved hydrologic prediction. With the increasing availability of satellite observations (such as soil moisture) in recent years, DA is emerging in operational forecast systems. Although these techniques have seen widespread application, developmental research has continued to further refine their effectiveness. This presentation will examine potential improvements to the Particle Filter (PF) through the inclusion of multivariate correlation structures. Applications of the PF typically rely on univariate DA schemes (such as assimilating the outlet observed discharge), and multivariate schemes generally ignore the spatial correlation of the observations. In this study, a multivariate DA scheme is proposed by introducing geostatistics into the newly developed particle filter with Markov chain Monte Carlo (PF-MCMC) method. This new method is assessed by a case study over one of the basin with natural hydrologic process in Model Parameter Estimation Experiment (MOPEX), located in Arizona. The multivariate PF-MCMC method is used to assimilate the Advanced Scatterometer (ASCAT) grid (12.5 km) soil moisture retrievals and the observed streamflow in five gages (four inlet and one outlet gages) into the Sacramento Soil Moisture Accounting (SAC-SMA) model for the same scale (12.5 km), leading to greater skill in hydrologic predictions.
14. Efficient Approximate Bayesian Computation Coupled With Markov Chain Monte Carlo Without Likelihood
PubMed Central
Wegmann, Daniel; Leuenberger, Christoph; Excoffier, Laurent
2009-01-01
Approximate Bayesian computation (ABC) techniques permit inferences in complex demographic models, but are computationally inefficient. A Markov chain Monte Carlo (MCMC) approach has been proposed (Marjoram et al. 2003), but it suffers from computational problems and poor mixing. We propose several methodological developments to overcome the shortcomings of this MCMC approach and hence realize substantial computational advances over standard ABC. The principal idea is to relax the tolerance within MCMC to permit good mixing, but retain a good approximation to the posterior by a combination of subsampling the output and regression adjustment. We also propose to use a partial least-squares (PLS) transformation to choose informative statistics. The accuracy of our approach is examined in the case of the divergence of two populations with and without migration. In that case, our ABC–MCMC approach needs considerably lower computation time to reach the same accuracy than conventional ABC. We then apply our method to a more complex case with the estimation of divergence times and migration rates between three African populations. PMID:19506307
15. Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation
Vrugt, Jasper A.; Ter Braak, Cajo J. F.; Clark, Martyn P.; Hyman, James M.; Robinson, Bruce A.
2008-12-01
There is increasing consensus in the hydrologic literature that an appropriate framework for streamflow forecasting and simulation should include explicit recognition of forcing and parameter and model structural error. This paper presents a novel Markov chain Monte Carlo (MCMC) sampler, entitled differential evolution adaptive Metropolis (DREAM), that is especially designed to efficiently estimate the posterior probability density function of hydrologic model parameters in complex, high-dimensional sampling problems. This MCMC scheme adaptively updates the scale and orientation of the proposal distribution during sampling and maintains detailed balance and ergodicity. It is then demonstrated how DREAM can be used to analyze forcing data error during watershed model calibration using a five-parameter rainfall-runoff model with streamflow data from two different catchments. Explicit treatment of precipitation error during hydrologic model calibration not only results in prediction uncertainty bounds that are more appropriate but also significantly alters the posterior distribution of the watershed model parameters. This has significant implications for regionalization studies. The approach also provides important new ways to estimate areal average watershed precipitation, information that is of utmost importance for testing hydrologic theory, diagnosing structural errors in models, and appropriately benchmarking rainfall measurement devices.
16. Markov chain Monte Carlo analysis to constrain dark matter properties with directional detection
SciTech Connect
Billard, J.; Mayet, F.; Santos, D.
2011-04-01
Directional detection is a promising dark matter search strategy. Indeed, weakly interacting massive particle (WIMP)-induced recoils would present a direction dependence toward the Cygnus constellation, while background-induced recoils exhibit an isotropic distribution in the Galactic rest frame. Taking advantage of these characteristic features, and even in the presence of a sizeable background, it has recently been shown that data from forthcoming directional detectors could lead either to a competitive exclusion or to a conclusive discovery, depending on the value of the WIMP-nucleon cross section. However, it is possible to further exploit these upcoming data by using the strong dependence of the WIMP signal with: the WIMP mass and the local WIMP velocity distribution. Using a Markov chain Monte Carlo analysis of recoil events, we show for the first time the possibility to constrain the unknown WIMP parameters, both from particle physics (mass and cross section) and Galactic halo (velocity dispersion along the three axis), leading to an identification of non-baryonic dark matter.
17. Extracting g tensor values from experimental data with Markov Chain Monte Carlo methods
Kulkarni, Anagha; Liu, Weiwen; Zurakowski, Ryan; Doty, Matthew
Quantum Dot Molecules(QDMs) have emerged as a new platform for optoelectronic and spintronic devices.QDMs consist of multiple Quantum Dots (QDs) arranged in close proximity such that interactions between them can tailor their optical and spin properties.These properties can be tuned during growth and in-situ by applying electric fields that vary the coupling between QDs,which controls the formation of delocalized molecular-like states.Engineering the formation of molecular states in QDMS can be used to achieve new functionalities unavailable with individual QDs. Using molecular engineering approaches to tailor QDMs require precise knowledge of parameters such as binding energies of charge complexes,magnitude of many body interactions or components of the g tensor.Precise values of these parameters are difficult to extract from either experimental measurements or theoretical calculations.We develop and demonstrate a Markov Chain Monte Carlo method for extracting elements of the g tensor for a single hole confined in a QDM from photoluminescence data obtained as a function of electric and magnetic fields.This method can be applied to extract precise quantitative values of other physical parameters from sparse experimental data on a variety of systems.
18. Estimating stepwise debromination pathways of polybrominated diphenyl ethers with an analogue Markov Chain Monte Carlo algorithm.
PubMed
Zou, Yonghong; Christensen, Erik R; Zheng, Wei; Wei, Hua; Li, An
2014-11-01
A stochastic process was developed to simulate the stepwise debromination pathways for polybrominated diphenyl ethers (PBDEs). The stochastic process uses an analogue Markov Chain Monte Carlo (AMCMC) algorithm to generate PBDE debromination profiles. The acceptance or rejection of the randomly drawn stepwise debromination reactions was determined by a maximum likelihood function. The experimental observations at certain time points were used as target profiles; therefore, the stochastic processes are capable of presenting the effects of reaction conditions on the selection of debromination pathways. The application of the model is illustrated by adopting the experimental results of decabromodiphenyl ether (BDE209) in hexane exposed to sunlight. Inferences that were not obvious from experimental data were suggested by model simulations. For example, BDE206 has much higher accumulation at the first 30 min of sunlight exposure. By contrast, model simulation suggests that, BDE206 and BDE207 had comparable yields from BDE209. The reason for the higher BDE206 level is that BDE207 has the highest depletion in producing octa products. Compared to a previous version of the stochastic model based on stochastic reaction sequences (SRS), the AMCMC approach was determined to be more efficient and robust. Due to the feature of only requiring experimental observations as input, the AMCMC model is expected to be applicable to a wide range of PBDE debromination processes, e.g. microbial, photolytic, or joint effects in natural environments. PMID:25113201
19. Testing the efficiency of Markov chain Monte Carlo with People using facial affect categories.
PubMed
Martin, Jay B; Griffiths, Thomas L; Sanborn, Adam N
2012-01-01
Exploring how people represent natural categories is a key step toward developing a better understanding of how people learn, form memories, and make decisions. Much research on categorization has focused on artificial categories that are created in the laboratory, since studying natural categories defined on high-dimensional stimuli such as images is methodologically challenging. Recent work has produced methods for identifying these representations from observed behavior, such as reverse correlation (RC). We compare RC against an alternative method for inferring the structure of natural categories called Markov chain Monte Carlo with People (MCMCP). Based on an algorithm used in computer science and statistics, MCMCP provides a way to sample from the set of stimuli associated with a natural category. We apply MCMCP and RC to the problem of recovering natural categories that correspond to two kinds of facial affect (happy and sad) from realistic images of faces. Our results show that MCMCP requires fewer trials to obtain a higher quality estimate of people's mental representations of these two categories. PMID:21972923
20. A Markov Chain Monte Carlo Approach to Estimate AIDS after HIV Infection.
PubMed
Apenteng, Ofosuhene O; Ismail, Noor Azina
2015-01-01
The spread of human immunodeficiency virus (HIV) infection and the resulting acquired immune deficiency syndrome (AIDS) is a major health concern in many parts of the world, and mathematical models are commonly applied to understand the spread of the HIV epidemic. To understand the spread of HIV and AIDS cases and their parameters in a given population, it is necessary to develop a theoretical framework that takes into account realistic factors. The current study used this framework to assess the interaction between individuals who developed AIDS after HIV infection and individuals who did not develop AIDS after HIV infection (pre-AIDS). We first investigated how probabilistic parameters affect the model in terms of the HIV and AIDS population over a period of time. We observed that there is a critical threshold parameter, R0, which determines the behavior of the model. If R0 ≤ 1, there is a unique disease-free equilibrium; if R0 < 1, the disease dies out; and if R0 > 1, the disease-free equilibrium is unstable. We also show how a Markov chain Monte Carlo (MCMC) approach could be used as a supplement to forecast the numbers of reported HIV and AIDS cases. An approach using a Monte Carlo analysis is illustrated to understand the impact of model-based predictions in light of uncertain parameters on the spread of HIV. Finally, to examine this framework and demonstrate how it works, a case study was performed of reported HIV and AIDS cases from an annual data set in Malaysia, and then we compared how these approaches complement each other. We conclude that HIV disease in Malaysia shows epidemic behavior, especially in the context of understanding and predicting emerging cases of HIV and AIDS. PMID:26147199
1. A Markov Chain Monte Carlo Approach to Estimate AIDS after HIV Infection
PubMed Central
Apenteng, Ofosuhene O.; Ismail, Noor Azina
2015-01-01
The spread of human immunodeficiency virus (HIV) infection and the resulting acquired immune deficiency syndrome (AIDS) is a major health concern in many parts of the world, and mathematical models are commonly applied to understand the spread of the HIV epidemic. To understand the spread of HIV and AIDS cases and their parameters in a given population, it is necessary to develop a theoretical framework that takes into account realistic factors. The current study used this framework to assess the interaction between individuals who developed AIDS after HIV infection and individuals who did not develop AIDS after HIV infection (pre-AIDS). We first investigated how probabilistic parameters affect the model in terms of the HIV and AIDS population over a period of time. We observed that there is a critical threshold parameter, R0, which determines the behavior of the model. If R0 ≤ 1, there is a unique disease-free equilibrium; if R0 < 1, the disease dies out; and if R0 > 1, the disease-free equilibrium is unstable. We also show how a Markov chain Monte Carlo (MCMC) approach could be used as a supplement to forecast the numbers of reported HIV and AIDS cases. An approach using a Monte Carlo analysis is illustrated to understand the impact of model-based predictions in light of uncertain parameters on the spread of HIV. Finally, to examine this framework and demonstrate how it works, a case study was performed of reported HIV and AIDS cases from an annual data set in Malaysia, and then we compared how these approaches complement each other. We conclude that HIV disease in Malaysia shows epidemic behavior, especially in the context of understanding and predicting emerging cases of HIV and AIDS. PMID:26147199
2. Approximate Bayesian Computation Using Markov Chain Monte Carlo Simulation: Theory, Concepts, and Applications
2013-12-01
The ever increasing pace of computational power, along with continued advances in measurement technologies and improvements in process understanding has stimulated the development of increasingly complex hydrologic models that simulate soil moisture flow, groundwater recharge, surface runoff, root water uptake, and river discharge at increasingly finer spatial and temporal scales. Reconciling these system models with field and remote sensing data is a difficult task, particularly because average measures of model/data similarity inherently lack the power to provide a meaningful comparative evaluation of the consistency in model form and function. The very construction of the likelihood function - as a summary variable of the (usually averaged) properties of the error residuals - dilutes and mixes the available information into an index having little remaining correspondence to specific behaviors of the system (Gupta et al., 2008). The quest for a more powerful method for model evaluation has inspired Vrugt and Sadegh [2013] to introduce "likelihood-free" inference as vehicle for diagnostic model evaluation. This class of methods is also referred to as Approximate Bayesian Computation (ABC) and relaxes the need for an explicit likelihood function in favor of one or multiple different summary statistics rooted in hydrologic theory that together have a much stronger and compelling diagnostic power than some aggregated measure of the size of the error residuals. Here, we will introduce an efficient ABC sampling method that is orders of magnitude faster in exploring the posterior parameter distribution than commonly used rejection and Population Monte Carlo (PMC) samplers. Our methodology uses Markov Chain Monte Carlo simulation with DREAM, and takes advantage of a simple computational trick to resolve discontinuity problems with the application of set-theoretic summary statistics. We will also demonstrate a set of summary statistics that are rather insensitive to
3. Assessment of Parametric Uncertainty in Groundwater Reactive Transport Modeling Using Markov Chain Monte Carlo Techniques
Shi, X.; Ye, M.; Curtis, G. P.; Lu, D.; Meyer, P. D.; Yabusaki, S.; Wu, J.
2011-12-01
Assessment of parametric uncertainty for groundwater reactive transport models is challenging, because the models are highly nonlinear with respect to their parameters due to nonlinear reaction equations and process coupling. The nonlinearity may yield parameter distributions that are non-Gaussian and have multiple modes. For such parameter distributions, the widely used nonlinear regression methods may not be able to accurately quantify predictive uncertainty. One solution to this problem is to use Markov Chain Monte Carlo (MCMC) techniques. Both the nonlinear regression and MCMC methods are used in this study for quantification of parametric uncertainty of a surface complexation model (SCM), developed to simulate hexavalent uranium [U(VI)] transport in column experiments. Firstly, a brute force Monte Carlo (MC) simulation with hundreds of thousands of model executions is conducted to understand the surface of objective function and predictive uncertainty of uranium concentration. Subsequently, the Gauss-Marquardt-Levenberg method is applied to calibrate the model. It shows that, even with multiple initial guesses, the local optimization method has difficulty of finding the global optimum because of the rough surface of the objective function and local optima/minima due to model nonlinearity. Another problem of the nonlinear regression is the underestimation of predictive uncertainty, as both the linear and nonlinear confidence intervals are narrower than that obtained from the native MC simulation. Since the naïve MC simulation is computationally expensive, the above challenges for parameter estimation and predictive uncertainty analysis are addressed using a computationally efficient MCMC technique, the DiffeRential Evolution Adaptive Metropolis algorithm (DREAM) algorithm. The results obtained from running DREAM compared with those from brute force Monte Carlo simulations shown that MCMC not only successfully infers the multi-modals posterior probability
4. A Markov Chain Monte Carlo Algorithm for Infrasound Atmospheric Sounding: Application to the Humming Roadrunner experiment in New Mexico
Lalande, Jean-Marie; Waxler, Roger; Velea, Doru
2016-04-01
As infrasonic waves propagate at long ranges through atmospheric ducts it has been suggested that observations of such waves can be used as a remote sensing techniques in order to update properties such as temperature and wind speed. In this study we investigate a new inverse approach based on Markov Chain Monte Carlo methods. This approach as the advantage of searching for the full Probability Density Function in the parameter space at a lower computational cost than extensive parameters search performed by the standard Monte Carlo approach. We apply this inverse methods to observations from the Humming Roadrunner experiment (New Mexico) and discuss implications for atmospheric updates, explosion characterization, localization and yield estimation.
5. Input estimation for drug discovery using optimal control and Markov chain Monte Carlo approaches.
PubMed
Trägårdh, Magnus; Chappell, Michael J; Ahnmark, Andrea; Lindén, Daniel; Evans, Neil D; Gennemark, Peter
2016-04-01
Input estimation is employed in cases where it is desirable to recover the form of an input function which cannot be directly observed and for which there is no model for the generating process. In pharmacokinetic and pharmacodynamic modelling, input estimation in linear systems (deconvolution) is well established, while the nonlinear case is largely unexplored. In this paper, a rigorous definition of the input-estimation problem is given, and the choices involved in terms of modelling assumptions and estimation algorithms are discussed. In particular, the paper covers Maximum a Posteriori estimates using techniques from optimal control theory, and full Bayesian estimation using Markov Chain Monte Carlo (MCMC) approaches. These techniques are implemented using the optimisation software CasADi, and applied to two example problems: one where the oral absorption rate and bioavailability of the drug eflornithine are estimated using pharmacokinetic data from rats, and one where energy intake is estimated from body-mass measurements of mice exposed to monoclonal antibodies targeting the fibroblast growth factor receptor (FGFR) 1c. The results from the analysis are used to highlight the strengths and weaknesses of the methods used when applied to sparsely sampled data. The presented methods for optimal control are fast and robust, and can be recommended for use in drug discovery. The MCMC-based methods can have long running times and require more expertise from the user. The rigorous definition together with the illustrative examples and suggestions for software serve as a highly promising starting point for application of input-estimation methods to problems in drug discovery. PMID:26932466
6. Cosmological constraints on generalized Chaplygin gas model: Markov Chain Monte Carlo approach
SciTech Connect
Xu, Lixin; Lu, Jianbo E-mail: lvjianbo819@163.com
2010-03-01
We use the Markov Chain Monte Carlo method to investigate a global constraints on the generalized Chaplygin gas (GCG) model as the unification of dark matter and dark energy from the latest observational data: the Constitution dataset of type supernovae Ia (SNIa), the observational Hubble data (OHD), the cluster X-ray gas mass fraction, the baryon acoustic oscillation (BAO), and the cosmic microwave background (CMB) data. In a non-flat universe, the constraint results for GCG model are, Ω{sub b}h{sup 2} = 0.0235{sup +0.0021}{sub −0.0018} (1σ) {sup +0.0028}{sub −0.0022} (2σ), Ω{sub k} = 0.0035{sup +0.0172}{sub −0.0182} (1σ) {sup +0.0226}{sub −0.0204} (2σ), A{sub s} = 0.753{sup +0.037}{sub −0.035} (1σ) {sup +0.045}{sub −0.044} (2σ), α = 0.043{sup +0.102}{sub −0.106} (1σ) {sup +0.134}{sub −0.117} (2σ), and H{sub 0} = 70.00{sup +3.25}{sub −2.92} (1σ) {sup +3.77}{sub −3.67} (2σ), which is more stringent than the previous results for constraint on GCG model parameters. Furthermore, according to the information criterion, it seems that the current observations much support ΛCDM model relative to the GCG model.
7. Asteroid orbital inversion using a virtual-observation Markov-chain Monte Carlo method
Muinonen, Karri; Granvik, Mikael; Oszkiewicz, Dagmara; Pieniluoma, Tuomo; Pentikäinen, Hanna
2012-12-01
A novel virtual-observation Markov-chain Monte Carlo method (MCMC) is presented for the asteroid orbital inverse problem posed by small to moderate numbers of astrometric observations. In the method, the orbital-element proposal probability density is chosen to mimic the convolution of the a posteriori density by itself: first, random errors are simulated for each observation, resulting in a set of virtual observations; second, least-squares orbital elements are derived for the virtual observations using the Nelder-Mead downhill simplex method; third, repeating the procedure gives a difference between two sets of what can be called virtual least-squares elements; and, fourth, the difference obtained constitutes a symmetric proposal in a random-walk Metropolis-Hastings algorithm, avoiding the explicit computation of the proposal density. In practice, the proposals are based on a large number of pre-computed sets of orbital elements. Virtual-observation MCMC is thus based on the characterization of the phase-space volume of solutions before the actual MCMC sampling. Virtual-observation MCMC is compared to MCMC orbital ranging, a random-walk Metropolis-Hastings algorithm based on sampling with the help of Cartesian positions at two observation dates, in the case of the near-Earth asteroid (85640) 1998 OX4. In the present preliminary comparison, the methods yield similar results for a 9.1-day observational time interval extracted from the full current astrometry of the asteroid. In the future, both of the methods are to be applied to the astrometric observations of the Gaia mission.
8. Recovering the inflationary potential: An analysis using flow methods and Markov chain Monte Carlo
Powell, Brian A.
Since its inception in 1980 by Guth [1], inflation has emerged as the dominant paradigm for describing the physics of the early universe. While inflation has matured theoretically over two decades, it has only recently begun to be rigorously tested observationally. Measurements of the cosmic microwave background (CMB) and large-scale structure surveys (LSS) have begun to unravel the mysteries of the inflationary epoch with exquisite and unprecedented accuracy. This thesis is a contribution to the effort of reconstructing the physics of inflation. This information is largely encoded in the potential energy function of the inflaton, the field that drives the inflationary expansion. With little theoretical guidance as to the probable form of this potential, reconstruction is a predominantly data-driven endeavor. This thesis presents an investigation of the constrainability of the inflaton potential given current CMB and LSS data. We develop a methodology based on the inflationary flow formalism that provides an assessment of our current ability to resolve the form of the inflaton potential in the face of experimental and statistical error. We find that there is uncertainty regarding the initial dynamics of the inflaton field, related to the poor constraints that can be drawn on the primordial power spectrum on large scales. We also investigate the future prospects of potential reconstruction, as might be expected when data from ESA's Planck Surveyor becomes available. We develop an approach that utilizes Markov chain Monte Carlo to analyze the statistical properties of the inflaton potential. Besides providing constraints on the parameters of the potential, this method makes it possible to perform model selection on the inflationary model space. While future data will likely determine the general features of the inflaton, there will likely be many different models that remain good fits to the data. Bayesian model selection will then be needed to draw comparisons
9. BENCHMARK TESTS FOR MARKOV CHAIN MONTE CARLO FITTING OF EXOPLANET ECLIPSE OBSERVATIONS
SciTech Connect
Rogers, Justin; Lopez-Morales, Mercedes; Apai, Daniel; Adams, Elisabeth
2013-04-10
Ground-based observations of exoplanet eclipses provide important clues to the planets' atmospheric physics, yet systematics in light curve analyses are not fully understood. It is unknown if measurements suggesting near-infrared flux densities brighter than models predict are real, or artifacts of the analysis processes. We created a large suite of model light curves, using both synthetic and real noise, and tested the common process of light curve modeling and parameter optimization with a Markov Chain Monte Carlo algorithm. With synthetic white noise models, we find that input eclipse signals are generally recovered within 10% accuracy for eclipse depths greater than the noise amplitude, and to smaller depths for higher sampling rates and longer baselines. Red noise models see greater discrepancies between input and measured eclipse signals, often biased in one direction. Finally, we find that in real data, systematic biases result even with a complex model to account for trends, and significant false eclipse signals may appear in a non-Gaussian distribution. To quantify the bias and validate an eclipse measurement, we compare both the planet-hosting star and several of its neighbors to a separately chosen control sample of field stars. Re-examining the Rogers et al. Ks-band measurement of CoRoT-1b finds an eclipse 3190{sup +370}{sub -440} ppm deep centered at {phi}{sub me} = 0.50418{sup +0.00197}{sub -0.00203}. Finally, we provide and recommend the use of selected data sets we generated as a benchmark test for eclipse modeling and analysis routines, and propose criteria to verify eclipse detections.
10. Stochastic Monte-Carlo Markov Chain Inversions on Models Regionalized Using Receiver Functions
Larmat, C. S.; Maceira, M.; Kato, Y.; Bodin, T.; Calo, M.; Romanowicz, B. A.; Chai, C.; Ammon, C. J.
2014-12-01
There is currently a strong interest in stochastic approaches to seismic modeling - versus deterministic methods such as gradient methods - due to the ability of these methods to better deal with highly non-linear problems. Another advantage of stochastic methods is that they allow the estimation of the a posteriori probability distribution of the derived parameters, meaning the envisioned Bayesian inversion of Tarantola allowing the quantification of the solution error. The cost to pay of stochastic methods is that they require testing thousands of variations of each unknown parameter and their associated weights to ensure reliable probabilistic inferences. Even with the best High-Performance Computing resources available, 3D stochastic full waveform modeling at the regional scale still remains out-of-reach. We are exploring regionalization as one way to reduce the dimension of the parameter space, allowing the identification of areas in the models that can be treated as one block in a subsequent stochastic inversion. Regionalization is classically performed through the identification of tectonic or structural elements. Lekic & Romanowicz (2011) proposed a new approach with a cluster analysis of the tomographic velocity models instead. Here we present the results of a clustering analysis on the P-wave receiver-functions used in the subsequent inversion. Different clustering algorithms and quality of clustering are tested for different datasets of North America and China. Preliminary results with the kmean clustering algorithm show that an interpolated receiver function wavefield (Chai et al., GRL, in review) improve the agreement with the geological and tectonic regions of North America compared to the traditional approach of stacked receiver functions. After regionalization, 1D profile for each region is stochastically inferred using a parallelized code based on Monte-Carlo Markov Chains (MCMC), and modeling surfacewave-dispersion and receiver
11. Markov chain formalism for polarized light transfer in plane-parallel atmospheres, with numerical comparison to the Monte Carlo method.
PubMed
Xu, Feng; Davis, Anthony B; West, Robert A; Esposito, Larry W
2011-01-17
Building on the Markov chain formalism for scalar (intensity only) radiative transfer, this paper formulates the solution to polarized diffuse reflection from and transmission through a vertically inhomogeneous atmosphere. For verification, numerical results are compared to those obtained by the Monte Carlo method, showing deviations less than 1% when 90 streams are used to compute the radiation from two types of atmospheres, pure Rayleigh and Rayleigh plus aerosol, when they are divided into sublayers of optical thicknesses of less than 0.03. PMID:21263634
12. Optimized Nested Markov Chain Monte Carlo Sampling: Application to the Liquid Nitrogen Hugoniot Using Density Functional Theory
Shaw, M. Sam; Coe, Joshua D.; Sewell, Thomas D.
2009-06-01
An optimized version of the Nested Markov Chain Monte Carlo sampling method is applied to the calculation of the Hugoniot for liquid nitrogen. The full'' system of interest is calculated using density functional theory (DFT) with a 6-31G* basis set for the configurational energies. The reference'' system is given by a model potential fit to the anisotropic pair interaction of two nitrogen molecules from DFT calculations. The EOS is sampled in the isobaric-isothermal (NPT) ensemble with a trial move constructed from many Monte Carlo steps in the reference system. The trial move is then accepted with a probability chosen to give the full system distribution. The P's and T's of the reference and full systems are chosen separately to optimize the computational time required to produce the full system EOS. The method is numerically very efficient and predicts a Hugoniot in excellent agreement with experimental data.
13. Optimized Nested Markov Chain Monte Carlo Sampling: Application to the Liquid Nitrogen Hugoniot Using Density Functional Theory
Shaw, M. Sam; Coe, Joshua D.; Sewell, Thomas D.
2009-12-01
An optimized version of the Nested Markov Chain Monte Carlo sampling method is applied to the calculation of the Hugoniot for liquid nitrogen. The "full" system of interest is calculated using density functional theory (DFT) with a 6-31G* basis set for the configurational energies. The "reference" system is given by a model potential fit to the anisotropic pair interaction of two nitrogen molecules from DFT calculations. The EOS is sampled in the isobaric-isothermal (NPT) ensemble with a trial move constructed from many Monte Carlo steps in the reference system. The trial move is then accepted with a probability chosen to give the full system distribution. The P's and T's of the reference and full systems are chosen separately to optimize the computational time required to produce the full system EOS. The method is numerically very efficient and predicts a Hugoniot in excellent agreement with experimental data.
14. Optimized nested Markov chain Monte Carlo sampling: application to the liquid nitrogen Hugoniot using density functional theory
SciTech Connect
Shaw, Milton Sam; Coe, Joshua D; Sewell, Thomas D
2009-01-01
An optimized version of the Nested Markov Chain Monte Carlo sampling method is applied to the calculation of the Hugoniot for liquid nitrogen. The 'full' system of interest is calculated using density functional theory (DFT) with a 6-31 G* basis set for the configurational energies. The 'reference' system is given by a model potential fit to the anisotropic pair interaction of two nitrogen molecules from DFT calculations. The EOS is sampled in the isobaric-isothermal (NPT) ensemble with a trial move constructed from many Monte Carlo steps in the reference system. The trial move is then accepted with a probability chosen to give the full system distribution. The P's and T's of the reference and full systems are chosen separately to optimize the computational time required to produce the full system EOS. The method is numerically very efficient and predicts a Hugoniot in excellent agreement with experimental data.
15. Geochemical Characterization Using Geophysical Data and Markov Chain Monte Carlo Methods
Chen, J.; Hubbard, S.; Rubin, Y.; Murray, C.; Roden, E.; Majer, E.
2002-12-01
if they were available from direct measurements or as variables otherwise. To estimate the geochemical parameters, we first assigned a prior model for each variable and a likelihood model for each type of data, which together define posterior probability distributions for each variable on the domain. Since the posterior probability distribution may involve hundreds of variables, we used a Markov Chain Monte Carlo (MCMC) method to explore each variable by generating and subsequently evaluating hundreds of realizations. Results from this case study showed that although geophysical attributes are not necessarily directly related to geochemical parameters, geophysical data could be very useful for providing accurate and high-resolution information about geochemical parameter distribution through their joint and indirect connections with hydrogeological properties such as lithofacies. This case study also demonstrated that MCMC methods were particularly useful for geochemical parameter estimation using geophysical data because they allow incorporation into the procedure of spatial correlation information, measurement errors, and cross correlations among different types of parameters.
16. Phasic Triplet Markov Chains.
PubMed
El Yazid Boudaren, Mohamed; Monfrini, Emmanuel; Pieczynski, Wojciech; Aïssani, Amar
2014-11-01
Hidden Markov chains have been shown to be inadequate for data modeling under some complex conditions. In this work, we address the problem of statistical modeling of phenomena involving two heterogeneous system states. Such phenomena may arise in biology or communications, among other fields. Namely, we consider that a sequence of meaningful words is to be searched within a whole observation that also contains arbitrary one-by-one symbols. Moreover, a word may be interrupted at some site to be carried on later. Applying plain hidden Markov chains to such data, while ignoring their specificity, yields unsatisfactory results. The Phasic triplet Markov chain, proposed in this paper, overcomes this difficulty by means of an auxiliary underlying process in accordance with the triplet Markov chains theory. Related Bayesian restoration techniques and parameters estimation procedures according to the new model are then described. Finally, to assess the performance of the proposed model against the conventional hidden Markov chain model, experiments are conducted on synthetic and real data. PMID:26353069
17. A Markov chain Monte Carlo (MCMC) methodology with bootstrap percentile estimates for predicting presidential election results in Ghana.
PubMed
Nortey, Ezekiel N N; Ansah-Narh, Theophilus; Asah-Asante, Richard; Minkah, Richard
2015-01-01
Although, there exists numerous literature on the procedure for forecasting or predicting election results, in Ghana only opinion poll strategies have been used. To fill this gap, the paper develops Markov chain models for forecasting the 2016 presidential election results at the Regional, Zonal (i.e. Savannah, Coastal and Forest) and the National levels using past presidential election results of Ghana. The methodology develops a model for prediction of the 2016 presidential election results in Ghana using the Markov chains Monte Carlo (MCMC) methodology with bootstrap estimates. The results were that the ruling NDC may marginally win the 2016 Presidential Elections but would not obtain the more than 50 % votes to be declared an outright winner. This means that there is going to be a run-off election between the two giant political parties: the ruling NDC and the major opposition party, NPP. The prediction for the 2016 Presidential run-off election between the NDC and the NPP was rather in favour of the major opposition party, the NPP with a little over the 50 % votes obtained. PMID:26435890
18. Fitting a distribution to censored contamination data using Markov Chain Monte Carlo methods and samples selected with unequal probabilities.
PubMed
Williams, Michael S; Ebel, Eric D
2014-11-18
The fitting of statistical distributions to chemical and microbial contamination data is a common application in risk assessment. These distributions are used to make inferences regarding even the most pedestrian of statistics, such as the population mean. The reason for the heavy reliance on a fitted distribution is the presence of left-, right-, and interval-censored observations in the data sets, with censored observations being the result of nondetects in an assay, the use of screening tests, and other practical limitations. Considerable effort has been expended to develop statistical distributions and fitting techniques for a wide variety of applications. Of the various fitting methods, Markov Chain Monte Carlo methods are common. An underlying assumption for many of the proposed Markov Chain Monte Carlo methods is that the data represent independent and identically distributed (iid) observations from an assumed distribution. This condition is satisfied when samples are collected using a simple random sampling design. Unfortunately, samples of food commodities are generally not collected in accordance with a strict probability design. Nevertheless, pseudosystematic sampling efforts (e.g., collection of a sample hourly or weekly) from a single location in the farm-to-table continuum are reasonable approximations of a simple random sample. The assumption that the data represent an iid sample from a single distribution is more difficult to defend if samples are collected at multiple locations in the farm-to-table continuum or risk-based sampling methods are employed to preferentially select samples that are more likely to be contaminated. This paper develops a weighted bootstrap estimation framework that is appropriate for fitting a distribution to microbiological samples that are collected with unequal probabilities of selection. An example based on microbial data, derived by the Most Probable Number technique, demonstrates the method and highlights the
19. Markov Chain Monte Carlo (MCMC) Inversion of Hillslope Elevation and Soil Thickness Data for the Baselevel History
Naylor, Mark; Mudd, Simon; Yoo, Kyungsoo
2010-05-01
Hillslope topography and soil thickness respond to changes in river incision or deposition. For example, accelerated river incision leads to a wave of steepening and soil thinning that begins at the channel and moves upslope [1]. Because of the coupled response of topography, soil thickness and channel incision or deposition rates, it may be possible to use hillslope properties to reconstruct the erosional or depositional history of channels. A prerequisite for such inversion of hillslope properties to reconstruct historical landscape dynamics is a method that allows one to quantify both the most likely channel history as well as the uncertainties in changing channel erosion or deposition rates through time. Here we present robust methods ideally suited for this purpose: Monte Carlo Markov Chain (MCMC) methods. Specifically, MCMC methods [2] involve (i) taking some assumed base level history, (ii) perturbing that history (iii) running a forward model to estimate new hillslope profiles (iv) choosing whether to accept the new history by a Metropolis-Hastings Algorithm [3] (v) storing the favoured history and repeating. In this way we iterate towards the most likely channel history whilst exploring parameter space in such a way that confidence intervals can quantified. Here we demonstrate how this approach returns not only a best estimate history, but also credibility intervals which reflect the progressive loss of information with time. These techniques are generic and should be employed more generally within geomorphology. [1] Mudd, S.M., and D.J. Furbish (2007), Responses of soil mantled hillslopes to transient channel incision rates, Journal of Geophysical Research-Earth Surface, 112, F03S18, doi:10.1029/2006JF000516 [2] K. Gallagher, K. Charvin, S. Nielsen, M. Sambridge and J. Stephenson (2009) Markov chain Monte Carlo (MCMC) sampling methods to determine optimal models, model resolution and model choice for Earth Science problems Marine and Petroleum Geology 26
20. Recovery of Item Parameters in the Nominal Response Model: A Comparison of Marginal Maximum Likelihood Estimation and Markov Chain Monte Carlo Estimation.
ERIC Educational Resources Information Center
Wollack, James A.; Bolt, Daniel M.; Cohen, Allan S.; Lee, Young-Sun
2002-01-01
Compared the quality of item parameter estimates for marginal maximum likelihood (MML) and Markov Chain Monte Carlo (MCMC) with the nominal response model using simulation. The quality of item parameter recovery was nearly identical for MML and MCMC, and both methods tended to produce good estimates. (SLD)
1. Assessment of parameter uncertainty in hydrological model using a Markov-Chain-Monte-Carlo-based multilevel-factorial-analysis method
Zhang, Junlong; Li, Yongping; Huang, Guohe; Chen, Xi; Bao, Anming
2016-07-01
Without a realistic assessment of parameter uncertainty, decision makers may encounter difficulties in accurately describing hydrologic processes and assessing relationships between model parameters and watershed characteristics. In this study, a Markov-Chain-Monte-Carlo-based multilevel-factorial-analysis (MCMC-MFA) method is developed, which can not only generate samples of parameters from a well constructed Markov chain and assess parameter uncertainties with straightforward Bayesian inference, but also investigate the individual and interactive effects of multiple parameters on model output through measuring the specific variations of hydrological responses. A case study is conducted for addressing parameter uncertainties in the Kaidu watershed of northwest China. Effects of multiple parameters and their interactions are quantitatively investigated using the MCMC-MFA with a three-level factorial experiment (totally 81 runs). A variance-based sensitivity analysis method is used to validate the results of parameters' effects. Results disclose that (i) soil conservation service runoff curve number for moisture condition II (CN2) and fraction of snow volume corresponding to 50% snow cover (SNO50COV) are the most significant factors to hydrological responses, implying that infiltration-excess overland flow and snow water equivalent represent important water input to the hydrological system of the Kaidu watershed; (ii) saturate hydraulic conductivity (SOL_K) and soil evaporation compensation factor (ESCO) have obvious effects on hydrological responses; this implies that the processes of percolation and evaporation would impact hydrological process in this watershed; (iii) the interactions of ESCO and SNO50COV as well as CN2 and SNO50COV have an obvious effect, implying that snow cover can impact the generation of runoff on land surface and the extraction of soil evaporative demand in lower soil layers. These findings can help enhance the hydrological model
2. Markov chain Monte Carlo study on dark matter property related to the cosmic e{sup {+-}}excesses
SciTech Connect
Liu Jie; Yuan Qiang; Bi Xiaojun; Li Hong; Zhang Xinmin
2010-01-15
In this paper we develop a Markov chain Monte Carlo code to study the dark matter properties in frameworks to interpret the recent observations of cosmic ray electron/positron excesses. We assume that the dark matter particles couple dominantly to leptons and consider two cases, annihilating or decaying into lepton pairs, respectively. The constraint on the central density profile from the H.E.S.S. observation of diffuse {gamma} rays around the Galactic center is also included in the Markov chain Monte Carlo code self-consistently. In the numerical study, we have considered two cases of the background: fixed e{sup +}e{sup -} background and the relaxed one. Two data sets of electrons/positrons, i.e. PAMELA+ATIC (Data set I) and PAMELA+Fermi-LAT+H.E.S.S. (Data set II), are fitted independently, considering the current inconsistence between the observational data. We find that for Data set I, dark matter with m{sub {chi}{approx_equal}0}.70 TeV for annihilation (or 1.4 TeV for decay) and a non-negligible branching ratio to e{sup +}e{sup -} channel is favored; while for Data set II, m{sub {chi}{approx_equal}2}.2 TeV for annihilation (or 4.5 TeV for decay) and the combination of {mu}{sup +{mu}-} and {tau}{sup +{tau}-} final states can best fit the data. We also show that the background of electrons and positrons actually will significantly affect the branching ratios. The H.E.S.S. observation of {gamma} rays in the Galactic center ridge puts a strong constraint on the central density profile of the dark matter halo for the annihilation dark matter scenario. In this case the Navarro-Frenk-White profile, which is regarded as the typical predication from the cold dark matter scenario, is excluded with a high significance (>3{sigma}). For the decaying dark matter scenario, the constraint is much weaker.
3. Weighted maximum posterior marginals for random fields using an ensemble of conditional densities from multiple Markov chain Monte Carlo simulations.
PubMed
2011-07-01
The ability of classification systems to adjust their performance (sensitivity/specificity) is essential for tasks in which certain errors are more significant than others. For example, mislabeling cancerous lesions as benign is typically more detrimental than mislabeling benign lesions as cancerous. Unfortunately, methods for modifying the performance of Markov random field (MRF) based classifiers are noticeably absent from the literature, and thus most such systems restrict their performance to a single, static operating point (a paired sensitivity/specificity). To address this deficiency we present weighted maximum posterior marginals (WMPM) estimation, an extension of maximum posterior marginals (MPM) estimation. Whereas the MPM cost function penalizes each error equally, the WMPM cost function allows misclassifications associated with certain classes to be weighted more heavily than others. This creates a preference for specific classes, and consequently a means for adjusting classifier performance. Realizing WMPM estimation (like MPM estimation) requires estimates of the posterior marginal distributions. The most prevalent means for estimating these--proposed by Marroquin--utilizes a Markov chain Monte Carlo (MCMC) method. Though Marroquin's method (M-MCMC) yields estimates that are sufficiently accurate for MPM estimation, they are inadequate for WMPM. To more accurately estimate the posterior marginals we present an equally simple, but more effective extension of the MCMC method (E-MCMC). Assuming an identical number of iterations, E-MCMC as compared to M-MCMC yields estimates with higher fidelity, thereby 1) allowing a far greater number and diversity of operating points and 2) improving overall classifier performance. To illustrate the utility of WMPM and compare the efficacies of M-MCMC and E-MCMC, we integrate them into our MRF-based classification system for detecting cancerous glands in (whole-mount or quarter) histological sections of the prostate
4. A MARKOV CHAIN MONTE CARLO ALGORITHM FOR ANALYSIS OF LOW SIGNAL-TO-NOISE COSMIC MICROWAVE BACKGROUND DATA
SciTech Connect
Jewell, J. B.; O'Dwyer, I. J.; Huey, Greg; Gorski, K. M.; Eriksen, H. K.; Wandelt, B. D. E-mail: h.k.k.eriksen@astro.uio.no
2009-05-20
We present a new Markov Chain Monte Carlo (MCMC) algorithm for cosmic microwave background (CMB) analysis in the low signal-to-noise regime. This method builds on and complements the previously described CMB Gibbs sampler, and effectively solves the low signal-to-noise inefficiency problem of the direct Gibbs sampler. The new algorithm is a simple Metropolis-Hastings sampler with a general proposal rule for the power spectrum, C {sub l}, followed by a particular deterministic rescaling operation of the sky signal, s. The acceptance probability for this joint move depends on the sky map only through the difference of {chi}{sup 2} between the original and proposed sky sample, which is close to unity in the low signal-to-noise regime. The algorithm is completed by alternating this move with a standard Gibbs move. Together, these two proposals constitute a computationally efficient algorithm for mapping out the full joint CMB posterior, both in the high and low signal-to-noise regimes.
5. A MONTE CARLO MARKOV CHAIN BASED INVESTIGATION OF BLACK HOLE SPIN IN THE ACTIVE GALAXY NGC 3783
SciTech Connect
Reynolds, Christopher S.; Lohfink, Anne M.; Trippe, Margaret L.; Brenneman, Laura W.; Miller, Jon M.; Fabian, Andrew C.; Nowak, Michael A. E-mail: alohfink@astro.umd.edu
2012-08-20
The analysis of relativistically broadened X-ray spectral features from the inner accretion disk provides a powerful tool for measuring the spin of supermassive black holes in active galactic nuclei (AGNs). However, AGN spectra are often complex and careful analysis employing appropriate and self-consistent models is required if one has to obtain robust results. In this paper, we revisit the deep 2009 July Suzaku observation of the Seyfert galaxy NGC 3783 in order to study in a rigorous manner the robustness of the inferred black hole spin parameter. Using Monte Carlo Markov chain techniques, we identify a (partial) modeling degeneracy between the iron abundance of the disk and the black hole spin parameter. We show that the data for NGC 3783 strongly require both supersolar iron abundance (Z{sub Fe} = 2-4 Z{sub Sun }) and a rapidly spinning black hole (a > 0.89). We discuss various astrophysical considerations that can affect the measured abundance. We note that, while the abundance enhancement inferred in NGC 3783 is modest, the X-ray analysis of some other objects has found extreme iron abundances. We introduce the hypothesis that the radiative levitation of iron ions in the innermost regions of radiation-dominated AGN disks can enhance the photospheric abundance of iron. We show that radiative levitation is a plausible mechanism in the very inner regions of high accretion rate AGN disks.
6. Markov Chain Monte Carlo Joint Analysis of Chandra X-Ray Imaging Spectroscopy and Sunyaev-Zel'dovich Effect Data
NASA Technical Reports Server (NTRS)
Bonamente, Massimillano; Joy, Marshall K.; Carlstrom, John E.; Reese, Erik D.; LaRoque, Samuel J.
2004-01-01
X-ray and Sunyaev-Zel'dovich effect data can be combined to determine the distance to galaxy clusters. High-resolution X-ray data are now available from Chandra, which provides both spatial and spectral information, and Sunyaev-Zel'dovich effect data were obtained from the BIMA and Owens Valley Radio Observatory (OVRO) arrays. We introduce a Markov Chain Monte Carlo procedure for the joint analysis of X-ray and Sunyaev- Zel'dovich effect data. The advantages of this method are the high computational efficiency and the ability to measure simultaneously the probability distribution of all parameters of interest, such as the spatial and spectral properties of the cluster gas and also for derivative quantities such as the distance to the cluster. We demonstrate this technique by applying it to the Chandra X-ray data and the OVRO radio data for the galaxy cluster A611. Comparisons with traditional likelihood ratio methods reveal the robustness of the method. This method will be used in follow-up paper to determine the distances to a large sample of galaxy cluster.
7. Application of the Markov Chain Monte Carlo method for snow water equivalent retrieval based on passive microwave measurements
Pan, J.; Durand, M. T.; Vanderjagt, B. J.
2015-12-01
Markov Chain Monte Carlo (MCMC) method is a retrieval algorithm based on Bayes' rule, which starts from an initial state of snow/soil parameters, and updates it to a series of new states by comparing the posterior probability of simulated snow microwave signals before and after each time of random walk. It is a realization of the Bayes' rule, which gives an approximation to the probability of the snow/soil parameters in condition of the measured microwave TB signals at different bands. Although this method could solve all snow parameters including depth, density, snow grain size and temperature at the same time, it still needs prior information of these parameters for posterior probability calculation. How the priors will influence the SWE retrieval is a big concern. Therefore, in this paper at first, a sensitivity test will be carried out to study how accurate the snow emission models and how explicit the snow priors need to be to maintain the SWE error within certain amount. The synthetic TB simulated from the measured snow properties plus a 2-K observation error will be used for this purpose. It aims to provide a guidance on the MCMC application under different circumstances. Later, the method will be used for the snowpits at different sites, including Sodankyla, Finland, Churchill, Canada and Colorado, USA, using the measured TB from ground-based radiometers at different bands. Based on the previous work, the error in these practical cases will be studied, and the error sources will be separated and quantified.
8. Assimilation of Satellite Soil Moisture observation with the Particle Filter-Markov Chain Monte Carlo and Geostatistical Modeling
2016-04-01
Soil moisture simulation and prediction are increasingly used to characterize agricultural droughts but the process suffers from data scarcity and quality. The satellite soil moisture observations could be used to improve model predictions with data assimilation. Remote sensing products, however, are typically discontinuous in spatial-temporal coverages; while simulated soil moisture products are potentially biased due to the errors in forcing data, parameters, and deficiencies of model physics. This study attempts to provide a detailed analysis of the joint and separate assimilation of streamflow and Advanced Scatterometer (ASCAT) surface soil moisture into a fully distributed hydrologic model, with the use of recently developed particle filter-Markov chain Monte Carlo (PF-MCMC) method. A geostatistical model is introduced to overcome the satellite soil moisture discontinuity issue where satellite data does not cover the whole study region or is significantly biased, and the dominant land cover is dense vegetation. The results indicate that joint assimilation of soil moisture and streamflow has minimal effect in improving the streamflow prediction, however, the surface soil moisture field is significantly improved. The combination of DA and geostatistical approach can further improve the surface soil moisture prediction.
9. Lifetime PCB 153 bioaccumulation and pharmacokinetics in pilot whales: Bayesian population PBPK modeling and Markov chain Monte Carlo simulations.
PubMed
Weijs, Liesbeth; Roach, Anthony C; Yang, Raymond S H; McDougall, Robin; Lyons, Michael; Housand, Conrad; Tibax, Detlef; Manning, Therese; Chapman, John; Edge, Katelyn; Covaci, Adrian; Blust, Ronny
2014-01-01
Physiologically based pharmacokinetic (PBPK) models for wild animal populations such as marine mammals typically have a high degree of model uncertainty and variability due to the scarcity of information and the embryonic nature of this field. Parameters values used in marine mammals models are usually taken from other mammalian species (e.g. rats or mice) and might not be entirely suitable to properly explain the kinetics of pollutants in marine mammals. Therefore, several parameters for a PBPK model for the bioaccumulation and pharmacokinetics of PCB 153 in long-finned pilot whales were estimated in the present study using the Bayesian approach executed with Markov chain Monte Carlo (MCMC) simulations. This method uses 'prior' information of the parameters, either from the literature or from previous model runs. The advantage is that this method uses such 'prior' parameters to calculate probability distributions to determine 'posterior' values that best explain the field observations. Those field observations or datasets were PCB 153 concentrations in blubber of long-finned pilot whales from Sandy Cape and Stanley, Tasmania, Australia. The model predictions showed an overall decrease in PCB 153 levels in blubber over the lifetime of the pilot whales. All parameters from the Sandy Cape model were updated using the Stanley dataset, except for the concentration of PCB 153 in the milk. The model presented here is a promising and preliminary start to PBPK modeling in long-finned pilot whales that would provide a basis for non-invasive studies in these protected marine mammals. PMID:24080004
10. Comparison of reversible-jump Markov-chain-Monte-Carlo learning approach with other methods for missing enzyme identification.
PubMed
Geng, Bo; Zhou, Xiaobo; Zhu, Jinmin; Hung, Y S; Wong, Stephen T C
2008-04-01
Computational identification of missing enzymes plays a significant role in accurate and complete reconstruction of metabolic network for both newly sequenced and well-studied organisms. For a metabolic reaction, given a set of candidate enzymes identified according to certain biological evidences, a powerful mathematical model is required to predict the actual enzyme(s) catalyzing the reactions. In this study, several plausible predictive methods are considered for the classification problem in missing enzyme identification, and comparisons are performed with an aim to identify a method with better performance than the Bayesian model used in previous work. In particular, a regression model consisting of a linear term and a nonlinear term is proposed to apply to the problem, in which the reversible jump Markov-chain-Monte-Carlo (MCMC) learning technique (developed in [Andrieu C, Freitas Nando de, Doucet A. Robust full Bayesian learning for radial basis networks 2001;13:2359-407.]) is adopted to estimate the model order and the parameters. We evaluated the models using known reactions in Escherichia coli, Mycobacterium tuberculosis, Vibrio cholerae and Caulobacter cresentus bacteria, as well as one eukaryotic organism, Saccharomyces Cerevisiae. Although support vector regression also exhibits comparable performance in this application, it was demonstrated that the proposed model achieves favorable prediction performance, particularly sensitivity, compared with the Bayesian method. PMID:17950040
11. Markov Chain Monte Carlo inversion of temperature and salinity structure of an internal solitary wave packet from marine seismic data
Tang, Qunshu; Hobbs, Richard; Zheng, Chan; Biescas, Berta; Caiado, Camila
2016-06-01
Marine seismic reflection technique is used to observe the strong ocean dynamic process of nonlinear internal solitary waves (ISWs or solitons) in the near-surface water. Analysis of ISWs is problematical because of their transient nature and limitations of classical physical oceanography methods. This work explores a Markov Chain Monte Carlo (MCMC) approach to recover the temperature and salinity of ISW field using the seismic reflectivity data and in situ hydrographic data. The MCMC approach is designed to directly sample the posterior probability distributions of temperature and salinity which are the solutions of the system under investigation. The principle improvement is the capability of incorporating uncertainties in observations and prior models which then provide quantified uncertainties in the output model parameters. We tested the MCMC approach on two acoustic reflectivity data sets one synthesized from a CTD cast and the other derived from multichannel seismic reflections. This method finds the solutions faithfully within the significantly narrowed confidence intervals from the provided priors. Combined with a low frequency initial model interpreted from seismic horizons of ISWs, the MCMC method is used to compute the finescale temperature, salinity, acoustic velocity, and density of ISW field. The statistically derived results are equivalent to the conventional linearized inversion method. However, the former provides us the quantified uncertainties of the temperature and salinity along the whole section whilst the latter does not. These results are the first time ISWs have been mapped with sufficient detail for further analysis of their dynamic properties.
12. A LINK TO THE PAST: USING MARKOV CHAIN MONTE CARLO FITTING TO CONSTRAIN FUNDAMENTAL PARAMETERS OF HIGH-REDSHIFT GALAXIES
SciTech Connect
Pirzkal, N.; Rothberg, B.; Koekemoer, Anton; Nilsson, Kim K.; Finkelstein, S.; Malhotra, Sangeeta; Rhoads, James
2012-04-01
We have developed a new method for fitting spectral energy distributions (SEDs) to identify and constrain the physical properties of high-redshift (4 < z < 8) galaxies. Our approach uses an implementation of Bayesian based Markov Chain Monte Carlo that we have dubbed '{pi}MC{sup 2}'. It allows us to compare observations to arbitrarily complex models and to compute 95% credible intervals that provide robust constraints for the model parameters. The work is presented in two sections. In the first, we test {pi}MC{sup 2} using simulated SEDs to not only confirm the recovery of the known inputs but to assess the limitations of the method and identify potential hazards of SED fitting when applied specifically to high-redshift (z > 4) galaxies. In the second part of the paper we apply {pi}MC{sup 2} to thirty-three 4 < z < 8 objects, including the spectroscopically confirmed Grism ACS Program for Extragalactic Science Ly{alpha} sample (4 < z < 6), supplemented by newly obtained Hubble Space Telescope/WFC3 near-IR observations, and several recently reported broadband selected z > 6 galaxies. Using {pi}MC{sup 2}, we are able to constrain the stellar mass of these objects and in some cases their stellar age and find no evidence that any of these sources formed at a redshift larger than z = 8, a time when the universe was Almost-Equal-To 0.6 Gyr old.
13. Multi-Resolution Markov-Chain-Monte-Carlo Approach for System Identification with an Application to Finite-Element Models
SciTech Connect
Johannesson, G; Glaser, R E; Lee, C L; Nitao, J J; Hanley, W G
2005-02-07
Estimating unknown system configurations/parameters by combining system knowledge gained from a computer simulation model on one hand and from observed data on the other hand is challenging. An example of such inverse problem is detecting and localizing potential flaws or changes in a structure by using a finite-element model and measured vibration/displacement data. We propose a probabilistic approach based on Bayesian methodology. This approach does not only yield a single best-guess solution, but a posterior probability distribution over the parameter space. In addition, the Bayesian approach provides a natural framework to accommodate prior knowledge. A Markov chain Monte Carlo (MCMC) procedure is proposed to generate samples from the posterior distribution (an ensemble of likely system configurations given the data). The MCMC procedure proposed explores the parameter space at different resolutions (scales), resulting in a more robust and efficient procedure. The large-scale exploration steps are carried out using coarser-resolution finite-element models, yielding a considerable decrease in computational time, which can be a crucial for large finite-element models. An application is given using synthetic displacement data from a simple cantilever beam with MCMC exploration carried out at three different resolutions.
14. A trans-dimensional Bayesian Markov chain Monte Carlo algorithm for model assessment using frequency-domain electromagnetic data
USGS Publications Warehouse
Minsley, B.J.
2011-01-01
A meaningful interpretation of geophysical measurements requires an assessment of the space of models that are consistent with the data, rather than just a single, 'best' model which does not convey information about parameter uncertainty. For this purpose, a trans-dimensional Bayesian Markov chain Monte Carlo (MCMC) algorithm is developed for assessing frequency-domain electromagnetic (FDEM) data acquired from airborne or ground-based systems. By sampling the distribution of models that are consistent with measured data and any prior knowledge, valuable inferences can be made about parameter values such as the likely depth to an interface, the distribution of possible resistivity values as a function of depth and non-unique relationships between parameters. The trans-dimensional aspect of the algorithm allows the number of layers to be a free parameter that is controlled by the data, where models with fewer layers are inherently favoured, which provides a natural measure of parsimony and a significant degree of flexibility in parametrization. The MCMC algorithm is used with synthetic examples to illustrate how the distribution of acceptable models is affected by the choice of prior information, the system geometry and configuration and the uncertainty in the measured system elevation. An airborne FDEM data set that was acquired for the purpose of hydrogeological characterization is also studied. The results compare favourably with traditional least-squares analysis, borehole resistivity and lithology logs from the site, and also provide new information about parameter uncertainty necessary for model assessment. ?? 2011. Geophysical Journal International ?? 2011 RAS.
15. A trans-dimensional Bayesian Markov chain Monte Carlo algorithm for model assessment using frequency-domain electromagnetic data
USGS Publications Warehouse
Minsley, Burke J.
2011-01-01
A meaningful interpretation of geophysical measurements requires an assessment of the space of models that are consistent with the data, rather than just a single, ‘best’ model which does not convey information about parameter uncertainty. For this purpose, a trans-dimensional Bayesian Markov chain Monte Carlo (MCMC) algorithm is developed for assessing frequencydomain electromagnetic (FDEM) data acquired from airborne or ground-based systems. By sampling the distribution of models that are consistent with measured data and any prior knowledge, valuable inferences can be made about parameter values such as the likely depth to an interface, the distribution of possible resistivity values as a function of depth and non-unique relationships between parameters. The trans-dimensional aspect of the algorithm allows the number of layers to be a free parameter that is controlled by the data, where models with fewer layers are inherently favoured, which provides a natural measure of parsimony and a significant degree of flexibility in parametrization. The MCMC algorithm is used with synthetic examples to illustrate how the distribution of acceptable models is affected by the choice of prior information, the system geometry and configuration and the uncertainty in the measured system elevation. An airborne FDEM data set that was acquired for the purpose of hydrogeological characterization is also studied. The results compare favorably with traditional least-squares analysis, borehole resistivity and lithology logs from the site, and also provide new information about parameter uncertainty necessary for model assessment.
16. Application of Markov chain Monte Carlo analysis to biomathematical modeling of respirable dust in US and UK coal miners
PubMed Central
Sweeney, Lisa M.; Parker, Ann; Haber, Lynne T.; Tran, C. Lang; Kuempel, Eileen D.
2015-01-01
A biomathematical model was previously developed to describe the long-term clearance and retention of particles in the lungs of coal miners. The model structure was evaluated and parameters were estimated in two data sets, one from the United States and one from the United Kingdom. The three-compartment model structure consists of deposition of inhaled particles in the alveolar region, competing processes of either clearance from the alveolar region or translocation to the lung interstitial region, and very slow, irreversible sequestration of interstitialized material in the lung-associated lymph nodes. Point estimates of model parameter values were estimated separately for the two data sets. In the current effort, Bayesian population analysis using Markov chain Monte Carlo simulation was used to recalibrate the model while improving assessments of parameter variability and uncertainty. When model parameters were calibrated simultaneously to the two data sets, agreement between the derived parameters for the two groups was very good, and the central tendency values were similar to those derived from the deterministic approach. These findings are relevant to the proposed update of the ICRP human respiratory tract model with revisions to the alveolar-interstitial region based on this long-term particle clearance and retention model. PMID:23454101
17. Modeling the effects and uncertainties of contaminated sediment remediation scenarios in a Norwegian fjord by Markov chain Monte Carlo simulation.
PubMed
Saloranta, Tuomo M; Armitage, James M; Haario, Heikki; Naes, Kristoffer; Cousins, Ian T; Barton, David N
2008-01-01
Multimedia environmental fate models are useful tools to investigate the long-term impacts of remediation measures designed to alleviate potential ecological and human health concerns in contaminated areas. Estimating and communicating the uncertainties associated with the model simulations is a critical task for demonstrating the transparency and reliability of the results. The Extended Fourier Amplitude Sensitivity Test(Extended FAST) method for sensitivity analysis and Bayesian Markov chain Monte Carlo (MCMC) method for uncertainty analysis and model calibration have several advantages over methods typically applied for multimedia environmental fate models. Most importantly, the simulation results and their uncertainties can be anchored to the available observations and their uncertainties. We apply these techniques for simulating the historical fate of polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs) in the Grenland fjords, Norway, and for predicting the effects of different contaminated sediment remediation (capping) scenarios on the future levels of PCDD/Fs in cod and crab therein. The remediation scenario simulations show that a significant remediation effect can first be seen when significant portions of the contaminated sediment areas are cleaned up, and that increase in capping area leads to both earlier achievement of good fjord status and narrower uncertainty in the predicted timing for this. PMID:18350897
18. Musical Markov Chains
Volchenkov, Dima; Dawin, Jean René
A system for using dice to compose music randomly is known as the musical dice game. The discrete time MIDI models of 804 pieces of classical music written by 29 composers have been encoded into the transition matrices and studied by Markov chains. Contrary to human languages, entropy dominates over redundancy, in the musical dice games based on the compositions of classical music. The maximum complexity is achieved on the blocks consisting of just a few notes (8 notes, for the musical dice games generated over Bach's compositions). First passage times to notes can be used to resolve tonality and feature a composer.
19. Snow Water Equivalent Retrieval By Markov Chain Monte Carlo Based on Memls and Hut Snow Emission Model
Pan, J.; Durand, M. T.; Vanderjagt, B. J.
2014-12-01
The Markov chain Monte Carlo (MCMC) method had been proved to be successful in snow water equivalent retrieval based on synthetic point-scale passive microwave brightness temperature (TB) observations. This method needs only general prior information about distribution of snow parameters, and could estimate layered snow properties, including the thickness, temperature, density and snow grain size (or exponential correlation length) of each layer. In this study, the multi-layer HUT (Helsinki University of Technology) model and the MEMLS (Microwave Emission Model of Layered Snowpacks) will be used as observation models to assimilate the observed TB into snow parameter prediction. Previous studies had shown that the multi-layer HUT model tends to underestimate TB at 37 GHz for deep snow, while the MEMLS does not show sensitivity of model bias to snow depth. Therefore, results using HUT model and MEMLS will be compared to see how the observation model will influence the retrieval of snow parameters. The radiometric measurements at 10.65, 18.7, 36.5 and 90 GHz at Sodankyla, Finland will be used as MCMC input, and the statistics of all snow property measurement will be used to calculate the prior information. 43 dry snowpits with complete measurements of all snow parameters will be used for validation. The entire dataset are from NorSREx (Nordic Snow Radar Experiment) experiments carried out by Juha Lemmetyinen, Anna Kontu and Jouni Pulliainen in FMI in 2009-2011 winters, and continued two more winters from 2011 to Spring of 2013. Besides the snow thickness and snow density that are directly related to snow water equivalent, other parameters will be compared with observations, too. For thin snow, the previous studies showed that influence of underlying soil is considerable, especially when the soil is half frozen with part of unfrozen liquid water and part of ice. Therefore, this study will also try to employ a simple frozen soil permittivity model to improve the
20. Application of Markov Chain Monte Carlo Method to Mantle Melting: An Example from REE Abundances in Abyssal Peridotites
LIU, B.; Liang, Y.
2015-12-01
Markov chain Monte Carlo (MCMC) simulation is a powerful statistical method in solving inverse problems that arise from a wide range of applications, such as nuclear physics, computational biology, financial engineering, among others. In Earth sciences applications of MCMC are primarily in the field of geophysics [1]. The purpose of this study is to introduce MCMC to geochemical inverse problems related to trace element fractionation during concurrent melting, melt transport and melt-rock reaction in the mantle. MCMC method has several advantages over linearized least squares methods in inverting trace element patterns in basalts and mantle rocks. First, MCMC can handle equations that have no explicit analytical solutions which are required by linearized least squares methods for gradient calculation. Second, MCMC converges to global minimum while linearized least squares methods may be stuck at a local minimum or converge slowly due to nonlinearity. Furthermore, MCMC can provide insight into uncertainties of model parameters with non-normal trade-off. We use MCMC to invert for extent of melting, amount of trapped melt, and extent of chemical disequilibrium between the melt and residual solid from REE data in abyssal peridotites from Central Indian Ridge and Mid-Atlantic Ridge. In the first step, we conduct forward calculation of REE evolution with melting models in a reasonable model space. We then build up a chain of melting models according to Metropolis-Hastings algorithm to represent the probability of specific model. We show that chemical disequilibrium is likely to play an important role in fractionating LREE in residual peridotites. In the future, MCMC will be applied to more realistic but also more complicated melting models in which partition coefficients, diffusion coefficients, as well as melting and melt suction rates vary as functions of temperature, pressure and mineral compositions. [1]. Sambridge & Mosegarrd [2002] Rev. Geophys.
1. Efficient Markov Chain Monte Carlo Implementation of Bayesian Analysis of Additive and Dominance Genetic Variances in Noninbred Pedigrees
PubMed Central
Waldmann, Patrik; Hallander, Jon; Hoti, Fabian; Sillanpää, Mikko J.
2008-01-01
Accurate and fast computation of quantitative genetic variance parameters is of great importance in both natural and breeding populations. For experimental designs with complex relationship structures it can be important to include both additive and dominance variance components in the statistical model. In this study, we introduce a Bayesian Gibbs sampling approach for estimation of additive and dominance genetic variances in the traditional infinitesimal model. The method can handle general pedigrees without inbreeding. To optimize between computational time and good mixing of the Markov chain Monte Carlo (MCMC) chains, we used a hybrid Gibbs sampler that combines a single site and a blocked Gibbs sampler. The speed of the hybrid sampler and the mixing of the single-site sampler were further improved by the use of pretransformed variables. Two traits (height and trunk diameter) from a previously published diallel progeny test of Scots pine (Pinus sylvestris L.) and two large simulated data sets with different levels of dominance variance were analyzed. We also performed Bayesian model comparison on the basis of the posterior predictive loss approach. Results showed that models with both additive and dominance components had the best fit for both height and diameter and for the simulated data with high dominance. For the simulated data with low dominance, we needed an informative prior to avoid the dominance variance component becoming overestimated. The narrow-sense heritability estimates in the Scots pine data were lower compared to the earlier results, which is not surprising because the level of dominance variance was rather high, especially for diameter. In general, the hybrid sampler was considerably faster than the blocked sampler and displayed better mixing properties than the single-site sampler. PMID:18558655
2. Efficient Markov chain Monte Carlo implementation of Bayesian analysis of additive and dominance genetic variances in noninbred pedigrees.
PubMed
Waldmann, Patrik; Hallander, Jon; Hoti, Fabian; Sillanpää, Mikko J
2008-06-01
Accurate and fast computation of quantitative genetic variance parameters is of great importance in both natural and breeding populations. For experimental designs with complex relationship structures it can be important to include both additive and dominance variance components in the statistical model. In this study, we introduce a Bayesian Gibbs sampling approach for estimation of additive and dominance genetic variances in the traditional infinitesimal model. The method can handle general pedigrees without inbreeding. To optimize between computational time and good mixing of the Markov chain Monte Carlo (MCMC) chains, we used a hybrid Gibbs sampler that combines a single site and a blocked Gibbs sampler. The speed of the hybrid sampler and the mixing of the single-site sampler were further improved by the use of pretransformed variables. Two traits (height and trunk diameter) from a previously published diallel progeny test of Scots pine (Pinus sylvestris L.) and two large simulated data sets with different levels of dominance variance were analyzed. We also performed Bayesian model comparison on the basis of the posterior predictive loss approach. Results showed that models with both additive and dominance components had the best fit for both height and diameter and for the simulated data with high dominance. For the simulated data with low dominance, we needed an informative prior to avoid the dominance variance component becoming overestimated. The narrow-sense heritability estimates in the Scots pine data were lower compared to the earlier results, which is not surprising because the level of dominance variance was rather high, especially for diameter. In general, the hybrid sampler was considerably faster than the blocked sampler and displayed better mixing properties than the single-site sampler. PMID:18558655
3. A stochastic Markov chain approach for tennis: Monte Carlo simulation and modeling
Aslam, Kamran
This dissertation describes the computational formulation of probability density functions (pdfs) that facilitate head-to-head match simulations in tennis along with ranking systems developed from their use. A background on the statistical method used to develop the pdfs , the Monte Carlo method, and the resulting rankings are included along with a discussion on ranking methods currently being used both in professional sports and in other applications. Using an analytical theory developed by Newton and Keller in [34] that defines a tennis player's probability of winning a game, set, match and single elimination tournament, a computational simulation has been developed in Matlab that allows further modeling not previously possible with the analytical theory alone. Such experimentation consists of the exploration of non-iid effects, considers the concept the varying importance of points in a match and allows an unlimited number of matches to be simulated between unlikely opponents. The results of these studies have provided pdfs that accurately model an individual tennis player's ability along with a realistic, fair and mathematically sound platform for ranking them.
4. Epistasis Test in Meta-Analysis: A Multi-Parameter Markov Chain Monte Carlo Model for Consistency of Evidence.
PubMed
Lin, Chin; Chu, Chi-Ming; Su, Sui-Lung
2016-01-01
Conventional genome-wide association studies (GWAS) have been proven to be a successful strategy for identifying genetic variants associated with complex human traits. However, there is still a large heritability gap between GWAS and transitional family studies. The "missing heritability" has been suggested to be due to lack of studies focused on epistasis, also called gene-gene interactions, because individual trials have often had insufficient sample size. Meta-analysis is a common method for increasing statistical power. However, sufficient detailed information is difficult to obtain. A previous study employed a meta-regression-based method to detect epistasis, but it faced the challenge of inconsistent estimates. Here, we describe a Markov chain Monte Carlo-based method, called "Epistasis Test in Meta-Analysis" (ETMA), which uses genotype summary data to obtain consistent estimates of epistasis effects in meta-analysis. We defined a series of conditions to generate simulation data and tested the power and type I error rates in ETMA, individual data analysis and conventional meta-regression-based method. ETMA not only successfully facilitated consistency of evidence but also yielded acceptable type I error and higher power than conventional meta-regression. We applied ETMA to three real meta-analysis data sets. We found significant gene-gene interactions in the renin-angiotensin system and the polycyclic aromatic hydrocarbon metabolism pathway, with strong supporting evidence. In addition, glutathione S-transferase (GST) mu 1 and theta 1 were confirmed to exert independent effects on cancer. We concluded that the application of ETMA to real meta-analysis data was successful. Finally, we developed an R package, etma, for the detection of epistasis in meta-analysis [etma is available via the Comprehensive R Archive Network (CRAN) at https://cran.r-project.org/web/packages/etma/index.html]. PMID:27045371
5. Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses
Feroz, F.; Hobson, M. P.
2008-02-01
In performing a Bayesian analysis of astronomical data, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multimodal or exhibit pronounced (curving) degeneracies, which can cause problems for traditional Markov Chain Monte Carlo (MCMC) sampling methods. Secondly, in selecting between a set of competing models, calculation of the Bayesian evidence for each model is computationally expensive using existing methods such as thermodynamic integration. The nested sampling method introduced by Skilling, has greatly reduced the computational expense of calculating evidence and also produces posterior inferences as a by-product. This method has been applied successfully in cosmological applications by Mukherjee, Parkinson & Liddle, but their implementation was efficient only for unimodal distributions without pronounced degeneracies. Shaw, Bridges & Hobson recently introduced a clustered nested sampling method which is significantly more efficient in sampling from multimodal posteriors and also determines the expectation and variance of the final evidence from a single run of the algorithm, hence providing a further increase in efficiency. In this paper, we build on the work of Shaw et al. and present three new methods for sampling and evidence evaluation from distributions that may contain multiple modes and significant degeneracies in very high dimensions; we also present an even more efficient technique for estimating the uncertainty on the evaluated evidence. These methods lead to a further substantial improvement in sampling efficiency and robustness, and are applied to two toy problems to demonstrate the accuracy and economy of the evidence calculation and parameter estimation. Finally, we discuss the use of these methods in performing Bayesian object detection in astronomical data sets, and show that they significantly outperform existing MCMC techniques. An implementation
6. Phase-coexistence simulations of fluid mixtures by the Markov Chain Monte Carlo method using single-particle models
SciTech Connect
Li, Jun; Calo, Victor M.
2013-09-15
We present a single-particle Lennard–Jones (L-J) model for CO{sub 2} and N{sub 2}. Simplified L-J models for other small polyatomic molecules can be obtained following the methodology described herein. The phase-coexistence diagrams of single-component systems computed using the proposed single-particle models for CO{sub 2} and N{sub 2} agree well with experimental data over a wide range of temperatures. These diagrams are computed using the Markov Chain Monte Carlo method based on the Gibbs-NVT ensemble. This good agreement validates the proposed simplified models. That is, with properly selected parameters, the single-particle models have similar accuracy in predicting gas-phase properties as more complex, state-of-the-art molecular models. To further test these single-particle models, three binary mixtures of CH{sub 4}, CO{sub 2} and N{sub 2} are studied using a Gibbs-NPT ensemble. These results are compared against experimental data over a wide range of pressures. The single-particle model has similar accuracy in the gas phase as traditional models although its deviation in the liquid phase is greater. Since the single-particle model reduces the particle number and avoids the time-consuming Ewald summation used to evaluate Coulomb interactions, the proposed model improves the computational efficiency significantly, particularly in the case of high liquid density where the acceptance rate of the particle-swap trial move increases. We compare, at constant temperature and pressure, the Gibbs-NPT and Gibbs-NVT ensembles to analyze their performance differences and results consistency. As theoretically predicted, the agreement between the simulations implies that Gibbs-NVT can be used to validate Gibbs-NPT predictions when experimental data is not available.
7. Corruption of accuracy and efficiency of Markov chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models
Schoups, G.; Vrugt, J. A.; Fenicia, F.; van de Giesen, N. C.
2010-10-01
Conceptual rainfall-runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics. Reliance on first-order, explicit, fixed-step integration methods leads to computationally cheap simulation models that are easy to implement. Computational speed is especially desirable for estimating parameter and predictive uncertainty using Markov chain Monte Carlo (MCMC) methods. Confirming earlier work of Kavetski et al. (2003), we show here that the computational speed of first-order, explicit, fixed-step integration methods comes at a cost: for a case study with a spatially lumped conceptual rainfall-runoff model, it introduces artificial bimodality in the marginal posterior parameter distributions, which is not present in numerically accurate implementations of the same model. The resulting effects on MCMC simulation include (1) inconsistent estimates of posterior parameter and predictive distributions, (2) poor performance and slow convergence of the MCMC algorithm, and (3) unreliable convergence diagnosis using the Gelman-Rubin statistic. We studied several alternative numerical implementations to remedy these problems, including various adaptive-step finite difference schemes and an operator splitting method. Our results show that adaptive-step, second-order methods, based on either explicit finite differencing or operator splitting with analytical integration, provide the best alternative for accurate and efficient MCMC simulation. Fixed-step or adaptive-step implicit methods may also be used for increased accuracy, but they cannot match the efficiency of adaptive-step explicit finite differencing or operator splitting. Of the latter two, explicit finite differencing is more generally applicable and is preferred if the individual hydrologic flux laws cannot be integrated analytically, as the splitting method then loses its advantage.
8. Epistasis Test in Meta-Analysis: A Multi-Parameter Markov Chain Monte Carlo Model for Consistency of Evidence
PubMed Central
Lin, Chin; Chu, Chi-Ming; Su, Sui-Lung
2016-01-01
Conventional genome-wide association studies (GWAS) have been proven to be a successful strategy for identifying genetic variants associated with complex human traits. However, there is still a large heritability gap between GWAS and transitional family studies. The “missing heritability” has been suggested to be due to lack of studies focused on epistasis, also called gene–gene interactions, because individual trials have often had insufficient sample size. Meta-analysis is a common method for increasing statistical power. However, sufficient detailed information is difficult to obtain. A previous study employed a meta-regression-based method to detect epistasis, but it faced the challenge of inconsistent estimates. Here, we describe a Markov chain Monte Carlo-based method, called “Epistasis Test in Meta-Analysis” (ETMA), which uses genotype summary data to obtain consistent estimates of epistasis effects in meta-analysis. We defined a series of conditions to generate simulation data and tested the power and type I error rates in ETMA, individual data analysis and conventional meta-regression-based method. ETMA not only successfully facilitated consistency of evidence but also yielded acceptable type I error and higher power than conventional meta-regression. We applied ETMA to three real meta-analysis data sets. We found significant gene–gene interactions in the renin–angiotensin system and the polycyclic aromatic hydrocarbon metabolism pathway, with strong supporting evidence. In addition, glutathione S-transferase (GST) mu 1 and theta 1 were confirmed to exert independent effects on cancer. We concluded that the application of ETMA to real meta-analysis data was successful. Finally, we developed an R package, etma, for the detection of epistasis in meta-analysis [etma is available via the Comprehensive R Archive Network (CRAN) at https://cran.r-project.org/web/packages/etma/index.html]. PMID:27045371
9. Multiresponse multilayer vadose zone model calibration using Markov chain Monte Carlo simulation and field water retention data
WöHling, Thomas; Vrugt, Jasper A.
2011-04-01
10. Estimation of soil salinity by using Markov Chain Monte Carlo simulation for multi-configuration electromagnetic induction measurements
Jadoon, K. Z.; Altaf, M. U.; McCabe, M. F.; Hoteit, I.; Moghadas, D.
2014-12-01
In arid and semi-arid regions, soil salinity has a major impact on agro-ecosystems, agricultural productivity, environment and sustainability. High levels of soil salinity adversely affect plant growth and productivity, soil and water quality, and may eventually result in soil erosion and land degradation. Being essentially a hazard, it's important to monitor and map soil salinity at an early stage to effectively use soil resources and maintain soil salinity level below the salt tolerance of crops. In this respect, low frequency electromagnetic induction (EMI) systems can be used as a noninvasive method to map the distribution of soil salinity at the field scale and at a high spatial resolution. In this contribution, an EMI system (the CMD Mini-Explorer) is used to estimate soil salinity using a Bayesian approach implemented via a Markov chain Monte Carlo (MCMC) sampling for inversion of multi-configuration EMI measurements. In-situ and EMI measurements were conducted across a farm where Acacia trees are irrigated with brackish water using a drip irrigation system. The electromagnetic forward model is based on the full solution of Maxwell's equation, and the subsurface is considered as a three-layer problem. In total, five parameters (electrical conductivity of three layers and thickness of top two layers) were inverted and modeled electrical conductivities were converted into the universal standard of soil salinity measurement (i.e. using the method of electrical conductivity of a saturated soil paste extract). Simulation results demonstrate that the proposed scheme successfully recovers soil salinity and reduces the uncertainties in the prior estimate. Analysis of the resulting posterior distribution of parameters indicates that electrical conductivity of the top two layers and the thickness of the first layer are well constrained by the EMI measurements. The proposed approach allows for quantitative mapping and monitoring of the spatial electrical conductivity
11. Holographic dark energy in a universe with spatial curvature and massive neutrinos: a full Markov Chain Monte Carlo exploration
SciTech Connect
Li, Yun-He; Wang, Shuang; Zhang, Xin; Li, Xiao-Dong E-mail: swang@mail.ustc.edu.cn E-mail: zhangxin@mail.neu.edu.cn
2013-02-01
In this paper, we report the results of constraining the holographic dark energy model with spatial curvature and massive neutrinos, based on a Markov Chain Monte Carlo global fit technique. The cosmic observational data include the full WMAP 7-yr temperature and polarization data, the type Ia supernova data from Union2.1 sample, the baryon acoustic oscillation data from SDSS DR7 and WiggleZ Dark Energy Survey, and the latest measurements of H{sub 0} from HST. To deal with the perturbations of dark energy, we adopt the parameterized post-Friedmann method. We find that, for the simplest holographic dark energy model without spatial curvature and massive neutrinos, the phenomenological parameter c < 1 at more than 4σ confidence level. The inclusion of spatial curvature enlarges the error bars and leads to c < 1 only in about 2.5σ range; in contrast, the inclusion of massive neutrinos does not have significant influence on c. We also find that, for the holographic dark energy model with spatial curvature but without massive neutrinos, the 3σ error bars of the current fractional curvature density Ω{sub k0} are still in order of 10{sup −2}; for the model with massive neutrinos but without spatial curvature, the 2σ upper bound of the total mass of neutrinos is Σm{sub ν} < 0.48 eV. Moreover, there exists clear degeneracy between spatial curvature and massive neutrinos in the holographic dark energy model, which enlarges the upper bound of Σm{sub ν} by more than 2 times. In addition, we demonstrate that, making use of the full WMAP data can give better constraints on the holographic dark energy model, compared with the case using the WMAP ''distance priors''.
12. Parameter Estimation Using Markov Chain Monte Carlo Methods for Gravitational Waves from Spinning Inspirals of Compact Objects
Raymond, Vivien
2012-05-01
Gravitational waves are on the verge of opening a brand new window on the Universe. However, gravitational wave astronomy comes with very unique challenges in data analysis and signal processing in order to lead to new discoveries in astrophysics. Among the sources of gravitational waves, inspiraling binary systems of compact objects, neutron stars and/or black holes in the mass range 1Msun--100Msun stand out as likely to be detected and relatively easy to model. The detection of a gravitational wave event is challenging and will be a rewarding achievement by itself. After such a detection, measurement of source properties holds major promise for improving our astrophysical understanding and requires reliable methods for parameter estimation and model selection. This is a complicated problem, because of the large number of parameters (15 for spinning compact objects in a quasi-circular orbit) and the degeneracies between them, the significant amount of structure in the parameter space, and the particularities of the detector noise. This work presents the development of a parameter-estimation and model-selection algorithm, based on Bayesian statistical theory and using Markov chain Monte Carlo methods for ground-based gravitational-wave detectors (LIGO and Virgo). This method started from existing non-spinning and single spin stand-alone analysis codes and was developed into a method able to tackle the complexity of fully spinning systems, and infer all spinning parameters of a compact binary. Not only are spinning parameters believed to be astrophysically significant, but this work has shown that not including them in the analysis can lead to biases in parameter recovery. This work made it possible to answer several scientific questions involving parameter estimation of inspiraling spinning compact objects, which are addressed in the chapters of this dissertation.
13. Bayesian Inversion of Soil-Plant-Atmosphere Interactions for an Oak-Savanna Ecosystem Using Markov Chain Monte Carlo Method
Chen, X.; Rubin, Y.; Baldocchi, D. D.
2005-12-01
Understanding the interactions between soil, plant, and the atmosphere under water-stressed conditions is important for ecosystems where water availability is limited. In such ecosystems, the amount of water transferred from the soil to the atmosphere is controlled not only by weather conditions and vegetation type but also by soil water availability. Although researchers have proposed different approaches to model the impact of soil moisture on plant activities, the parameters involved are difficult to measure. However, using measurements of observed latent heat and carbon fluxes, as well as soil moisture data, Bayesian inversion methods can be employed to estimate the various model parameters. In our study, actual Evapotranspiration (ET) of an ecosystem is approximated by the Priestley-Taylor relationship, with the Priestley-Taylor coefficient modeled as a function of soil moisture content. Soil moisture limitation on root uptake is characterized in a similar manner as the Feddes' model. The inference of Bayesian inversion is processed within the framework of graphical theories. Due to the difficulty of obtaining exact inference, the Markov chain Monte Carlo (MCMC) method is implemented using a free software package, BUGS (Bayesian inference Using Gibbs Sampling). The proposed methodology is applied to a Mediterranean Oak-Savanna FLUXNET site in California, where continuous measurements of actual ET are obtained from eddy-covariance technique and soil moisture contents are monitored by several time domain reflectometry probes located within the footprint of the flux tower. After the implementation of Bayesian inversion, the posterior distributions of all the parameters exhibit enhancement in information compared to the prior distributions. The generated samples based on data in year 2003 are used to predict the actual ET in year 2004 and the prediction uncertainties are assessed in terms of confidence intervals. Our tests also reveal the usefulness of various
14. An integrated Markov chain Monte Carlo algorithm for upscaling hydrological and geochemical parameters from column to field scale.
PubMed
Arora, Bhavna; Mohanty, Binayak P; McGuire, Jennifer T
2015-04-15
Predicting and controlling the concentrations of redox-sensitive elements are primary concerns for environmental remediation of contaminated sites. These predictions are complicated by dynamic flow processes as hydrologic variability is a governing control on conservative and reactive chemical concentrations. Subsurface heterogeneity in the form of layers and lenses further complicates the flow dynamics of the system impacting chemical concentrations including redox-sensitive elements. In response to these complexities, this study investigates the role of heterogeneity and hydrologic processes in an effective parameter upscaling scheme from the column to the landfill scale. We used a Markov chain Monte Carlo (MCMC) algorithm to derive upscaling coefficients for hydrological and geochemical parameters, which were tested for variations across heterogeneous systems (layers and lenses) and interaction of flow processes based on the output uncertainty of dominant biogeochemical concentrations at the Norman Landfill site, a closed municipal landfill with prevalent organic and trace metal contamination. The results from MCMC analysis indicated that geochemical upscaling coefficients based on effective concentration ratios incorporating local heterogeneity across layered and lensed systems produced better estimates of redox-sensitive biogeochemistry at the field scale. MCMC analysis also suggested that inclusion of hydrological parameters in the upscaling scheme reduced the output uncertainty of effective mean geochemical concentrations by orders of magnitude at the Norman Landfill site. This was further confirmed by posterior density plots of the scaling coefficients that revealed unimodal characteristics when only geochemical processes were involved, but produced multimodal distributions when hydrological parameters were included. The multimodality again suggests the effect of heterogeneity and lithologic variability on the distribution of redox-sensitive elements at the
15. Behavioral Analysis of Visitors to a Medical Institution’s Website Using Markov Chain Monte Carlo Methods
PubMed Central
Tani, Yuji
2016-01-01
Background Consistent with the “attention, interest, desire, memory, action” (AIDMA) model of consumer behavior, patients collect information about available medical institutions using the Internet to select information for their particular needs. Studies of consumer behavior may be found in areas other than medical institution websites. Such research uses Web access logs for visitor search behavior. At this time, research applying the patient searching behavior model to medical institution website visitors is lacking. Objective We have developed a hospital website search behavior model using a Bayesian approach to clarify the behavior of medical institution website visitors and determine the probability of their visits, classified by search keyword. Methods We used the website data access log of a clinic of internal medicine and gastroenterology in the Sapporo suburbs, collecting data from January 1 through June 31, 2011. The contents of the 6 website pages included the following: home, news, content introduction for medical examinations, mammography screening, holiday person-on-duty information, and other. The search keywords we identified as best expressing website visitor needs were listed as the top 4 headings from the access log: clinic name, clinic name + regional name, clinic name + medical examination, and mammography screening. Using the search keywords as the explaining variable, we built a binomial probit model that allows inspection of the contents of each purpose variable. Using this model, we determined a beta value and generated a posterior distribution. We performed the simulation using Markov Chain Monte Carlo methods with a noninformation prior distribution for this model and determined the visit probability classified by keyword for each category. Results In the case of the keyword “clinic name,” the visit probability to the website, repeated visit to the website, and contents page for medical examination was positive. In the case of the
16. Neutrino masses and cosmological parameters from a Euclid-like survey: Markov Chain Monte Carlo forecasts including theoretical errors
SciTech Connect
Audren, Benjamin; Lesgourgues, Julien; Bird, Simeon; Haehnelt, Martin G.; Viel, Matteo E-mail: julien.lesgourgues@cern.ch E-mail: haehnelt@ast.cam.ac.uk
2013-01-01
We present forecasts for the accuracy of determining the parameters of a minimal cosmological model and the total neutrino mass based on combined mock data for a future Euclid-like galaxy survey and Planck. We consider two different galaxy surveys: a spectroscopic redshift survey and a cosmic shear survey. We make use of the Monte Carlo Markov Chains (MCMC) technique and assume two sets of theoretical errors. The first error is meant to account for uncertainties in the modelling of the effect of neutrinos on the non-linear galaxy power spectrum and we assume this error to be fully correlated in Fourier space. The second error is meant to parametrize the overall residual uncertainties in modelling the non-linear galaxy power spectrum at small scales, and is conservatively assumed to be uncorrelated and to increase with the ratio of a given scale to the scale of non-linearity. It hence increases with wavenumber and decreases with redshift. With these two assumptions for the errors and assuming further conservatively that the uncorrelated error rises above 2% at k = 0.4 h/Mpc and z = 0.5, we find that a future Euclid-like cosmic shear/galaxy survey achieves a 1-σ error on M{sub ν} close to 32 meV/25 meV, sufficient for detecting the total neutrino mass with good significance. If the residual uncorrelated errors indeed rises rapidly towards smaller scales in the non-linear regime as we have assumed here then the data on non-linear scales does not increase the sensitivity to the total neutrino mass. Assuming instead a ten times smaller theoretical error with the same scale dependence, the error on the total neutrino mass decreases moderately from σ(M{sub ν}) = 18 meV to 14 meV when mildly non-linear scales with 0.1 h/Mpc < k < 0.6 h/Mpc are included in the analysis of the galaxy survey data.
17. Markov chain Monte Carlo estimation of species distributions: A case study of the swift fox in western Kansas
USGS Publications Warehouse
Sargeant, G.A.; Sovada, M.A.; Slivinski, C.C.; Johnson, D.H.
2005-01-01
Accurate maps of species distributions are essential tools for wildlife research and conservation. Unfortunately, biologists often are forced to rely on maps derived from observed occurrences recorded opportunistically during observation periods of variable length. Spurious inferences are likely to result because such maps are profoundly affected by the duration and intensity of observation and by methods used to delineate distributions, especially when detection is uncertain. We conducted a systematic survey of swift fox (Vulpes velox) distribution in western Kansas, USA, and used Markov chain Monte Carlo (MCMC) image restoration to rectify these problems. During 1997-1999, we searched 355 townships (ca. 93 km2) 1-3 times each for an average cost of $7,315 per year and achieved a detection rate (probability of detecting swift foxes, if present, during a single search) of ?? = 0.69 (95% Bayesian confidence interval [BCI] = [0.60, 0.77]). Our analysis produced an estimate of the underlying distribution, rather than a map of observed occurrences, that reflected the uncertainty associated with estimates of model parameters. To evaluate our results, we analyzed simulated data with similar properties. Results of our simulations suggest negligible bias and good precision when probabilities of detection on ???1 survey occasions (cumulative probabilities of detection) exceed 0.65. Although the use of MCMC image restoration has been limited by theoretical and computational complexities, alternatives do not possess the same advantages. Image models accommodate uncertain detection, do not require spatially independent data or a census of map units, and can be used to estimate species distributions directly from observations without relying on habitat covariates or parameters that must be estimated subjectively. These features facilitate economical surveys of large regions, the detection of temporal trends in distribution, and assessments of landscape-level relations between 18. Balancing Particle Diversity in Markov Chain Monte Carlo Methods for Dual Calibration-Data Assimilation Problems in Hydrologic Modeling NASA Astrophysics Data System (ADS) Hernandez, F.; Liang, X. 2014-12-01 Given the inherent uncertainty in almost all of the variables involved, recent research is re-addressing the problem of calibrating hydrologic models from a stochastic perspective: the focus is shifting from finding a single parameter configuration that minimizes the model error, to approximating the maximum likelihood multivariate probability distribution of the parameters. To this end, Markov chain Monte Carlo (MCMC) formulations are widely used, where the distribution is defined as a smoothed ensemble of particles or members, each of which represents a feasible parameterization. However, the updating of these ensembles needs to strike a careful balance so that the particles adequately resemble the real distribution without either clustering or drifting excessively. In this study, we explore the implementation of two techniques that attempt to improve the quality of the resulting ensembles, both for the approximation of the model parameters and of the unknown states, in a dual calibration-data assimilation framework. The first feature of our proposed algorithm, in an effort to keep members from clustering on areas of high likelihood in light of the observations, is the introduction of diversity-inducing operators after each resampling. This approach has been successfully used before, and here we aim at testing additional operators which are also borrowed from the Evolutionary Computation literature. The second feature is a novel arrangement of the particles into two alternative data structures. The first one is a non-sorted Pareto population which favors 1) particles with high likelihood, and 2) particles that introduce a certain level of heterogeneity. The second structure is a partitioned array, in which each partition requires its members to have increasing levels of divergence from the particles in the areas of larger likelihood. Our newly proposed algorithm will be evaluated and compared to traditional MCMC methods in terms of convergence speed, and the 19. Bibliometric Application of Markov Chains. ERIC Educational Resources Information Center Pao, Miranda Lee; McCreery, Laurie 1986-01-01 A rudimentary description of Markov Chains is presented in order to introduce its use to describe and to predict authors' movements among subareas of the discipline of ethnomusicology. Other possible applications are suggested. (Author) 20. A Comparison of Bayesian Monte Carlo Markov Chain and Maximum Likelihood Estimation Methods for the Statistical Analysis of Geodetic Time Series NASA Astrophysics Data System (ADS) Olivares, G.; Teferle, F. N. 2013-12-01 Geodetic time series provide information which helps to constrain theoretical models of geophysical processes. It is well established that such time series, for example from GPS, superconducting gravity or mean sea level (MSL), contain time-correlated noise which is usually assumed to be a combination of a long-term stochastic process (characterized by a power-law spectrum) and random noise. Therefore, when fitting a model to geodetic time series it is essential to also estimate the stochastic parameters beside the deterministic ones. Often the stochastic parameters include the power amplitudes of both time-correlated and random noise, as well as, the spectral index of the power-law process. To date, the most widely used method for obtaining these parameter estimates is based on maximum likelihood estimation (MLE). We present an integration method, the Bayesian Monte Carlo Markov Chain (MCMC) method, which, by using Markov chains, provides a sample of the posteriori distribution of all parameters and, thereby, using Monte Carlo integration, all parameters and their uncertainties are estimated simultaneously. This algorithm automatically optimizes the Markov chain step size and estimates the convergence state by spectral analysis of the chain. We assess the MCMC method through comparison with MLE, using the recently released GPS position time series from JPL and apply it also to the MSL time series from the Revised Local Reference data base of the PSMSL. Although the parameter estimates for both methods are fairly equivalent, they suggest that the MCMC method has some advantages over MLE, for example, without further computations it provides the spectral index uncertainty, is computationally stable and detects multimodality. 1. Sequence-based Parameter Estimation for an Epidemiological Temporal Aftershock Forecasting Model using Markov Chain Monte Carlo Simulation NASA Astrophysics Data System (ADS) Jalayer, Fatemeh; Ebrahimian, Hossein 2014-05-01 Introduction The first few days elapsed after the occurrence of a strong earthquake and in the presence of an ongoing aftershock sequence are quite critical for emergency decision-making purposes. Epidemic Type Aftershock Sequence (ETAS) models are used frequently for forecasting the spatio-temporal evolution of seismicity in the short-term (Ogata, 1988). The ETAS models are epidemic stochastic point process models in which every earthquake is a potential triggering event for subsequent earthquakes. The ETAS model parameters are usually calibrated a priori and based on a set of events that do not belong to the on-going seismic sequence (Marzocchi and Lombardi 2009). However, adaptive model parameter estimation, based on the events in the on-going sequence, may have several advantages such as, tuning the model to the specific sequence characteristics, and capturing possible variations in time of the model parameters. Simulation-based methods can be employed in order to provide a robust estimate for the spatio-temporal seismicity forecasts in a prescribed forecasting time interval (i.e., a day) within a post-main shock environment. This robust estimate takes into account the uncertainty in the model parameters expressed as the posterior joint probability distribution for the model parameters conditioned on the events that have already occurred (i.e., before the beginning of the forecasting interval) in the on-going seismic sequence. The Markov Chain Monte Carlo simulation scheme is used herein in order to sample directly from the posterior probability distribution for ETAS model parameters. Moreover, the sequence of events that is going to occur during the forecasting interval (and hence affecting the seismicity in an epidemic type model like ETAS) is also generated through a stochastic procedure. The procedure leads to two spatio-temporal outcomes: (1) the probability distribution for the forecasted number of events, and (2) the uncertainty in estimating the 2. The effects of LIGO detector noise on a 15-dimensional Markov-chain Monte Carlo analysis of gravitational-wave signals NASA Astrophysics Data System (ADS) Raymond, V.; van der Sluys, M. V.; Mandel, I.; Kalogera, V.; Röver, C.; Christensen, N. 2010-06-01 Gravitational-wave signals from inspirals of binary compact objects (black holes and neutron stars) are primary targets of the ongoing searches by ground-based gravitational-wave (GW) interferometers (LIGO, Virgo and GEO-600). We present parameter estimation results from our Markov-chain Monte Carlo code SPINspiral on signals from binaries with precessing spins. Two data sets are created by injecting simulated GW signals either into synthetic Gaussian noise or into LIGO detector data. We compute the 15-dimensional probability-density functions (PDFs) for both data sets, as well as for a data set containing LIGO data with a known, loud artefact ('glitch'). We show that the analysis of the signal in detector noise yields accuracies similar to those obtained using simulated Gaussian noise. We also find that while the Markov chains from the glitch do not converge, the PDFs would look consistent with a GW signal present in the data. While our parameter estimation results are encouraging, further investigations into how to differentiate an actual GW signal from noise are necessary. 3. Integrated Markov Chain Monte Carlo (MCMC) analysis of primordial non-Gaussianity (f{sub NL}) in the recent CMB data SciTech Connect Kim, Jaiseung 2011-04-01 We have made a Markov Chain Monte Carlo (MCMC) analysis of primordial non-Gaussianity (f{sub NL}) using the WMAP bispectrum and power spectrum. In our analysis, we have simultaneously constrained f{sub NL} and cosmological parameters so that the uncertainties of cosmological parameters can properly propagate into the f{sub NL} estimation. Investigating the parameter likelihoods deduced from MCMC samples, we find slight deviation from Gaussian shape, which makes a Fisher matrix estimation less accurate. Therefore, we have estimated the confidence interval of f{sub NL} by exploring the parameter likelihood without using the Fisher matrix. We find that the best-fit values of our analysis make a good agreement with other results, but the confidence interval is slightly different. 4. Reconstruction of Exposure to m-Xylene from Human Biomonitoring Data Using PBPK Modelling, Bayesian Inference, and Markov Chain Monte Carlo Simulation PubMed Central McNally, Kevin; Cotton, Richard; Cocker, John; Jones, Kate; Bartels, Mike; Rick, David; Price, Paul; Loizou, George 2012-01-01 There are numerous biomonitoring programs, both recent and ongoing, to evaluate environmental exposure of humans to chemicals. Due to the lack of exposure and kinetic data, the correlation of biomarker levels with exposure concentrations leads to difficulty in utilizing biomonitoring data for biological guidance values. Exposure reconstruction or reverse dosimetry is the retrospective interpretation of external exposure consistent with biomonitoring data. We investigated the integration of physiologically based pharmacokinetic modelling, global sensitivity analysis, Bayesian inference, and Markov chain Monte Carlo simulation to obtain a population estimate of inhalation exposure to m-xylene. We used exhaled breath and venous blood m-xylene and urinary 3-methylhippuric acid measurements from a controlled human volunteer study in order to evaluate the ability of our computational framework to predict known inhalation exposures. We also investigated the importance of model structure and dimensionality with respect to its ability to reconstruct exposure. PMID:22719759 5. (1)H NMR z-spectra of acetate methyl in stretched hydrogels: quantum-mechanical description and Markov chain Monte Carlo relaxation-parameter estimation. PubMed Shishmarev, Dmitry; Chapman, Bogdan E; Naumann, Christoph; Mamone, Salvatore; Kuchel, Philip W 2015-01-01 The (1)H NMR signal of the methyl group of sodium acetate is shown to be a triplet in the anisotropic environment of stretched gelatin gel. The multiplet structure of the signal is due to the intra-methyl residual dipolar couplings. The relaxation properties of the spin system were probed by recording steady-state irradiation envelopes ('z-spectra'). A quantum-mechanical model based on irreducible spherical tensors formed by the three magnetically equivalent spins of the methyl group was used to simulate and fit experimental z-spectra. The multiple parameter values of the relaxation model were estimated by using a Bayesian-based Markov chain Monte Carlo algorithm. PMID:25486634 6. On a Result for Finite Markov Chains ERIC Educational Resources Information Center Kulathinal, Sangita; Ghosh, Lagnojita 2006-01-01 In an undergraduate course on stochastic processes, Markov chains are discussed in great detail. Textbooks on stochastic processes provide interesting properties of finite Markov chains. This note discusses one such property regarding the number of steps in which a state is reachable or accessible from another state in a finite Markov chain with M… 7. Reconciling a geophysical model to data using a Markov chain Monte Carlo algorithm: An application to the Yellow Sea-Korean Peninsula region NASA Astrophysics Data System (ADS) Pasyanos, Michael E.; Franz, Gregory A.; Ramirez, Abelardo L. 2006-03-01 In an effort to build seismic models that are the most consistent with multiple data sets we have applied a new probabilistic inverse technique. This method uses a Markov chain Monte Carlo (MCMC) algorithm to sample models from a prior distribution and test them against multiple data types to generate a posterior distribution. While computationally expensive, this approach has several advantages over deterministic models, notably the seamless reconciliation of different data types that constrain the model, the proper handling of both data and model uncertainties, and the ability to easily incorporate a variety of prior information, all in a straightforward, natural fashion. A real advantage of the technique is that it provides a more complete picture of the solution space. By mapping out the posterior probability density function, we can avoid simplistic assumptions about the model space and allow alternative solutions to be identified, compared, and ranked. Here we use this method to determine the crust and upper mantle structure of the Yellow Sea and Korean Peninsula region. The model is parameterized as a series of seven layers in a regular latitude-longitude grid, each of which is characterized by thickness and seismic parameters (Vp, Vs, and density). We use surface wave dispersion and body wave traveltime data to drive the model. We find that when properly tuned (i.e., the Markov chains have had adequate time to fully sample the model space and the inversion has converged), the technique behaves as expected. The posterior model reflects the prior information at the edge of the model where there is little or no data to constrain adjustments, but the range of acceptable models is significantly reduced in data-rich regions, producing values of sediment thickness, crustal thickness, and upper mantle velocities consistent with expectations based on knowledge of the regional tectonic setting. 8. A more efficient approach to parallel-tempered Markov-chain Monte Carlo for the highly structured posteriors of gravitational-wave signals NASA Astrophysics Data System (ADS) Farr, Benjamin; Kalogera, Vicky; Luijten, Erik 2014-07-01 We introduce a new Markov-chain Monte Carlo (MCMC) approach designed for the efficient sampling of highly correlated and multimodal posteriors. Parallel tempering, though effective, is a costly technique for sampling such posteriors. Our approach minimizes the use of parallel tempering, only applying it for a short time to build a proposal distribution that is based upon estimation of the kernel density and tuned to the target posterior. This proposal makes subsequent use of parallel tempering unnecessary, allowing all chains to be cooled to sample the target distribution. Gains in efficiency are found to increase with increasing posterior complexity, ranging from tens of percent in the simplest cases to over a factor of 10 for the more complex cases. Our approach is particularly useful in the context of parameter estimation of gravitational-wave signals measured by ground-based detectors, which is currently done through Bayesian inference with MCMC, one of the leading sampling methods. Posteriors for these signals are typically multimodal with strong nonlinear correlations, making sampling difficult. As we enter the advanced-detector era, improved sensitivities and wider bandwidths will drastically increase the computational cost of analyses, demanding more efficient search algorithms to meet these challenges. 9. Application and Evaluation of a Snowmelt Runoff Model in the Tamor River Basin, Eastern Himalaya Using a Markov Chain Monte Carlo (MCMC) Data Assimilation Approach NASA Technical Reports Server (NTRS) Panday, Prajjwal K.; Williams, Christopher A.; Frey, Karen E.; Brown, Molly E. 2013-01-01 Previous studies have drawn attention to substantial hydrological changes taking place in mountainous watersheds where hydrology is dominated by cryospheric processes. Modelling is an important tool for understanding these changes but is particularly challenging in mountainous terrain owing to scarcity of ground observations and uncertainty of model parameters across space and time. This study utilizes a Markov Chain Monte Carlo data assimilation approach to examine and evaluate the performance of a conceptual, degree-day snowmelt runoff model applied in the Tamor River basin in the eastern Nepalese Himalaya. The snowmelt runoff model is calibrated using daily streamflow from 2002 to 2006 with fairly high accuracy (average Nash-Sutcliffe metric approx. 0.84, annual volume bias <3%). The Markov Chain Monte Carlo approach constrains the parameters to which the model is most sensitive (e.g. lapse rate and recession coefficient) and maximizes model fit and performance. Model simulated streamflow using an interpolated precipitation data set decreases the fractional contribution from rainfall compared with simulations using observed station precipitation. The average snowmelt contribution to total runoff in the Tamor River basin for the 2002-2006 period is estimated to be 29.7+/-2.9% (which includes 4.2+/-0.9% from snowfall that promptly melts), whereas 70.3+/-2.6% is attributed to contributions from rainfall. On average, the elevation zone in the 4000-5500m range contributes the most to basin runoff, averaging 56.9+/-3.6% of all snowmelt input and 28.9+/-1.1% of all rainfall input to runoff. Model simulated streamflow using an interpolated precipitation data set decreases the fractional contribution from rainfall versus snowmelt compared with simulations using observed station precipitation. Model experiments indicate that the hydrograph itself does not constrain estimates of snowmelt versus rainfall contributions to total outflow but that this derives from the degree 10. Bayesian approach to the study of white dwarf binaries in LISA data: The application of a reversible jump Markov chain Monte Carlo method SciTech Connect Stroeer, Alexander; Veitch, John 2009-09-15 The Laser Interferometer Space Antenna (LISA) defines new demands on data analysis efforts in its all-sky gravitational wave survey, recording simultaneously thousands of galactic compact object binary foreground sources and tens to hundreds of background sources like binary black hole mergers and extreme-mass ratio inspirals. We approach this problem with an adaptive and fully automatic Reversible Jump Markov Chain Monte Carlo sampler, able to sample from the joint posterior density function (as established by Bayes theorem) for a given mixture of signals ''out of the box'', handling the total number of signals as an additional unknown parameter beside the unknown parameters of each individual source and the noise floor. We show in examples from the LISA Mock Data Challenge implementing the full response of LISA in its TDI description that this sampler is able to extract monochromatic Double White Dwarf signals out of colored instrumental noise and additional foreground and background noise successfully in a global fitting approach. We introduce 2 examples with fixed number of signals (MCMC sampling), and 1 example with unknown number of signals (RJ-MCMC), the latter further promoting the idea behind an experimental adaptation of the model indicator proposal densities in the main sampling stage. We note that the experienced runtimes and degeneracies in parameter extraction limit the shown examples to the extraction of a low but realistic number of signals. 11. Accelerating Monte Carlo molecular simulations by reweighting and reconstructing Markov chains: Extrapolation of canonical ensemble averages and second derivatives to different temperature and density conditions SciTech Connect Kadoura, Ahmad; Sun, Shuyu Salama, Amgad 2014-08-01 Accurate determination of thermodynamic properties of petroleum reservoir fluids is of great interest to many applications, especially in petroleum engineering and chemical engineering. Molecular simulation has many appealing features, especially its requirement of fewer tuned parameters but yet better predicting capability; however it is well known that molecular simulation is very CPU expensive, as compared to equation of state approaches. We have recently introduced an efficient thermodynamically consistent technique to regenerate rapidly Monte Carlo Markov Chains (MCMCs) at different thermodynamic conditions from the existing data points that have been pre-computed with expensive classical simulation. This technique can speed up the simulation more than a million times, making the regenerated molecular simulation almost as fast as equation of state approaches. In this paper, this technique is first briefly reviewed and then numerically investigated in its capability of predicting ensemble averages of primary quantities at different neighboring thermodynamic conditions to the original simulated MCMCs. Moreover, this extrapolation technique is extended to predict second derivative properties (e.g. heat capacity and fluid compressibility). The method works by reweighting and reconstructing generated MCMCs in canonical ensemble for Lennard-Jones particles. In this paper, system's potential energy, pressure, isochoric heat capacity and isothermal compressibility along isochors, isotherms and paths of changing temperature and density from the original simulated points were extrapolated. Finally, an optimized set of Lennard-Jones parameters (ε, σ) for single site models were proposed for methane, nitrogen and carbon monoxide. 12. Geochemical Characterization Using Geophysical Data and Markov Chain Monte Carlo Methods: A Case Study at the South Oyster Bacterial Transport Site in Virginia SciTech Connect Chen, Jinsong; Hubbard, Susan; Rubin, Yoram; Murray, Christopher J.; Roden, Eric E.; Majer, Ernest L. 2004-12-22 The paper demonstrates the use of ground-penetrating radar (GPR) tomographic data for estimating extractable Fe(II) and Fe(III) concentrations using a Markov chain Monte Carlo (MCMC) approach, based on data collected at the DOE South Oyster Bacterial Transport Site in Virginia. Analysis of multidimensional data including physical, geophysical, geochemical, and hydrogeological measurements collected at the site shows that GPR attenuation and lithofacies are most informative for the estimation. A statistical model is developed for integrating the GPR attenuation and lithofacies data. In the model, lithofacies is considered as a spatially correlated random variable and petrophysical models for linking GPR attenuation to geochemical parameters were derived from data at and near boreholes. Extractable Fe(II) and Fe(III) concentrations at each pixel between boreholes are estimated by conditioning to the co-located GPR data and the lithofacies measurements along boreholes through spatial correlation. Cross-validation results show that geophysical data, constrained by lithofacies, provided information about extractable Fe(II) and Fe(III) concentration in a minimally invasive manner and with a resolution unparalleled by other geochemical characterization methods. The developed model is effective and flexible, and should be applicable for estimating other geochemical parameters at other sites. 13. Aeolus: A Markov Chain Monte Carlo Code for Mapping Ultracool Atmospheres. An Application on Jupiter and Brown Dwarf HST Light Curves NASA Astrophysics Data System (ADS) Karalidi, Theodora; Apai, Dániel; Schneider, Glenn; Hanson, Jake R.; Pasachoff, Jay M. 2015-11-01 Deducing the cloud cover and its temporal evolution from the observed planetary spectra and phase curves can give us major insight into the atmospheric dynamics. In this paper, we present Aeolus, a Markov chain Monte Carlo code that maps the structure of brown dwarf and other ultracool atmospheres. We validated Aeolus on a set of unique Jupiter Hubble Space Telescope (HST) light curves. Aeolus accurately retrieves the properties of the major features of the Jovian atmosphere, such as the Great Red Spot and a major 5 μm hot spot. Aeolus is the first mapping code validated on actual observations of a giant planet over a full rotational period. For this study, we applied Aeolus to J- and H-band HST light curves of 2MASS J21392676+0220226 and 2MASS J0136565+093347. Aeolus retrieves three spots at the top of the atmosphere (per observational wavelength) of these two brown dwarfs, with a surface coverage of 21% ± 3% and 20.3% ± 1.5%, respectively. The Jupiter HST light curves will be publicly available via ADS/VIZIR. 14. Geochemical Characterization Using Geophysical Data and Markov Chain Monte Carolo methods: A Case Study at the South Oyster Bacterial Transport Site in Virginia SciTech Connect Chen, Jinsong; Hubbard, Susan; Rubin, Yoram; Murray, Chris; Roden, Eric; Majer, Ernest 2003-11-18 The spatial distribution of field-scale geochemical parameters, such as extractable Fe(II) and Fe(III), influences microbial processes and thus the efficacy of bioremediation. Because traditional characterization of those parameters is invasive and laborious, it is rarely performed sufficiently at the field-scale. Since both geochemical and geophysical parameters often correlate to some common physical properties (such as lithofacies), we investigated the utility of tomographic radar attenuation data for improving estimation of geochemical parameters using a Markov Chain Monte Carlo (MCMC) approach. The data used in this study included physical, geophysical, and geochemical measurements collected in and between several boreholes at the DOE South Oyster Bacterial Transport Site in Virginia. Results show that geophysical data, constrained by physical data, provided field-scale information about extractable Fe(II) and Fe(III) in a minimally invasive manner and with a resolution unparalleled by other geochemical characterization methods. This study presents our estimation framework for estimating Fe(II) and Fe(III), and its application to a specific site. Our hypothesis--that geochemical parameters and geophysical attributes can be linked through their mutual dependence on physical properties--should be applicable for estimating other geochemical parameters at other sites. 15. A comparison between Gauss-Newton and Markov chain Monte Carlo basedmethods for inverting spectral induced polarization data for Cole-Coleparameters SciTech Connect Chen, Jinsong; Kemna, Andreas; Hubbard, Susan S. 2008-05-15 We develop a Bayesian model to invert spectral induced polarization (SIP) data for Cole-Cole parameters using Markov chain Monte Carlo (MCMC) sampling methods. We compare the performance of the MCMC based stochastic method with an iterative Gauss-Newton based deterministic method for Cole-Cole parameter estimation through inversion of synthetic and laboratory SIP data. The Gauss-Newton based method can provide an optimal solution for given objective functions under constraints, but the obtained optimal solution generally depends on the choice of initial values and the estimated uncertainty information is often inaccurate or insufficient. In contrast, the MCMC based inversion method provides extensive global information on unknown parameters, such as the marginal probability distribution functions, from which we can obtain better estimates and tighter uncertainty bounds of the parameters than with the deterministic method. Additionally, the results obtained with the MCMC method are independent of the choice of initial values. Because the MCMC based method does not explicitly offer single optimal solution for given objective functions, the deterministic and stochastic methods can complement each other. For example, the stochastic method can first be used to obtain the means of the unknown parameters by starting from an arbitrary set of initial values and the deterministic method can then be initiated using the means as starting values to obtain the optimal estimates of the Cole-Cole parameters. 16. Stochastic seismic tomography by interacting Markov chains NASA Astrophysics Data System (ADS) Bottero, Alexis; Gesret, Alexandrine; Romary, Thomas; Noble, Mark; Maisons, Christophe 2016-07-01 Markov chain Monte Carlo sampling methods are widely used for non-linear Bayesian inversion where no analytical expression for the forward relation between data and model parameters is available. Contrary to the linear(ized) approaches they naturally allow to evaluate the uncertainties on the model found. Nevertheless their use is problematic in high dimensional model spaces especially when the computational cost of the forward problem is significant and/or the a posteriori distribution is multimodal. In this case the chain can stay stuck in one of the modes and hence not provide an exhaustive sampling of the distribution of interest. We present here a still relatively unknown algorithm that allows interaction between several Markov chains at different temperatures. These interactions (based on Importance Resampling) ensure a robust sampling of any posterior distribution and thus provide a way to efficiently tackle complex fully non linear inverse problems. The algorithm is easy to implement and is well adapted to run on parallel supercomputers. In this paper the algorithm is first introduced and applied to a synthetic multimodal distribution in order to demonstrate its robustness and efficiency compared to a Simulated Annealing method. It is then applied in the framework of first arrival traveltime seismic tomography on real data recorded in the context of hydraulic fracturing. To carry out this study a wavelet based adaptive model parametrization has been used. This allows to integrate the a priori information provided by sonic logs and to reduce optimally the dimension of the problem. 17. Many hepatitis C reinfections that spontaneously clear may be undetected: Markov-chain Monte Carlo analysis of observational study data PubMed Central Sacks-Davis, Rachel; McBryde, Emma; Grebely, Jason; Hellard, Margaret; Vickerman, Peter 2015-01-01 Hepatitis C virus (HCV) reinfection rates are probably underestimated due to reinfection episodes occurring between study visits. A Markov model of HCV reinfection and spontaneous clearance was fitted to empirical data. Bayesian post-estimation was used to project reinfection rates, reinfection spontaneous clearance probability and duration of reinfection. Uniform prior probability distributions were assumed for reinfection rate (more than 0), spontaneous clearance probability (0–1) and duration (0.25–6.00 months). Model estimates were 104 per 100 person-years (95% CrI: 21–344), 0.84 (95% CrI: 0.59–0.98) and 1.3 months (95% CrI: 0.3–4.1) for reinfection rate, spontaneous clearance probability and duration, respectively. Simulation studies were used to assess model validity, demonstrating that the Bayesian model estimates provided useful information about the possible sources and magnitude of bias in epidemiological estimates of reinfection rates, probability of reinfection clearance and duration or reinfection. The quality of the Bayesian estimates improved for larger samples and shorter test intervals. Uncertainty in model estimates notwithstanding, findings suggest that HCV reinfections frequently and quickly result in spontaneous clearance, with many reinfection events going unobserved. PMID:25589564 18. Using Games to Teach Markov Chains ERIC Educational Resources Information Center Johnson, Roger W. 2003-01-01 Games are promoted as examples for classroom discussion of stationary Markov chains. In a game context Markov chain terminology and results are made concrete, interesting, and entertaining. Game length for several-player games such as "Hi Ho! Cherry-O" and "Chutes and Ladders" is investigated and new, simple formulas are given. Slight… 19. Some Interesting Characteristics of Markov Chain Transition Matrices. ERIC Educational Resources Information Center Egelston, Richard L. A Monte Carlo investigation of Markov chain matrices was conducted to create empirical distributions for two statistics created from the transition matrices. Curve fitting techniques developed by Karl Pearson were used to deduce if theoretical equations could be fit to the two sets of distributions. The set of distributions which describe the… 20. Recurrent Urinary Tract Infections Among Women: Comparative Effectiveness of 5 Prevention and Management Strategies Using a Markov Chain Monte Carlo Model PubMed Central Eells, Samantha J.; Bharadwa, Kiran; McKinnell, James A.; Miller, Loren G. 2014-01-01 Background. Recurrent urinary tract infections (UTIs) are a common problem among women. However, comparative effectiveness strategies for managing recurrent UTIs are lacking. Methods. We performed a systematic literature review of management of women experiencing ≥3 UTIs per year. We then developed a Markov chain Monte Carlo model of recurrent UTI for each management strategy with ≥2 adequate trials published. We simulated a cohort that experienced 3 UTIs/year and a secondary cohort that experienced 8 UTIs/year. Model outcomes were treatment efficacy, patient and payer cost, and health-related quality of life. Results. Five strategies had ≥2 clinical trials published: (1) daily antibiotic (nitrofurantoin) prophylaxis; (2) daily estrogen prophylaxis; (3) daily cranberry prophylaxis; (4) acupuncture prophylaxis; and (5) symptomatic self-treatment. In the 3 UTIs/year model, nitrofurantoin prophylaxis was most effective, reducing the UTI rate to 0.4 UTIs/year, and the most expensive to the payer ($821/year). All other strategies resulted in payer cost savings but were less efficacious. Symptomatic self-treatment was the only strategy that resulted in patient cost savings, and was the most favorable strategy in term of cost per quality-adjusted life-year (QALY) gained. Conclusions. Daily antibiotic use is the most effective strategy for recurrent UTI prevention compared to daily cranberry pills, daily estrogen therapy, and acupuncture. Cost savings to payers and patients were seen for most regimens, and improvement in QALYs were seen with all. Our findings provide clinically meaningful data to guide the physician–patient partnership in determining a preferred method of prevention for this common clinical problem. PMID:24065333
1. Elucid—exploring the local universe with the reconstructed initial density field. I. Hamiltonian Markov chain Monte Carlo method with particle mesh dynamics
SciTech Connect
Wang, Huiyuan; Mo, H. J.; Yang, Xiaohu; Lin, W. P.; Jing, Y. P.
2014-10-10
Simulating the evolution of the local universe is important for studying galaxies and the intergalactic medium in a way free of cosmic variance. Here we present a method to reconstruct the initial linear density field from an input nonlinear density field, employing the Hamiltonian Markov Chain Monte Carlo (HMC) algorithm combined with Particle-mesh (PM) dynamics. The HMC+PM method is applied to cosmological simulations, and the reconstructed linear density fields are then evolved to the present day with N-body simulations. These constrained simulations accurately reproduce both the amplitudes and phases of the input simulations at various z. Using a PM model with a grid cell size of 0.75 h {sup –1} Mpc and 40 time steps in the HMC can recover more than half of the phase information down to a scale k ∼ 0.85 h Mpc{sup –1} at high z and to k ∼ 3.4 h Mpc{sup –1} at z = 0, which represents a significant improvement over similar reconstruction models in the literature, and indicates that our model can reconstruct the formation histories of cosmic structures over a large dynamical range. Adopting PM models with higher spatial and temporal resolutions yields even better reconstructions, suggesting that our method is limited more by the availability of computer resource than by principle. Dynamic models of structure evolution adopted in many earlier investigations can induce non-Gaussianity in the reconstructed linear density field, which in turn can cause large systematic deviations in the predicted halo mass function. Such deviations are greatly reduced or absent in our reconstruction.
2. Monte Carlo Integration Using Spatial Structure of Markov Random Field
Yasuda, Muneki
2015-03-01
Monte Carlo integration (MCI) techniques are important in various fields. In this study, a new MCI technique for Markov random fields (MRFs) is proposed. MCI consists of two successive parts: the first involves sampling using a technique such as the Markov chain Monte Carlo method, and the second involves an averaging operation using the obtained sample points. In the averaging operation, a simple sample averaging technique is often employed. The method proposed in this paper improves the averaging operation by addressing the spatial structure of the MRF and is mathematically guaranteed to statistically outperform standard MCI using the simple sample averaging operation. Moreover, the proposed method can be improved in a systematic manner and is numerically verified by numerical simulations using planar Ising models. In the latter part of this paper, the proposed method is applied to the inverse Ising problem and we observe that it outperforms the maximum pseudo-likelihood estimation.
3. Lotic ecosystem response to chronic metal contamination assessed by the resazurin-resorufin smart tracer with data assimilation by the Markov chain Monte Carlo method
Stanaway, D. J.; Flores, A. N.; Haggerty, R.; Benner, S. G.; Feris, K. P.
2011-12-01
Concurrent assessment of biogeochemical and solute transport data (i.e. advection, dispersion, transient storage) within lotic systems remains a challenge in eco-hydrological research. Recently, the Resazurin-Resorufin Smart Tracer System (RRST) was proposed as a mechanism to measure microbial activity at the sediment-water interface [Haggerty et al., 2008, 2009] associating metabolic and hydrologic processes and allowing for the reach scale extrapolation of biotic function in the context of a dynamic physical environment. This study presents a Markov Chain Monte Carlo (MCMC) data assimilation technique to solve the inverse model of the Raz Rru Advection Dispersion Equation (RRADE). The RRADE is a suite of dependent 1-D reactive ADEs, associated through the microbially mediated reduction of Raz to Rru (k12). This reduction is proportional to DO consumption (R^2=0.928). MCMC is a suite of algorithms that solve Bayes theorem to condition uncertain model states and parameters on imperfect observations. Here, the RRST is employed to quantify the effect of chronic metal exposure on hyporheic microbial metabolism along a 100+ year old metal contamination gradient in the Clark Fork River (CF). We hypothesized that 1) the energetic cost of metal tolerance limits heterotrophic microbial respiration in communities evolved in chronic metal contaminated environments, with respiration inhibition directly correlated to degree of contamination (observational experiment) and 2) when experiencing acute metal stress, respiration rate inhibition of metal tolerant communities is less than that of naïve communities (manipulative experiment). To test these hypotheses, 4 replicate columns containing sediment collected from differently contaminated CF reaches and reference sites were fed a solution of RRST, NaCl, and cadmium (manipulative experiment only) within 24 hrs post collection. Column effluent was collected and measured for Raz, Rru, and EC to determine the Raz Rru breakthrough
4. Parameter estimation of gravitational waves from nonprecessing black hole-neutron star inspirals with higher harmonics: Comparing Markov-chain Monte Carlo posteriors to an effective Fisher matrix
O'Shaughnessy, Richard; Farr, Ben; Ochsner, Evan; Cho, Hee-Suk; Kim, Chunglee; Lee, Chang-Hwan
2014-03-01
Most calculations of the gravitational wave signal from merging compact binaries limit attention to the leading-order quadrupole when constructing models for detection or parameter estimation. Some studies have claimed that if additional "higher harmonics" are included consistently in the gravitational wave signal and search model, binary parameters can be measured much more precisely. Using the lalinference Markov-chain Monte Carlo parameter estimation code, we construct posterior parameter constraints associated with two distinct nonprecessing black hole-neutron star (BH-NS) binaries, each with and without higher-order harmonics. All simulations place a plausible signal into a three-detector network with Gaussian noise. Our simulations suggest that higher harmonics provide little information, principally allowing us to measure a previously unconstrained angle associated with the source geometry well but otherwise improving knowledge of all other parameters by a few percent for our loud fiducial signal (ρ =20). Even at this optimistic signal amplitude, different noise realizations have a more significant impact on parameter accuracy than higher harmonics. We compare our results with the "effective Fisher matrix" introduced previously as a method to obtain robust analytic predictions for complicated signals with multiple significant harmonics. We find generally good agreement with these predictions, confirm that intrinsic parameter measurement accuracy is nearly independent of detector network geometry, and show that uncertainties in extrinsic and intrinsic parameters can, to a good approximation, be separated. For our fiducial example, the individual masses can be determined to lie between 7.11-11.48M⊙ and 1.77-1.276M⊙ at greater than 99% confidence level, accounting for unknown BH spin. Assuming comparable control over waveform systematics, measurements of BH-NS binaries can constrain the BH and perhaps NS mass distributions. Using analytic arguments to
5. Monte Carlo without chains
SciTech Connect
Chorin, Alexandre J.
2007-12-12
A sampling method for spin systems is presented. The spin lattice is written as the union of a nested sequence of sublattices, all but the last with conditionally independent spins, which are sampled in succession using their marginals. The marginals are computed concurrently by a fast algorithm; errors in the evaluation of the marginals are offset by weights. There are no Markov chains and each sample is independent of the previous ones; the cost of a sample is proportional to the number of spins (but the number of samples needed for good statistics may grow with array size). The examples include the Edwards-Anderson spin glass in three dimensions.
6. Statistical significance test for transition matrices of atmospheric Markov chains
NASA Technical Reports Server (NTRS)
Vautard, Robert; Mo, Kingtse C.; Ghil, Michael
1990-01-01
Low-frequency variability of large-scale atmospheric dynamics can be represented schematically by a Markov chain of multiple flow regimes. This Markov chain contains useful information for the long-range forecaster, provided that the statistical significance of the associated transition matrix can be reliably tested. Monte Carlo simulation yields a very reliable significance test for the elements of this matrix. The results of this test agree with previously used empirical formulae when each cluster of maps identified as a distinct flow regime is sufficiently large and when they all contain a comparable number of maps. Monte Carlo simulation provides a more reliable way to test the statistical significance of transitions to and from small clusters. It can determine the most likely transitions, as well as the most unlikely ones, with a prescribed level of statistical significance.
7. Markov chains for testing redundant software
NASA Technical Reports Server (NTRS)
White, Allan L.; Sjogren, Jon A.
1988-01-01
A preliminary design for a validation experiment has been developed that addresses several problems unique to assuring the extremely high quality of multiple-version programs in process-control software. The procedure uses Markov chains to model the error states of the multiple version programs. The programs are observed during simulated process-control testing, and estimates are obtained for the transition probabilities between the states of the Markov chain. The experimental Markov chain model is then expanded into a reliability model that takes into account the inertia of the system being controlled. The reliability of the multiple version software is computed from this reliability model at a given confidence level using confidence intervals obtained for the transition probabilities during the experiment. An example demonstrating the method is provided.
8. Entropy Computation in Partially Observed Markov Chains
Desbouvries, François
2006-11-01
Let X = {Xn}n∈N be a hidden process and Y = {Yn}n∈N be an observed process. We assume that (X,Y) is a (pairwise) Markov Chain (PMC). PMC are more general than Hidden Markov Chains (HMC) and yet enable the development of efficient parameter estimation and Bayesian restoration algorithms. In this paper we propose a fast (i.e., O(N)) algorithm for computing the entropy of {Xn}n=0N given an observation sequence {yn}n=0N.
9. Document Ranking Based upon Markov Chains.
ERIC Educational Resources Information Center
Danilowicz, Czeslaw; Balinski, Jaroslaw
2001-01-01
Considers how the order of documents in information retrieval responses are determined and introduces a method that uses a probabilistic model of a document set where documents are regarded as states of a Markov chain and where transition probabilities are directly proportional to similarities between documents. (Author/LRW)
10. Markov Chain Estimation of Avian Seasonal Fecundity
EPA Science Inventory
To explore the consequences of modeling decisions on inference about avian seasonal fecundity we generalize previous Markov chain (MC) models of avian nest success to formulate two different MC models of avian seasonal fecundity that represent two different ways to model renestin...
11. The cutoff phenomenon in finite Markov chains.
PubMed Central
Diaconis, P
1996-01-01
Natural mixing processes modeled by Markov chains often show a sharp cutoff in their convergence to long-time behavior. This paper presents problems where the cutoff can be proved (card shuffling, the Ehrenfests' urn). It shows that chains with polynomial growth (drunkard's walk) do not show cutoffs. The best general understanding of such cutoffs (high multiplicity of second eigenvalues due to symmetry) is explored. Examples are given where the symmetry is broken but the cutoff phenomenon persists. PMID:11607633
12. Using satellite observations to improve model estimates of CO2 and CH4 flux: a Metropolis Hastings Markov Chain Monte Carlo approach
MacBean, Natasha; Disney, Mathias; Lewis, Philip; Ineson, Phil
2010-05-01
profile as a whole. We present results from an Observing System Simulation Experiment (OSSE) designed to investigate the impact of management and climate change on peatland carbon fluxes, as well as how observations from satellites may be able to constrain modeled carbon fluxes. We use an adapted version of the Carnegie-Ames-Stanford Approach (CASA) model (Potter et al., 1993) that includes a representation of methane dynamics (Potter, 1997). The model formulation is further modified to allow for assimilation of satellite observations of surface soil moisture and land surface temperature. The observations are used to update model estimates using a Metropolis Hastings Markov Chain Monte Carlo (MCMC) approach. We examine the effect of temporal frequency and precision of satellite observations with a view to establishing how, and at what level, such observations would make a significant improvement in model uncertainty. We compare this with the system characteristics of existing and future satellites. We believe this is the first attempt to assimilate surface soil moisture and land surface temperature into an ecosystem model that includes a full representation of CH4 flux. Bubier, J., and T. Moore (1994), An ecological perspective on methane emissions from northern wetlands, TREE, 9, 460-464. Charman, D. (2002), Peatlands and Environmental Change, JohnWiley and Sons, Ltd, England. Gorham, E. (1991), Northern peatlands: Role in the carbon cycle and probable responses to climatic warming, Ecological Applications, 1, 182-195. Lai, D. (2009), Methane dynamics in northern peatlands: A review, Pedosphere, 19, 409-421. Le Mer, J., and P. Roger (2001), Production, oxidation, emission and consumption of methane by soils: A review, European Journal of Soil Biology, 37, 25-50. Limpens, J., F. Berendse, J. Canadell, C. Freeman, J. Holden, N. Roulet, H. Rydin, and Potter, C. (1997), An ecosystem simulation model for methane production and emission from wetlands, Global Biogeochemical
13. Bayesian restoration of a hidden Markov chain with applications to DNA sequencing.
PubMed
Churchill, G A; Lazareva, B
1999-01-01
Hidden Markov models (HMMs) are a class of stochastic models that have proven to be powerful tools for the analysis of molecular sequence data. A hidden Markov model can be viewed as a black box that generates sequences of observations. The unobservable internal state of the box is stochastic and is determined by a finite state Markov chain. The observable output is stochastic with distribution determined by the state of the hidden Markov chain. We present a Bayesian solution to the problem of restoring the sequence of states visited by the hidden Markov chain from a given sequence of observed outputs. Our approach is based on a Monte Carlo Markov chain algorithm that allows us to draw samples from the full posterior distribution of the hidden Markov chain paths. The problem of estimating the probability of individual paths and the associated Monte Carlo error of these estimates is addressed. The method is illustrated by considering a problem of DNA sequence multiple alignment. The special structure for the hidden Markov model used in the sequence alignment problem is considered in detail. In conclusion, we discuss certain interesting aspects of biological sequence alignments that become accessible through the Bayesian approach to HMM restoration. PMID:10421527
14. Numerical methods in Markov chain modeling
NASA Technical Reports Server (NTRS)
Philippe, Bernard; Saad, Youcef; Stewart, William J.
1989-01-01
Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.
15. Radiative transfer calculated from a Markov chain formalism
NASA Technical Reports Server (NTRS)
Esposito, L. W.; House, L. L.
1978-01-01
The theory of Markov chains is used to formulate the radiative transport problem in a general way by modeling the successive interactions of a photon as a stochastic process. Under the minimal requirement that the stochastic process is a Markov chain, the determination of the diffuse reflection or transmission from a scattering atmosphere is equivalent to the solution of a system of linear equations. This treatment is mathematically equivalent to, and thus has many of the advantages of, Monte Carlo methods, but can be considerably more rapid than Monte Carlo algorithms for numerical calculations in particular applications. We have verified the speed and accuracy of this formalism for the standard problem of finding the intensity of scattered light from a homogeneous plane-parallel atmosphere with an arbitrary phase function for scattering. Accurate results over a wide range of parameters were obtained with computation times comparable to those of a standard 'doubling' routine. The generality of this formalism thus allows fast, direct solutions to problems that were previously soluble only by Monte Carlo methods. Some comparisons are made with respect to integral equation methods.
16. Growth and Dissolution of Macromolecular Markov Chains
Gaspard, Pierre
2016-07-01
The kinetics and thermodynamics of free living copolymerization are studied for processes with rates depending on k monomeric units of the macromolecular chain behind the unit that is attached or detached. In this case, the sequence of monomeric units in the growing copolymer is a kth-order Markov chain. In the regime of steady growth, the statistical properties of the sequence are determined analytically in terms of the attachment and detachment rates. In this way, the mean growth velocity as well as the thermodynamic entropy production and the sequence disorder can be calculated systematically. These different properties are also investigated in the regime of depolymerization where the macromolecular chain is dissolved by the surrounding solution. In this regime, the entropy production is shown to satisfy Landauer's principle.
17. SHARP ENTRYWISE PERTURBATION BOUNDS FOR MARKOV CHAINS
PubMed Central
THIEDE, ERIK; VAN KOTEN, BRIAN; WEARE, JONATHAN
2015-01-01
For many Markov chains of practical interest, the invariant distribution is extremely sensitive to perturbations of some entries of the transition matrix, but insensitive to others; we give an example of such a chain, motivated by a problem in computational statistical physics. We have derived perturbation bounds on the relative error of the invariant distribution that reveal these variations in sensitivity. Our bounds are sharp, we do not impose any structural assumptions on the transition matrix or on the perturbation, and computing the bounds has the same complexity as computing the invariant distribution or computing other bounds in the literature. Moreover, our bounds have a simple interpretation in terms of hitting times, which can be used to draw intuitive but rigorous conclusions about the sensitivity of a chain to various types of perturbations. PMID:26491218
18. Markov Chain Analysis of Musical Dice Games
Volchenkov, D.; Dawin, J. R.
2012-07-01
A system for using dice to compose music randomly is known as the musical dice game. The discrete time MIDI models of 804 pieces of classical music written by 29 composers have been encoded into the transition matrices and studied by Markov chains. Contrary to human languages, entropy dominates over redundancy, in the musical dice games based on the compositions of classical music. The maximum complexity is achieved on the blocks consisting of just a few notes (8 notes, for the musical dice games generated over Bach's compositions). First passage times to notes can be used to resolve tonality and feature a composer.
19. Approximating Markov Chains: What and why
SciTech Connect
Pincus, S.
1996-06-01
Much of the current study of dynamical systems is focused on geometry (e.g., chaos and bifurcations) and ergodic theory. Yet dynamical systems were originally motivated by an attempt to {open_quote}{open_quote}solve,{close_quote}{close_quote} or at least understand, a discrete-time analogue of differential equations. As such, numerical, analytical solution techniques for dynamical systems would seem desirable. We discuss an approach that provides such techniques, the approximation of dynamical systems by suitable finite state Markov Chains. Steady state distributions for these Markov Chains, a straightforward calculation, will converge to the true dynamical system steady state distribution, with appropriate limit theorems indicated. Thus (i) approximation by a computable, linear map holds the promise of vastly faster steady state solutions for nonlinear, multidimensional differential equations; (ii) the solution procedure is unaffected by the presence or absence of a probability density function for the {ital attractor}, entirely skirting singularity, fractal/multifractal, and renormalization considerations. The theoretical machinery underpinning this development also implies that under very general conditions, steady state measures are weakly continuous with control parameter evolution. This means that even though a system may change periodicity, or become chaotic in its limiting behavior, such statistical parameters as the mean, standard deviation, and tail probabilities change continuously, not abruptly with system evolution. {copyright} {ital 1996 American Institute of Physics.}
20. Equilibrium Control Policies for Markov Chains
SciTech Connect
Malikopoulos, Andreas
2011-01-01
The average cost criterion has held great intuitive appeal and has attracted considerable attention. It is widely employed when controlling dynamic systems that evolve stochastically over time by means of formulating an optimization problem to achieve long-term goals efficiently. The average cost criterion is especially appealing when the decision-making process is long compared to other timescales involved, and there is no compelling motivation to select short-term optimization. This paper addresses the problem of controlling a Markov chain so as to minimize the average cost per unit time. Our approach treats the problem as a dual constrained optimization problem. We derive conditions guaranteeing that a saddle point exists for the new dual problem and we show that this saddle point is an equilibrium control policy for each state of the Markov chain. For practical situations with constraints consistent to those we study here, our results imply that recognition of such saddle points may be of value in deriving in real time an optimal control policy.
1. Multivariate Markov chain modeling for stock markets
2003-06-01
We study a multivariate Markov chain model as a stochastic model of the price changes of portfolios in the framework of the mean field approximation. The time series of price changes are coded into the sequences of up and down spins according to their signs. We start with the discussion for small portfolios consisting of two stock issues. The generalization of our model to arbitrary size of portfolio is constructed by a recurrence relation. The resultant form of the joint probability of the stationary state coincides with Gibbs measure assigned to each configuration of spin glass model. Through the analysis of actual portfolios, it has been shown that the synchronization of the direction of the price changes is well described by the model.
2. SATMC: Spectral energy distribution Analysis Through Markov Chains
Johnson, S. P.; Wilson, G. W.; Tang, Y.; Scott, K. S.
2013-12-01
We present the general purpose spectral energy distribution (SED) fitting tool SED Analysis Through Markov Chains (SATMC). Utilizing Monte Carlo Markov Chain (MCMC) algorithms, SATMC fits an observed SED to SED templates or models of the user's choice to infer intrinsic parameters, generate confidence levels and produce the posterior parameter distribution. Here, we describe the key features of SATMC from the underlying MCMC engine to specific features for handling SED fitting. We detail several test cases of SATMC, comparing results obtained from traditional least-squares methods, which highlight its accuracy, robustness and wide range of possible applications. We also present a sample of submillimetre galaxies (SMGs) that have been fitted using the SED synthesis routine GRASIL as input. In general, these SMGs are shown to occupy a large volume of parameter space, particularly in regards to their star formation rates which range from ˜30 to 3000 M⊙ yr-1 and stellar masses which range from ˜1010 to 1012 M⊙. Taking advantage of the Bayesian formalism inherent to SATMC, we also show how the fitting results may change under different parametrizations (i.e. different initial mass functions) and through additional or improved photometry, the latter being crucial to the study of high-redshift galaxies.
3. Multiple pattern matching: a Markov chain approach.
PubMed
Lladser, Manuel E; Betterton, M D; Knight, Rob
2008-01-01
RNA motifs typically consist of short, modular patterns that include base pairs formed within and between modules. Estimating the abundance of these patterns is of fundamental importance for assessing the statistical significance of matches in genomewide searches, and for predicting whether a given function has evolved many times in different species or arose from a single common ancestor. In this manuscript, we review in an integrated and self-contained manner some basic concepts of automata theory, generating functions and transfer matrix methods that are relevant to pattern analysis in biological sequences. We formalize, in a general framework, the concept of Markov chain embedding to analyze patterns in random strings produced by a memoryless source. This conceptualization, together with the capability of automata to recognize complicated patterns, allows a systematic analysis of problems related to the occurrence and frequency of patterns in random strings. The applications we present focus on the concept of synchronization of automata, as well as automata used to search for a finite number of keywords (including sets of patterns generated according to base pairing rules) in a general text. PMID:17668213
4. Manpower planning using Markov Chain model
2014-07-01
Manpower planning is a planning model which understands the flow of manpower based on the policies changes. For such purpose, numerous attempts have been made by researchers to develop a model to investigate the track of movements of lecturers for various universities. As huge number of lecturers in a university, it is difficult to track the movement of lecturers and also there is no quantitative way used in tracking the movement of lecturers. This research is aimed to determine the appropriate manpower model to understand the flow of lecturers in a university in Malaysia by determine the probability and mean time of lecturers remain in the same status rank. In addition, this research also intended to estimate the number of lecturers in different status rank (lecturer, senior lecturer and associate professor). From the previous studies, there are several methods applied in manpower planning model and appropriate method used in this research is Markov Chain model. Results obtained from this study indicate that the appropriate manpower planning model used is validated by compare to the actual data. The smaller margin of error gives a better result which means that the projection is closer to actual data. These results would give some suggestions for the university to plan the hiring lecturers and budgetary for university in future.
5. Weighted Markov chains for forecasting and analysis in Incidence of infectious diseases in jiangsu Province, China☆
PubMed Central
Peng, Zhihang; Bao, Changjun; Zhao, Yang; Yi, Honggang; Xia, Letian; Yu, Hao; Shen, Hongbing; Chen, Feng
2010-01-01
This paper first applies the sequential cluster method to set up the classification standard of infectious disease incidence state based on the fact that there are many uncertainty characteristics in the incidence course. Then the paper presents a weighted Markov chain, a method which is used to predict the future incidence state. This method assumes the standardized self-coefficients as weights based on the special characteristics of infectious disease incidence being a dependent stochastic variable. It also analyzes the characteristics of infectious diseases incidence via the Markov chain Monte Carlo method to make the long-term benefit of decision optimal. Our method is successfully validated using existing incidents data of infectious diseases in Jiangsu Province. In summation, this paper proposes ways to improve the accuracy of the weighted Markov chain, specifically in the field of infection epidemiology. PMID:23554632
6. Differential evolution Markov chain with snooker updater and fewer chains
SciTech Connect
Vrugt, Jasper A; Ter Braak, Cajo J F
2008-01-01
Differential Evolution Markov Chain (DE-MC) is an adaptive MCMC algorithm, in which multiple chains are run in parallel. Standard DE-MC requires at least N=2d chains to be run in parallel, where d is the dimensionality of the posterior. This paper extends DE-MC with a snooker updater and shows by simulation and real examples that DE-MC can work for d up to 50--100 with fewer parallel chains (e.g. N=3) by exploiting information from their past by generating jumps from differences of pairs of past states. This approach extends the practical applicability of DE-MC and is shown to be about 5--26 times more efficient than the optimal Normal random walk Metropolis sampler for the 97.5% point of a variable from a 25--50 dimensional Student T{sub 3} distribution. In a nonlinear mixed effects model example the approach outperformed a block-updater geared to the specific features of the model.
7. Bayesian seismic tomography by parallel interacting Markov chains
Gesret, Alexandrine; Bottero, Alexis; Romary, Thomas; Noble, Mark; Desassis, Nicolas
2014-05-01
The velocity field estimated by first arrival traveltime tomography is commonly used as a starting point for further seismological, mineralogical, tectonic or similar analysis. In order to interpret quantitatively the results, the tomography uncertainty values as well as their spatial distribution are required. The estimated velocity model is obtained through inverse modeling by minimizing an objective function that compares observed and computed traveltimes. This step is often performed by gradient-based optimization algorithms. The major drawback of such local optimization schemes, beyond the possibility of being trapped in a local minimum, is that they do not account for the multiple possible solutions of the inverse problem. They are therefore unable to assess the uncertainties linked to the solution. Within a Bayesian (probabilistic) framework, solving the tomography inverse problem aims at estimating the posterior probability density function of velocity model using a global sampling algorithm. Markov chains Monte-Carlo (MCMC) methods are known to produce samples of virtually any distribution. In such a Bayesian inversion, the total number of simulations we can afford is highly related to the computational cost of the forward model. Although fast algorithms have been recently developed for computing first arrival traveltimes of seismic waves, the complete browsing of the posterior distribution of velocity model is hardly performed, especially when it is high dimensional and/or multimodal. In the latter case, the chain may even stay stuck in one of the modes. In order to improve the mixing properties of classical single MCMC, we propose to make interact several Markov chains at different temperatures. This method can make efficient use of large CPU clusters, without increasing the global computational cost with respect to classical MCMC and is therefore particularly suited for Bayesian inversion. The exchanges between the chains allow a precise sampling of the
8. Unsupervised Segmentation of Hidden Semi-Markov Non Stationary Chains
2006-11-01
In the classical hidden Markov chain (HMC) model we have a hidden chain X, which is a Markov one and an observed chain Y. HMC are widely used; however, in some situations they have to be replaced by the more general "hidden semi-Markov chains" (HSMC) which are particular "triplet Markov chains" (TMC) T = (X, U, Y), where the auxiliary chain U models the semi-Markovianity of X. Otherwise, non stationary classical HMC can also be modeled by a triplet Markov stationary chain with, as a consequence, the possibility of parameters' estimation. The aim of this paper is to use simultaneously both properties. We consider a non stationary HSMC and model it as a TMC T = (X, U1, U2, Y), where U1 models the semi-Markovianity and U2 models the non stationarity. The TMC T being itself stationary, all parameters can be estimated by the general "Iterative Conditional Estimation" (ICE) method, which leads to unsupervised segmentation. We present some experiments showing the interest of the new model and related processing in image segmentation area.
9. Markov Chains For Testing Redundant Software
NASA Technical Reports Server (NTRS)
White, Allan L.; Sjogren, Jon A.
1990-01-01
Preliminary design developed for validation experiment that addresses problems unique to assuring extremely high quality of multiple-version programs in process-control software. Approach takes into account inertia of controlled system in sense it takes more than one failure of control program to cause controlled system to fail. Verification procedure consists of two steps: experimentation (numerical simulation) and computation, with Markov model for each step.
10. On a Markov chain roulette-type game
El-Shehawey, M. A.; El-Shreef, Gh A.
2009-05-01
A Markov chain on non-negative integers which arises in a roulette-type game is discussed. The transition probabilities are p01 = ρ, pNj = δNj, pi,i+W = q, pi,i-1 = p = 1 - q, 1 <= W < N, 0 <= ρ <= 1, N - W < j <= N and i = 1, 2, ..., N - W. Using formulae for the determinant of a partitioned matrix, a closed form expression for the solution of the Markov chain roulette-type game is deduced. The present analysis is supported by two mathematical models from tumor growth and war with bargaining.
11. Influence of credit scoring on the dynamics of Markov chain
Galina, Timofeeva
2015-11-01
Markov processes are widely used to model the dynamics of a credit portfolio and forecast the portfolio risk and profitability. In the Markov chain model the loan portfolio is divided into several groups with different quality, which determined by presence of indebtedness and its terms. It is proposed that dynamics of portfolio shares is described by a multistage controlled system. The article outlines mathematical formalization of controls which reflect the actions of the bank's management in order to improve the loan portfolio quality. The most important control is the organization of approval procedure of loan applications. The credit scoring is studied as a control affecting to the dynamic system. Different formalizations of "good" and "bad" consumers are proposed in connection with the Markov chain model.
12. Markov chain for estimating human mitochondrial DNA mutation pattern
Vantika, Sandy; Pasaribu, Udjianna S.
2015-12-01
The Markov chain was proposed to estimate the human mitochondrial DNA mutation pattern. One DNA sequence was taken randomly from 100 sequences in Genbank. The nucleotide transition matrix and mutation transition matrix were estimated from this sequence. We determined whether the states (mutation/normal) are recurrent or transient. The results showed that both of them are recurrent.
13. Students' Progress throughout Examination Process as a Markov Chain
ERIC Educational Resources Information Center
Hlavatý, Robert; Dömeová, Ludmila
2014-01-01
The paper is focused on students of Mathematical methods in economics at the Czech university of life sciences (CULS) in Prague. The idea is to create a model of students' progress throughout the whole course using the Markov chain approach. Each student has to go through various stages of the course requirements where his success depends on the…
14. Building Higher-Order Markov Chain Models with EXCEL
ERIC Educational Resources Information Center
Ching, Wai-Ki; Fung, Eric S.; Ng, Michael K.
2004-01-01
Categorical data sequences occur in many applications such as forecasting, data mining and bioinformatics. In this note, we present higher-order Markov chain models for modelling categorical data sequences with an efficient algorithm for solving the model parameters. The algorithm can be implemented easily in a Microsoft EXCEL worksheet. We give a…
15. Analyzing Sequential Categorical Data: Individual Variation in Markov Chains.
ERIC Educational Resources Information Center
Gardner, William
1990-01-01
This paper provides a method for analyzing data consisting of event sequences and covariate observations associated with Markov chains. The objective is to use the covariate data to explain differences between individuals in the transition probability matrices characterizing their sequential data. (TJH)
16. Operations and support cost modeling using Markov chains
NASA Technical Reports Server (NTRS)
Unal, Resit
1989-01-01
Systems for future missions will be selected with life cycle costs (LCC) as a primary evaluation criterion. This reflects the current realization that only systems which are considered affordable will be built in the future due to the national budget constaints. Such an environment calls for innovative cost modeling techniques which address all of the phases a space system goes through during its life cycle, namely: design and development, fabrication, operations and support; and retirement. A significant portion of the LCC for reusable systems are generated during the operations and support phase (OS). Typically, OS costs can account for 60 to 80 percent of the total LCC. Clearly, OS costs are wholly determined or at least strongly influenced by decisions made during the design and development phases of the project. As a result OS costs need to be considered and estimated early in the conceptual phase. To be effective, an OS cost estimating model needs to account for actual instead of ideal processes by associating cost elements with probabilities. One approach that may be suitable for OS cost modeling is the use of the Markov Chain Process. Markov chains are an important method of probabilistic analysis for operations research analysts but they are rarely used for life cycle cost analysis. This research effort evaluates the use of Markov Chains in LCC analysis by developing OS cost model for a hypothetical reusable space transportation vehicle (HSTV) and suggests further uses of the Markov Chain process as a design-aid tool.
17. Adiabatic condition and the quantum hitting time of Markov chains
SciTech Connect
Krovi, Hari; Ozols, Maris; Roland, Jeremie
2010-08-15
We present an adiabatic quantum algorithm for the abstract problem of searching marked vertices in a graph, or spatial search. Given a random walk (or Markov chain) P on a graph with a set of unknown marked vertices, one can define a related absorbing walk P{sup '} where outgoing transitions from marked vertices are replaced by self-loops. We build a Hamiltonian H(s) from the interpolated Markov chain P(s)=(1-s)P+sP{sup '} and use it in an adiabatic quantum algorithm to drive an initial superposition over all vertices to a superposition over marked vertices. The adiabatic condition implies that, for any reversible Markov chain and any set of marked vertices, the running time of the adiabatic algorithm is given by the square root of the classical hitting time. This algorithm therefore demonstrates a novel connection between the adiabatic condition and the classical notion of hitting time of a random walk. It also significantly extends the scope of previous quantum algorithms for this problem, which could only obtain a full quadratic speedup for state-transitive reversible Markov chains with a unique marked vertex.
18. Using Markov Chain Analyses in Counselor Education Research
ERIC Educational Resources Information Center
Duys, David K.; Headrick, Todd C.
2004-01-01
This study examined the efficacy of an infrequently used statistical analysis in counselor education research. A Markov chain analysis was used to examine hypothesized differences between students' use of counseling skills in an introductory course. Thirty graduate students participated in the study. Independent raters identified the microskills…
19. Fuzzy Markov random fields versus chains for multispectral image segmentation.
PubMed
Salzenstein, Fabien; Collet, Christophe
2006-11-01
This paper deals with a comparison of recent statistical models based on fuzzy Markov random fields and chains for multispectral image segmentation. The fuzzy scheme takes into account discrete and continuous classes which model the imprecision of the hidden data. In this framework, we assume the dependence between bands and we express the general model for the covariance matrix. A fuzzy Markov chain model is developed in an unsupervised way. This method is compared with the fuzzy Markovian field model previously proposed by one of the authors. The segmentation task is processed with Bayesian tools, such as the well-known MPM (Mode of Posterior Marginals) criterion. Our goal is to compare the robustness and rapidity for both methods (fuzzy Markov fields versus fuzzy Markov chains). Indeed, such fuzzy-based procedures seem to be a good answer, e.g., for astronomical observations when the patterns present diffuse structures. Moreover, these approaches allow us to process missing data in one or several spectral bands which correspond to specific situations in astronomy. To validate both models, we perform and compare the segmentation on synthetic images and raw multispectral astronomical data. PMID:17063681
20. A Markov Chain-based quantitative study of angular distribution of photons through turbid slabs via isotropic light scattering
Li, Xuesong; Northrop, William F.
2016-04-01
This paper describes a quantitative approach to approximate multiple scattering through an isotropic turbid slab based on Markov Chain theorem. There is an increasing need to utilize multiple scattering for optical diagnostic purposes; however, existing methods are either inaccurate or computationally expensive. Here, we develop a novel Markov Chain approximation approach to solve multiple scattering angular distribution (AD) that can accurately calculate AD while significantly reducing computational cost compared to Monte Carlo simulation. We expect this work to stimulate ongoing multiple scattering research and deterministic reconstruction algorithm development with AD measurements.
1. An Overview of Markov Chain Methods for the Study of Stage-Sequential Developmental Processes
ERIC Educational Resources Information Center
Kapland, David
2008-01-01
This article presents an overview of quantitative methodologies for the study of stage-sequential development based on extensions of Markov chain modeling. Four methods are presented that exemplify the flexibility of this approach: the manifest Markov model, the latent Markov model, latent transition analysis, and the mixture latent Markov model.…
2. Bayesian Smoothing Algorithms in Partially Observed Markov Chains
Ait-el-Fquih, Boujemaa; Desbouvries, François
2006-11-01
Let x = {xn}n∈N be a hidden process, y = {yn}n∈N an observed process and r = {rn}n∈N some auxiliary process. We assume that t = {tn}n∈N with tn = (xn, rn, yn-1) is a (Triplet) Markov Chain (TMC). TMC are more general than Hidden Markov Chains (HMC) and yet enable the development of efficient restoration and parameter estimation algorithms. This paper is devoted to Bayesian smoothing algorithms for TMC. We first propose twelve algorithms for general TMC. In the Gaussian case, these smoothers reduce to a set of algorithms which include, among other solutions, extensions to TMC of classical Kalman-like smoothing algorithms (originally designed for HMC) such as the RTS algorithms, the Two-Filter algorithms or the Bryson and Frazier algorithm.
3. Constructing 1/ωα noise from reversible Markov chains
Erland, Sveinung; Greenwood, Priscilla E.
2007-09-01
This paper gives sufficient conditions for the output of 1/ωα noise from reversible Markov chains on finite state spaces. We construct several examples exhibiting this behavior in a specified range of frequencies. We apply simple representations of the covariance function and the spectral density in terms of the eigendecomposition of the probability transition matrix. The results extend to hidden Markov chains. We generalize the results for aggregations of AR1-processes of C. W. J. Granger [J. Econometrics 14, 227 (1980)]. Given the eigenvalue function, there is a variety of ways to assign values to the states such that the 1/ωα condition is satisfied. We show that a random walk on a certain state space is complementary to the point process model of 1/ω noise of B. Kaulakys and T. Meskauskas [Phys. Rev. E 58, 7013 (1998)]. Passing to a continuous state space, we construct 1/ωα noise which also has a long memory.
4. Constructing 1/omegaalpha noise from reversible Markov chains.
PubMed
Erland, Sveinung; Greenwood, Priscilla E
2007-09-01
This paper gives sufficient conditions for the output of 1/omegaalpha noise from reversible Markov chains on finite state spaces. We construct several examples exhibiting this behavior in a specified range of frequencies. We apply simple representations of the covariance function and the spectral density in terms of the eigendecomposition of the probability transition matrix. The results extend to hidden Markov chains. We generalize the results for aggregations of AR1-processes of C. W. J. Granger [J. Econometrics 14, 227 (1980)]. Given the eigenvalue function, there is a variety of ways to assign values to the states such that the 1/omegaalpha condition is satisfied. We show that a random walk on a certain state space is complementary to the point process model of 1/omega noise of B. Kaulakys and T. Meskauskas [Phys. Rev. E 58, 7013 (1998)]. Passing to a continuous state space, we construct 1/omegaalpha noise which also has a long memory. PMID:17930206
5. Space system operations and support cost analysis using Markov chains
NASA Technical Reports Server (NTRS)
Unal, Resit; Dean, Edwin B.; Moore, Arlene A.; Fairbairn, Robert E.
1990-01-01
This paper evaluates the use of Markov chain process in probabilistic life cycle cost analysis and suggests further uses of the process as a design aid tool. A methodology is developed for estimating operations and support cost and expected life for reusable space transportation systems. Application of the methodology is demonstrated for the case of a hypothetical space transportation vehicle. A sensitivity analysis is carried out to explore the effects of uncertainty in key model inputs.
6. Parallel algorithms for simulating continuous time Markov chains
NASA Technical Reports Server (NTRS)
Nicol, David M.; Heidelberger, Philip
1992-01-01
We have previously shown that the mathematical technique of uniformization can serve as the basis of synchronization for the parallel simulation of continuous-time Markov chains. This paper reviews the basic method and compares five different methods based on uniformization, evaluating their strengths and weaknesses as a function of problem characteristics. The methods vary in their use of optimism, logical aggregation, communication management, and adaptivity. Performance evaluation is conducted on the Intel Touchstone Delta multiprocessor, using up to 256 processors.
7. Markov chain evaluation of acute postoperative pain transition states.
PubMed
Tighe, Patrick J; Bzdega, Matthew; Fillingim, Roger B; Rashidi, Parisa; Aytug, Haldun
2016-03-01
Previous investigations on acute postoperative pain dynamicity have focused on daily pain assessments, and so were unable to examine intraday variations in acute pain intensity. We analyzed 476,108 postoperative acute pain intensity ratings, which were clinically documented on postoperative days 1 to 7 from 8346 surgical patients using Markov chain modeling to describe how patients are likely to transition from one pain state to another in a probabilistic fashion. The Markov chain was found to be irreducible and positive recurrent, with no absorbing states. Transition probabilities ranged from 0.0031, for the transition from state 10 to state 1, to 0.69 for the transition from state 0 to state 0. The greatest density of transitions was noted in the diagonal region of the transition matrix, suggesting that patients were generally most likely to transition to the same pain state as their current state. There were also slightly increased probability densities in transitioning to a state of asleep or 0 from the current state. An examination of the number of steps required to traverse from a particular first pain score to a target state suggested that overall, fewer steps were required to reach a state of 0 (range 6.1-8.8 steps) or asleep (range 9.1-11) than were required to reach a mild pain intensity state. Our results suggest that using Markov chains is a feasible method for describing probabilistic postoperative pain trajectories, pointing toward the possibility of using Markov decision processes to model sequential interactions between pain intensity ratings, and postoperative analgesic interventions. PMID:26588689
8. Robust Dynamics and Control of a Partially Observed Markov Chain
SciTech Connect
Elliott, R. J. Malcolm, W. P. Moore, J. P.
2007-12-15
In a seminal paper, Martin Clark (Communications Systems and Random Process Theory, Darlington, 1977, pp. 721-734, 1978) showed how the filtered dynamics giving the optimal estimate of a Markov chain observed in Gaussian noise can be expressed using an ordinary differential equation. These results offer substantial benefits in filtering and in control, often simplifying the analysis and an in some settings providing numerical benefits, see, for example Malcolm et al. (J. Appl. Math. Stoch. Anal., 2007, to appear).Clark's method uses a gauge transformation and, in effect, solves the Wonham-Zakai equation using variation of constants. In this article, we consider the optimal control of a partially observed Markov chain. This problem is discussed in Elliott et al. (Hidden Markov Models Estimation and Control, Applications of Mathematics Series, vol. 29, 1995). The innovation in our results is that the robust dynamics of Clark are used to compute forward in time dynamics for a simplified adjoint process. A stochastic minimum principle is established.
9. Gapped alignment of protein sequence motifs through Monte Carlo optimization of a hidden Markov model
PubMed Central
Neuwald, Andrew F; Liu, Jun S
2004-01-01
Background Certain protein families are highly conserved across distantly related organisms and belong to large and functionally diverse superfamilies. The patterns of conservation present in these protein sequences presumably are due to selective constraints maintaining important but unknown structural mechanisms with some constraints specific to each family and others shared by a larger subset or by the entire superfamily. To exploit these patterns as a source of functional information, we recently devised a statistically based approach called contrast hierarchical alignment and interaction network (CHAIN) analysis, which infers the strengths of various categories of selective constraints from co-conserved patterns in a multiple alignment. The power of this approach strongly depends on the quality of the multiple alignments, which thus motivated development of theoretical concepts and strategies to improve alignment of conserved motifs within large sets of distantly related sequences. Results Here we describe a hidden Markov model (HMM), an algebraic system, and Markov chain Monte Carlo (MCMC) sampling strategies for alignment of multiple sequence motifs. The MCMC sampling strategies are useful both for alignment optimization and for adjusting position specific background amino acid frequencies for alignment uncertainties. Associated statistical formulations provide an objective measure of alignment quality as well as automatic gap penalty optimization. Improved alignments obtained in this way are compared with PSI-BLAST based alignments within the context of CHAIN analysis of three protein families: Giα subunits, prolyl oligopeptidases, and transitional endoplasmic reticulum (p97) AAA+ ATPases. Conclusion While not entirely replacing PSI-BLAST based alignments, which likewise may be optimized for CHAIN analysis using this approach, these motif-based methods often more accurately align very distantly related sequences and thus can provide a better measure of
10. Effective degree Markov-chain approach for discrete-time epidemic processes on uncorrelated networks
Cai, Chao-Ran; Wu, Zhi-Xi; Guan, Jian-Yue
2014-11-01
Recently, Gómez et al. proposed a microscopic Markov-chain approach (MMCA) [S. Gómez, J. Gómez-Gardeñes, Y. Moreno, and A. Arenas, Phys. Rev. E 84, 036105 (2011), 10.1103/PhysRevE.84.036105] to the discrete-time susceptible-infected-susceptible (SIS) epidemic process and found that the epidemic prevalence obtained by this approach agrees well with that by simulations. However, we found that the approach cannot be straightforwardly extended to a susceptible-infected-recovered (SIR) epidemic process (due to its irreversible property), and the epidemic prevalences obtained by MMCA and Monte Carlo simulations do not match well when the infection probability is just slightly above the epidemic threshold. In this contribution we extend the effective degree Markov-chain approach, proposed for analyzing continuous-time epidemic processes [J. Lindquist, J. Ma, P. Driessche, and F. Willeboordse, J. Math. Biol. 62, 143 (2011), 10.1007/s00285-010-0331-2], to address discrete-time binary-state (SIS) or three-state (SIR) epidemic processes on uncorrelated complex networks. It is shown that the final epidemic size as well as the time series of infected individuals obtained from this approach agree very well with those by Monte Carlo simulations. Our results are robust to the change of different parameters, including the total population size, the infection probability, the recovery probability, the average degree, and the degree distribution of the underlying networks.
11. Topological Charge Evolution in the Markov-Chain of QCD
SciTech Connect
Derek Leinweber; Anthony Williams; Jian-bo Zhang; Frank Lee
2004-04-01
The topological charge is studied on lattices of large physical volume and fine lattice spacing. We illustrate how a parity transformation on the SU(3) link-variables of lattice gauge configurations reverses the sign of the topological charge and leaves the action invariant. Random applications of the parity transformation are proposed to traverse from one topological charge sign to the other. The transformation provides an improved unbiased estimator of the ensemble average and is essential in improving the ergodicity of the Markov chain process.
12. On Construction of Quantum Markov Chains on Cayley trees
Accardi, Luigi; Mukhamedov, Farrukh; Souissi, Abdessatar
2016-03-01
The main aim of the present paper is to provide a new construction of quantum Markov chain (QMC) on arbitrary order Cayley tree. In that construction, a QMC is defined as a weak limit of finite volume states with boundary conditions, i.e. QMC depends on the boundary conditions. Note that this construction reminds statistical mechanics models with competing interactions on trees. If one considers one dimensional tree, then the provided construction reduces to well-known one, which was studied by the first author. Our construction will allow to investigate phase transition problem in a quantum setting.
13. Deterioration Prediction Model of Irrigation Facilities by Markov Chain Model
Mori, Takehisa; Nishino, Noriyasu; Fujiwara, Tetsuro
"Stock Management" launched in all over Japan is an activity to use irrigation facilities effectively and to reduce life cycle costs of theirs. Deterioration prediction of the irrigation facility condition is a vital process for the study of maintenance measures and the estimation of maintenance cost. It is important issue to establish the prediction technique with higher accuracy. Thereupon, we established a deterioration prediction model by a statistical method "Markov chain", and analyzed a function diagnosis data of irrigation facilities. As a result, we clarified the deterioration characteristics into each structure type and facilities.
14. Markov chain Mote Carlo solution of BK equation through Newton-Kantorovich method
BoŻek, Krzysztof; Kutak, Krzysztof; Placzek, Wieslaw
2013-07-01
We propose a new method for Monte Carlo solution of non-linear integral equations by combining the Newton-Kantorovich method for solving non-linear equations with the Markov Chain Monte Carlo (MCMC) method for solving linear equations. The Newton-Kantorovich method allows to express the non-linear equation as a system of the linear equations which then can be treated by the MCMC (random walk) algorithm. We apply this method to the Balitsky-Kovchegov (BK) equation describing evolution of gluon density at low x. Results of numerical computations show that the MCMC method is both precise and efficient. The presented algorithm may be particularly suited for solving more complicated and higher-dimensional non-linear integral equation, for which traditional methods become unfeasible.
15. First and second order semi-Markov chains for wind speed modeling
Prattico, F.; Petroni, F.; D'Amico, G.
2012-04-01
-order Markov chain with different number of states, and Weibull distribution. All this model use Markov chains to generate synthetic wind speed time series but the search for a better model is still open. Approaching this issue, we applied new models which are generalization of Markov models. More precisely we applied semi-Markov models to generate synthetic wind speed time series. Semi-Markov processes (SMP) are a wide class of stochastic processes which generalize at the same time both Markov chains and renewal processes. Their main advantage is that of using whatever type of waiting time distribution for modeling the time to have a transition from one state to another one. This major flexibility has a price to pay: availability of data to estimate the parameters of the model which are more numerous. Data availability is not an issue in wind speed studies, therefore, semi-Markov models can be used in a statistical efficient way. In this work we present three different semi-Markov chain models: the first one is a first-order SMP where the transition probabilities from two speed states (at time Tn and Tn-1) depend on the initial state (the state at Tn-1), final state (the state at Tn) and on the waiting time (given by t=Tn-Tn-1), the second model is a second order SMP where we consider the transition probabilities as depending also on the state the wind speed was before the initial state (which is the state at Tn-2) and the last one is still a second order SMP where the transition probabilities depends on the three states at Tn-2,Tn-1 and Tn and on the waiting times t_1=Tn-1-Tn-2 and t_2=Tn-Tn-1. The three models are used to generate synthetic time series for wind speed by means of Monte Carlo simulations and the time lagged autocorrelation is used to compare statistical properties of the proposed models with those of real data and also with a time series generated though a simple Markov chain. [1] F. Youcef Ettoumi, H. Sauvageot, A.-E.-H. Adane, Statistical bivariate modeling
16. Efficient Parallel Learning of Hidden Markov Chain Models on SMPs
Li, Lei; Fu, Bin; Faloutsos, Christos
Quad-core cpus have been a common desktop configuration for today's office. The increasing number of processors on a single chip opens new opportunity for parallel computing. Our goal is to make use of the multi-core as well as multi-processor architectures to speed up large-scale data mining algorithms. In this paper, we present a general parallel learning framework, Cut-And-Stitch, for training hidden Markov chain models. Particularly, we propose two model-specific variants, CAS-LDS for learning linear dynamical systems (LDS) and CAS-HMM for learning hidden Markov models (HMM). Our main contribution is a novel method to handle the data dependencies due to the chain structure of hidden variables, so as to parallelize the EM-based parameter learning algorithm. We implement CAS-LDS and CAS-HMM using OpenMP on two supercomputers and a quad-core commercial desktop. The experimental results show that parallel algorithms using Cut-And-Stitch achieve comparable accuracy and almost linear speedups over the traditional serial version.
17. A Markov chain model for reliability growth and decay
NASA Technical Reports Server (NTRS)
Siegrist, K.
1982-01-01
A mathematical model is developed to describe a complex system undergoing a sequence of trials in which there is interaction between the internal states of the system and the outcomes of the trials. For example, the model might describe a system undergoing testing that is redesigned after each failure. The basic assumptions for the model are that the state of the system after a trial depends probabilistically only on the state before the trial and on the outcome of the trial and that the outcome of a trial depends probabilistically only on the state of the system before the trial. It is shown that under these basic assumptions, the successive states form a Markov chain and the successive states and outcomes jointly form a Markov chain. General results are obtained for the transition probabilities, steady-state distributions, etc. A special case studied in detail describes a system that has two possible state ('repaired' and 'unrepaired') undergoing trials that have three possible outcomes ('inherent failure', 'assignable-cause' 'failure' and 'success'). For this model, the reliability function is computed explicitly and an optimal repair policy is obtained.
18. On the Multilevel Solution Algorithm for Markov Chains
NASA Technical Reports Server (NTRS)
Horton, Graham
1997-01-01
We discuss the recently introduced multilevel algorithm for the steady-state solution of Markov chains. The method is based on an aggregation principle which is well established in the literature and features a multiplicative coarse-level correction. Recursive application of the aggregation principle, which uses an operator-dependent coarsening, yields a multi-level method which has been shown experimentally to give results significantly faster than the typical methods currently in use. When cast as a multigrid-like method, the algorithm is seen to be a Galerkin-Full Approximation Scheme with a solution-dependent prolongation operator. Special properties of this prolongation lead to the cancellation of the computationally intensive terms of the coarse-level equations.
19. Kinetics and thermodynamics of first-order Markov chain copolymerization
Gaspard, P.; Andrieux, D.
2014-07-01
We report a theoretical study of stochastic processes modeling the growth of first-order Markov copolymers, as well as the reversed reaction of depolymerization. These processes are ruled by kinetic equations describing both the attachment and detachment of monomers. Exact solutions are obtained for these kinetic equations in the steady regimes of multicomponent copolymerization and depolymerization. Thermodynamic equilibrium is identified as the state at which the growth velocity is vanishing on average and where detailed balance is satisfied. Away from equilibrium, the analytical expression of the thermodynamic entropy production is deduced in terms of the Shannon disorder per monomer in the copolymer sequence. The Mayo-Lewis equation is recovered in the fully irreversible growth regime. The theory also applies to Bernoullian chains in the case where the attachment and detachment rates only depend on the reacting monomer.
20. Kinetics and thermodynamics of first-order Markov chain copolymerization.
PubMed
Gaspard, P; Andrieux, D
2014-07-28
We report a theoretical study of stochastic processes modeling the growth of first-order Markov copolymers, as well as the reversed reaction of depolymerization. These processes are ruled by kinetic equations describing both the attachment and detachment of monomers. Exact solutions are obtained for these kinetic equations in the steady regimes of multicomponent copolymerization and depolymerization. Thermodynamic equilibrium is identified as the state at which the growth velocity is vanishing on average and where detailed balance is satisfied. Away from equilibrium, the analytical expression of the thermodynamic entropy production is deduced in terms of the Shannon disorder per monomer in the copolymer sequence. The Mayo-Lewis equation is recovered in the fully irreversible growth regime. The theory also applies to Bernoullian chains in the case where the attachment and detachment rates only depend on the reacting monomer. PMID:25084957
1. Nonequilibrium thermodynamic potentials for continuous-time Markov chains
Verley, Gatien
2016-01-01
We connect the rare fluctuations of an equilibrium (EQ) process and the typical fluctuations of a nonequilibrium (NE) stationary process. In the framework of large deviation theory, this observation allows us to introduce NE thermodynamic potentials. For continuous-time Markov chains, we identify the relevant pairs of conjugated variables and propose two NE ensembles: one with fixed dynamics and fluctuating time-averaged variables, and another with fixed time-averaged variables, but a fluctuating dynamics. Accordingly, we show that NE processes are equivalent to conditioned EQ processes ensuring that NE potentials are Legendre dual. We find a variational principle satisfied by the NE potentials that reach their maximum in the NE stationary state and whose first derivatives produce the NE equations of state and second derivatives produce the NE Maxwell relations generalizing the Onsager reciprocity relations.
2. Projection methods for the numerical solution of Markov chain models
NASA Technical Reports Server (NTRS)
1989-01-01
Projection methods for computing stationary probability distributions for Markov chain models are presented. A general projection method is a method which seeks an approximation from a subspace of small dimension to the original problem. Thus, the original matrix problem of size N is approximated by one of dimension m, typically much smaller than N. A particularly successful class of methods based on this principle is that of Krylov subspace methods which utilize subspaces of the form span(v,av,...,A(exp m-1)v). These methods are effective in solving linear systems and eigenvalue problems (Lanczos, Arnoldi,...) as well as nonlinear equations. They can be combined with more traditional iterative methods such as successive overrelaxation, symmetric successive overrelaxation, or with incomplete factorization methods to enhance convergence.
3. Kinetics and thermodynamics of first-order Markov chain copolymerization
SciTech Connect
Gaspard, P.; Andrieux, D.
2014-07-28
We report a theoretical study of stochastic processes modeling the growth of first-order Markov copolymers, as well as the reversed reaction of depolymerization. These processes are ruled by kinetic equations describing both the attachment and detachment of monomers. Exact solutions are obtained for these kinetic equations in the steady regimes of multicomponent copolymerization and depolymerization. Thermodynamic equilibrium is identified as the state at which the growth velocity is vanishing on average and where detailed balance is satisfied. Away from equilibrium, the analytical expression of the thermodynamic entropy production is deduced in terms of the Shannon disorder per monomer in the copolymer sequence. The Mayo-Lewis equation is recovered in the fully irreversible growth regime. The theory also applies to Bernoullian chains in the case where the attachment and detachment rates only depend on the reacting monomer.
4. A Quantum Algorithm for Estimating Hitting Times of Markov Chains
Narayan Chowdhury, Anirban; Somma, Rolando
We present a quantum algorithm to estimate the hitting time of a reversible Markov chain faster than classically possible. To this end, we show that the hitting time is given by an expected value of the inverse of a Hermitian matrix. To obtain this expected value, our algorithm combines three important techniques developed in the literature. One such a technique is called spectral gap amplification and we use it to amplify the gap of the Hermitian matrix or reduce its condition number. We then use a new algorithm by Childs, Kothari, and Somma to implement the inverse of a matrix, and finally use methods developed in the context of quantum metrology to reduce the complexity of expected-value estimation for a given precision. The authors acknowledge support from AFOSR Grant Number FA9550-12-1-0057 and the Google Research Award.
5. On the multi-level solution algorithm for Markov chains
SciTech Connect
Horton, G.
1996-12-31
We discuss the recently introduced multi-level algorithm for the steady-state solution of Markov chains. The method is based on the aggregation principle, which is well established in the literature. Recursive application of the aggregation yields a multi-level method which has been shown experimentally to give results significantly faster than the methods currently in use. The algorithm can be reformulated as an algebraic multigrid scheme of Galerkin-full approximation type. The uniqueness of the scheme stems from its solution-dependent prolongation operator which permits significant computational savings in the evaluation of certain terms. This paper describes the modeling of computer systems to derive information on performance, measured typically as job throughput or component utilization, and availability, defined as the proportion of time a system is able to perform a certain function in the presence of component failures and possibly also repairs.
6. Sampling graphs with a prescribed joint degree distribution using Markov Chains.
SciTech Connect
Pinar, Ali; Stanton, Isabelle
2010-10-01
One of the most influential results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent work has shown that while these generative models do have the right degree distribution, they are not good models for real life networks due to their differences on other important metrics like conductance. We believe this is, in part, because many of these real-world networks have very different joint degree distributions, i.e. the probability that a randomly selected edge will be between nodes of degree k and l. Assortativity is a sufficient statistic of the joint degree distribution, and it has been previously noted that social networks tend to be assortative, while biological and technological networks tend to be disassortative. We suggest that the joint degree distribution of graphs is an interesting avenue of study for further research into network structure. We provide a simple greedy algorithm for constructing simple graphs from a given joint degree distribution, and a Monte Carlo Markov Chain method for sampling them. We also show that the state space of simple graphs with a fixed degree distribution is connected via endpoint switches. We empirically evaluate the mixing time of this Markov Chain by using experiments based on the autocorrelation of each edge.
7. Psychotherapy as Stochastic Process: Fitting a Markov Chain Model to Interviews of Ellis and Rogers. University of Minnesota Office of Student Affairs Research Bulletin, Vol. 15, No. 18.
ERIC Educational Resources Information Center
Lichtenberg, James W.; Hummel, Thomas J.
This investigation tested the hypothesis that the probabilistic structure underlying psychotherapy interviews is Markovian. The "goodness of fit" of a first-order Markov chain model to actual therapy interviews was assessed using a x squared test of homogeneity, and by generating by Monte Carlo methods empirical sampling distributions of selected…
8. A graph theoretic approach to global earthquake sequencing: A Markov chain model
Vasudevan, K.; Cavers, M. S.
2012-12-01
We construct a directed graph to represent a Markov chain of global earthquake sequences and analyze the statistics of transition probabilities linked to earthquake zones. For earthquake zonation, we consider the simplified plate boundary template of Kagan, Bird, and Jackson (KBJ template, 2010). We demonstrate the applicability of the directed graph approach to hazard-related forecasting using some of the properties of graphs that represent the finite Markov chain. We extend the present study to consider Bird's 52-plate zonation (2003) describing the global earthquakes at and within plate boundaries to gain further insight into the usefulness of digraphs corresponding to a Markov chain model.
9. Hidden Markov chain modeling for epileptic networks identification.
PubMed
Le Cam, Steven; Louis-Dorr, Valérie; Maillard, Louis
2013-01-01
The partial epileptic seizures are often considered to be caused by a wrong balance between inhibitory and excitatory interneuron connections within a focal brain area. These abnormal balances are likely to result in loss of functional connectivities between remote brain structures, while functional connectivities within the incriminated zone are enhanced. The identification of the epileptic networks underlying these hypersynchronies are expected to contribute to a better understanding of the brain mechanisms responsible for the development of the seizures. In this objective, threshold strategies are commonly applied, based on synchrony measurements computed from recordings of the electrophysiologic brain activity. However, such methods are reported to be prone to errors and false alarms. In this paper, we propose a hidden Markov chain modeling of the synchrony states with the aim to develop a reliable machine learning methods for epileptic network inference. The method is applied on a real Stereo-EEG recording, demonstrating consistent results with the clinical evaluations and with the current knowledge on temporal lobe epilepsy. PMID:24110697
10. ENSO informed Drought Forecasting Using Nonhomogeneous Hidden Markov Chain Model
Kwon, H.; Yoo, J.; Kim, T.
2013-12-01
The study aims at developing a new scheme to investigate the potential use of ENSO (El Niño/Southern Oscillation) for drought forecasting. In this regard, objective of this study is to extend a previously developed nonhomogeneous hidden Markov chain model (NHMM) to identify climate states associated with drought that can be potentially used to forecast drought conditions using climate information. As a target variable for forecasting, SPI(standardized precipitation index) is mainly utilized. This study collected monthly precipitation data over 56 stations that cover more than 30 years and K-means cluster analysis using drought properties was applied to partition regions into mutually exclusive clusters. In this study, six main clusters were distinguished through the regionalization procedure. For each cluster, the NHMM was applied to estimate the transition probability of hidden states as well as drought conditions informed by large scale climate indices (e.g. SOI, Nino1.2, Nino3, Nino3.4, MJO and PDO). The NHMM coupled with large scale climate information shows promise as a technique for forecasting drought scenarios. A more detailed explanation of large scale climate patterns associated with the identified hidden states will be provided with anomaly composites of SSTs and SLPs. Acknowledgement This research was supported by a grant(11CTIPC02) from Construction Technology Innovation Program (CTIP) funded by Ministry of Land, Transport and Maritime Affairs of Korean government.
11. Finding and Testing Network Communities by Lumped Markov Chains
PubMed Central
Piccardi, Carlo
2011-01-01
Identifying communities (or clusters), namely groups of nodes with comparatively strong internal connectivity, is a fundamental task for deeply understanding the structure and function of a network. Yet, there is a lack of formal criteria for defining communities and for testing their significance. We propose a sharp definition that is based on a quality threshold. By means of a lumped Markov chain model of a random walker, a quality measure called “persistence probability” is associated to a cluster, which is then defined as an “-community” if such a probability is not smaller than . Consistently, a partition composed of -communities is an “-partition.” These definitions turn out to be very effective for finding and testing communities. If a set of candidate partitions is available, setting the desired -level allows one to immediately select the -partition with the finest decomposition. Simultaneously, the persistence probabilities quantify the quality of each single community. Given its ability in individually assessing each single cluster, this approach can also disclose single well-defined communities even in networks that overall do not possess a definite clusterized structure. PMID:22073245
12. Threshold partitioning of sparse matrices and applications to Markov chains
SciTech Connect
Choi, Hwajeong; Szyld, D.B.
1996-12-31
It is well known that the order of the variables and equations of a large, sparse linear system influences the performance of classical iterative methods. In particular if, after a symmetric permutation, the blocks in the diagonal have more nonzeros, classical block methods have a faster asymptotic rate of convergence. In this paper, different ordering and partitioning algorithms for sparse matrices are presented. They are modifications of PABLO. In the new algorithms, in addition to the location of the nonzeros, the values of the entries are taken into account. The matrix resulting after the symmetric permutation has dense blocks along the diagonal, and small entries in the off-diagonal blocks. Parameters can be easily adjusted to obtain, for example, denser blocks, or blocks with elements of larger magnitude. In particular, when the matrices represent Markov chains, the permuted matrices are well suited for block iterative methods that find the corresponding probability distribution. Applications to three types of methods are explored: (1) Classical block methods, such as Block Gauss Seidel. (2) Preconditioned GMRES, where a block diagonal preconditioner is used. (3) Iterative aggregation method (also called aggregation/disaggregation) where the partition obtained from the ordering algorithm with certain parameters is used as an aggregation scheme. In all three cases, experiments are presented which illustrate the performance of the methods with the new orderings. The complexity of the new algorithms is linear in the number of nonzeros and the order of the matrix, and thus adding little computational effort to the overall solution.
13. User’s manual for basic version of MCnest Markov chain nest productivity model
EPA Science Inventory
The Markov Chain Nest Productivity Model (or MCnest) integrates existing toxicity information from three standardized avian toxicity tests with information on species life history and the timing of pesticide applications relative to the timing of avian breeding seasons to quantit...
14. Technical manual for basic version of the Markov chain nest productivity model (MCnest)
EPA Science Inventory
The Markov Chain Nest Productivity Model (or MCnest) integrates existing toxicity information from three standardized avian toxicity tests with information on species life history and the timing of pesticide applications relative to the timing of avian breeding seasons to quantit...
15. Markov chain analysis of succession in a rocky subtidal community.
PubMed
Hill, M Forrest; Witman, Jon D; Caswell, Hal
2004-08-01
We present a Markov chain model of succession in a rocky subtidal community based on a long-term (1986-1994) study of subtidal invertebrates (14 species) at Ammen Rock Pinnacle in the Gulf of Maine. The model describes successional processes (disturbance, colonization, species persistence, and replacement), the equilibrium (stationary) community, and the rate of convergence. We described successional dynamics by species turnover rates, recurrence times, and the entropy of the transition matrix. We used perturbation analysis to quantify the response of diversity to successional rates and species removals. The equilibrium community was dominated by an encrusting sponge (Hymedesmia) and a bryozoan (Crisia eburnea). The equilibrium structure explained 98% of the variance in observed species frequencies. Dominant species have low probabilities of disturbance and high rates of colonization and persistence. On average, species turn over every 3.4 years. Recurrence times varied among species (7-268 years); rare species had the longest recurrence times. The community converged to equilibrium quickly (9.5 years), as measured by Dobrushin's coefficient of ergodicity. The largest changes in evenness would result from removal of the dominant sponge Hymedesmia. Subdominant species appear to increase evenness by slowing the dominance of Hymedesmia. Comparison of the subtidal community with intertidal and coral reef communities revealed that disturbance rates are an order of magnitude higher in coral reef than in rocky intertidal and subtidal communities. Colonization rates and turnover times, however, are lowest and longest in coral reefs, highest and shortest in intertidal communities, and intermediate in subtidal communities. PMID:15278851
16. Enhancement of Markov chain model by integrating exponential smoothing: A case study on Muslims marriage and divorce
2015-12-01
Markov Chain has been introduced since the 1913 for the purpose of studying the flow of data for a consecutive number of years of the data and also forecasting. The important feature in Markov Chain is obtaining the accurate Transition Probability Matrix (TPM). However to obtain the suitable TPM is hard especially in involving long-term modeling due to unavailability of data. This paper aims to enhance the classical Markov Chain by introducing Exponential Smoothing technique in developing the appropriate TPM.
17. Weighted Markov Chains and Graphic State Nodes for Information Retrieval.
ERIC Educational Resources Information Center
Benoit, G.
2002-01-01
Discusses users' search behavior and decision making in data mining and information retrieval. Describes iterative information seeking as a Markov process during which users advance through states of nodes; and explains how the information system records the decision as weights, allowing the incorporation of users' decisions into the Markov…
18. Reliability analysis and prediction of mixed mode load using Markov Chain Model
Nikabdullah, N.; Singh, S. S. K.; Alebrahim, R.; Azizi, M. A.; K, Elwaleed A.; Noorani, M. S. M.
2014-06-01
The aim of this paper is to present the reliability analysis and prediction of mixed mode loading by using a simple two state Markov Chain Model for an automotive crankshaft. The reliability analysis and prediction for any automotive component or structure is important for analyzing and measuring the failure to increase the design life, eliminate or reduce the likelihood of failures and safety risk. The mechanical failures of the crankshaft are due of high bending and torsion stress concentration from high cycle and low rotating bending and torsional stress. The Markov Chain was used to model the two states based on the probability of failure due to bending and torsion stress. In most investigations it revealed that bending stress is much serve than torsional stress, therefore the probability criteria for the bending state would be higher compared to the torsion state. A statistical comparison between the developed Markov Chain Model and field data was done to observe the percentage of error. The reliability analysis and prediction was derived and illustrated from the Markov Chain Model were shown in the Weibull probability and cumulative distribution function, hazard rate and reliability curve and the bathtub curve. It can be concluded that Markov Chain Model has the ability to generate near similar data with minimal percentage of error and for a practical application; the proposed model provides a good accuracy in determining the reliability for the crankshaft under mixed mode loading.
19. Reliability analysis and prediction of mixed mode load using Markov Chain Model
SciTech Connect
Nikabdullah, N.; Singh, S. S. K.; Alebrahim, R.; Azizi, M. A.; K, Elwaleed A.; Noorani, M. S. M.
2014-06-19
The aim of this paper is to present the reliability analysis and prediction of mixed mode loading by using a simple two state Markov Chain Model for an automotive crankshaft. The reliability analysis and prediction for any automotive component or structure is important for analyzing and measuring the failure to increase the design life, eliminate or reduce the likelihood of failures and safety risk. The mechanical failures of the crankshaft are due of high bending and torsion stress concentration from high cycle and low rotating bending and torsional stress. The Markov Chain was used to model the two states based on the probability of failure due to bending and torsion stress. In most investigations it revealed that bending stress is much serve than torsional stress, therefore the probability criteria for the bending state would be higher compared to the torsion state. A statistical comparison between the developed Markov Chain Model and field data was done to observe the percentage of error. The reliability analysis and prediction was derived and illustrated from the Markov Chain Model were shown in the Weibull probability and cumulative distribution function, hazard rate and reliability curve and the bathtub curve. It can be concluded that Markov Chain Model has the ability to generate near similar data with minimal percentage of error and for a practical application; the proposed model provides a good accuracy in determining the reliability for the crankshaft under mixed mode loading.
20. A Markov Chain Monte Carlo Based Method for System Identification
SciTech Connect
Glaser, R E; Lee, C L; Nitao, J J; Hanley, W G
2002-10-22
This paper describes a novel methodology for the identification of mechanical systems and structures from vibration response measurements. It combines prior information, observational data and predictive finite element models to produce configurations and system parameter values that are most consistent with the available data and model. Bayesian inference and a Metropolis simulation algorithm form the basis for this approach. The resulting process enables the estimation of distributions of both individual parameters and system-wide states. Attractive features of this approach include its ability to: (1) provide quantitative measures of the uncertainty of a generated estimate; (2) function effectively when exposed to degraded conditions including: noisy data, incomplete data sets and model misspecification; (3) allow alternative estimates to be produced and compared, and (4) incrementally update initial estimates and analysis as more data becomes available. A series of test cases based on a simple fixed-free cantilever beam is presented. These results demonstrate that the algorithm is able to identify the system, based on the stiffness matrix, given applied force and resultant nodal displacements. Moreover, it effectively identifies locations on the beam where damage (represented by a change in elastic modulus) was specified.
1. Uncovering Mental Representations with Markov Chain Monte Carlo
ERIC Educational Resources Information Center
Sanborn, Adam N.; Griffiths, Thomas L.; Shiffrin, Richard M.
2010-01-01
A key challenge for cognitive psychology is the investigation of mental representations, such as object categories, subjective probabilities, choice utilities, and memory traces. In many cases, these representations can be expressed as a non-negative function defined over a set of objects. We present a behavioral method for estimating these…
2. Recognizing Chromospheric Objects via Markov Chain Monte Carlo
NASA Technical Reports Server (NTRS)
Mukhtar, Saleem; Turmon, Michael J.
1997-01-01
The solar chromosphere consists of three classes which contribute differentially to ultraviolet radiation reaching the earth. We describe a data set of solar images, means of segmenting the images into the constituent classes, and a novel high-level representation for compact objects based on a triangulated spatial membership function.
3. Deriving non-homogeneous DNA Markov chain models by cluster analysis algorithm minimizing multiple alignment entropy.
PubMed
Borodovsky, M; Peresetsky, A
1994-09-01
Non-homogeneous Markov chain models can represent biologically important regions of DNA sequences. The statistical pattern that is described by these models is usually weak and was found primarily because of strong biological indications. The general method for extracting similar patterns is presented in the current paper. The algorithm incorporates cluster analysis, multiple alignment and entropy minimization. The method was first tested using the set of DNA sequences produced by Markov chain generators. It was shown that artificial gene sequences, which initially have been randomly set up along the multiple alignment panels, are aligned according to the hidden triplet phase. Then the method was applied to real protein-coding sequences and the resulting alignment clearly indicated the triplet phase and produced the parameters of the optimal 3-periodic non-homogeneous Markov chain model. These Markov models were already employed in the GeneMark gene prediction algorithm, which is used in genome sequencing projects. The algorithm can also handle the case in which the sequences to be aligned reveal different statistical patterns, such as Escherichia coli protein-coding sequences belonging to Class II and Class III. The algorithm accepts a random mix of sequences from different classes, and is able to separate them into two groups (clusters), align each cluster separately, and define a non-homogeneous Markov chain model for each sequence cluster. PMID:7952897
4. Simplification of irreversible Markov chains by removal of states with fast leaving rates.
PubMed
Jia, Chen
2016-07-01
In the recent work of Ullah et al. (2012a), the authors developed an effective method to simplify reversible Markov chains by removal of states with low equilibrium occupancies. In this paper, we extend this result to irreversible Markov chains. We show that an irreversible chain can be simplified by removal of states with fast leaving rates. Moreover, we reveal that the irreversibility of the chain will always decrease after model simplification. This suggests that although model simplification can retain almost all the dynamic information of the chain, it will lose some thermodynamic information as a trade-off. Examples from biology are also given to illustrate the main results of this paper. PMID:27067245
5. Avian life history profiles for use in the Markov chain nest productivity model (MCnest)
EPA Science Inventory
The Markov Chain nest productivity model, or MCnest, quantitatively estimates the effects of pesticides or other toxic chemicals on annual reproductive success of avian species (Bennett and Etterson 2013, Etterson and Bennett 2013). The Basic Version of MCnest was developed as a...
6. Metastates in Mean-Field Models with Random External Fields Generated by Markov Chains
Formentin, M.; Külske, C.; Reichenbachs, A.
2012-01-01
We extend the construction by Külske and Iacobelli of metastates in finite-state mean-field models in independent disorder to situations where the local disorder terms are a sample of an external ergodic Markov chain in equilibrium. We show that for non-degenerate Markov chains, the structure of the theorems is analogous to the case of i.i.d. variables when the limiting weights in the metastate are expressed with the aid of a CLT for the occupation time measure of the chain. As a new phenomenon we also show in a Potts example that for a degenerate non-reversible chain this CLT approximation is not enough, and that the metastate can have less symmetry than the symmetry of the interaction and a Gaussian approximation of disorder fluctuations would suggest.
7. Fitting optimum order of Markov chain models for daily rainfall occurrences in Peninsular Malaysia
Deni, Sayang Mohd; Jemain, Abdul Aziz; Ibrahim, Kamarulzaman
2009-06-01
The analysis of the daily rainfall occurrence behavior is becoming more important, particularly in water-related sectors. Many studies have identified a more comprehensive pattern of the daily rainfall behavior based on the Markov chain models. One of the aims in fitting the Markov chain models of various orders to the daily rainfall occurrence is to determine the optimum order. In this study, the optimum order of the Markov chain models for a 5-day sequence will be examined in each of the 18 rainfall stations in Peninsular Malaysia, which have been selected based on the availability of the data, using the Akaike’s (AIC) and Bayesian information criteria (BIC). The identification of the most appropriate order in describing the distribution of the wet (dry) spells for each of the rainfall stations is obtained using the Kolmogorov-Smirnov goodness-of-fit test. It is found that the optimum order varies according to the levels of threshold used (e.g., either 0.1 or 10.0 mm), the locations of the region and the types of monsoon seasons. At most stations, the Markov chain models of a higher order are found to be optimum for rainfall occurrence during the northeast monsoon season for both levels of threshold. However, it is generally found that regardless of the monsoon seasons, the first-order model is optimum for the northwestern and eastern regions of the peninsula when the level of thresholds of 10.0 mm is considered. The analysis indicates that the first order of the Markov chain model is found to be most appropriate for describing the distribution of wet spells, whereas the higher-order models are found to be adequate for the dry spells in most of the rainfall stations for both threshold levels and monsoon seasons.
8. Application of Markov chain to the pattern of mitochondrial deoxyribonucleic acid mutations
Vantika, Sandy; Pasaribu, Udjianna S.
2014-03-01
This research explains how Markov chain used to model the pattern of deoxyribonucleic acid mutations in mitochondrial (mitochondrial DNA). First, sign test was used to see a pattern of nucleotide bases that will appear at one position after the position of mutated nucleotide base. Results obtained from the sign test showed that for most cases, there exist a pattern of mutation except in the mutation cases of adenine to cytosine, adenine to thymine, and cytosine to guanine. Markov chain analysis results on data of mutations that occur in mitochondrial DNA indicate that one and two positions after the position of mutated nucleotide bases tend to be occupied by particular nucleotide bases. From this analysis, it can be said that the adenine, cytosine, guanine and thymine will mutate if the nucelotide base at one and/or two positions after them is cytosine.
9. An 'adding' algorithm for the Markov chain formalism for radiation transfer
NASA Technical Reports Server (NTRS)
Esposito, L. W.
1979-01-01
An adding algorithm is presented, that extends the Markov chain method and considers a preceding calculation as a single state of a new Markov chain. This method takes advantage of the description of the radiation transport as a stochastic process. Successive application of this procedure makes calculation possible for any optical depth without increasing the size of the linear system used. It is determined that the time required for the algorithm is comparable to that for a doubling calculation for homogeneous atmospheres. For an inhomogeneous atmosphere the new method is considerably faster than the standard adding routine. It is concluded that the algorithm is efficient, accurate, and suitable for smaller computers in calculating the diffuse intensity scattered by an inhomogeneous planetary atmosphere.
10. A Markov Chain Model for evaluating the effectiveness of randomized surveillance procedures
SciTech Connect
Edmunds, T.A.
1994-01-01
A Markov Chain Model has been developed to evaluate the effectiveness of randomized surveillance procedures. The model is applicable for surveillance systems that monitor a collection of assets by randomly selecting and inspecting the assets. The model provides an estimate of the detection probability as a function of the amount of time that an adversary would require to steal or sabotage the asset. An interactive computer code has been written to perform the necessary computations.
11. Probabilistic approach of water residence time and connectivity using Markov chains with application to tidal embayments
Bacher, C.; Filgueira, R.; Guyondet, T.
2016-01-01
Markov chain analysis was recently proposed to assess the time scales and preferential pathways into biological or physical networks by computing residence time, first passage time, rates of transfer between nodes and number of passages in a node. We propose to adapt an algorithm already published for simple systems to physical systems described with a high resolution hydrodynamic model. The method is applied to bays and estuaries on the Eastern Coast of Canada for their interest in shellfish aquaculture. Current velocities have been computed by using a 2 dimensional grid of elements and circulation patterns were summarized by averaging Eulerian flows between adjacent elements. Flows and volumes allow computing probabilities of transition between elements and to assess the average time needed by virtual particles to move from one element to another, the rate of transfer between two elements, and the average residence time of each system. We also combined transfer rates and times to assess the main pathways of virtual particles released in farmed areas and the potential influence of farmed areas on other areas. We suggest that Markov chain is complementary to other sets of ecological indicators proposed to analyse the interactions between farmed areas - e.g., depletion index, carrying capacity assessment. Markov chain has several advantages with respect to the estimation of connectivity between pair of sites. It makes possible to estimate transfer rates and times at once in a very quick and efficient way, without the need to perform long term simulations of particle or tracer concentration.
12. Bayesian clustering of DNA sequences using Markov chains and a stochastic partition model.
PubMed
Jääskinen, Väinö; Parkkinen, Ville; Cheng, Lu; Corander, Jukka
2014-02-01
In many biological applications it is necessary to cluster DNA sequences into groups that represent underlying organismal units, such as named species or genera. In metagenomics this grouping needs typically to be achieved on the basis of relatively short sequences which contain different types of errors, making the use of a statistical modeling approach desirable. Here we introduce a novel method for this purpose by developing a stochastic partition model that clusters Markov chains of a given order. The model is based on a Dirichlet process prior and we use conjugate priors for the Markov chain parameters which enables an analytical expression for comparing the marginal likelihoods of any two partitions. To find a good candidate for the posterior mode in the partition space, we use a hybrid computational approach which combines the EM-algorithm with a greedy search. This is demonstrated to be faster and yield highly accurate results compared to earlier suggested clustering methods for the metagenomics application. Our model is fairly generic and could also be used for clustering of other types of sequence data for which Markov chains provide a reasonable way to compress information, as illustrated by experiments on shotgun sequence type data from an Escherichia coli strain. PMID:24246289
13. State space orderings for Gauss-Seidel in Markov chains revisited
SciTech Connect
Dayar, T.
1996-12-31
Symmetric state space orderings of a Markov chain may be used to reduce the magnitude of the subdominant eigenvalue of the (Gauss-Seidel) iteration matrix. Orderings that maximize the elemental mass or the number of nonzero elements in the dominant term of the Gauss-Seidel splitting (that is, the term approximating the coefficient matrix) do not necessarily converge faster. An ordering of a Markov chain that satisfies Property-R is semi-convergent. On the other hand, there are semi-convergent symmetric state space orderings that do not satisfy Property-R. For a given ordering, a simple approach for checking Property-R is shown. An algorithm that orders the states of a Markov chain so as to increase the likelihood of satisfying Property-R is presented. The computational complexity of the ordering algorithm is less than that of a single Gauss-Seidel iteration (for sparse matrices). In doing all this, the aim is to gain an insight for faster converging orderings. Results from a variety of applications improve the confidence in the algorithm.
14. Markov chains or the game of structure and chance. From complex networks, to language evolution, to musical compositions
Blanchard, Ph.; Dawin, J. R.; Volchenkov, D.
2010-06-01
Markov chains provide us with a powerful tool for studying the structure of graphs and databases in details. We review the method of generalized inverses for Markov chains and apply it for the analysis of urban structures, evolution of languages, and musical compositions. We also discuss a generalization of Lévy flights over large complex networks and study the interplay between the nonlinearity of diffusion process and the topological structure of the network.
15. Predicting transient particle transport in enclosed environments with the combined computational fluid dynamics and Markov chain method.
PubMed
Chen, C; Lin, C-H; Long, Z; Chen, Q
2014-02-01
To quickly obtain information about airborne infectious disease transmission in enclosed environments is critical in reducing the infection risk to the occupants. This study developed a combined computational fluid dynamics (CFD) and Markov chain method for quickly predicting transient particle transport in enclosed environments. The method first calculated a transition probability matrix using CFD simulations. Next, the Markov chain technique was applied to calculate the transient particle concentration distributions. This investigation used three cases, particle transport in an isothermal clean room, an office with an underfloor air distribution system, and the first-class cabin of an MD-82 airliner, to validate the combined CFD and Markov chain method. The general trends of the particle concentrations vs. time predicted by the Markov chain method agreed with the CFD simulations for these cases. The proposed Markov chain method can provide faster-than-real-time information about particle transport in enclosed environments. Furthermore, for a fixed airflow field, when the source location is changed, the Markov chain method can be used to avoid recalculation of the particle transport equation and thus reduce computing costs. PMID:23789964
16. Animal vocal sequences: not the Markov chains we thought they were
PubMed Central
Kershenbaum, Arik; Bowles, Ann E.; Freeberg, Todd M.; Jin, Dezhe Z.; Lameira, Adriano R.; Bohn, Kirsten
2014-01-01
Many animals produce vocal sequences that appear complex. Most researchers assume that these sequences are well characterized as Markov chains (i.e. that the probability of a particular vocal element can be calculated from the history of only a finite number of preceding elements). However, this assumption has never been explicitly tested. Furthermore, it is unclear how language could evolve in a single step from a Markovian origin, as is frequently assumed, as no intermediate forms have been found between animal communication and human language. Here, we assess whether animal taxa produce vocal sequences that are better described by Markov chains, or by non-Markovian dynamics such as the ‘renewal process’ (RP), characterized by a strong tendency to repeat elements. We examined vocal sequences of seven taxa: Bengalese finches Lonchura striata domestica, Carolina chickadees Poecile carolinensis, free-tailed bats Tadarida brasiliensis, rock hyraxes Procavia capensis, pilot whales Globicephala macrorhynchus, killer whales Orcinus orca and orangutans Pongo spp. The vocal systems of most of these species are more consistent with a non-Markovian RP than with the Markovian models traditionally assumed. Our data suggest that non-Markovian vocal sequences may be more common than Markov sequences, which must be taken into account when evaluating alternative hypotheses for the evolution of signalling complexity, and perhaps human language origins. PMID:25143037
17. A Markov Chain Analysis of Fish Movements to Determine Entrainment Zones
SciTech Connect
Johnson, Gary E.; Hedgepeth, J; Skalski, John R.; Giorgi, Albert E.
2004-10-01
Fish can become entrained at water withdrawal locations such as fish bypasses or cooling water intakes. Accordingly, the size of a fish entrainment zone (FEZ) is often of interest to fisheries managers and facility operators. This study developed a new technique to map the FEZ, defined here as the region immediately upstream of a portal where the probability of fish movement toward the portal is greater than 90%. To map the FEZ, we applied a Markov chain analysis to fish movement data collected with an active tracking sonar. This device locks onto and follows a target, recording positions through a set of volumetric cells comprising the sampled volume. The probability of a fish moving from one cell to another was calculated from fish position data, which was used to populate a Markov transition matrix. We developed and applied the technique using data on salmon smolts migrating near the ice/trash sluiceway at The Dalles Dam on the Columbia River. The FEZ of the sluiceway entrance in 2000 as determined with this procedure was approximately 5 m across and extended 6-8 m out from the face of the dam in the surface layer 2-3 m deep. In conclusion, using a Markov chain analysis of fish track data we were able to describe and quantify the FEZ of the sluiceway at The Dalles Dam. This technique for FEZ mapping is applicable to other bioengineering efforts aimed at protecting fish populations affected by water withdrawals.
18. Animal vocal sequences: not the Markov chains we thought they were.
PubMed
Kershenbaum, Arik; Bowles, Ann E; Freeberg, Todd M; Jin, Dezhe Z; Lameira, Adriano R; Bohn, Kirsten
2014-10-01
Many animals produce vocal sequences that appear complex. Most researchers assume that these sequences are well characterized as Markov chains (i.e. that the probability of a particular vocal element can be calculated from the history of only a finite number of preceding elements). However, this assumption has never been explicitly tested. Furthermore, it is unclear how language could evolve in a single step from a Markovian origin, as is frequently assumed, as no intermediate forms have been found between animal communication and human language. Here, we assess whether animal taxa produce vocal sequences that are better described by Markov chains, or by non-Markovian dynamics such as the 'renewal process' (RP), characterized by a strong tendency to repeat elements. We examined vocal sequences of seven taxa: Bengalese finches Lonchura striata domestica, Carolina chickadees Poecile carolinensis, free-tailed bats Tadarida brasiliensis, rock hyraxes Procavia capensis, pilot whales Globicephala macrorhynchus, killer whales Orcinus orca and orangutans Pongo spp. The vocal systems of most of these species are more consistent with a non-Markovian RP than with the Markovian models traditionally assumed. Our data suggest that non-Markovian vocal sequences may be more common than Markov sequences, which must be taken into account when evaluating alternative hypotheses for the evolution of signalling complexity, and perhaps human language origins. PMID:25143037
19. Ancestry inference in complex admixtures via variable-length Markov chain linkage models.
PubMed
Rodriguez, Jesse M; Bercovici, Sivan; Elmore, Megan; Batzoglou, Serafim
2013-03-01
Inferring the ancestral origin of chromosomal segments in admixed individuals is key for genetic applications, ranging from analyzing population demographics and history, to mapping disease genes. Previous methods addressed ancestry inference by using either weak models of linkage disequilibrium, or large models that make explicit use of ancestral haplotypes. In this paper we introduce ALLOY, an efficient method that incorporates generalized, but highly expressive, linkage disequilibrium models. ALLOY applies a factorial hidden Markov model to capture the parallel process producing the maternal and paternal admixed haplotypes, and models the background linkage disequilibrium in the ancestral populations via an inhomogeneous variable-length Markov chain. We test ALLOY in a broad range of scenarios ranging from recent to ancient admixtures with up to four ancestral populations. We show that ALLOY outperforms the previous state of the art, and is robust to uncertainties in model parameters. PMID:23421795
20. Ancestry Inference in Complex Admixtures via Variable-length Markov Chain Linkage Models
PubMed Central
Bercovici, Sivan; Elmore, Megan; Batzoglou, Serafim
2013-01-01
Abstract Inferring the ancestral origin of chromosomal segments in admixed individuals is key for genetic applications, ranging from analyzing population demographics and history, to mapping disease genes. Previous methods addressed ancestry inference by using either weak models of linkage disequilibrium, or large models that make explicit use of ancestral haplotypes. In this paper we introduce ALLOY, an efficient method that incorporates generalized, but highly expressive, linkage disequilibrium models. ALLOY applies a factorial hidden Markov model to capture the parallel process producing the maternal and paternal admixed haplotypes, and models the background linkage disequilibrium in the ancestral populations via an inhomogeneous variable-length Markov chain. We test ALLOY in a broad range of scenarios ranging from recent to ancient admixtures with up to four ancestral populations. We show that ALLOY outperforms the previous state of the art, and is robust to uncertainties in model parameters. PMID:23421795
1. The optimum order of a Markov chain model for daily rainfall in Nigeria
Jimoh, O. D.; Webster, P.
1996-11-01
Markov type models are often used to describe the occurrence of daily rainfall. Although models of Order 1 have been successfully employed, there remains uncertainty concerning the optimum order for such models. This paper is concerned with estimation of the optimum order of Markov chains and, in particular, the use of objective criteria of the Akaike and Bayesian Information Criteria (AIC and BIC, respectively). Using daily rainfall series for five stations in Nigeria, it has been found that the AIC and BIC estimates vary with month as well as the value of the rainfall threshold used to define a wet day. There is no apparent system to this variation, although AIC estimates are consistently greater than or equal to BIC estimates, with values of the latter limited to zero or unity. The optimum order is also investigated through generation of synthetic sequences of wet and dry days using the transition matrices of zero-, first- and second-order Markov chains. It was found that the first-order model is superior to the zero-order model in representing the characteristics of the historical sequence as judged using frequency duration curves. There was no discernible difference between the model performance for first- and second-order models. There was no seasonal varation in the model performance, which contrasts with the optimum models identified using AIC and BIC estimates. It is concluded that caution is needed with the use of objective criteria for determining the optimum order of the Markov model and that the use of frequency duration curves can provide a robust alternative method of model identification. Comments are also made on the importance of record length and non-stationarity for model identification
2. Global characterization of geophysical data using lagrangean data and Markov-chain statistics.
Pares-Sierra, Alejandro; Flores-Morales, Ana Laura
2015-04-01
A method for the global analysis of geophysical data is presented. Using short-period Lagrangean transports, calculated off-line from a numerical circulation ocean model (ROMS), a stochastic transition matrix is constructed. Iteration methods for this last, sparse, very-large matrix are used to solve standard Markov chain problem of time of arrival and destination. The method permits the identification of areas of influence, time of residence and connectivity between regions. Application for the Gulf of Mexico and the Eastern Tropical Pacific circulation is presented.
3. A multi-level solution algorithm for steady-state Markov chains
NASA Technical Reports Server (NTRS)
Horton, Graham; Leutenegger, Scott T.
1993-01-01
A new iterative algorithm, the multi-level algorithm, for the numerical solution of steady state Markov chains is presented. The method utilizes a set of recursively coarsened representations of the original system to achieve accelerated convergence. It is motivated by multigrid methods, which are widely used for fast solution of partial differential equations. Initial results of numerical experiments are reported, showing significant reductions in computation time, often an order of magnitude or more, relative to the Gauss-Seidel and optimal SOR algorithms for a variety of test problems. The multi-level method is compared and contrasted with the iterative aggregation-disaggregation algorithm of Takahashi.
4. A Markov chain technique for determining the acquisition behavior of a digital tracking loop
NASA Technical Reports Server (NTRS)
1972-01-01
An iterative procedure is presented for determining the acquisition behavior of discrete or digital implementations of a tracking loop. The technique is based on the theory of Markov chains and provides the cumulative probability of acquisition in the loop as a function of time in the presence of noise and a given set of initial condition probabilities. A digital second-order tracking loop to be used in the Viking command receiver for continuous tracking of the command subcarrier phase was analyzed using this technique, and the results agree closely with experimental data.
5. MonteCUBES
SciTech Connect
Blennow, Mattias
2010-03-30
We introduce the software package MonteCUBES, which is designed to easily and effectively perform Markov Chain Monte Carlo simulations for analyzing neutrino oscillation experiments. We discuss the methods used in the software as well as why we believe that it is particularly useful for simulating new physics effects.
6. Relocation hypocenter of microearthquake using Markov Chain simulation: Case study on geothermal field
Adu, Nurlia; Indriati Retno, P.; Suharsono
2016-02-01
Monitoring of micro seismic activity in the geothermal field is useful to know the fracture controllers in the geothermal reservoir area. However, in determining the point of micro earthquake, hypocenters still contain inherent uncertainties due to several factors such as mismatches velocity model used by the actual subsurface conditions. For that reason, hypocenter relocation by Markov Chain method is used, to simulate the hypocenter point spatially based opportunities transition containing the principle of conditional probability. The purpose of this relocation is to improve the models of the hypocenter so that the interpretation of the subsurface structure is better. From the result of the relocation of using Markov Chain identified fault structures trending below the surface of the northeast-southwest (NE-SW) with approximately N38°E. This structure is suspected as the continuity of the structure in the surface. The depth of the hypocenter is located 758 m above mean sea level more than 800 m below mean sea level.
7. Short-term droughts forecast using Markov chain model in Victoria, Australia
Rahmat, Siti Nazahiyah; Jayasuriya, Niranjali; Bhuiyan, Muhammed A.
2016-04-01
A comprehensive risk management strategy for dealing with drought should include both short-term and long-term planning. The objective of this paper is to present an early warning method to forecast drought using the Standardised Precipitation Index (SPI) and a non-homogeneous Markov chain model. A model such as this is useful for short-term planning. The developed method has been used to forecast droughts at a number of meteorological monitoring stations that have been regionalised into six (6) homogenous clusters with similar drought characteristics based on SPI. The non-homogeneous Markov chain model was used to estimate drought probabilities and drought predictions up to 3 months ahead. The drought severity classes defined using the SPI were computed at a 12-month time scale. The drought probabilities and the predictions were computed for six clusters that depict similar drought characteristics in Victoria, Australia. Overall, the drought severity class predicted was quite similar for all the clusters, with the non-drought class probabilities ranging from 49 to 57 %. For all clusters, the near normal class had a probability of occurrence varying from 27 to 38 %. For the more moderate and severe classes, the probabilities ranged from 2 to 13 % and 3 to 1 %, respectively. The developed model predicted drought situations 1 month ahead reasonably well. However, 2 and 3 months ahead predictions should be used with caution until the models are developed further.
8. Modeling of stratigraphic columns using Markov Chains and Gibbs sampling algorithms, Campo Oritupano, Venezuela.
Durán, E.
2012-04-01
The interbeded sandstones, siltstones and shale layers within the stratigraphic units of the Oficina Formation were stochastically characterized. The units within the Oritupano field are modeled using the information from 12 wells and a post-stack 3-D seismic cube. The Markov Chain algorithm was successful at maintaining the proportion of lithotypes of the columns in the study area. Different transition probability matrixes are evaluated by changing the length of the sequences represented in the transition matrix and how this choice of length affects ciclicity and the genetic relations between lithotypes. The Gibbs algorithm, using small sequences as building blocks for modeling, kept the main stratigraphic succession according to the geology. Although the modeled stratigraphy depends strongly on initial conditions, the use of longer sequences in the substitution helps not to overweight the transition counts from one lithotype to the same in the main diagonal of the probability matrix of the Markov Chain in the Gibbs algorithm. A methodology based on the phase spectrum of the seismic trace for tying the modeled sequences with the seismic data is evaluated and discussed. The results point to the phase spectrum as an alternate way to cross-correlate synthetic seismograms with the seismic trace in favor of the well known amplitude correlation. Finally, a map of net sand over the study area is generated from the modeled columns and compared with previous stratigraphic and facies analysis at the levels of interest.
9. Markov chain modelling of reliability analysis and prediction under mixed mode loading
Singh, Salvinder; Abdullah, Shahrum; Nik Mohamed, Nik Abdullah; Mohd Noorani, Mohd Salmi
2015-03-01
The reliability assessment for an automobile crankshaft provides an important understanding in dealing with the design life of the component in order to eliminate or reduce the likelihood of failure and safety risks. The failures of the crankshafts are considered as a catastrophic failure that leads towards a severe failure of the engine block and its other connecting subcomponents. The reliability of an automotive crankshaft under mixed mode loading using the Markov Chain Model is studied. The Markov Chain is modelled by using a two-state condition to represent the bending and torsion loads that would occur on the crankshaft. The automotive crankshaft represents a good case study of a component under mixed mode loading due to the rotating bending and torsion stresses. An estimation of the Weibull shape parameter is used to obtain the probability density function, cumulative distribution function, hazard and reliability rate functions, the bathtub curve and the mean time to failure. The various properties of the shape parameter is used to model the failure characteristic through the bathtub curve is shown. Likewise, an understanding of the patterns posed by the hazard rate onto the component can be used to improve the design and increase the life cycle based on the reliability and dependability of the component. The proposed reliability assessment provides an accurate, efficient, fast and cost effective reliability analysis in contrast to costly and lengthy experimental techniques.
10. Predicting seasonal fate of phenanthrene in aquatic environment with a Markov chain.
PubMed
Sun, Caiyun; Ma, Qiyun; Zhang, Jiquan; Zhou, Mo; Chen, Yanan
2016-08-01
Phenanthrene (Phe) with carcinogenicity is ubiquitous in the environment, especially in aquatic environment; its toxicity is greater. To help determine toxicity risk and remediation strategies, this study predicted seasonal fate of Phe in aquatic environment. Candidate mechanisms including biodegradation, sorption, desorption, photodegradation, hydrolysis and volatility were studied; the results for experiments under simulated conditions for normal, wet and dry seasons in the Yinma River Basin indicated that biodegradation in sediment, sorption, desorption, and volatility were important pathways for elimination of Phe from aquatic environment and showed seasonal variations. A microcosm which was used to mimic sediment/water system was set up to illustrate seasonal distribution and transport of Phe. A Markov chain was applied to predict seasonal fate of Phe in air/water/sediment environment, the predicted results were perfectly agreed with results of microcosm experiments. Predicted results with a Markov chain suggested that volatility and biodegradation in sediment were main elimination pathways, and contributions of elimination pathways showed seasonal variations; Phe was eliminated from water and sediment to negligible levels over around 250 h in August and over 1000 h in May; in November, Phe was eliminated from water to a negligible level while about 31 % of Phe amount still remained in sediment over 1000 h. PMID:27180837
11. Controlling influenza disease: Comparison between discrete time Markov chain and deterministic model
Novkaniza, F.; Ivana, Aldila, D.
2016-04-01
Mathematical model of respiratory diseases spread with Discrete Time Markov Chain (DTMC) and deterministic approach for constant total population size are analyzed and compared in this article. Intervention of medical treatment and use of medical mask included in to the model as a constant parameter to controlling influenza spreads. Equilibrium points and basic reproductive ratio as the endemic criteria and it level set depend on some variable are given analytically and numerically as a results from deterministic model analysis. Assuming total of human population is constant from deterministic model, number of infected people also analyzed with Discrete Time Markov Chain (DTMC) model. Since Δt → 0, we could assume that total number of infected people might change only from i to i + 1, i - 1, or i. Approximation probability of an outbreak with gambler's ruin problem will be presented. We find that no matter value of basic reproductive ℛ0, either its larger than one or smaller than one, number of infection will always tends to 0 for t → ∞. Some numerical simulation to compare between deterministic and DTMC approach is given to give a better interpretation and a better understanding about the models results.
12. Brief Communication: Earthquake sequencing: analysis of time series constructed from the Markov chain model
Cavers, M. S.; Vasudevan, K.
2015-10-01
Directed graph representation of a Markov chain model to study global earthquake sequencing leads to a time series of state-to-state transition probabilities that includes the spatio-temporally linked recurrent events in the record-breaking sense. A state refers to a configuration comprised of zones with either the occurrence or non-occurrence of an earthquake in each zone in a pre-determined time interval. Since the time series is derived from non-linear and non-stationary earthquake sequencing, we use known analysis methods to glean new information. We apply decomposition procedures such as ensemble empirical mode decomposition (EEMD) to study the state-to-state fluctuations in each of the intrinsic mode functions. We subject the intrinsic mode functions, derived from the time series using the EEMD, to a detailed analysis to draw information content of the time series. Also, we investigate the influence of random noise on the data-driven state-to-state transition probabilities. We consider a second aspect of earthquake sequencing that is closely tied to its time-correlative behaviour. Here, we extend the Fano factor and Allan factor analysis to the time series of state-to-state transition frequencies of a Markov chain. Our results support not only the usefulness of the intrinsic mode functions in understanding the time series but also the presence of power-law behaviour exemplified by the Fano factor and the Allan factor.
13. MBMC: An Effective Markov Chain Approach for Binning Metagenomic Reads from Environmental Shotgun Sequencing Projects.
PubMed
Wang, Ying; Hu, Haiyan; Li, Xiaoman
2016-08-01
14. Quantum Markov chains, sufficiency of quantum channels, and Rényi information measures
Datta, Nilanjana; Wilde, Mark M.
2015-12-01
A short quantum Markov chain is a tripartite state {ρ }{ABC} such that system A can be recovered perfectly by acting on system C of the reduced state {ρ }{BC}. Such states have conditional mutual information I(A;B| C) equal to zero and are the only states with this property. A quantum channel {N} is sufficient for two states ρ and σ if there exists a recovery channel using which one can perfectly recover ρ from {N}(ρ ) and σ from {N}(σ ). The relative entropy difference D(ρ \\parallel σ )-D({N}(ρ )\\parallel {N}(σ )) is equal to zero if and only if {N} is sufficient for ρ and σ. In this paper, we show that these properties extend to Rényi generalizations of these information measures which were proposed in (Berta et al 2015 J. Math. Phys. 56 022205; Seshadreesan et al 2015 J. Phys. A: Math. Theor. 48 395303), thus providing an alternate characterization of short quantum Markov chains and sufficient quantum channels. These results give further support to these quantities as being legitimate Rényi generalizations of the conditional mutual information and the relative entropy difference. Along the way, we solve some open questions of Ruskai and Zhang, regarding the trace of particular matrices that arise in the study of monotonicity of relative entropy under quantum operations and strong subadditivity of the von Neumann entropy.
15. Entropy and long-range memory in random symbolic additive Markov chains
Melnik, S. S.; Usatenko, O. V.
2016-06-01
The goal of this paper is to develop an estimate for the entropy of random symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the high-order additive stationary ergodic Markov chain with long-range memory. Supposing that the correlations between random elements of the chain are weak, we express the conditional entropy of the sequence by means of the symbolic pair correlation function. We also examine an algorithm for estimating the conditional entropy of finite symbolic sequences. We show that the entropy contains two contributions, i.e., the correlation and the fluctuation. The obtained analytical results are used for numerical evaluation of the entropy of written English texts and DNA nucleotide sequences. The developed theory opens the way for constructing a more consistent and sophisticated approach to describe the systems with strong short-range and weak long-range memory.
16. Markov chains at the interface of combinatorics, computing, and statistical physics
Streib, Amanda Pascoe
The fields of statistical physics, discrete probability, combinatorics, and theoretical computer science have converged around efforts to understand random structures and algorithms. Recent activity in the interface of these fields has enabled tremendous breakthroughs in each domain and has supplied a new set of techniques for researchers approaching related problems. This thesis makes progress on several problems in this interface whose solutions all build on insights from multiple disciplinary perspectives. First, we consider a dynamic growth process arising in the context of DNA-based self-assembly. The assembly process can be modeled as a simple Markov chain. We prove that the chain is rapidly mixing for large enough bias in regions of Zd. The proof uses a geometric distance function and a variant of path coupling in order to handle distances that can be exponentially large. We also provide the first results in the case of fluctuating bias, where the bias can vary depending on the location of the tile, which arises in the nanotechnology application. Moreover, we use intuition from statistical physics to construct a choice of the biases for which the Markov chain Mmon requires exponential time to converge. Second, we consider a related problem regarding the convergence rate of biased permutations that arises in the context of self-organizing lists. The Markov chain Mnn in this case is a nearest-neighbor chain that allows adjacent transpositions, and the rate of these exchanges is governed by various input parameters. It was conjectured that the chain is always rapidly mixing when the inversion probabilities are positively biased, i.e., we put nearest neighbor pair x < y in order with bias 1/2 ≤ pxy ≤ 1 and out of order with bias 1 - pxy. The Markov chain Mmon was known to have connections to a simplified version of this biased card-shuffling. We provide new connections between Mnn and Mmon by using simple combinatorial bijections, and we prove that Mnn is
17. Entropy and long-range memory in random symbolic additive Markov chains.
PubMed
Melnik, S S; Usatenko, O V
2016-06-01
The goal of this paper is to develop an estimate for the entropy of random symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the high-order additive stationary ergodic Markov chain with long-range memory. Supposing that the correlations between random elements of the chain are weak, we express the conditional entropy of the sequence by means of the symbolic pair correlation function. We also examine an algorithm for estimating the conditional entropy of finite symbolic sequences. We show that the entropy contains two contributions, i.e., the correlation and the fluctuation. The obtained analytical results are used for numerical evaluation of the entropy of written English texts and DNA nucleotide sequences. The developed theory opens the way for constructing a more consistent and sophisticated approach to describe the systems with strong short-range and weak long-range memory. PMID:27415245
18. Fisher information and asymptotic normality in system identification for quantum Markov chains
SciTech Connect
2011-06-15
This paper deals with the problem of estimating the coupling constant {theta} of a mixing quantum Markov chain. For a repeated measurement on the chain's output we show that the outcomes' time average has an asymptotically normal (Gaussian) distribution, and we give the explicit expressions of its mean and variance. In particular, we obtain a simple estimator of {theta} whose classical Fisher information can be optimized over different choices of measured observables. We then show that the quantum state of the output together with the system is itself asymptotically Gaussian and compute its quantum Fisher information, which sets an absolute bound to the estimation error. The classical and quantum Fisher information are compared in a simple example. In the vicinity of {theta}=0 we find that the quantum Fisher information has a quadratic rather than linear scaling in output size, and asymptotically the Fisher information is localized in the system, while the output is independent of the parameter.
NASA Technical Reports Server (NTRS)
Horton, Graham
1994-01-01
We consider a variant of the well-known Gauss-Seidel method for the solution of Markov chains in steady state. Whereas the standard algorithm visits each state exactly once per iteration in a predetermined order, the alternative approach uses a dynamic strategy. A set of states to be visited is maintained which can grow and shrink as the computation progresses. In this manner, we hope to concentrate the computational work in those areas of the chain in which maximum improvement in the solution can be achieved. We consider the adaptive approach both as a solver in its own right and as a relaxation method within the multi-level algorithm. Experimental results show significant computational savings in both cases.
20. On the utility of the multi-level algorithm for the solution of nearly completely decomposable Markov chains
NASA Technical Reports Server (NTRS)
Leutenegger, Scott T.; Horton, Graham
1994-01-01
Recently the Multi-Level algorithm was introduced as a general purpose solver for the solution of steady state Markov chains. In this paper, we consider the performance of the Multi-Level algorithm for solving Nearly Completely Decomposable (NCD) Markov chains, for which special-purpose iteractive aggregation/disaggregation algorithms such as the Koury-McAllister-Stewart (KMS) method have been developed that can exploit the decomposability of the the Markov chain. We present experimental results indicating that the general-purpose Multi-Level algorithm is competitive, and can be significantly faster than the special-purpose KMS algorithm when Gauss-Seidel and Gaussian Elimination are used for solving the individual blocks.
1. Kullback-Leibler Divergence-Based Differential Evolution Markov Chain Filter for Global Localization of Mobile Robots
PubMed Central
Martín, Fernando; Moreno, Luis; Garrido, Santiago; Blanco, Dolores
2015-01-01
One of the most important skills desired for a mobile robot is the ability to obtain its own location even in challenging environments. The information provided by the sensing system is used here to solve the global localization problem. In our previous work, we designed different algorithms founded on evolutionary strategies in order to solve the aforementioned task. The latest developments are presented in this paper. The engine of the localization module is a combination of the Markov chain Monte Carlo sampling technique and the Differential Evolution method, which results in a particle filter based on the minimization of a fitness function. The robot’s pose is estimated from a set of possible locations weighted by a cost value. The measurements of the perceptive sensors are used together with the predicted ones in a known map to define a cost function to optimize. Although most localization methods rely on quadratic fitness functions, the sensed information is processed asymmetrically in this filter. The Kullback-Leibler divergence is the basis of a cost function that makes it possible to deal with different types of occlusions. The algorithm performance has been checked in a real map. The results are excellent in environments with dynamic and unmodeled obstacles, a fact that causes occlusions in the sensing area. PMID:26389914
2. Kullback-Leibler Divergence-Based Differential Evolution Markov Chain Filter for Global Localization of Mobile Robots.
PubMed
Martín, Fernando; Moreno, Luis; Garrido, Santiago; Blanco, Dolores
2015-01-01
One of the most important skills desired for a mobile robot is the ability to obtain its own location even in challenging environments. The information provided by the sensing system is used here to solve the global localization problem. In our previous work, we designed different algorithms founded on evolutionary strategies in order to solve the aforementioned task. The latest developments are presented in this paper. The engine of the localization module is a combination of the Markov chain Monte Carlo sampling technique and the Differential Evolution method, which results in a particle filter based on the minimization of a fitness function. The robot's pose is estimated from a set of possible locations weighted by a cost value. The measurements of the perceptive sensors are used together with the predicted ones in a known map to define a cost function to optimize. Although most localization methods rely on quadratic fitness functions, the sensed information is processed asymmetrically in this filter. The Kullback-Leibler divergence is the basis of a cost function that makes it possible to deal with different types of occlusions. The algorithm performance has been checked in a real map. The results are excellent in environments with dynamic and unmodeled obstacles, a fact that causes occlusions in the sensing area. PMID:26389914
3. A multiple-state discrete-time Markov chain for estimating suspended sediment concentrations in open channel flow
Tsai, Christina; Wu, Nai-Kuang
2015-04-01
In this study, transport processes of uniform size sediment particles under steady and uniform flow are described by the multi-state discrete-time Markov chain. The multi-state discrete-time Markov chain is employed to estimate the suspended sediment concentration distribution versus water depth for various steady and uniform flow conditions. Model results are validated against available measurement data and the Rouse profile. Moreover, the multi-state discrete-time Markov chain can be used to quantify the average time spent for the flow to reach the dynamic equilibrium of particle deposition and entrainment processes. In the first part of this study, suspended sediment concentration under three different flow conditions are discussed. As the Rouse number decreases, the difference between the suspended sediment concentration estimated by the Markov chain model and the Rouse profile becomes more significant, and such discrepancy can be observed at a larger relative height from the bed. It can be attributed to the fact that the use of the terminal settling velocity in the transport process can lead to underestimation of the model residence probability and overestimation of the deposition probability. In the second part, laboratory experiments are used to validate the proposed multi-state discrete-time Markov chain model. It is observed that it would take more time for the sediment concentration to reach a dynamic equilibrium as the Rouse number decreases. In addition, the flow depth is found to be a contributing factor that impacts the time spent to reach the concentration dynamic equilibrium. It is recognized that the performance of the proposed multi-state discrete-time Markov chain model relies significantly on the knowledge of the vertical distribution of the turbulence intensity.
4. Unsupervised SAR images change detection with hidden Markov chains on a sliding window
Bouyahia, Zied; Benyoussef, Lamia; Derrode, Stéphane
2007-10-01
This work deals with unsupervised change detection in bi-date Synthetic Aperture Radar (SAR) images. Whatever the indicator of change used, e.g. log-ratio or Kullback-Leibler divergence, we have observed poor quality change maps for some events when using the Hidden Markov Chain (HMC) model we focus on in this work. The main reason comes from the stationary assumption involved in this model - and in most Markovian models such as Hidden Markov Random Fields-, which can not be justified in most observed scenes: changed areas are not necessarily stationary in the image. Besides the few non stationary Markov models proposed in the literature, the aim of this paper is to describe a pragmatic solution to tackle stationarity by using a sliding window strategy. In this algorithm, the criterion image is scanned pixel by pixel, and a classical HMC model is applied only on neighboring pixels. By moving the window through the image, the process is able to produce a change map which can better exhibit non stationary changes than the classical HMC applied directly on the whole criterion image. Special care is devoted to the estimation of the number of classes in each window, which can vary from one (no change) to three (positive change, negative change and no change) by using the corrected Akaike Information Criterion (AICc) suited to small samples. The quality assessment of the proposed approach is achieved with speckle-simulated images in which simulated changes is introduced. The windowed strategy is also evaluated with a pair of RADARSAT images bracketing the Nyiragongo volcano eruption event in January 2002. The available ground truth confirms the effectiveness of the proposed approach compared to a classical HMC-based strategy.
5. Modeling and computing of stock index forecasting based on neural network and Markov chain.
PubMed
Dai, Yonghui; Han, Dongmei; Dai, Weihui
2014-01-01
The stock index reflects the fluctuation of the stock market. For a long time, there have been a lot of researches on the forecast of stock index. However, the traditional method is limited to achieving an ideal precision in the dynamic market due to the influences of many factors such as the economic situation, policy changes, and emergency events. Therefore, the approach based on adaptive modeling and conditional probability transfer causes the new attention of researchers. This paper presents a new forecast method by the combination of improved back-propagation (BP) neural network and Markov chain, as well as its modeling and computing technology. This method includes initial forecasting by improved BP neural network, division of Markov state region, computing of the state transition probability matrix, and the prediction adjustment. Results of the empirical study show that this method can achieve high accuracy in the stock index prediction, and it could provide a good reference for the investment in stock market. PMID:24782659
6. A Markov chain analysis of fish movements to determine entrainment zones
SciTech Connect
Johnson, Gary E.; Hedgepeth, J.; Skalski, John R.; Giorgi, Albert E.
2004-06-01
The extent of the biological zone of influence (BZI) of a water withdrawal port, such as a cooling water intake or a smolt bypass, directly reflects its local effect on fish. This study produced a new technique to determine the BZI, defined as the region immediately upstream of a portal where the probability of fish movement toward the portal is greater than 90%. We developed and applied the technique at The Dalles Dam on the Columbia River, where the ice/trash sluiceway functions as a surface flow smolt bypass. To map the BZI, we applied a Markov-Chain analysis to smolt movement data collected with an active fish tracking sonar system. Probabilities of fish movement from cell to cell in the sample volume, calculated from tracked fish data, formed a Markov transition matrix. Multiplying this matrix by itself many times with absorption at the boundaries produced estimates of probability of passage out each side of the sample volume from the cells within. The BZI of a sluiceway entrance at The Dalles Dam was approximately 5 m across and extended 6-8 m out from the face of the dam in the surface layer 2-3 m deep. BZI mapping is applicable to many bioengineering efforts to protect fish populations.
7. Markov chain algorithms: a template for building future robust low-power systems
PubMed Central
Deka, Biplab; Birklykke, Alex A.; Duwe, Henry; Mansinghka, Vikash K.; Kumar, Rakesh
2014-01-01
Although computational systems are looking towards post CMOS devices in the pursuit of lower power, the expected inherent unreliability of such devices makes it difficult to design robust systems without additional power overheads for guaranteeing robustness. As such, algorithmic structures with inherent ability to tolerate computational errors are of significant interest. We propose to cast applications as stochastic algorithms based on Markov chains (MCs) as such algorithms are both sufficiently general and tolerant to transition errors. We show with four example applications—Boolean satisfiability, sorting, low-density parity-check decoding and clustering—how applications can be cast as MC algorithms. Using algorithmic fault injection techniques, we demonstrate the robustness of these implementations to transition errors with high error rates. Based on these results, we make a case for using MCs as an algorithmic template for future robust low-power systems. PMID:24842030
8. Study of behavior and determination of customer lifetime value(CLV) using Markov chain model
Permana, Dony; Indratno, Sapto Wahyu; Pasaribu, Udjianna S.
2014-03-01
Customer Lifetime Value or CLV is a restriction on interactive marketing to help a company in arranging financial for the marketing of new customer acquisition and customer retention. Additionally CLV can be able to segment customers for financial arrangements. Stochastic models for the fairly new CLV used a Markov chain. In this model customer retention probability and new customer acquisition probability play an important role. This model is originally introduced by Pfeifer and Carraway in 2000 [1]. They introduced several CLV models, one of them only involves customer and former customer. In this paper we expand the model by adding the assumption of the transition from former customer to customer. In the proposed model, the CLV value is higher than the CLV value obtained by Pfeifer and Caraway model. But our model still requires a longer convergence time.
9. 3D+t brain MRI segmentation using robust 4D Hidden Markov Chain.
PubMed
Lavigne, François; Collet, Christophe; Armspach, Jean-Paul
2014-01-01
In recent years many automatic methods have been developed to help physicians diagnose brain disorders, but the problem remains complex. In this paper we propose a method to segment brain structures on two 3D multi-modal MR images taken at different times (longitudinal acquisition). A bias field correction is performed with an adaptation of the Hidden Markov Chain (HMC) allowing us to take into account the temporal correlation in addition to spatial neighbourhood information. To improve the robustness of the segmentation of the principal brain structures and to detect Multiple Sclerosis Lesions as outliers the Trimmed Likelihood Estimator (TLE) is used during the process. The method is validated on 3D+t brain MR images. PMID:25571045
10. Study of behavior and determination of customer lifetime value(CLV) using Markov chain model
SciTech Connect
Permana, Dony; Indratno, Sapto Wahyu; Pasaribu, Udjianna S.
2014-03-24
Customer Lifetime Value or CLV is a restriction on interactive marketing to help a company in arranging financial for the marketing of new customer acquisition and customer retention. Additionally CLV can be able to segment customers for financial arrangements. Stochastic models for the fairly new CLV used a Markov chain. In this model customer retention probability and new customer acquisition probability play an important role. This model is originally introduced by Pfeifer and Carraway in 2000 [1]. They introduced several CLV models, one of them only involves customer and former customer. In this paper we expand the model by adding the assumption of the transition from former customer to customer. In the proposed model, the CLV value is higher than the CLV value obtained by Pfeifer and Caraway model. But our model still requires a longer convergence time.
11. A methodology for stochastic analysis of share prices as Markov chains with finite states.
PubMed
Mettle, Felix Okoe; Quaye, Enoch Nii Boi; Laryea, Ravenhill Adjetey
2014-01-01
Price volatilities make stock investments risky, leaving investors in critical position when uncertain decision is made. To improve investor evaluation confidence on exchange markets, while not using time series methodology, we specify equity price change as a stochastic process assumed to possess Markov dependency with respective state transition probabilities matrices following the identified state pace (i.e. decrease, stable or increase). We established that identified states communicate, and that the chains are aperiodic and ergodic thus possessing limiting distributions. We developed a methodology for determining expected mean return time for stock price increases and also establish criteria for improving investment decision based on highest transition probabilities, lowest mean return time and highest limiting distributions. We further developed an R algorithm for running the methodology introduced. The established methodology is applied to selected equities from Ghana Stock Exchange weekly trading data. PMID:25520904
12. Markov Chain-Like Quantum Biological Modeling of Mutations, Aging, and Evolution
PubMed Central
Djordjevic, Ivan B.
2015-01-01
Recent evidence suggests that quantum mechanics is relevant in photosynthesis, magnetoreception, enzymatic catalytic reactions, olfactory reception, photoreception, genetics, electron-transfer in proteins, and evolution; to mention few. In our recent paper published in Life, we have derived the operator-sum representation of a biological channel based on codon basekets, and determined the quantum channel model suitable for study of the quantum biological channel capacity. However, this model is essentially memoryless and it is not able to properly model the propagation of mutation errors in time, the process of aging, and evolution of genetic information through generations. To solve for these problems, we propose novel quantum mechanical models to accurately describe the process of creation spontaneous, induced, and adaptive mutations and their propagation in time. Different biological channel models with memory, proposed in this paper, include: (i) Markovian classical model, (ii) Markovian-like quantum model, and (iii) hybrid quantum-classical model. We then apply these models in a study of aging and evolution of quantum biological channel capacity through generations. We also discuss key differences of these models with respect to a multilevel symmetric channel-based Markovian model and a Kimura model-based Markovian process. These models are quite general and applicable to many open problems in biology, not only biological channel capacity, which is the main focus of the paper. We will show that the famous quantum Master equation approach, commonly used to describe different biological processes, is just the first-order approximation of the proposed quantum Markov chain-like model, when the observation interval tends to zero. One of the important implications of this model is that the aging phenotype becomes determined by different underlying transition probabilities in both programmed and random (damage) Markov chain-like models of aging, which are mutually
13. Fuzzy hidden Markov chains segmentation for volume determination and quantitation in PET
Hatt, M.; Lamare, F.; Boussion, N.; Turzo, A.; Collet, C.; Salzenstein, F.; Roux, C.; Jarritt, P.; Carson, K.; Cheze-LeRest, C.; Visvikis, D.
2007-07-01
Accurate volume of interest (VOI) estimation in PET is crucial in different oncology applications such as response to therapy evaluation and radiotherapy treatment planning. The objective of our study was to evaluate the performance of the proposed algorithm for automatic lesion volume delineation; namely the fuzzy hidden Markov chains (FHMC), with that of current state of the art in clinical practice threshold based techniques. As the classical hidden Markov chain (HMC) algorithm, FHMC takes into account noise, voxel intensity and spatial correlation, in order to classify a voxel as background or functional VOI. However the novelty of the fuzzy model consists of the inclusion of an estimation of imprecision, which should subsequently lead to a better modelling of the 'fuzzy' nature of the object of interest boundaries in emission tomography data. The performance of the algorithms has been assessed on both simulated and acquired datasets of the IEC phantom, covering a large range of spherical lesion sizes (from 10 to 37 mm), contrast ratios (4:1 and 8:1) and image noise levels. Both lesion activity recovery and VOI determination tasks were assessed in reconstructed images using two different voxel sizes (8 mm3 and 64 mm3). In order to account for both the functional volume location and its size, the concept of % classification errors was introduced in the evaluation of volume segmentation using the simulated datasets. Results reveal that FHMC performs substantially better than the threshold based methodology for functional volume determination or activity concentration recovery considering a contrast ratio of 4:1 and lesion sizes of <28 mm. Furthermore differences between classification and volume estimation errors evaluated were smaller for the segmented volumes provided by the FHMC algorithm. Finally, the performance of the automatic algorithms was less susceptible to image noise levels in comparison to the threshold based techniques. The analysis of both
14. A stochastic Markov chain model to describe lung cancer growth and metastasis.
PubMed
Newton, Paul K; Mason, Jeremy; Bethel, Kelly; Bazhenova, Lyudmila A; Nieva, Jorge; Kuhn, Peter
2012-01-01
A stochastic Markov chain model for metastatic progression is developed for primary lung cancer based on a network construction of metastatic sites with dynamics modeled as an ensemble of random walkers on the network. We calculate a transition matrix, with entries (transition probabilities) interpreted as random variables, and use it to construct a circular bi-directional network of primary and metastatic locations based on postmortem tissue analysis of 3827 autopsies on untreated patients documenting all primary tumor locations and metastatic sites from this population. The resulting 50 potential metastatic sites are connected by directed edges with distributed weightings, where the site connections and weightings are obtained by calculating the entries of an ensemble of transition matrices so that the steady-state distribution obtained from the long-time limit of the Markov chain dynamical system corresponds to the ensemble metastatic distribution obtained from the autopsy data set. We condition our search for a transition matrix on an initial distribution of metastatic tumors obtained from the data set. Through an iterative numerical search procedure, we adjust the entries of a sequence of approximations until a transition matrix with the correct steady-state is found (up to a numerical threshold). Since this constrained linear optimization problem is underdetermined, we characterize the statistical variance of the ensemble of transition matrices calculated using the means and variances of their singular value distributions as a diagnostic tool. We interpret the ensemble averaged transition probabilities as (approximately) normally distributed random variables. The model allows us to simulate and quantify disease progression pathways and timescales of progression from the lung position to other sites and we highlight several key findings based on the model. PMID:22558094
15. A Markov Chain Model for Changes in Users’ Assessment of Search Results
PubMed Central
Zhitomirsky-Geffet, Maayan; Bar-Ilan, Judit; Levene, Mark
2016-01-01
Previous research shows that users tend to change their assessment of search results over time. This is a first study that investigates the factors and reasons for these changes, and describes a stochastic model of user behaviour that may explain these changes. In particular, we hypothesise that most of the changes are local, i.e. between results with similar or close relevance to the query, and thus belong to the same”coarse” relevance category. According to the theory of coarse beliefs and categorical thinking, humans tend to divide the range of values under consideration into coarse categories, and are thus able to distinguish only between cross-category values but not within them. To test this hypothesis we conducted five experiments with about 120 subjects divided into 3 groups. Each student in every group was asked to rank and assign relevance scores to the same set of search results over two or three rounds, with a period of three to nine weeks between each round. The subjects of the last three-round experiment were then exposed to the differences in their judgements and were asked to explain them. We make use of a Markov chain model to measure change in users’ judgments between the different rounds. The Markov chain demonstrates that the changes converge, and that a majority of the changes are local to a neighbouring relevance category. We found that most of the subjects were satisfied with their changes, and did not perceive them as mistakes but rather as a legitimate phenomenon, since they believe that time has influenced their relevance assessment. Both our quantitative analysis and user comments support the hypothesis of the existence of coarse relevance categories resulting from categorical thinking in the context of user evaluation of search results. PMID:27171426
16. Effects of tour boats on dolphin activity examined with sensitivity analysis of Markov chains.
PubMed
Dans, Silvana Laura; Degrati, Mariana; Pedraza, Susana Noemí; Crespo, Enrique Alberto
2012-08-01
In Patagonia, Argentina, watching dolphins, especially dusky dolphins (Lagenorhynchus obscurus), is a new tourist activity. Feeding time decreases and time to return to feeding after feeding is abandoned and time it takes a group of dolphins to feed increase in the presence of boats. Such effects on feeding behavior may exert energetic costs on dolphins and thus reduce an individual's survival and reproductive capacity or maybe associated with shifts in distribution. We sought to predict which behavioral changes modify the activity pattern of dolphins the most. We modeled behavioral sequences of dusky dolphins with Markov chains. We calculated transition probabilities from one activity to another and arranged them in a stochastic matrix model. The proportion of time dolphins dedicated to a given activity (activity budget) and the time it took a dolphin to resume that activity after it had been abandoned (recurrence time) were calculated. We used a sensitivity analysis of Markov chains to calculate the sensitivity of the time budget and the activity-resumption time to changes in behavioral transition probabilities. Feeding-time budget was most sensitive to changes in the probability of dolphins switching from traveling to feeding behavior and of maintaining feeding behavior. Thus, an increase in these probabilities would be associated with the largest reduction in the time dedicated to feeding. A reduction in the probability of changing from traveling to feeding would also be associated with the largest increases in the time it takes dolphins to resume feeding. To approach dolphins when they are traveling would not affect behavior less because presence of the boat may keep dolphins from returning to feeding. Our results may help operators of dolphin-watching vessels minimize negative effects on dolphins. PMID:22624561
17. Binary 3-D Markov Chain Random Fields: Finite-size Scaling Analysis of Percolation Properties
Harter, T.
2004-12-01
Percolation phenomena in random media have been extensively studied in a wide variety of fields in physics, chemistry, engineering, bio-, earth-, and environmental sciences. Most work has focused on uncorrelated random fields. The critical behavior in media with short-range correlations is thought to be identical to that in uncorrelated systems. However, the percolation threshold, pc, which is 0.3116 in uncorrelated media, has been observed to vary with the correlation scale and also with the random field type. Here, we present percolation properties and finite-size scaling effects in three-dimensional binary cubic lattices represented by correlated Markov-chain random fields and compare them to those in sequential Gaussian and sequential indicator random fields. We find that the computed percolation threshold in correlated random fields is significantly lower than in the uncorrelated lattice and decreases with increasing correlation scale. The rate of decrease rapidly flattens out for correlation lengths larger than 2-3 grid-blocks. At correlation scales of 5-6 grid blocks, pc is found to be 0.126 for the Markov chain random fields and slightly higher for sequential Gaussian and indicator random fields. The universal scaling constants for mean cluster size, backbone fraction, and connectivity are found to be consistent with results on uncorrelated lattices. For numerical studies, it is critical to understand finite-size effects on the percolation and associated phase connectivity properties of lattices. We present detailed statistical results on the percolation properties in finite sized lattice and their dependence on correlation scale. We show that appropriate grid resolution and choice of simulation boundaries is critical to properly simulate correlated natural geologic systems, which may display significant finite-size effects.
18. A Markov Chain Model for Changes in Users' Assessment of Search Results.
PubMed
Zhitomirsky-Geffet, Maayan; Bar-Ilan, Judit; Levene, Mark
2016-01-01
Previous research shows that users tend to change their assessment of search results over time. This is a first study that investigates the factors and reasons for these changes, and describes a stochastic model of user behaviour that may explain these changes. In particular, we hypothesise that most of the changes are local, i.e. between results with similar or close relevance to the query, and thus belong to the same"coarse" relevance category. According to the theory of coarse beliefs and categorical thinking, humans tend to divide the range of values under consideration into coarse categories, and are thus able to distinguish only between cross-category values but not within them. To test this hypothesis we conducted five experiments with about 120 subjects divided into 3 groups. Each student in every group was asked to rank and assign relevance scores to the same set of search results over two or three rounds, with a period of three to nine weeks between each round. The subjects of the last three-round experiment were then exposed to the differences in their judgements and were asked to explain them. We make use of a Markov chain model to measure change in users' judgments between the different rounds. The Markov chain demonstrates that the changes converge, and that a majority of the changes are local to a neighbouring relevance category. We found that most of the subjects were satisfied with their changes, and did not perceive them as mistakes but rather as a legitimate phenomenon, since they believe that time has influenced their relevance assessment. Both our quantitative analysis and user comments support the hypothesis of the existence of coarse relevance categories resulting from categorical thinking in the context of user evaluation of search results. PMID:27171426
19. Assessing the Progress and the Underlying Nature of the Flows of Doctoral and Master Degree Candidates Using Absorbing Markov Chains
ERIC Educational Resources Information Center
Nicholls, Miles G.
2007-01-01
In this paper, absorbing markov chains are used to analyse the flows of higher degree by research candidates (doctoral and master) within an Australian faculty of business. The candidates are analysed according to whether they are full time or part time. The need for such analysis stemmed from what appeared to be a rather poor completion rate (as…
20. A Markov Random Field Framework for Protein Side-Chain Resonance Assignment
Zeng, Jianyang; Zhou, Pei; Donald, Bruce Randall
Nuclear magnetic resonance (NMR) spectroscopy plays a critical role in structural genomics, and serves as a primary tool for determining protein structures, dynamics and interactions in physiologically-relevant solution conditions. The current speed of protein structure determination via NMR is limited by the lengthy time required in resonance assignment, which maps spectral peaks to specific atoms and residues in the primary sequence. Although numerous algorithms have been developed to address the backbone resonance assignment problem [68,2,10,37,14,64,1,31,60], little work has been done to automate side-chain resonance assignment [43, 48, 5]. Most previous attempts in assigning side-chain resonances depend on a set of NMR experiments that record through-bond interactions with side-chain protons for each residue. Unfortunately, these NMR experiments have low sensitivity and limited performance on large proteins, which makes it difficult to obtain enough side-chain resonance assignments. On the other hand, it is essential to obtain almost all of the side-chain resonance assignments as a prerequisite for high-resolution structure determination. To overcome this deficiency, we present a novel side-chain resonance assignment algorithm based on alternative NMR experiments measuring through-space interactions between protons in the protein, which also provide crucial distance restraints and are normally required in high-resolution structure determination. We cast the side-chain resonance assignment problem into a Markov Random Field (MRF) framework, and extend and apply combinatorial protein design algorithms to compute the optimal solution that best interprets the NMR data. Our MRF framework captures the contact map information of the protein derived from NMR spectra, and exploits the structural information available from the backbone conformations determined by orientational restraints and a set of discretized side-chain conformations (i.e., rotamers). A Hausdorff
1. SU-E-J-115: Using Markov Chain Modeling to Elucidate Patterns in Breast Cancer Metastasis Over Time and Space
SciTech Connect
Comen, E; Mason, J; Kuhn, P; Nieva, J; Newton, P; Norton, L; Venkatappa, N; Jochelson, M
2014-06-01
2. Efficient variants of the minimal diffusion formulation of Markov chain ensembles.
PubMed
Güler, Marifi
2016-02-01
This study is concerned with ensembles of continuous-time Markov chains evolving independently under a common transition rate matrix in some finite state space. In this context, our prior work [Phys. Rev. E 91, 062116 (2015)] has formulated an approximation scheme, called the minimal diffusion formulation, to deduce how the number of chains in a prescribed relevant state evolves in time. The formulation consists of two specifically coupled Ornstein-Uhlenbeck processes in a stochastic differential equation representation; it is minimal in the sense that its structure does not change with the state space size or the transition matrix density, and it requires no matrix square-root operations. In the present study, we first calculate the autocorrelation function of the relevant state density in the minimal diffusion formulation, which is fundamental to the identification of the ensemble dynamics. The obtained autocorrelation function is then employed to develop two diffusion formulations that reduce the structural complexity of the minimal diffusion formulation without significant loss of accuracy in the dynamics. One of these variant formulations includes one less noise term than the minimal diffusion formulation and still satisfies the above-mentioned autocorrelation function in its dynamics. The second variant is in the form of a one-dimensional Langevin equation, therefore it is the simplest possible diffusion formulation one can obtain for the problem, yet its autocorrelation function is first-order accurate in time gap. Numerical simulations supporting the theoretical analysis are delivered. PMID:26986304
3. Efficient variants of the minimal diffusion formulation of Markov chain ensembles
Güler, Marifi
2016-02-01
This study is concerned with ensembles of continuous-time Markov chains evolving independently under a common transition rate matrix in some finite state space. In this context, our prior work [Phys. Rev. E 91, 062116 (2015), 10.1103/PhysRevE.91.062116] has formulated an approximation scheme, called the minimal diffusion formulation, to deduce how the number of chains in a prescribed relevant state evolves in time. The formulation consists of two specifically coupled Ornstein-Uhlenbeck processes in a stochastic differential equation representation; it is minimal in the sense that its structure does not change with the state space size or the transition matrix density, and it requires no matrix square-root operations. In the present study, we first calculate the autocorrelation function of the relevant state density in the minimal diffusion formulation, which is fundamental to the identification of the ensemble dynamics. The obtained autocorrelation function is then employed to develop two diffusion formulations that reduce the structural complexity of the minimal diffusion formulation without significant loss of accuracy in the dynamics. One of these variant formulations includes one less noise term than the minimal diffusion formulation and still satisfies the above-mentioned autocorrelation function in its dynamics. The second variant is in the form of a one-dimensional Langevin equation, therefore it is the simplest possible diffusion formulation one can obtain for the problem, yet its autocorrelation function is first-order accurate in time gap. Numerical simulations supporting the theoretical analysis are delivered.
4. The ATLAS Fast Monte Carlo Production Chain Project
Jansky, Roland
2015-12-01
During the last years ATLAS has successfully deployed a new integrated simulation framework (ISF) which allows a flexible mixture of full and fast detector simulation techniques within the processing of one event. The thereby achieved possible speed-up in detector simulation of up to a factor 100 makes subsequent digitization and reconstruction the dominant contributions to the Monte Carlo (MC) production CPU cost. The slowest components of both digitization and reconstruction are inside the Inner Detector due to the complex signal modeling needed in the emulation of the detector readout and in reconstruction due to the combinatorial nature of the problem to solve, respectively. Alternative fast approaches have been developed for these components: for the silicon based detectors a simpler geometrical clustering approach has been deployed replacing the charge drift emulation in the standard digitization modules, which achieves a very high accuracy in describing the standard output. For the Inner Detector track reconstruction, a Monte Carlo generator information based trajectory building has been deployed with the aim of bypassing the CPU intensive pattern recognition. Together with the ISF all components have been integrated into a new fast MC production chain, aiming to produce fast MC simulated data with sufficient agreement with fully simulated and reconstructed data at a processing time of seconds per event, compared to several minutes for full simulation.
5. Nonpoint source solute transport normal to aquifer bedding in heterogeneous, Markov chain random fields
Zhang, Hua; Harter, Thomas; Sivakumar, Bellie
2006-06-01
Facies-based geostatistical models have become important tools for analyzing flow and mass transport processes in heterogeneous aquifers. Yet little is known about the relationship between these latter processes and the parameters of facies-based geostatistical models. In this study, we examine the transport of a nonpoint source solute normal (perpendicular) to the major bedding plane of an alluvial aquifer medium that contains multiple geologic facies, including interconnected, high-conductivity (coarse textured) facies. We also evaluate the dependence of the transport behavior on the parameters of the constitutive facies model. A facies-based Markov chain geostatistical model is used to quantify the spatial variability of the aquifer system's hydrostratigraphy. It is integrated with a groundwater flow model and a random walk particle transport model to estimate the solute traveltime probability density function (pdf) for solute flux from the water table to the bottom boundary (the production horizon) of the aquifer. The cases examined include two-, three-, and four-facies models, with mean length anisotropy ratios for horizontal to vertical facies, ek, from 25:1 to 300:1 and with a wide range of facies volume proportions (e.g., from 5 to 95% coarse-textured facies). Predictions of traveltime pdfs are found to be significantly affected by the number of hydrostratigraphic facies identified in the aquifer. Those predictions of traveltime pdfs also are affected by the proportions of coarse-textured sediments, the mean length of the facies (particularly the ratio of length to thickness of coarse materials), and, to a lesser degree, the juxtapositional preference among the hydrostratigraphic facies. In transport normal to the sedimentary bedding plane, traveltime is not lognormally distributed as is often assumed. Also, macrodispersive behavior (variance of the traveltime) is found not to be a unique function of the conductivity variance. For the parameter range
6. Sanov and central limit theorems for output statistics of quantum Markov chains
SciTech Connect
2015-02-15
In this paper, we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov’s theorem for the multi-site empirical measure associated to finite sequences of consecutive outcomes of a classical stochastic process. Our result relies on the construction of an extended quantum transition operator (which keeps track of previous outcomes) in terms of which we compute moment generating functions, and whose spectral radius is related to the large deviations rate function. As a corollary to this, we obtain a central limit theorem for the empirical measure. Such higher level statistics may be used to uncover critical behaviour such as dynamical phase transitions, which are not captured by lower level statistics such as the sample mean. As a step in this direction, we give an example of a finite system whose level-1 (empirical mean) rate function is independent of a model parameter while the level-2 (empirical measure) rate is not.
7. Markov-chain approach to the distribution of ancestors in species of biparental reproduction
Caruso, M.; Jarne, C.
2014-08-01
We studied how to obtain a distribution for the number of ancestors in species of sexual reproduction. Present models concentrate on the estimation of distributions repetitions of ancestors in genealogical trees. It has been shown that it is not possible to reconstruct the genealogical history of each species along all its generations by means of a geometric progression. This analysis demonstrates that it is possible to rebuild the tree of progenitors by modeling the problem with a Markov chain. For each generation, the maximum number of possible ancestors is different. This presents huge problems for the resolution. We found a solution through a dilation of the sample space, although the distribution defined there takes smaller values with respect to the initial problem. In order to correct the distribution for each generation, we introduced the invariance under a gauge (local) group of dilations. These ideas can be used to study the interaction of several processes and provide a new approach on the problem of the common ancestor. In the same direction, this model also provides some elements that can be used to improve models of animal reproduction.
8. Two-state Markov-chain Poisson nature of individual cellphone call statistics
Jiang, Zhi-Qiang; Xie, Wen-Jie; Li, Ming-Xia; Zhou, Wei-Xing; Sornette, Didier
2016-07-01
Unfolding the burst patterns in human activities and social interactions is a very important issue especially for understanding the spreading of disease and information and the formation of groups and organizations. Here, we conduct an in-depth study of the temporal patterns of cellphone conversation activities of 73 339 anonymous cellphone users, whose inter-call durations are Weibull distributed. We find that the individual call events exhibit a pattern of bursts, that high activity periods are alternated with low activity periods. In both periods, the number of calls are exponentially distributed for individuals, but power-law distributed for the population. Together with the exponential distributions of inter-call durations within bursts and of the intervals between consecutive bursts, we demonstrate that the individual call activities are driven by two independent Poisson processes, which can be combined within a minimal model in terms of a two-state first-order Markov chain, giving significant fits for nearly half of the individuals. By measuring directly the distributions of call rates across the population, which exhibit power-law tails, we purport the existence of power-law distributions, via the ‘superposition of distributions’ mechanism. Our findings shed light on the origins of bursty patterns in other human activities.
9. Study on the calculation models of bus delay at bays using queueing theory and Markov chain.
PubMed
Sun, Feng; Sun, Li; Sun, Shao-Wei; Wang, Dian-Hai
2015-01-01
Traffic congestion at bus bays has decreased the service efficiency of public transit seriously in China, so it is crucial to systematically study its theory and methods. However, the existing studies lack theoretical model on computing efficiency. Therefore, the calculation models of bus delay at bays are studied. Firstly, the process that buses are delayed at bays is analyzed, and it was found that the delay can be divided into entering delay and exiting delay. Secondly, the queueing models of bus bays are formed, and the equilibrium distribution functions are proposed by applying the embedded Markov chain to the traditional model of queuing theory in the steady state; then the calculation models of entering delay are derived at bays. Thirdly, the exiting delay is studied by using the queueing theory and the gap acceptance theory. Finally, the proposed models are validated using field-measured data, and then the influencing factors are discussed. With these models the delay is easily assessed knowing the characteristics of the dwell time distribution and traffic volume at the curb lane in different locations and different periods. It can provide basis for the efficiency evaluation of bus bays. PMID:25759720
10. Markov chain decomposition of monthly rainfall into daily rainfall: Evaluation of climate change impact
DOE PAGESBeta
Yoo, Chulsang; Lee, Jinwook; Ro, Yonghun
2016-01-01
This paper evaluates the effect of climate change on daily rainfall, especially on the mean number of wet days and the mean rainfall intensity. Assuming that the mechanism of daily rainfall occurrences follows the first-order Markov chain model, the possible changes in the transition probabilities are estimated by considering the climate change scenarios. Also, the change of the stationary probabilities of wet and dry day occurrences and finally the change in the number of wet days are derived for the comparison of current (1x CO2) and 2x CO2conditions. As a result of this study, the increase or decrease in themore » mean number of wet days was found to be not enough to explain all of the change in monthly rainfall amounts, so rainfall intensity should also be modified. The application to the Seoul weather station in Korea shows that about 30% of the total change in monthly rainfall amount can be explained by the change in the number of wet days and the remaining 70% by the change in the rainfall intensity. That is, as an effect of climate change, the increase in the rainfall intensity could be more significant than the increase in the wet days and, thus, the risk of flood will be much highly increased.« less
11. Solving inverse problem for Markov chain model of customer lifetime value using flower pollination algorithm
Al-Ma'shumah, Fathimah; Permana, Dony; Sidarto, Kuntjoro Adji
2015-12-01
Customer Lifetime Value is an important and useful concept in marketing. One of its benefits is to help a company for budgeting marketing expenditure for customer acquisition and customer retention. Many mathematical models have been introduced to calculate CLV considering the customer retention/migration classification scheme. A fairly new class of these models which will be described in this paper uses Markov Chain Models (MCM). This class of models has the major advantage for its flexibility to be modified to several different cases/classification schemes. In this model, the probabilities of customer retention and acquisition play an important role. From Pfeifer and Carraway, 2000, the final formula of CLV obtained from MCM usually contains nonlinear form of the transition probability matrix. This nonlinearity makes the inverse problem of CLV difficult to solve. This paper aims to solve this inverse problem, yielding the approximate transition probabilities for the customers, by applying metaheuristic optimization algorithm developed by Yang, 2013, Flower Pollination Algorithm. The major interpretation of obtaining the transition probabilities are to set goals for marketing teams in keeping the relative frequencies of customer acquisition and customer retention.
12. DIM SUM: demography and individual migration simulated using a Markov chain.
PubMed
Brown, Jeremy M; Savidge, Kevin; McTavish, Emily Jane B
2011-03-01
An increasing number of studies seek to infer demographic history, often jointly with genetic relationships. Despite numerous analytical methods for such data, few simulations have investigated the methods' power and robustness, especially when underlying assumptions have been violated. DIM SUM (Demography and Individual Migration Simulated Using a Markov chain) is a stand-alone Java program for the simulation of population demography and individual migration while recording ancestor-descendant relationships. It does not employ coalescent assumptions or discrete population boundaries. It is extremely flexible, allowing the user to specify border positions, reactions of organisms to borders, local and global carrying capacities, individual dispersal kernels, rates of reproduction and strategies for sampling individuals. Spatial variables may be specified using image files (e.g., as exported from gis software) and may vary through time. In combination with software for genetic marker simulation, DIM SUM will be useful for testing phylogeographic (e.g., nested clade phylogeographic analysis, coalescent-based tests and continuous-landscape frameworks) and landscape-genetic methods, specifically regarding violations of coalescent assumptions. It can also be used to explore the qualitative features of proposed demographic scenarios (e.g. regarding biological invasions) and as a pedagogical tool. DIM SUM (with user's manual) can be downloaded from http://code.google.com/p/bio-dimsum. PMID:21429144
13. A Markov chain model for image ranking system in social networks
Zin, Thi Thi; Tin, Pyke; Toriu, Takashi; Hama, Hiromitsu
2014-03-01
In today world, different kinds of networks such as social, technological, business and etc. exist. All of the networks are similar in terms of distributions, continuously growing and expanding in large scale. Among them, many social networks such as Facebook, Twitter, Flickr and many others provides a powerful abstraction of the structure and dynamics of diverse kinds of inter personal connection and interaction. Generally, the social network contents are created and consumed by the influences of all different social navigation paths that lead to the contents. Therefore, identifying important and user relevant refined structures such as visual information or communities become major factors in modern decision making world. Moreover, the traditional method of information ranking systems cannot be successful due to their lack of taking into account the properties of navigation paths driven by social connections. In this paper, we propose a novel image ranking system in social networks by using the social data relational graphs from social media platform jointly with visual data to improve the relevance between returned images and user intentions (i.e., social relevance). Specifically, we propose a Markov chain based Social-Visual Ranking algorithm by taking social relevance into account. By using some extensive experiments, we demonstrated the significant and effectiveness of the proposed social-visual ranking method.
14. Mapping absorption processes onto a Markov chain, conserving the mean first passage time
Biswas, Katja
2013-04-01
The dynamics of a multidimensional system is projected onto a discrete state master equation using the transition rates W(k → k‧ t, t + dt) between a set of states {k} represented by the regions {ζk} in phase or discrete state space. Depending on the dynamics Γi(t) of the original process and the choice of ζk, the discretized process can be Markovian or non-Markovian. For absorption processes, it is shown that irrespective of these properties of the projection, a master equation with time-independent transition rates \\bar{W}(k\\rightarrow k^{\\prime }) can be obtained, which conserves the total occupation time of the partitions of the phase or discrete state space of the original process. An expression for the transition probabilities \\bar{p}(k^{\\prime }|k) is derived based on either time-discrete measurements {ti} with variable time stepping Δ(i + 1)i = ti + 1 - ti or the theoretical knowledge at continuous times t. This allows computational methods of absorbing Markov chains to be used to obtain the mean first passage time (MFPT) of the system. To illustrate this approach, the procedure is applied to obtain the MFPT for the overdamped Brownian motion of particles subject to a system with dichotomous noise and the escape from an entropic barrier. The high accuracy of the simulation results confirms with the theory.
15. Phase Transitions for Quantum Markov Chains Associated with Ising Type Models on a Cayley Tree
Mukhamedov, Farrukh; Barhoumi, Abdessatar; Souissi, Abdessatar
2016-05-01
The main aim of the present paper is to prove the existence of a phase transition in quantum Markov chain (QMC) scheme for the Ising type models on a Cayley tree. Note that this kind of models do not have one-dimensional analogous, i.e. the considered model persists only on trees. In this paper, we provide a more general construction of forward QMC. In that construction, a QMC is defined as a weak limit of finite volume states with boundary conditions, i.e. QMC depends on the boundary conditions. Our main result states the existence of a phase transition for the Ising model with competing interactions on a Cayley tree of order two. By the phase transition we mean the existence of two distinct QMC which are not quasi-equivalent and their supports do not overlap. We also study some algebraic property of the disordered phase of the model, which is a new phenomena even in a classical setting.
16. Markov chain decomposition of monthly rainfall into daily rainfall: Evaluation of climate change impact
SciTech Connect
Yoo, Chulsang; Lee, Jinwook; Ro, Yonghun
2016-01-01
This paper evaluates the effect of climate change on daily rainfall, especially on the mean number of wet days and the mean rainfall intensity. Assuming that the mechanism of daily rainfall occurrences follows the first-order Markov chain model, the possible changes in the transition probabilities are estimated by considering the climate change scenarios. Also, the change of the stationary probabilities of wet and dry day occurrences and finally the change in the number of wet days are derived for the comparison of current (1x CO2) and 2x CO2conditions. As a result of this study, the increase or decrease in the mean number of wet days was found to be not enough to explain all of the change in monthly rainfall amounts, so rainfall intensity should also be modified. The application to the Seoul weather station in Korea shows that about 30% of the total change in monthly rainfall amount can be explained by the change in the number of wet days and the remaining 70% by the change in the rainfall intensity. That is, as an effect of climate change, the increase in the rainfall intensity could be more significant than the increase in the wet days and, thus, the risk of flood will be much highly increased.
17. Exceptional motifs in different Markov chain models for a statistical analysis of DNA sequences.
PubMed
Schbath, S; Prum, B; de Turckheim, E
1995-01-01
Identifying exceptional motifs is often used for extracting information from long DNA sequences. The two difficulties of the method are the choice of the model that defines the expected frequencies of words and the approximation of the variance of the difference T(W) between the number of occurrences of a word W and its estimation. We consider here different Markov chain models, either with stationary or periodic transition probabilities. We estimate the variance of the difference T(W) by the conditional variance of the number of occurrences of W given the oligonucleotides counts that define the model. Two applications show how to use asymptotically standard normal statistics associated with the counts to describe a given sequence in terms of its outlying words. Sequences of Escherichia coli and of Bacillus subtilis are compared with respect to their exceptional tri- and tetranucleotides. For both bacteria, exceptional 3-words are mainly found in the coding frame. E. coli palindrome counts are analyzed in different models, showing that many overabundant words are one-letter mutations of avoided palindromes. PMID:8521272
18. Study on the Calculation Models of Bus Delay at Bays Using Queueing Theory and Markov Chain
PubMed Central
Sun, Li; Sun, Shao-wei; Wang, Dian-hai
2015-01-01
Traffic congestion at bus bays has decreased the service efficiency of public transit seriously in China, so it is crucial to systematically study its theory and methods. However, the existing studies lack theoretical model on computing efficiency. Therefore, the calculation models of bus delay at bays are studied. Firstly, the process that buses are delayed at bays is analyzed, and it was found that the delay can be divided into entering delay and exiting delay. Secondly, the queueing models of bus bays are formed, and the equilibrium distribution functions are proposed by applying the embedded Markov chain to the traditional model of queuing theory in the steady state; then the calculation models of entering delay are derived at bays. Thirdly, the exiting delay is studied by using the queueing theory and the gap acceptance theory. Finally, the proposed models are validated using field-measured data, and then the influencing factors are discussed. With these models the delay is easily assessed knowing the characteristics of the dwell time distribution and traffic volume at the curb lane in different locations and different periods. It can provide basis for the efficiency evaluation of bus bays. PMID:25759720
19. Integration of logistic regression, Markov chain and cellular automata models to simulate urban expansion
Jokar Arsanjani, Jamal; Helbich, Marco; Kainz, Wolfgang; Darvishi Boloorani, Ali
2013-04-01
This research analyses the suburban expansion in the metropolitan area of Tehran, Iran. A hybrid model consisting of logistic regression model, Markov chain (MC), and cellular automata (CA) was designed to improve the performance of the standard logistic regression model. Environmental and socio-economic variables dealing with urban sprawl were operationalised to create a probability surface of spatiotemporal states of built-up land use for the years 2006, 2016, and 2026. For validation, the model was evaluated by means of relative operating characteristic values for different sets of variables. The approach was calibrated for 2006 by cross comparing of actual and simulated land use maps. The achieved outcomes represent a match of 89% between simulated and actual maps of 2006, which was satisfactory to approve the calibration process. Thereafter, the calibrated hybrid approach was implemented for forthcoming years. Finally, future land use maps for 2016 and 2026 were predicted by means of this hybrid approach. The simulated maps illustrate a new wave of suburban development in the vicinity of Tehran at the western border of the metropolis during the next decades.
20. Identifying the role of typhoons as drought busters in South Korea based on hidden Markov chain models
Yoo, Jiyoung; Kwon, Hyun-Han; So, Byung-Jin; Rajagopalan, Balaji; Kim, Tae-Woong
2015-04-01
This study proposed a hidden Markov chain model-based drought analysis (HMM-DA) tool to understand the beginning and ending of meteorological drought and to further characterize typhoon-induced drought busters (TDB) by exploring spatiotemporal drought patterns in South Korea. It was found that typhoons have played a dominant role in ending drought events (EDE) during the typhoon season (July-September) over the last four decades (1974-2013). The percentage of EDEs terminated by TDBs was about 43-90% mainly along coastal regions in South Korea. Furthermore, the TDBs, mainly during summer, have a positive role in managing extreme droughts during the subsequent autumn and spring seasons. The HMM-DA models the temporal dependencies between drought states using Markov chain, consequently capturing the dependencies between droughts and typhoons well, thus, enabling a better performance in modeling spatiotemporal drought attributes compared to traditional methods.
1. An open Markov chain scheme model for a credit consumption portfolio fed by ARIMA and SARMA processes
Esquível, Manuel L.; Fernandes, José Moniz; Guerreiro, Gracinda R.
2016-06-01
We introduce a schematic formalism for the time evolution of a random population entering some set of classes and such that each member of the population evolves among these classes according to a scheme based on a Markov chain model. We consider that the flow of incoming members is modeled by a time series and we detail the time series structure of the elements in each of the classes. We present a practical application to data from a credit portfolio of a Cape Verdian bank; after modeling the entering population in two different ways - namely as an ARIMA process and as a deterministic sigmoid type trend plus a SARMA process for the residues - we simulate the behavior of the population and compare the results. We get that the second method is more accurate in describing the behavior of the populations when compared to the observed values in a direct simulation of the Markov chain.
2. Development of a Compound Distribution Markov Chain Model for Stochastic Generation of Rainfall with Long Term Persistence
Kamal Chowdhury, AFM; Lockart, Natalie; Willgoose, Garry; Kuczera, George
2015-04-01
One of the overriding issues in the rainfall simulation is the underestimation of observed rainfall variability in longer timescales (e.g. monthly, annual and multi-year), which usually results into under-estimation of reservoir reliability in urban water planning. This study has developed a Compound Distribution Markov Chain (CDMC) model for stochastic generation of daily rainfall. We used two parameters of Markov Chain process (transition probabilities of wet-to-wet and dry-to-dry days) for simulating rainfall occurrence and two parameters of gamma distribution (calculated from mean and standard deviation of wet-day rainfall) for simulating wet-day rainfall amounts. While two models with deterministic parameters underestimated long term variability, our investigation found that the long term variability of rainfall in the model is predominantly governed by the long term variability of gamma parameters, rather than the variability of Markov Chain parameters. Therefore, in the third approach, we developed the CDMC model with deterministic parameters of Markov Chain process, but stochastic parameters of gamma distribution by sampling the mean and standard deviation of wet-day rainfall from their log-normal and bivariate-normal distribution. We have found that the CDMC is able to replicate both short term and long term rainfall variability, when we calibrated the model at two sites in east coast of Australia using three types of daily rainfall data - (1) dynamically downscaled, 10 km resolution gridded data produced by NSW/ACT Regional Climate Modelling project, (2) 5 km resolution gridded data by Australian Water Availability Project and (3) point scale raingauge stations data by Bureau of Meteorology, Australia. We also examined the spatial variability of parameters and their link with local orography at our field site. The suitability of the model in runoff generation and urban reservoir-water simulation will be discussed.
3. Derivation of a Markov state model of the dynamics of a protein-like chain immersed in an implicit solvent
Schofield, Jeremy; Bayat, Hanif
2014-09-01
A Markov state model of the dynamics of a protein-like chain immersed in an implicit hard sphere solvent is derived from first principles for a system of monomers that interact via discontinuous potentials designed to account for local structure and bonding in a coarse-grained sense. The model is based on the assumption that the implicit solvent interacts on a fast time scale with the monomers of the chain compared to the time scale for structural rearrangements of the chain and provides sufficient friction so that the motion of monomers is governed by the Smoluchowski equation. A microscopic theory for the dynamics of the system is developed that reduces to a Markovian model of the kinetics under well-defined conditions. Microscopic expressions for the rate constants that appear in the Markov state model are analyzed and expressed in terms of a temperature-dependent linear combination of escape rates that themselves are independent of temperature. Excellent agreement is demonstrated between the theoretical predictions of the escape rates and those obtained through simulation of a stochastic model of the dynamics of bond formation. Finally, the Markov model is studied by analyzing the eigenvalues and eigenvectors of the matrix of transition rates, and the equilibration process for a simple helix-forming system from an ensemble of initially extended configurations to mainly folded configurations is investigated as a function of temperature for a number of different chain lengths. For short chains, the relaxation is primarily single-exponential and becomes independent of temperature in the low-temperature regime. The profile is more complicated for longer chains, where multi-exponential relaxation behavior is seen at intermediate temperatures followed by a low temperature regime in which the folding becomes rapid and single exponential. It is demonstrated that the behavior of the equilibration profile as the temperature is lowered can be understood in terms of the
4. Discovering Beaten Paths in Collaborative Ontology-Engineering Projects using Markov Chains
PubMed Central
Walk, Simon; Singer, Philipp; Strohmaier, Markus; Tudorache, Tania; Musen, Mark A.; Noy, Natalya F.
2014-01-01
Biomedical taxonomies, thesauri and ontologies in the form of the International Classification of Diseases as a taxonomy or the National Cancer Institute Thesaurus as an OWL-based ontology, play a critical role in acquiring, representing and processing information about human health. With increasing adoption and relevance, biomedical ontologies have also significantly increased in size. For example, the 11th revision of the International Classification of Diseases, which is currently under active development by the World Health Organization contains nearly 50, 000 classes representing a vast variety of different diseases and causes of death. This evolution in terms of size was accompanied by an evolution in the way ontologies are engineered. Because no single individual has the expertise to develop such large-scale ontologies, ontology-engineering projects have evolved from small-scale efforts involving just a few domain experts to large-scale projects that require effective collaboration between dozens or even hundreds of experts, practitioners and other stakeholders. Understanding the way these different stakeholders collaborate will enable us to improve editing environments that support such collaborations. In this paper, we uncover how large ontology-engineering projects, such as the International Classification of Diseases in its 11th revision, unfold by analyzing usage logs of five different biomedical ontology-engineering projects of varying sizes and scopes using Markov chains. We discover intriguing interaction patterns (e.g., which properties users frequently change after specific given ones) that suggest that large collaborative ontology-engineering projects are governed by a few general principles that determine and drive development. From our analysis, we identify commonalities and differences between different projects that have implications for project managers, ontology editors, developers and contributors working on collaborative ontology
5. Stochastic Simulation of Rainfall Data Using a Markov Chain Model Calibrated to Dynamically Downscaled Climate Data
Chowdhury, A. F. M. K.; Lockart, N.; Willgoose, G. R.; Kuczera, G. A.; Nadeeka, P. M.
2014-12-01
This study used high resolution spatially distributed rainfall data produced by NSW/ACT Regional Climate Modelling (NARCliM) project. NARCliM dynamically downscaled four Global Climate Models using three Regional Climate Models within the Weather Research and Forecasting model to generate gridded climate data at 10 km spatial resolution for south eastern Australia. These dataset are being used in this project to evaluate the urban water security of reservoirs on the east coast of Australia. A stochastic model to simulate rainfall series was developed for runoff generation using parameters calibrated to NARCliM. This study has developed a Markov Chain model, which simulates the occurrence of daily rainfall using the transition probability of dry and wet days, while the precipitation for the wet days are generated using a two parameter gamma distribution. We have identified significant seasonal and intra- to inter-decadal variations of the model parameters at our field site. Incorporating the temporal variability (for instance, calibrating the model parameters to each decade independently), we have found that the model satisfactorily preserves the daily, monthly and annual characteristics of the NARCliM rainfall. In addition to the temporal variability, we have observed that the model parameters vary spatially at our site with potential orographic effects that vary both seasonally and decadally. However, the parameters of the model fitted to the NARCliM rainfall are significantly different from the parameters fitted to the ground-based climate station rainfall. Suitability of the model for the generation of long time series (e.g. 1000 years) required for reservoir simulation will be discussed.
6. An informational transition in conditioned Markov chains: Applied to genetics and evolution.
PubMed
Zhao, Lei; Lascoux, Martin; Waxman, David
2016-08-01
In this work we assume that we have some knowledge about the state of a population at two known times, when the dynamics is governed by a Markov chain such as a Wright-Fisher model. Such knowledge could be obtained, for example, from observations made on ancient and contemporary DNA, or during laboratory experiments involving long term evolution. A natural assumption is that the behaviour of the population, between observations, is related to (or constrained by) what was actually observed. The present work shows that this assumption has limited validity. When the time interval between observations is larger than a characteristic value, which is a property of the population under consideration, there is a range of intermediate times where the behaviour of the population has reduced or no dependence on what was observed and an equilibrium-like distribution applies. Thus, for example, if the frequency of an allele is observed at two different times, then for a large enough time interval between observations, the population has reduced or no dependence on the two observed frequencies for a range of intermediate times. Given observations of a population at two times, we provide a general theoretical analysis of the behaviour of the population at all intermediate times, and determine an expression for the characteristic time interval, beyond which the observations do not constrain the population's behaviour over a range of intermediate times. The findings of this work relate to what can be meaningfully inferred about a population at intermediate times, given knowledge of terminal states. PMID:27105672
7. Discovering beaten paths in collaborative ontology-engineering projects using Markov chains.
PubMed
Walk, Simon; Singer, Philipp; Strohmaier, Markus; Tudorache, Tania; Musen, Mark A; Noy, Natalya F
2014-10-01
Biomedical taxonomies, thesauri and ontologies in the form of the International Classification of Diseases as a taxonomy or the National Cancer Institute Thesaurus as an OWL-based ontology, play a critical role in acquiring, representing and processing information about human health. With increasing adoption and relevance, biomedical ontologies have also significantly increased in size. For example, the 11th revision of the International Classification of Diseases, which is currently under active development by the World Health Organization contains nearly 50,000 classes representing a vast variety of different diseases and causes of death. This evolution in terms of size was accompanied by an evolution in the way ontologies are engineered. Because no single individual has the expertise to develop such large-scale ontologies, ontology-engineering projects have evolved from small-scale efforts involving just a few domain experts to large-scale projects that require effective collaboration between dozens or even hundreds of experts, practitioners and other stakeholders. Understanding the way these different stakeholders collaborate will enable us to improve editing environments that support such collaborations. In this paper, we uncover how large ontology-engineering projects, such as the International Classification of Diseases in its 11th revision, unfold by analyzing usage logs of five different biomedical ontology-engineering projects of varying sizes and scopes using Markov chains. We discover intriguing interaction patterns (e.g., which properties users frequently change after specific given ones) that suggest that large collaborative ontology-engineering projects are governed by a few general principles that determine and drive development. From our analysis, we identify commonalities and differences between different projects that have implications for project managers, ontology editors, developers and contributors working on collaborative ontology
8. Large Deviations for Stationary Probabilities of a Family of Continuous Time Markov Chains via Aubry-Mather Theory
2015-05-01
In the present paper, we consider a family of continuous time symmetric random walks indexed by , . For each the matching random walk take values in the finite set of states ; notice that is a subset of , where is the unitary circle. The infinitesimal generator of such chain is denoted by . The stationary probability for such process converges to the uniform distribution on the circle, when . Here we want to study other natural measures, obtained via a limit on , that are concentrated on some points of . We will disturb this process by a potential and study for each the perturbed stationary measures of this new process when . We disturb the system considering a fixed potential and we will denote by the restriction of to . Then, we define a non-stochastic semigroup generated by the matrix , where is the infinifesimal generator of . From the continuous time Perron's Theorem one can normalized such semigroup, and, then we get another stochastic semigroup which generates a continuous time Markov Chain taking values on . This new chain is called the continuous time Gibbs state associated to the potential , see (Lopes et al. in J Stat Phys 152:894-933, 2013). The stationary probability vector for such Markov Chain is denoted by . We assume that the maximum of is attained in a unique point of , and from this will follow that . Thus, here, our main goal is to analyze the large deviation principle for the family , when . The deviation function , which is defined on , will be obtained from a procedure based on fixed points of the Lax-Oleinik operator and Aubry-Mather theory. In order to obtain the associated Lax-Oleinik operator we use the Varadhan's Lemma for the process . For a careful analysis of the problem we present full details of the proof of the Large Deviation Principle, in the Skorohod space, for such family of Markov Chains, when . Finally, we compute the entropy of the invariant probabilities on the Skorohod space associated to the Markov Chains we analyze.
9. Markov chains and entropy tests in genetic-based lithofacies analysis of deep-water clastic depositional systems
Borka, Szabolcs
2016-01-01
The aim of this study was to examine the relationship between structural elements and the so-called genetic lithofacies in a clastic deep-water depositional system. Process-sedimentology has recently been gaining importance in the characterization of these systems. This way the recognized facies attributes can be associated with the depositional processes establishing the genetic lithofacies. In this paper this approach was presented through a case study of a Tertiary deep-water sequence of the Pannonian-basin. Of course it was necessary to interpret the stratigraphy of the sequences in terms of "general" sedimentology, focusing on the structural elements. For this purpose, well-logs and standard deep-water models were applied. The cyclicity of sedimentary sequences can be easily revealed by using Markov chains. Though Markov chain analysis has broad application in mainly fluvial depositional environments, its utilization is uncommon in deep-water systems. In this context genetic lithofacies was determined and analysed by embedded Markov chains. The randomness in the presence of a lithofacies within a cycle was estimated by entropy tests (entropy after depositional, before depositional, for the whole system). Subsequently the relationships between lithofacies were revealed and a depositional model (i.e. modal cycle) was produced with 90% confidence level of stationarity. The non-randomness of the latter was tested by chi-square test. The consequences coming from the comparison of "general" sequences (composed of architectural elements), the genetic-based sequences (showing the distributions of the genetic lithofacies) and the lithofacies relationships were discussed in details. This way main depositional channel has the best, channelized lobes have good potential hydrocarbon reservoir attributes, with symmetric alternation of persistent fine-grained sandstone (Facies D) and muddy fine-grained sandstone with traction structures (Facies F)
10. A Thermodynamic Formalism for Continuous Time Markov Chains with Values on the Bernoulli Space: Entropy, Pressure and Large Deviations
Lopes, Artur; Neumann, Adriana; Thieullen, Philippe
2013-09-01
Through this paper we analyze the ergodic properties of continuous time Markov chains with values on the one-dimensional spin lattice (also known as the Bernoulli space). Initially, we consider as the infinitesimal generator the operator [InlineEquation not available: see fulltext.], where [InlineEquation not available: see fulltext.] is a discrete time Ruelle operator (transfer operator), and is a given fixed Lipschitz function. The associated continuous time stationary Markov chain will define the a priori probability. Given a Lipschitz interaction , we are interested in Gibbs (equilibrium) state for such V. This will be another continuous time stationary Markov chain. In order to analyze this problem we will use a continuous time Ruelle operator (transfer operator) naturally associated to V. Among other things we will show that a continuous time Perron-Frobenius Theorem is true in the case V is a Lipschitz function. We also introduce an entropy, which is negative (see also Lopes et al. in Entropy and Variational Principle for one-dimensional Lattice Systems with a general a-priori probability: positive and zero temperature. Arxiv, 2012), and we consider a variational principle of pressure. Finally, we analyze large deviations properties for the empirical measure in the continuous time setting using results by Y. Kifer (Tamsui Oxf. J. Manag. Sci. 321(2):505-524, 1990). In the last appendix of the paper we explain why the techniques we develop here have the capability to be applied to the analysis of convergence of a certain version of the Metropolis algorithm.
11. Derivation of a Markov state model of the dynamics of a protein-like chain immersed in an implicit solvent
SciTech Connect
Schofield, Jeremy Bayat, Hanif
2014-09-07
A Markov state model of the dynamics of a protein-like chain immersed in an implicit hard sphere solvent is derived from first principles for a system of monomers that interact via discontinuous potentials designed to account for local structure and bonding in a coarse-grained sense. The model is based on the assumption that the implicit solvent interacts on a fast time scale with the monomers of the chain compared to the time scale for structural rearrangements of the chain and provides sufficient friction so that the motion of monomers is governed by the Smoluchowski equation. A microscopic theory for the dynamics of the system is developed that reduces to a Markovian model of the kinetics under well-defined conditions. Microscopic expressions for the rate constants that appear in the Markov state model are analyzed and expressed in terms of a temperature-dependent linear combination of escape rates that themselves are independent of temperature. Excellent agreement is demonstrated between the theoretical predictions of the escape rates and those obtained through simulation of a stochastic model of the dynamics of bond formation. Finally, the Markov model is studied by analyzing the eigenvalues and eigenvectors of the matrix of transition rates, and the equilibration process for a simple helix-forming system from an ensemble of initially extended configurations to mainly folded configurations is investigated as a function of temperature for a number of different chain lengths. For short chains, the relaxation is primarily single-exponential and becomes independent of temperature in the low-temperature regime. The profile is more complicated for longer chains, where multi-exponential relaxation behavior is seen at intermediate temperatures followed by a low temperature regime in which the folding becomes rapid and single exponential. It is demonstrated that the behavior of the equilibration profile as the temperature is lowered can be understood in terms of the
12. Obesity status transitions across the elementary years: Use of Markov chain modeling
Technology Transfer Automated Retrieval System (TEKTRAN)
Overweight and obesity status transition probabilities using first-order Markov transition models applied to elementary school children were assessed. Complete longitudinal data across eleven assessments were available from 1,494 elementary school children (from 7,599 students in 41 out of 45 school...
13. spMC: an R-package for 3D lithological reconstructions based on spatial Markov chains
Sartore, Luca; Fabbri, Paolo; Gaetan, Carlo
2016-09-01
The paper presents the spatial Markov Chains (spMC) R-package and a case study of subsoil simulation/prediction located in a plain site of Northeastern Italy. spMC is a quite complete collection of advanced methods for data inspection, besides spMC implements Markov Chain models to estimate experimental transition probabilities of categorical lithological data. Furthermore, simulation methods based on most known prediction methods (as indicator Kriging and CoKriging) were implemented in spMC package. Moreover, other more advanced methods are available for simulations, e.g. path methods and Bayesian procedures, that exploit the maximum entropy. Since the spMC package was developed for intensive geostatistical computations, part of the code is implemented for parallel computations via the OpenMP constructs. A final analysis of this computational efficiency compares the simulation/prediction algorithms by using different numbers of CPU cores, and considering the example data set of the case study included in the package.
14. The monoculture vs. rotation strategies in forestry: formalization and prediction by means of Markov-chain modelling.
PubMed
Feldman, Olga; Korotkov, Vladimir N; Logofet, Dmitrii O
2005-10-01
The monoculture strategy of forest management, where the same tree species (e.g., Picea abies) is cultivated in a number of successive planting-growing-felling cycles, is generally considered to be economically efficient, yet not sustainable as it reduces biodiversity in the forest. The sound alternative suggests a long-term strategy of forest management in which different forest types rotate either with planting after clear cutting, or by natural forest succession, yet the commercial output remains dubious. We suggest an approach to formalization and modelling forest dynamics in the long-term by means of Markov chains, the monoculture strategy resulting in an absorbing chain and the rotation one in a regular chain. The approach is illustrated with a case study of Russkii Les, a managed forest located in the Moscow Region, Russia, and the nearby forest reserve having been used as a data source for undisturbed forest dynamics. Starting with conceptual schemes of transitions among certain forest types (states of the chain) in the monoculture and rotation cases, we estimated the transition probabilities by an original method based on average duration of the corresponding states and on the likelihood of alternative transitions from a state into the next one. Formal analysis of the regular chain reveals an opportunity to achieve particular management objectives within the rotation strategy, in particular, to get the distribution of forest types in accordance with an adopted hierarchy of their commercial values, i.e. more valuable types have greater shares. PMID:16111801
15. The distribution of genome shared identical by descent for a pair of full sibs by means of the continuous time Markov chain
Julie, Hongki; Pasaribu, Udjianna S.; Pancoro, Adi
2015-12-01
This paper will allow Markov Chain's application in genome shared identical by descent by two individual at full sibs model. The full sibs model was a continuous time Markov Chain with three state. In the full sibs model, we look for the cumulative distribution function of the number of sub segment which have 2 IBD haplotypes from a segment of the chromosome which the length is t Morgan and the cumulative distribution function of the number of sub segment which have at least 1 IBD haplotypes from a segment of the chromosome which the length is t Morgan. This cumulative distribution function will be developed by the moment generating function.
16. Using Data Augmentation and Markov Chain Monte Carlo for the Estimation of Unfolding Response Models
ERIC Educational Resources Information Center
Johnson, Matthew S.; Junker, Brian W.
2003-01-01
Unfolding response models, a class of item response theory (IRT) models that assume a unimodal item response function (IRF), are often used for the measurement of attitudes. Verhelst and Verstralen (1993)and Andrich and Luo (1993) independently developed unfolding response models by relating the observed responses to a more common monotone IRT…
17. Probabilistic parameter estimation of activated sludge processes using Markov Chain Monte Carlo.
PubMed
Sharifi, Soroosh; Murthy, Sudhir; Takács, Imre; Massoudieh, Arash
2014-03-01
One of the most important challenges in making activated sludge models (ASMs) applicable to design problems is identifying the values of its many stoichiometric and kinetic parameters. When wastewater characteristics data from full-scale biological treatment systems are used for parameter estimation, several sources of uncertainty, including uncertainty in measured data, external forcing (e.g. influent characteristics), and model structural errors influence the value of the estimated parameters. This paper presents a Bayesian hierarchical modeling framework for the probabilistic estimation of activated sludge process parameters. The method provides the joint probability density functions (JPDFs) of stoichiometric and kinetic parameters by updating prior information regarding the parameters obtained from expert knowledge and literature. The method also provides the posterior correlations between the parameters, as well as a measure of sensitivity of the different constituents with respect to the parameters. This information can be used to design experiments to provide higher information content regarding certain parameters. The method is illustrated using the ASM1 model to describe synthetically generated data from a hypothetical biological treatment system. The results indicate that data from full-scale systems can narrow down the ranges of some parameters substantially whereas the amount of information they provide regarding other parameters is small, due to either large correlations between some of the parameters or a lack of sensitivity with respect to the parameters. PMID:24384542
18. Transport map-accelerated Markov chain Monte Carlo for Bayesian parameter inference
Marzouk, Y.; Parno, M.
2014-12-01
We introduce a new framework for efficient posterior sampling in Bayesian inference, using a combination of optimal transport maps and the Metropolis-Hastings rule. The core idea is to use transport maps to transform typical Metropolis proposal mechanisms (e.g., random walks, Langevin methods, Hessian-preconditioned Langevin methods) into non-Gaussian proposal distributions that can more effectively explore the target density. Our approach adaptively constructs a lower triangular transport map—i.e., a Knothe-Rosenblatt re-arrangement—using information from previous MCMC states, via the solution of an optimization problem. Crucially, this optimization problem is convex regardless of the form of the target distribution. It is solved efficiently using Newton or quasi-Newton methods, but the formulation is such that these methods require no derivative information from the target probability distribution; the target distribution is instead represented via samples. Sequential updates using the alternating direction method of multipliers enable efficient and parallelizable adaptation of the map even for large numbers of samples. We show that this approach uses inexact or truncated maps to produce an adaptive MCMC algorithm that is ergodic for the exact target distribution. Numerical demonstrations on a range of parameter inference problems involving both ordinary and partial differential equations show multiple order-of-magnitude speedups over standard MCMC techniques, measured by the number of effectively independent samples produced per model evaluation and per unit of wallclock time.
19. Stochastic Inversion of Electrical Resistivity Changes Using a Markov Chain, Monte Carlo Approach
SciTech Connect
Ramirez, A; Nitao, J; Hanley, W; Aines, R; Glaser, R; Sengupta, S; Dyer, K; Hickling, T; Daily, W
2004-09-21
We describe a stochastic inversion method for mapping subsurface regions where the electrical resistivity is changing. The technique combines prior information, electrical resistance data and forward models to produce subsurface resistivity models that are most consistent with all available data. Bayesian inference and a Metropolis simulation algorithm form the basis for this approach. Attractive features include its ability to: (1) provide quantitative measures of the uncertainty of a generated estimate and, (2) allow alternative model estimates to be identified, compared and ranked. Methods that monitor convergence and summarize important trends of the posterior distribution are introduced. Results from a physical model test and a field experiment were used to assess performance. The stochastic inversions presented provide useful estimates of the most probable location, shape, and volume of the changing region, and the most likely resistivity change. The proposed method is computationally expensive, requiring the use of extensive computational resources to make its application practical.
20. Testing the Efficiency of Markov Chain Monte Carlo with People Using Facial Affect Categories
ERIC Educational Resources Information Center
Martin, Jay B.; Griffiths, Thomas L.; Sanborn, Adam N.
2012-01-01
Exploring how people represent natural categories is a key step toward developing a better understanding of how people learn, form memories, and make decisions. Much research on categorization has focused on artificial categories that are created in the laboratory, since studying natural categories defined on high-dimensional stimuli such as…
1. Approximate Bayesian Computation using Markov Chain Monte Carlo simulation: DREAM(ABC)
2014-08-01
The quest for a more powerful method for model evaluation has inspired Vrugt and Sadegh (2013) to introduce "likelihood-free" inference as vehicle for diagnostic model evaluation. This class of methods is also referred to as Approximate Bayesian Computation (ABC) and relaxes the need for a residual-based likelihood function in favor of one or multiple different summary statistics that exhibit superior diagnostic power. Here we propose several methodological improvements over commonly used ABC sampling methods to permit inference of complex system models. Our methodology entitled DREAM(ABC) uses the DiffeRential Evolution Adaptive Metropolis algorithm as its main building block and takes advantage of a continuous fitness function to efficiently explore the behavioral model space. Three case studies demonstrate that DREAM(ABC) is at least an order of magnitude more efficient than commonly used ABC sampling methods for more complex models. DREAM(ABC) is also more amenable to distributed, multi-processor, implementation, a prerequisite to diagnostic inference of CPU-intensive system models.
2. Application of Markov chain theory to ASTP natural environment launch criteria at Kennedy Space Center
NASA Technical Reports Server (NTRS)
Graves, M. E.; Perlmutter, M.
1974-01-01
To aid the planning of the Apollo Soyuz Test Program (ASTP), certain natural environment statistical relationships are presented, based on Markov theory and empirical counts. The practical results are in terms of conditional probability of favorable and unfavorable launch conditions at Kennedy Space Center (KSC). They are based upon 15 years of recorded weather data which are analyzed under a set of natural environmental launch constraints. Three specific forecasting problems were treated: (1) the length of record of past weather which is useful to a prediction; (2) the effect of persistence in runs of favorable and unfavorable conditions; and (3) the forecasting of future weather in probabilistic terms.
3. Application of stochastic automata networks for creation of continuous time Markov chain models of voltage gating of gap junction channels.
PubMed
Snipas, Mindaugas; Pranevicius, Henrikas; Pranevicius, Mindaugas; Pranevicius, Osvaldas; Paulauskas, Nerijus; Bukauskas, Feliksas F
2015-01-01
The primary goal of this work was to study advantages of numerical methods used for the creation of continuous time Markov chain models (CTMC) of voltage gating of gap junction (GJ) channels composed of connexin protein. This task was accomplished by describing gating of GJs using the formalism of the stochastic automata networks (SANs), which allowed for very efficient building and storing of infinitesimal generator of the CTMC that allowed to produce matrices of the models containing a distinct block structure. All of that allowed us to develop efficient numerical methods for a steady-state solution of CTMC models. This allowed us to accelerate CPU time, which is necessary to solve CTMC models, ~20 times. PMID:25705700
4. Geodesic Monte Carlo on Embedded Manifolds.
PubMed
Byrne, Simon; Girolami, Mark
2013-12-01
Markov chain Monte Carlo methods explicitly defined on the manifold of probability distributions have recently been established. These methods are constructed from diffusions across the manifold and the solution of the equations describing geodesic flows in the Hamilton-Jacobi representation. This paper takes the differential geometric basis of Markov chain Monte Carlo further by considering methods to simulate from probability distributions that themselves are defined on a manifold, with common examples being classes of distributions describing directional statistics. Proposal mechanisms are developed based on the geodesic flows over the manifolds of support for the distributions, and illustrative examples are provided for the hypersphere and Stiefel manifold of orthonormal matrices. PMID:25309024
5. Geodesic Monte Carlo on Embedded Manifolds
PubMed Central
Byrne, Simon; Girolami, Mark
2013-01-01
Markov chain Monte Carlo methods explicitly defined on the manifold of probability distributions have recently been established. These methods are constructed from diffusions across the manifold and the solution of the equations describing geodesic flows in the Hamilton–Jacobi representation. This paper takes the differential geometric basis of Markov chain Monte Carlo further by considering methods to simulate from probability distributions that themselves are defined on a manifold, with common examples being classes of distributions describing directional statistics. Proposal mechanisms are developed based on the geodesic flows over the manifolds of support for the distributions, and illustrative examples are provided for the hypersphere and Stiefel manifold of orthonormal matrices. PMID:25309024
6. Topological coarse graining of polymer chains using wavelet-accelerated Monte Carlo. II. Self-avoiding chains.
PubMed
Ismail, Ahmed E; Stephanopoulos, George; Rutledge, Gregory C
2005-06-15
In the preceding paper [A. E. Ismail, G. C. Rutledge, and G. Stephanopoulos J. Chem. Phys. (in press)] we introduced wavelet-accelerated Monte Carlo (WAMC), a coarse-graining methodology based on the wavelet transform, as a method for sampling polymer chains. In the present paper, we extend our analysis to consider excluded-volume effects by studying self-avoiding chains. We provide evidence that the coarse-grained potentials developed using the WAMC method obey phenomenological scaling laws, and use simple physical arguments for freely jointed chains to motivate these laws. We show that coarse-grained self-avoiding random walks can reproduce results obtained from simulations of the original, more-detailed chains to a high degree of accuracy, in orders of magnitude less time. PMID:16008482
7. Time series segmentation with shifting means hidden markov models
Kehagias, Ath.; Fortin, V.
2006-08-01
We present a new family of hidden Markov models and apply these to the segmentation of hydrological and environmental time series. The proposed hidden Markov models have a discrete state space and their structure is inspired from the shifting means models introduced by Chernoff and Zacks and by Salas and Boes. An estimation method inspired from the EM algorithm is proposed, and we show that it can accurately identify multiple change-points in a time series. We also show that the solution obtained using this algorithm can serve as a starting point for a Monte-Carlo Markov chain Bayesian estimation method, thus reducing the computing time needed for the Markov chain to converge to a stationary distribution.
8. Mesoscopic dynamic Monte Carlo simulations of the adsorption of proteinlike HP chains within laterally constricted spaces.
PubMed
Liu, Susan M; Haynes, Charles A
2005-02-15
9. Application of Markov chain model to daily maximum temperature for thermal comfort in Malaysia
SciTech Connect
Nordin, Muhamad Asyraf bin Che; Hassan, Husna
2015-10-22
The Markov chain’s first order principle has been widely used to model various meteorological fields, for prediction purposes. In this study, a 14-year (2000-2013) data of daily maximum temperatures in Bayan Lepas were used. Earlier studies showed that the outdoor thermal comfort range based on physiologically equivalent temperature (PET) index in Malaysia is less than 34°C, thus the data obtained were classified into two state: normal state (within thermal comfort range) and hot state (above thermal comfort range). The long-run results show the probability of daily temperature exceed TCR will be only 2.2%. On the other hand, the probability daily temperature within TCR will be 97.8%.
10. Quantum Monte Carlo Simulations of Adulteration Effect on Bond Alternating Spin=1/2 Chain
Zhang, Peng; Xu, Zhaoxin; Ying, Heping; Dai, Jianhui; Crompton, Peter
The S=1/2 Heisenberg chain with bond alternation and randomness of antiferromagnetic (AFM) and ferromagnetic (FM) interactions is investigated by quantum Monte Carlo simulations of loop/cluster algorithm. Our results have shown interesting finite temperature magnetic properties of this model. The relevance of our study to former investigation results is discussed.
11. Bayesian Gibbs Markov chain: MRF-based Stochastic Joint Inversion of Hydrological and Geophysical Datasets for Improved Characterization of Aquifer Heterogeneities.
Oware, E. K.
2015-12-01
Modeling aquifer heterogeneities (AH) is a complex, multidimensional problem that mostly requires stochastic imaging strategies for tractability. While the traditional Bayesian Markov chain Monte Carlo (McMC) provides a powerful framework to model AH, the generic McMC is computationally prohibitive and, thus, unappealing for large-scale problems. An innovative variant of the McMC scheme that imposes priori spatial statistical constraints on model parameter updates, for improved characterization in a computationally efficient manner is proposed. The proposed algorithm (PA) is based on Markov random field (MRF) modeling, which is an image processing technique that infers the global behavior of a random field from its local properties, making the MRF approach well suited for imaging AH. MRF-based modeling leverages the equivalence of Gibbs (or Boltzmann) distribution (GD) and MRF to identify the local properties of an MRF in terms of the easily quantifiable Gibbs energy. The PA employs the two-step approach to model the lithological structure of the aquifer and the hydraulic properties within the identified lithologies simultaneously. It performs local Gibbs energy minimizations along a random path, which requires parameters of the GD (spatial statistics) to be specified. A PA that implicitly infers site-specific GD parameters within a Bayesian framework is also presented. The PA is illustrated with a synthetic binary facies aquifer with a lognormal heterogeneity simulated within each facies. GD parameters of 2.6, 1.2, -0.4, and -0.2 were estimated for the horizontal, vertical, NESW, and NWSE directions, respectively. Most of the high hydraulic conductivity zones (facies 2) were fairly resolved (see results below) with facies identification accuracy rate of 81%, 89%, and 90% for the inversions conditioned on concentration (R1), resistivity (R2), and joint (R3), respectively. The incorporation of the conditioning datasets improved on the root mean square error (RMSE
12. Markov Chain Modelling Analysis of HIV/AIDS Progression: A Race-based Forecast in the United States
PubMed Central
Lee, S.; Ko, J.; Tan, Xi; Patel, Isha; Balkrishnan, R.; Chang, J.
2014-01-01
HIV/AIDS has reached a pandemic level across the world with more than 33 million people who are living with HIV. In the United States, more than half a million people have been victims of AIDS. This study investigates the most vulnerable racial minority population (the African Americans) in the United States and the second least affected (the Caucasians) in order to predict the trends of the epidemic. A Markov chain analysis was used to model the progression of the disease among vulnerable people, infective people and AIDS cases for the two races separately, based on the 2009 Centers of Disease Control and Prevention HIV/AIDS Surveillance Report. Based on the Markov model, our study predicts that the number of African American people living with AIDS diagnosis and HIV infection and dead due to HIV/AIDS will be 662.2, 1225.3 and 62.9 in 2015 and 794.9, 1566.5 and 79.2 in 2030, respectively. The number of Caucasian people living with AIDS diagnosis and HIV infection and dead due to HIV/AIDS will be 96.4, 160 and 6.5 in 2015 and 118.6, 206.9 and 8.3 in 2030, respectively. The numbers of deaths due to HIV/AIDS are quite stable over the years in both the races. There is an increasing trend in the number of people living with HIV infection and AIDS diagnosis in Caucasians compared with African Americans. The absolute number of Caucasians living with AIDS diagnosis and HIV infection is quite smaller compared with African Americans. The results reveal discrepancy in HIV infection, AIDS diagnosis and deaths due to HIV/AIDS among the African Americans and the Caucasians races. There is a need for interventions focusing on HIV/AIDS prevention and management, optimum resource allocation and development of antiAIDS campaigns to reduce the infection rate. PMID:24843183
13. The condition of a finite Markov chain and perturbation bounds for the limiting probabilities
NASA Technical Reports Server (NTRS)
Meyer, C. D., Jr.
1979-01-01
The inequalities bounding the relative error the norm of w- w squiggly/the norm of w are exhibited by a very simple function of E and A. Let T denote the transition matrix of an ergodic chain, C, and let A = I - T. Let E be a perturbation matrix such that T squiggly = T - E is also the transition matrix of an ergodic chain, C squiggly. Let w and w squiggly denote the limiting probability (row) vectors for C and C squiggly. The inequality is the best one possible. This bound can be significant in the numerical determination of the limiting probabilities for an ergodic chain. In addition to presenting a sharp bound for the norm of w-w squiggly/the norm of w an explicit expression for w squiggly will be derived in which w squiggly is given as a function of E, A, w and some other related terms.
14. FREYA-a new Monte Carlo code for improved modeling of fission chains
SciTech Connect
Hagmann, C A; Randrup, J; Vogt, R L
2012-06-12
A new simulation capability for modeling of individual fission events and chains and the transport of fission products in materials is presented. FREYA ( Fission Yield Event Yield Algorithm ) is a Monte Carlo code for generating fission events providing correlated kinematic information for prompt neutrons, gammas, and fragments. As a standalone code, FREYA calculates quantities such as multiplicity-energy, angular, and gamma-neutron energy sharing correlations. To study materials with multiplication, shielding effects, and detectors, we have integrated FREYA into the general purpose Monte Carlo code MCNP. This new tool will allow more accurate modeling of detector responses including correlations and the development of SNM detectors with increased sensitivity.
15. Monte Carlo simulations for a fluctuating sphere labeled on a flexible polymer chain in good solvents
Chen, Yong; Shew, Chwen-Yang
2001-11-01
Monte Carlo simulations are conducted to investigate a model composed of a fluctuating sphere labeled on one chain end of an isolated flexible chain polymer in good solvents. The labeled sphere is to model the instantaneous size of a bound flexible chain segment or a vibrating chromophore on a polymer chain. We assume the vibration of the sphere is governed by a harmoniclike potential, and the sphere size stays positive. We first address the issue regarding the confinement effect induced by a flexible chain. To rationalize the simulation results, we carry out a detailed analysis for a simple case containing a dimer grafted onto a fluctuating sphere. Using the sphere with a large size fluctuation, we find that the fluctuating sphere can be confined within the coiled polymer chain, and even trapped inside the grooves between neighboring monomers. The results imply the confinement effects may influence the properties of chromophores labeled on polymers or drugs bound to biopolymers. Moreover, in a separate study, we show the fluctuating sphere model can be used to fit a bound flexible chain segment, and provides a means to parameterize a polymer chain to a dumbbell, with possible applications in the dynamics of dilute polymer solutions.
16. Monte-Carlo analysis of rarefied-gas diffusion including variance reduction using the theory of Markov random walks
NASA Technical Reports Server (NTRS)
Perlmutter, M.
1973-01-01
Molecular diffusion through a rarefied gas is analyzed by using the theory of Markov random walks. The Markov walk is simulated on the computer by using random numbers to find the new states from the appropriate transition probabilities. As the sample molecule during its random walk passes a scoring position, which is a location at which the macroscopic diffusing flow variables such as molecular flux and molecular density are desired, an appropriate payoff is scored. The payoff is a function of the sample molecule velocity. For example, in obtaining the molecular flux across a scoring position, the random walk payoff is the net number of times the scoring position has been crossed in the positive direction. Similarly, when the molecular density is required, the payoff is the sum of the inverse velocity of the sample molecule passing the scoring position. The macroscopic diffusing flow variables are then found from the expected payoff of the random walks.
17. Markov Chain Method for Radiative Transfer Modeling: A Case Study of Aerosol/Surface Retrieval using AirMSPI Measurements
Xu, F.; Diner, D. J.; Davis, A. B.; Latyshev, S.; Garay, M. J.; Kalashnikova, O.; Ge, C.; Wang, J.
2013-12-01
A vector Markov chain (MarCh) radiative transfer (RT) code developed at JPL that includes forward modeling of radiance and polarization fields and linearization (analytical estimation of Jacobians) was incorporated into an aerosol and surface retrieval package for a plane-parallel atmosphere/surface system. The RT computation by MarCh is based on matrix operations. To improve the code's computational efficiency, the forward model is currently undergoing acceleration through the exploration of different strategies for matrix operation and inversion, including numerical optimization, multi-threading/multi-processing techniques on a CPU. Implementation on a graphics processing unit (GPU) is also planned. Following a benchmarking study of the forward model, the performance of MarCh in aerosol and surface retrieval is being tested. With an optimized algorithm, we started from aerosol optical depth and surface retrieval using imagery acquired by Airborne Multiangle SpectroPolarimetric Imager (AirMSPI) over Fresno, CA. Aerosol properties including concentration and size distribution of different species provided by the Weather Research and Forecasting (WRF)-Chem model were used to constrain the retrieval and reduce the parameter space. The assumptions of spectral invariance in the angular shape of surface bidirectional reflectance factors (BRFs) and the magnitude of polarized surface BRFs were tested. The aerosol and surface properties are then relaxed in a stepwise way to refine the aerosol retrieval results and enable comparison with independent retrievals obtained from a collocated AErosol RObotic NETwork (AERONET) station.
18. Efficient search and responsiveness trade-offs in a Markov chain model of evolution in dynamic environments.
PubMed
Menezes, Amor A; Kabamba, Pierre T
2016-06-01
Motivated by the desire to study evolutionary responsiveness in fluctuating environments, and by the current interest in analyses of evolution that merge notions of fitness maximization with dynamical systems concepts such as Lyapunov functions, this paper models natural evolution with a simple stochastic dynamical system that can be represented as a Markov chain. The process maximizes fitness globally via search and has links to information and entropy. These links suggest that a possible rationale for evolution with the exponential fitness functions observed in nature is that of optimally-efficient search in a dynamic environment, which represents the quickest trade-off of prior information about the genotype search space for search effort savings after an environment perturbation. A Lyapunov function is also provided that relates the stochastic dynamical system model with search information, and the model shows that evolution is not gradient-based but dwells longer on more fit outcomes. The model further indicates that tuning the amount of selection trades off environment responsiveness with the time to reach fit outcomes, and that excessive selection causes a loss of responsiveness, a result that is validated by the literature and impacts efforts in directed evolution. PMID:26976482
19. Detection and prediction of land cover changes using Markov chain model in semi-arid rangeland in western Iran.
PubMed
Fathizad, Hassan; Rostami, Noredin; Faramarzi, Marzban
2015-10-01
The study of changes and destruction rate in the previous years as well as the possibility of prediction of these changes in the following years has a key role in optimal planning, controlling, and restricting non-normative changes in the future. This research was approached to detecting land use/cover changes (1985-2007) and to forecast the changes in the future (2021) use of multitemporal satellite imagery in semi-arid area in western Iran. A supervised classification of multilayer perceptron (MLP) was applied for detecting land use changes. The study area was classified into five classes, those of forest, rangeland, agriculture, residential, and barren lands. The change detection analysis indicated a decreasing trend in forest cover by 30.42%, while other land uses were increased during 1985 to 2007. The land use changes were predicted using Markov chain model for 2021. The model was calibrated by comparing the simulated map with the real detected classes of land cover in 2007. Then, for further model processing, an acceptable accuracy at 83% was achieved between them. Finally, land use changes were predicted by using transition matrix derived from calibrated approach. The findings of this study demonstrate a rapid change in land use/cover for the coming years. Transforming the forest into other land uses especially rangeland and cropland is the main land cover changes in the future. Therefore, the planning of protection and restoration of forest cover should be an essential program for decision-makers in the study area. PMID:26373304
20. MODELING PAVEMENT DETERIORATION PROCESSES BY POISSON HIDDEN MARKOV MODELS
Nam, Le Thanh; Kaito, Kiyoyuki; Kobayashi, Kiyoshi; Okizuka, Ryosuke
In pavement management, it is important to estimate lifecycle cost, which is composed of the expenses for repairing local damages, including potholes, and repairing and rehabilitating the surface and base layers of pavements, including overlays. In this study, a model is produced under the assumption that the deterioration process of pavement is a complex one that includes local damages, which occur frequently, and the deterioration of the surface and base layers of pavement, which progresses slowly. The variation in pavement soundness is expressed by the Markov deterioration model and the Poisson hidden Markov deterioration model, in which the frequency of local damage depends on the distribution of pavement soundness, is formulated. In addition, the authors suggest a model estimation method using the Markov Chain Monte Carlo (MCMC) method, and attempt to demonstrate the applicability of the proposed Poisson hidden Markov deterioration model by studying concrete application cases.
1. Static and dynamic properties of tethered chains at adsorbing surfaces: A Monte Carlo study
Descas, Radu; Sommer, Jens-Uwe; Blumen, Alexander
2004-05-01
We present extensive Monte Carlo simulations of tethered chains of length N on adsorbing surfaces, considering the dilute case in good solvents, and analyze our results using scaling arguments. We focus on the mean number M of chain contacts with the adsorbing wall, on the chain's extension (the radius of gyration) perpendicular and parallel to the adsorbing surface, on the probability distribution of the free end and on the density profile for all monomers. At the critical adsorption strength ɛc one has Mc˜Nφ, and we find (using the above results) as best candidate φ to equal 0.59. However, slight changes in the estimation of ɛc lead to large deviations in the resulting φ; this might be a possible reason for the difference in the φ values reported in the literature. We also investigate the dynamical scaling behavior at ɛc, by focusing on the end-to-end correlation function and on the correlation function of monomers adsorbed at the wall. We find that at ɛc the dynamic scaling exponent a (which describes the relaxation time of the chain as a function of N) is the same as that of free chains. Furthermore, we find that for tethered chains the modes perpendicular to the surface relax quicker than those parallel to it, which may be seen as a splitting in the relaxation spectrum.
2. A clustering approach for estimating parameters of a profile hidden Markov model.
PubMed
Aghdam, Rosa; Pezeshk, Hamid; Malekpour, Seyed Amir; Shemehsavar, Soudabeh; Eslahchi, Changiz
2013-01-01
A Profile Hidden Markov Model (PHMM) is a standard form of a Hidden Markov Models used for modeling protein and DNA sequence families based on multiple alignment. In this paper, we implement Baum-Welch algorithm and the Bayesian Monte Carlo Markov Chain (BMCMC) method for estimating parameters of small artificial PHMM. In order to improve the prediction accuracy of the estimation of the parameters of the PHMM, we classify the training data using the weighted values of sequences in the PHMM then apply an algorithm for estimating parameters of the PHMM. The results show that the BMCMC method performs better than the Maximum Likelihood estimation. PMID:23865165
3. Changes in mangrove species assemblages and future prediction of the Bangladesh Sundarbans using Markov chain model and cellular automata.
PubMed
Mukhopadhyay, Anirban; Mondal, Parimal; Barik, Jyotiskona; Chowdhury, S M; Ghosh, Tuhin; Hazra, Sugata
2015-06-01
The composition and assemblage of mangroves in the Bangladesh Sundarbans are changing systematically in response to several environmental factors. In order to understand the impact of the changing environmental conditions on the mangrove forest, species composition maps for the years 1985, 1995 and 2005 were studied. In the present study, 1985 and 1995 species zonation maps were considered as base data and the cellular automata-Markov chain model was run to predict the species zonation for the year 2005. The model output was validated against the actual dataset for 2005 and calibrated. Finally, using the model, mangrove species zonation maps for the years 2025, 2055 and 2105 have been prepared. The model was run with the assumption that the continuation of the current tempo and mode of drivers of environmental factors (temperature, rainfall, salinity change) of the last two decades will remain the same in the next few decades. Present findings show that the area distribution of the following species assemblages like Goran (Ceriops), Sundari (Heritiera), Passur (Xylocarpus), and Baen (Avicennia) would decrease in the descending order, whereas the area distribution of Gewa (Excoecaria), Keora (Sonneratia) and Kankra (Bruguiera) dominated assemblages would increase. The spatial distribution of projected mangrove species assemblages shows that more salt tolerant species will dominate in the future; which may be used as a proxy to predict the increase of salinity and its spatial variation in Sundarbans. Considering the present rate of loss of forest land, 17% of the total mangrove cover is predicted to be lost by the year 2105 with a significant loss of fresh water loving mangroves and related ecosystem services. This paper describes a unique approach to assess future changes in species composition and future forest zonation in mangroves under the 'business as usual' scenario of climate change. PMID:25719448
4. Analyses of rainfall using probability distribution and Markov chain models for crop planning in Daspalla region in Odisha, India
Mandal, K. G.; Padhi, J.; Kumar, A.; Ghosh, S.; Panda, D. K.; Mohanty, R. K.; Raychaudhuri, M.
2015-08-01
Rainfed agriculture plays and will continue to play a dominant role in providing food and livelihoods for an increasing world population. Rainfall analyses are helpful for proper crop planning under changing environment in any region. Therefore, in this paper, an attempt has been made to analyse 16 years of rainfall (1995-2010) at the Daspalla region in Odisha, eastern India for prediction using six probability distribution functions, forecasting the probable date of onset and withdrawal of monsoon, occurrence of dry spells by using Markov chain model and finally crop planning for the region. For prediction of monsoon and post-monsoon rainfall, log Pearson type III and Gumbel distribution were the best-fit probability distribution functions. The earliest and most delayed week of the onset of rainy season was the 20th standard meteorological week (SMW) (14th-20th May) and 25th SMW (18th-24th June), respectively. Similarly, the earliest and most delayed week of withdrawal of rainfall was the 39th SMW (24th-30th September) and 47th SMW (19th-25th November), respectively. The longest and shortest length of rainy season was 26 and 17 weeks, respectively. The chances of occurrence of dry spells are high from the 1st-22nd SMW and again the 42nd SMW to the end of the year. The probability of weeks (23rd-40th SMW) remaining wet varies between 62 and 100 % for the region. Results obtained through this analysis would be utilised for agricultural planning and mitigation of dry spells at the Daspalla region in Odisha, India.
5. Case studies of aerosol and ocean color retrieval using a Markov chain radiative transfer model and AirMSPI measurements
Xu, F.; Diner, D. J.; Seidel, F. C.; Dubovik, O.; Zhai, P.
2014-12-01
A vector Markov chain radiative transfer method was developed for forward modeling of radiance and polarization fields in a coupled atmosphere-ocean system. The method was benchmarked against an independent Successive Orders of Scattering code and linearized through the use of Jacobians. Incorporated with the multi-patch optimization algorithm and look-up-table method, simultaneous aerosol and ocean color retrievals were performed using imagery acquired by the Airborne Multiangle SpectroPolarimetric Imager (AirMSPI) when it was operated in step-and-stare mode with 9 viewing angles ranging between ±67°. Data from channels near 355, 380, 445, 470*, 555, 660*, and 865* nm were used in the retrievals, where the asterisk denotes the polarimetric bands. Retrievals were run for AirMSPI overflights over Southern California and Monterey Bay, CA. For the relatively high aerosol optical depth (AOD) case (~0.28 at 550 nm), the retrieved aerosol concentration, size distribution, water-leaving radiance, and chlorophyll concentration were compared to those reported by the USC SeaPRISM AERONET-OC site off the coast of Southern California on 6 February 2013. For the relatively low AOD case (~0.08 at 550 nm), the retrieved aerosol concentration and size distribution were compared to those reported by the Monterey Bay AERONET site on 28 April 2014. Further, we evaluate the benefits of multi-angle and polarimetric observations by performing the retrievals using (a) all view angles and channels; (b) all view angles but radiances only (no polarization); (c) the nadir view angle only with both radiance and polarization; and (d) the nadir view angle without polarization. Optimized retrievals using different initial guesses were performed to provide a measure of retrieval uncertainty. Removal of multi-angular or polarimetric information resulted in increases in both parameter uncertainty and systematic bias. Potential accuracy improvements afforded by applying constraints on the surface
6. Drift of a polymer chain in a porous medium —A Monte Carlo study
Avramova, K.; Milchev, A.
2002-01-01
We investigate the drift of an end-labeled telehelic polymer chain in a frozen disordered medium under the action of a constant force applied to the one end of the macromolecule by means of an off-lattice bead spring Monte Carlo model. The length of the polymers N is varied in the range 8chains can be interpreted as described by a scaling theory based on Pincus blobs. The variation of drag velocity with C in this interval of field intensities is qualitatively described by the law of Mackie-Meares. The threshold field intensity B_ab{c} itself is found to decrease linearly with C.
7. Accelerating population balance-Monte Carlo simulation for coagulation dynamics from the Markov jump model, stochastic algorithm and GPU parallel computing
Xu, Zuwei; Zhao, Haibo; Zheng, Chuguang
2015-01-01
This paper proposes a comprehensive framework for accelerating population balance-Monte Carlo (PBMC) simulation of particle coagulation dynamics. By combining Markov jump model, weighted majorant kernel and GPU (graphics processing unit) parallel computing, a significant gain in computational efficiency is achieved. The Markov jump model constructs a coagulation-rule matrix of differentially-weighted simulation particles, so as to capture the time evolution of particle size distribution with low statistical noise over the full size range and as far as possible to reduce the number of time loopings. Here three coagulation rules are highlighted and it is found that constructing appropriate coagulation rule provides a route to attain the compromise between accuracy and cost of PBMC methods. Further, in order to avoid double looping over all simulation particles when considering the two-particle events (typically, particle coagulation), the weighted majorant kernel is introduced to estimate the maximum coagulation rates being used for acceptance-rejection processes by single-looping over all particles, and meanwhile the mean time-step of coagulation event is estimated by summing the coagulation kernels of rejected and accepted particle pairs. The computational load of these fast differentially-weighted PBMC simulations (based on the Markov jump model) is reduced greatly to be proportional to the number of simulation particles in a zero-dimensional system (single cell). Finally, for a spatially inhomogeneous multi-dimensional (multi-cell) simulation, the proposed fast PBMC is performed in each cell, and multiple cells are parallel processed by multi-cores on a GPU that can implement the massively threaded data-parallel tasks to obtain remarkable speedup ratio (comparing with CPU computation, the speedup ratio of GPU parallel computing is as high as 200 in a case of 100 cells with 10 000 simulation particles per cell). These accelerating approaches of PBMC are
8. Accelerating population balance-Monte Carlo simulation for coagulation dynamics from the Markov jump model, stochastic algorithm and GPU parallel computing
SciTech Connect
Xu, Zuwei; Zhao, Haibo Zheng, Chuguang
2015-01-15
This paper proposes a comprehensive framework for accelerating population balance-Monte Carlo (PBMC) simulation of particle coagulation dynamics. By combining Markov jump model, weighted majorant kernel and GPU (graphics processing unit) parallel computing, a significant gain in computational efficiency is achieved. The Markov jump model constructs a coagulation-rule matrix of differentially-weighted simulation particles, so as to capture the time evolution of particle size distribution with low statistical noise over the full size range and as far as possible to reduce the number of time loopings. Here three coagulation rules are highlighted and it is found that constructing appropriate coagulation rule provides a route to attain the compromise between accuracy and cost of PBMC methods. Further, in order to avoid double looping over all simulation particles when considering the two-particle events (typically, particle coagulation), the weighted majorant kernel is introduced to estimate the maximum coagulation rates being used for acceptance–rejection processes by single-looping over all particles, and meanwhile the mean time-step of coagulation event is estimated by summing the coagulation kernels of rejected and accepted particle pairs. The computational load of these fast differentially-weighted PBMC simulations (based on the Markov jump model) is reduced greatly to be proportional to the number of simulation particles in a zero-dimensional system (single cell). Finally, for a spatially inhomogeneous multi-dimensional (multi-cell) simulation, the proposed fast PBMC is performed in each cell, and multiple cells are parallel processed by multi-cores on a GPU that can implement the massively threaded data-parallel tasks to obtain remarkable speedup ratio (comparing with CPU computation, the speedup ratio of GPU parallel computing is as high as 200 in a case of 100 cells with 10 000 simulation particles per cell). These accelerating approaches of PBMC are
9. Intraglobular structures in multiblock copolymer chains from a Monte Carlo simulation
Lewandowski, K.; Banaszak, M.
2011-07-01
Multiblock copolymer chains in implicit nonselective solvents are studied by using a Monte Carlo method, which employs a parallel tempering algorithm. Chains consisting of 120A and 120B monomers, arranged in three distinct microarchitectures: (10-10)12,(6-6)20, and (3-3)40, collapse to globular states upon cooling, as expected. By varying both the reduced temperature T* and the compatibility between monomers ω, numerous intraglobular structures are obtained: diclusters (handshake, spiral, torus with a core, etc.), triclusters, and n clusters with n>3 (lamellar and other), which are reminiscent of the block copolymer nanophases for spherically confined geometries. Phase diagrams for various chains in the (T*,ω) space are mapped. The structure factor S(k), for a selected microarchitecture and ω, is calculated. Since S(k) can be measured in scattering experiments, it can be used to relate simulation results to an experiment. Self-assembly in those systems is interpreted in terms of competition between minimization of the interfacial area separating different types of monomers and minimization of contacts between chain and solvent. Finally, the relevance of this model to the protein folding is addressed.
10. Quantum speedup of Monte Carlo methods
PubMed Central
Montanaro, Ashley
2015-01-01
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently. PMID:26528079
11. Markov information sources
NASA Technical Reports Server (NTRS)
Massey, J. L.
1975-01-01
A regular Markov source is defined as the output of a deterministic, but noisy, channel driven by the state sequence of a regular finite-state Markov chain. The rate of such a source is the per letter uncertainty of its digits. The well-known result that the rate of a unifilar regular Markov source is easily calculable is demonstrated, where unifilarity means that the present state of the Markov chain and the next output of the deterministic channel uniquely determine the next state. At present, there is no known method to calculate the rate of a nonunifilar source. Two tentative approaches to this unsolved problem are given, namely source identical twins and the master-slave source, which appear to shed some light on the question of rate calculation for a nonunifilar source.
12. Stretching semiflexible polymer chains: evidence for the importance of excluded volume effects from Monte Carlo simulation.
PubMed
Hsu, Hsiao-Ping; Binder, Kurt
2012-01-14
Semiflexible macromolecules in dilute solution under very good solvent conditions are modeled by self-avoiding walks on the simple cubic lattice (d = 3 dimensions) and square lattice (d = 2 dimensions), varying chain stiffness by an energy penalty ε(b) for chain bending. In the absence of excluded volume interactions, the persistence length l(p) of the polymers would then simply be l(p) = l(b)(2d - 2)(-1)q(b) (-1) with q(b) = exp(-ε(b)/k(B)T), the bond length l(b) being the lattice spacing, and k(B)T is the thermal energy. Using Monte Carlo simulations applying the pruned-enriched Rosenbluth method (PERM), both q(b) and the chain length N are varied over a wide range (0.005 ≤ q(b) ≤ 1, N ≤ 50,000), and also a stretching force f is applied to one chain end (fixing the other end at the origin). In the absence of this force, in d = 2 a single crossover from rod-like behavior (for contour lengths less than l(p)) to swollen coils occurs, invalidating the Kratky-Porod model, while in d = 3 a double crossover occurs, from rods to Gaussian coils (as implied by the Kratky-Porod model) and then to coils that are swollen due to the excluded volume interaction. If the stretching force is applied, excluded volume interactions matter for the force versus extension relation irrespective of chain stiffness in d = 2, while theories based on the Kratky-Porod model are found to work in d = 3 for stiff chains in an intermediate regime of chain extensions. While for q(b) ≪ 1 in this model a persistence length can be estimated from the initial decay of bond-orientational correlations, it is argued that this is not possible for more complex wormlike chains (e.g., bottle-brush polymers). Consequences for the proper interpretation of experiments are briefly discussed. PMID:22260610
13. Weighted-indexed semi-Markov models for modeling financial returns
D'Amico, Guglielmo; Petroni, Filippo
2012-07-01
In this paper we propose a new stochastic model based on a generalization of semi-Markov chains for studying the high frequency price dynamics of traded stocks. We assume that the financial returns are described by a weighted-indexed semi-Markov chain model. We show, through Monte Carlo simulations, that the model is able to reproduce important stylized facts of financial time series such as the first-passage-time distributions and the persistence of volatility. The model is applied to data from the Italian and German stock markets from 1 January 2007 until the end of December 2010.
14. Insight into earthquake sequencing: analysis and interpretation of time-series constructed from the directed graph of the Markov chain model
Cavers, M. S.; Vasudevan, K.
2015-02-01
Directed graph representation of a Markov chain model to study global earthquake sequencing leads to a time-series of state-to-state transition probabilities that includes the spatio-temporally linked recurrent events in the record-breaking sense. A state refers to a configuration comprised of zones with either the occurrence or non-occurrence of an earthquake in each zone in a pre-determined time interval. Since the time-series is derived from non-linear and non-stationary earthquake sequencing, we use known analysis methods to glean new information. We apply decomposition procedures such as ensemble empirical mode decomposition (EEMD) to study the state-to-state fluctuations in each of the intrinsic mode functions. We subject the intrinsic mode functions, the orthogonal basis set derived from the time-series using the EEMD, to a detailed analysis to draw information-content of the time-series. Also, we investigate the influence of random-noise on the data-driven state-to-state transition probabilities. We consider a second aspect of earthquake sequencing that is closely tied to its time-correlative behavior. Here, we extend the Fano factor and Allan factor analysis to the time-series of state-to state transition frequencies of a Markov chain. Our results support not only the usefulness the intrinsic mode functions in understanding the time-series but also the presence of power-law behaviour exemplified by the Fano factor and the Allan factor.
15. Diagram of states and morphologies of flexible-semiflexible copolymer chains: A Monte Carlo simulation
Zablotskiy, Sergey V.; Martemyanova, Julia A.; Ivanov, Viktor A.; Paul, Wolfgang
2016-06-01
A single copolymer chain consisting of multiple flexible (F) and semiflexible (S) blocks has been studied using a continuum bead-spring model by Stochastic Approximation Monte Carlo simulations, which determine the density of states of the model. The only difference between F and S blocks is the intramolecular bending potential, all non-bonded interactions are equal. The state diagrams for this class of models display multiple nematic phases in the collapsed state, characterized through a demixing of the blocks of different stiffness and orientational ordering of the stiff blocks. We observe dumbbell-like morphologies, lamellar phases, and for the larger block lengths also Saturn-like structures with a core of flexible segments and the stiff segments forming a ring around the core.
16. Diagram of states and morphologies of flexible-semiflexible copolymer chains: A Monte Carlo simulation.
PubMed
Zablotskiy, Sergey V; Martemyanova, Julia A; Ivanov, Viktor A; Paul, Wolfgang
2016-06-28
A single copolymer chain consisting of multiple flexible (F) and semiflexible (S) blocks has been studied using a continuum bead-spring model by Stochastic Approximation Monte Carlo simulations, which determine the density of states of the model. The only difference between F and S blocks is the intramolecular bending potential, all non-bonded interactions are equal. The state diagrams for this class of models display multiple nematic phases in the collapsed state, characterized through a demixing of the blocks of different stiffness and orientational ordering of the stiff blocks. We observe dumbbell-like morphologies, lamellar phases, and for the larger block lengths also Saturn-like structures with a core of flexible segments and the stiff segments forming a ring around the core. PMID:27369540
17. Reference hypernetted chain theory for ferrofluid bilayer: distribution functions compared with Monte Carlo.
PubMed
Polyakov, Evgeny A; Vorontsov-Velyaminov, Pavel N
2014-08-28
Properties of ferrofluid bilayer (modeled as a system of two planar layers separated by a distance h and each layer carrying a soft sphere dipolar liquid) are calculated in the framework of inhomogeneous Ornstein-Zernike equations with reference hypernetted chain closure (RHNC). The bridge functions are taken from a soft sphere (1/r(12)) reference system in the pressure-consistent closure approximation. In order to make the RHNC problem tractable, the angular dependence of the correlation functions is expanded into special orthogonal polynomials according to Lado. The resulting equations are solved using the Newton-GRMES algorithm as implemented in the public-domain solver NITSOL. Orientational densities and pair distribution functions of dipoles are compared with Monte Carlo simulation results. A numerical algorithm for the Fourier-Hankel transform of any positive integer order on a uniform grid is presented. PMID:25173007
18. Monte Carlo methods in genetic analysis
SciTech Connect
Lin, Shili
1996-12-31
Many genetic analyses require computation of probabilities and likelihoods of pedigree data. With more and more genetic marker data deriving from new DNA technologies becoming available to researchers, exact computations are often formidable with standard statistical methods and computational algorithms. The desire to utilize as much available data as possible, coupled with complexities of realistic genetic models, push traditional approaches to their limits. These methods encounter severe methodological and computational challenges, even with the aid of advanced computing technology. Monte Carlo methods are therefore increasingly being explored as practical techniques for estimating these probabilities and likelihoods. This paper reviews the basic elements of the Markov chain Monte Carlo method and the method of sequential imputation, with an emphasis upon their applicability to genetic analysis. Three areas of applications are presented to demonstrate the versatility of Markov chain Monte Carlo for different types of genetic problems. A multilocus linkage analysis example is also presented to illustrate the sequential imputation method. Finally, important statistical issues of Markov chain Monte Carlo and sequential imputation, some of which are unique to genetic data, are discussed, and current solutions are outlined. 72 refs.
19. Monte Carlo studies of the temperature-dependent size of polyelectrolyte chains
Severin, Mattias
1995-08-01
We have performed off-lattice Monte Carlo simulations of isolated, short (N=40), fully ionized polyelectrolytes in the presence of a low molecular mass, monovalent salt in the concentration range 0.0<=C<=1.0 mol dm-3. The polyelectrolyte is modeled as a freely jointed chain of N hard spherical beads of radius a=2.0 Å. The mean-square end-to-end distance and the radius of gyration have been calculated as functions of the Bjerrum length Λ, where Λ=e2/ɛ0ɛrkT. \$1/ LAMBDA- is thus proportional to the temperature. The results show an interesting temperature dependence; at high temperatures the polyion size decreases with increasing temperature, which is to be expected from simple considerations of the en- ergy/entropy balance. On lowering the temperature, however, we have found that the polyion reaches a maximum size at a certain temperature, which depends on the salt concentration. Further cooling then results in a contraction of the chain. For low salt concentrations, the maximum size represents a rodlike configuration, and the polymer shows a coil-to-rod-to-coil transition as the temperature is increased. We suggest that this behavior is due to the increased screening at low temperatures. The Debye-Hückel approximation does not take into account the fact that for Λ/2a>1 Manning condensation will reduce the effective charge of the chain. We have therefore also incorporated this phenomenon into the model in an ad hoc fashion by reducing the charge of each band according to the Manning fraction.
20. Minimising biases in full configuration interaction quantum Monte Carlo.
PubMed
Vigor, W A; Spencer, J S; Bearpark, M J; Thom, A J W
2015-03-14
We show that Full Configuration Interaction Quantum Monte Carlo (FCIQMC) is a Markov chain in its present form. We construct the Markov matrix of FCIQMC for a two determinant system and hence compute the stationary distribution. These solutions are used to quantify the dependence of the population dynamics on the parameters defining the Markov chain. Despite the simplicity of a system with only two determinants, it still reveals a population control bias inherent to the FCIQMC algorithm. We investigate the effect of simulation parameters on the population control bias for the neon atom and suggest simulation setups to, in general, minimise the bias. We show a reweight ing scheme to remove the bias caused by population control commonly used in diffusion Monte Carlo [Umrigar et al., J. Chem. Phys. 99, 2865 (1993)] is effective and recommend its use as a post processing step. PMID:25770522
1. Monte Carlo simulations of a polymer chain conformation. The effectiveness of local moves algorithms and estimation of entropy.
PubMed
Mańka, Agnieszka; Nowicki, Waldemar; Nowicka, Grażyna
2013-09-01
A linear chain on a simple cubic lattice was simulated by the Metropolis Monte Carlo method using a combination of local and non-local chain modifications. Kink-jump, crankshaft, reptation and end-segment moves were used for local changes of the chain conformation, while for non-local chain rearrangements the "cut-and-paste" algorithm was employed. The statistics of local micromodifications was examined. An approximate method for estimating the conformational entropy of a polymer chain, based on the efficiency of the kink-jump motion respecting chain continuity and excluded volume constraints, was proposed. The method was tested by calculating the conformational entropy of the undisturbed chain, the chain under tension and in different solvent conditions (athermal, theta and poor) and also of the chain confined in a slit. The results of these test calculations are qualitatively consistent with expectations. Moreover, the obtained values of the conformational entropy of self avoiding chain with ends fixed over different separations, agree very well with the available literature data. PMID:23765038
2. An Application of Markov Chains and a Monte-Carlo Simulation to Decision-Making Behavior of an Educational Administrator
ERIC Educational Resources Information Center
Yoda, Koji
1973-01-01
Develops models to systematically forecast the tendency of an educational administrator in charge of personnel selection processes to shift from one decision strategy to another under generally stable environmental conditions. Urges further research on these processes by educational planners. (JF)
3. A Mixture Rasch Model with a Covariate: A Simulation Study via Bayesian Markov Chain Monte Carlo Estimation
ERIC Educational Resources Information Center
Dai, Yunyun
2013-01-01
Mixtures of item response theory (IRT) models have been proposed as a technique to explore response patterns in test data related to cognitive strategies, instructional sensitivity, and differential item functioning (DIF). Estimation proves challenging due to difficulties in identification and questions of effect size needed to recover underlying…
4. A Markov Chain Monte Carlo Approach for Joint Inference of Population Structure and Inbreeding Rates From Multilocus Genotype Data
PubMed Central
Gao, Hong; Williamson, Scott; Bustamante, Carlos D.
2007-01-01
Nonrandom mating induces correlations in allelic states within and among loci that can be exploited to understand the genetic structure of natural populations (Wright 1965). For many species, it is of considerable interest to quantify the contribution of two forms of nonrandom mating to patterns of standing genetic variation: inbreeding (mating among relatives) and population substructure (limited dispersal of gametes). Here, we extend the popular Bayesian clustering approach STRUCTURE (Pritchard et al. 2000) for simultaneous inference of inbreeding or selfing rates and population-of-origin classification using multilocus genetic markers. This is accomplished by eliminating the assumption of Hardy–Weinberg equilibrium within clusters and, instead, calculating expected genotype frequencies on the basis of inbreeding or selfing rates. We demonstrate the need for such an extension by showing that selfing leads to spurious signals of population substructure using the standard STRUCTURE algorithm with a bias toward spurious signals of admixture. We gauge the performance of our method using extensive coalescent simulations and demonstrate that our approach can correct for this bias. We also apply our approach to understanding the population structure of the wild relative of domesticated rice, Oryza rufipogon, an important partially selfing grass species. Using a sample of n = 16 individuals sequenced at 111 random loci, we find strong evidence for existence of two subpopulations, which correlates well with geographic location of sampling, and estimate selfing rates for both groups that are consistent with estimates from experimental data (s ≈ 0.48–0.70). PMID:17483417
5. 21CMMC: Parallelized Monte Carlo Markov Chain analysis tool for the epoch of reionization (EoR)
2016-08-01
21CMMC is an efficient Python sampler of the semi-numerical reionization simulation code 21cmFAST (ascl:1102.023). It can recover constraints on astrophysical parameters from current or future 21 cm EoR experiments, accommodating a variety of EoR models, as well as priors on individual model parameters and the reionization history. By studying the resulting impact on the EoR astrophysical constraints, 21CMMC can be used to optimize foreground cleaning algorithms; interferometer designs; observing strategies; alternate statistics characterizing the 21cm signal; and synergies with other observational programs.
6. Improvement and comparison of likelihood functions for model calibration and parameter uncertainty analysis within a Markov chain Monte Carlo scheme
Cheng, Qin-Bo; Chen, Xi; Xu, Chong-Yu; Reinhardt-Imjela, Christian; Schulte, Achim
2014-11-01
In this study, the likelihood functions for uncertainty analysis of hydrological models are compared and improved through the following steps: (1) the equivalent relationship between the Nash-Sutcliffe Efficiency coefficient (NSE) and the likelihood function with Gaussian independent and identically distributed residuals is proved; (2) a new estimation method of the Box-Cox transformation (BC) parameter is developed to improve the effective elimination of the heteroscedasticity of model residuals; and (3) three likelihood functions-NSE, Generalized Error Distribution with BC (BC-GED) and Skew Generalized Error Distribution with BC (BC-SGED)-are applied for SWAT-WB-VSA (Soil and Water Assessment Tool - Water Balance - Variable Source Area) model calibration in the Baocun watershed, Eastern China. Performances of calibrated models are compared using the observed river discharges and groundwater levels. The result shows that the minimum variance constraint can effectively estimate the BC parameter. The form of the likelihood function significantly impacts on the calibrated parameters and the simulated results of high and low flow components. SWAT-WB-VSA with the NSE approach simulates flood well, but baseflow badly owing to the assumption of Gaussian error distribution, where the probability of the large error is low, but the small error around zero approximates equiprobability. By contrast, SWAT-WB-VSA with the BC-GED or BC-SGED approach mimics baseflow well, which is proved in the groundwater level simulation. The assumption of skewness of the error distribution may be unnecessary, because all the results of the BC-SGED approach are nearly the same as those of the BC-GED approach.
7. An Efficient Independence Sampler for Updating Branches in Bayesian Markov chain Monte Carlo Sampling of Phylogenetic Trees.
PubMed
Aberer, Andre J; Stamatakis, Alexandros; Ronquist, Fredrik
2016-01-01
Sampling tree space is the most challenging aspect of Bayesian phylogenetic inference. The sheer number of alternative topologies is problematic by itself. In addition, the complex dependency between branch lengths and topology increases the difficulty of moving efficiently among topologies. Current tree proposals are fast but sample new trees using primitive transformations or re-mappings of old branch lengths. This reduces acceptance rates and presumably slows down convergence and mixing. Here, we explore branch proposals that do not rely on old branch lengths but instead are based on approximations of the conditional posterior. Using a diverse set of empirical data sets, we show that most conditional branch posteriors can be accurately approximated via a [Formula: see text] distribution. We empirically determine the relationship between the logarithmic conditional posterior density, its derivatives, and the characteristics of the branch posterior. We use these relationships to derive an independence sampler for proposing branches with an acceptance ratio of ~90% on most data sets. This proposal samples branches between 2× and 3× more efficiently than traditional proposals with respect to the effective sample size per unit of runtime. We also compare the performance of standard topology proposals with hybrid proposals that use the new independence sampler to update those branches that are most affected by the topological change. Our results show that hybrid proposals can sometimes noticeably decrease the number of generations necessary for topological convergence. Inconsistent performance gains indicate that branch updates are not the limiting factor in improving topological convergence for the currently employed set of proposals. However, our independence sampler might be essential for the construction of novel tree proposals that apply more radical topology changes. PMID:26231183
8. Monte Carlo simulations to study the effect of chain stiffness on static and dynamic properties of polymer melts
Khanal, Kiran; Luettmer-Strathmann, Jutta
2009-04-01
Static and dynamic properties of polymers are affected by the stiffness of the chains. In this work, we investigate structural and thermodynamic properties of a lattice model for semiflexible polymer chains. The model is an extension of Shaffer's bond- fluctuation model and includes attractive interactions between monomers and an adjustable bending penalty that determines the Kuhn segment length. This allows us to model melts of flexible and semiflexible chains. For this work, we performed Monte Carlo simulations for polymer melts with a range of bending parameters and densities. Results for chain dimensions show that the Kuhn segment length increases monotonously with the bending penalty and has a linear dependence for a range of bending parameters. Results for self diffusion constants show that the translational mobility is strongly reduced by increasing chain stiffness. We also investigate equation-of-state properties of the melts.
9. Metrics for Labeled Markov Systems
NASA Technical Reports Server (NTRS)
1999-01-01
Partial Labeled Markov Chains are simultaneously generalizations of process algebra and of traditional Markov chains. They provide a foundation for interacting discrete probabilistic systems, the interaction being synchronization on labels as in process algebra. Existing notions of process equivalence are too sensitive to the exact probabilities of various transitions. This paper addresses contextual reasoning principles for reasoning about more robust notions of "approximate" equivalence between concurrent interacting probabilistic systems. The present results indicate that:We develop a family of metrics between partial labeled Markov chains to formalize the notion of distance between processes. We show that processes at distance zero are bisimilar. We describe a decision procedure to compute the distance between two processes. We show that reasoning about approximate equivalence can be done compositionally by showing that process combinators do not increase distance. We introduce an asymptotic metric to capture asymptotic properties of Markov chains; and show that parallel composition does not increase asymptotic distance.
10. Monte Carlo simulation of the data acquisition chain of scintillation detectors
SciTech Connect
Binda, F.; Ericsson, G.; Hellesen, C.; Hjalmarsson, A.; Eriksson, J.; Skiba, M.; Conroy, S.; Weiszflog, M.
2014-08-21
The good performance of a detector can be strongly affected by the instrumentation used to acquire the data. The possibility of anticipating how the acquisition chain will affect the signal can help in finding the best solution among different set-ups. In this work we developed a Monte Carlo code that aims to simulate the effect of the various components of a digital Data Acquisition system (DAQ) applied to scintillation detectors. The components included in the model are: the scintillator, the photomultiplier tube (PMT), the signal cable and the digitizer. We benchmarked the code against real data acquired with a NE213 scintillator, comparing simulated and real signal pulses induced by gamma-ray interaction. Then we studied the dependence of the energy resolution of a pulse height spectrum (PHS) on the sampling frequency and the bit resolution of the digitizer. We found that exceeding some values of the sampling frequency and the bit resolution improves only marginally the performance of the system. The method can be applied for the study of various detector systems relevant for nuclear techniques, such as in fusion diagnostics.
11. Monte Carlo simulation of the data acquisition chain of scintillation detectors
Binda, F.; Ericsson, G.; Hellesen, C.; Hjalmarsson, A.; Eriksson, J.; Skiba, M.; Conroy, S.; Weiszflog, M.
2014-08-01
The good performance of a detector can be strongly affected by the instrumentation used to acquire the data. The possibility of anticipating how the acquisition chain will affect the signal can help in finding the best solution among different set-ups. In this work we developed a Monte Carlo code that aims to simulate the effect of the various components of a digital Data Acquisition system (DAQ) applied to scintillation detectors. The components included in the model are: the scintillator, the photomultiplier tube (PMT), the signal cable and the digitizer. We benchmarked the code against real data acquired with a NE213 scintillator, comparing simulated and real signal pulses induced by gamma-ray interaction. Then we studied the dependence of the energy resolution of a pulse height spectrum (PHS) on the sampling frequency and the bit resolution of the digitizer. We found that exceeding some values of the sampling frequency and the bit resolution improves only marginally the performance of the system. The method can be applied for the study of various detector systems relevant for nuclear techniques, such as in fusion diagnostics.
12. Semi-Markov Graph Dynamics
PubMed Central
Raberto, Marco; Rapallo, Fabio; Scalas, Enrico
2011-01-01
In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting process. In simple words, this means that the chain transitions occur at random time instants called epochs. The model is quite rich and its possible connections with algebraic geometry are briefly discussed. Moreover, for the sake of simplicity, we focus on the space of undirected graphs with a fixed number of nodes. However, in an example, we present an interbank market model where it is meaningful to use directed graphs or even weighted graphs. PMID:21887245
13. A Bayesian Markov-Chain-Based Heteroscedastic Regression Model for the Analysis of 18O-Labeled Mass Spectra
Zhu, Qi; Burzykowski, Tomasz
2011-03-01
To reduce the influence of the between-spectra variability on the results of peptide quantification, one can consider the 18O-labeling approach. Ideally, with such labeling technique, a mass shift of 4 Da of the isotopic distributions of peptides from the labeled sample is induced, which allows one to distinguish the two samples and to quantify the relative abundance of the peptides. It is worth noting, however, that the presence of small quantities of 16O and 17O atoms during the labeling step can cause incomplete labeling. In practice, ignoring incomplete labeling may result in the biased estimation of the relative abundance of the peptide in the compared samples. A Markov model was developed to address this issue (Zhu, Valkenborg, Burzykowski. J. Proteome Res. 9, 2669-2677, 2010). The model assumed that the peak intensities were normally distributed with heteroscedasticity using a power-of-the-mean variance funtion. Such a dependence has been observed in practice. Alternatively, we formulate the model within the Bayesian framework. This opens the possibility to further extend the model by the inclusion of random effects that can be used to capture the biological/technical variability of the peptide abundance. The operational characteristics of the model were investigated by applications to real-life mass-spectrometry data sets and a simulation study.
14. A Markov chain analysis of the movements of juvenile salmonids in the forebay of McNary Dam, Washington and Oregon, 2006-09
USGS Publications Warehouse
Adams, Noah S.; Hatton, Tyson W.
2012-01-01
Passage and survival data for yearling and subyearling Chinook salmon and juvenile steelhead were collected at McNary Dam between 2006 and 2009. These data have provided critical information for resource managers to implement structural and operational changes designed to improve the survival of juvenile salmonids as they migrate past the dam. Much of the information collected at McNary Dam was in the form of three-dimensional tracks of fish movements in the forebay. These data depicted the behavior of multiple species (in three dimensions) during different diel periods, spill conditions, powerhouse operations, and test configurations of the surface bypass structures (temporary spillway weirs; TSWs). One of the challenges in reporting three-dimensional results is presenting the information in a manner that allows interested parties to summarize the behavior of many fish over many different conditions across multiple years. To accomplish this, we investigated the feasibility of using a Markov chain analysis to characterize fish movement patterns in the forebay of McNary Dam. The Markov chain analysis is one way that can be used to summarize numerically the behavior of fish in the forebay. Numerically summarizing the behavior of juvenile salmonids in the forebay of McNary Dam using the Markov chain analysis allowed us to confirm what had been previously summarized using visualization software. For example, proportions of yearling and subyearling Chinook salmon passing the three powerhouse areas was often greater in the southern and middle areas, compared to the northern area. The opposite generally was observed for steelhead. Results of this analysis also allowed us to confirm and quantify the extent of milling behavior that had been observed for steelhead. For fish that were first detected in the powerhouse region, less than 0.10 of the steelhead, on average, passed within each of the powerhouse areas. Instead, steelhead transitioned to adjoining areas in the
15. Characterization of environmental quality of forest fragments changes in Jundiaí-Mirim river basin-Brazil using the Markov Chain model
Hasimoto Fengler, Felipe; Leite de Moraes, Jener Fernando; Irio Ribeiro, Admilson; Peche Filho, Afonso; Araujo de Medeiros, Gerson; Baldin Damame, Desirée; Márcia Longo, Regina
2015-04-01
In Brazil is common practice the concurrency of large urban centers water catchment in distant sites. There's no policy to preserve strategic springs in the urban territory. Thus, rural areas, located in the surrounds of municipals, usually provide water and others environment services to the population that reside on cities. The Jundiaí-Mirim river basin, located in the most urbanized state in Brazil, São Paulo, composes an interesting example of this situation. It is located in a rural area near large urban centers, with large industrial parks, near the capital of state. As result of expansion of the cities on its surrounds their lands have had a historic of monetary valorization, making its territories attractive to the housing market. Consequently, the region has an intense process of urbanization that resulted in an increasing environmental disturbance in the areas of natural vegetation. In the other hand, the watershed is the principal water supplier of Jundiaí city, and houses forest remaining of an important Biome in Brazil, the Atlantic Rain Forest. Given the need to preserve its water production capacity and the forest remnants there, this study modeled the environmental quality of forest fragments through indicators of disturbance and evaluated the changes that occur between 1972 and 2013 using the Markov Chain model. The environment quality was determined by nine indicators of environmental disturbance (distance of urban areas, roads, edge land use, size, distance of others forest fragments, land capacity of use, watershed forest cover, number of forest fragments in the watersheds, shape of the forest fragment), obtained by techniques of Geoprocessing, and integrated by Multicriteria Analysis. The Markov Chain model showed a constant tendency of deteriorating in natural vegetation environmental quality, attributed to the intense process of occupation of the river basin. The results showed a historical trend of transformation in forest fragments with
16. Uniaxial magnetic anisotropy of quasi-one-dimensional Fe chains on Pb/Si: A Monte Carlo simulation
Du, Hai-Feng; He, Wei; Liu, Hao-Liang; Sun, Da-Li; Fang, Ya-Peng; Gao, Jian-Hua; Zhang, Xiang-Qun; Cheng, Zhao-Hua
2010-10-01
Magnetic behaviors of Fe nanowires grown on 4° miscut Si(111) substrate with Pb buffer layers have been investigated by means of Monte Carlo method. A simple model is constructed, in which the Fe chains are assumed to be assemblies of single domain Fe nanoclusters with magnetostatic energy and exchange coupling energy. The coverage dependence of the magnetic ordering temperature TC of the system is discussed. By accurately calculating the magnetostatic energy of the Fe chains, the simulated results are in agreement with the experimental ones measured by in situ surface magneto-optical Kerr effect. In addition to the magnetostatic energy, the exchange coupling between the overlapping islands is also responsible for the ferromagnetic ordering of high coverage Fe chains at room temperature. Our model was able to predict the essential features of the system.
17. Multivariate longitudinal data analysis with mixed effects hidden Markov models.
PubMed
Raffa, Jesse D; Dubin, Joel A
2015-09-01
Multiple longitudinal responses are often collected as a means to capture relevant features of the true outcome of interest, which is often hidden and not directly measurable. We outline an approach which models these multivariate longitudinal responses as generated from a hidden disease process. We propose a class of models which uses a hidden Markov model with separate but correlated random effects between multiple longitudinal responses. This approach was motivated by a smoking cessation clinical trial, where a bivariate longitudinal response involving both a continuous and a binomial response was collected for each participant to monitor smoking behavior. A Bayesian method using Markov chain Monte Carlo is used. Comparison of separate univariate response models to the bivariate response models was undertaken. Our methods are demonstrated on the smoking cessation clinical trial dataset, and properties of our approach are examined through extensive simulation studies. PMID:25761965
18. Analysis of transtheoretical model of health behavioral changes in a nutrition intervention study--a continuous time Markov chain model with Bayesian approach.
PubMed
Ma, Junsheng; Chan, Wenyaw; Tsai, Chu-Lin; Xiong, Momiao; Tilley, Barbara C
2015-11-30
Continuous time Markov chain (CTMC) models are often used to study the progression of chronic diseases in medical research but rarely applied to studies of the process of behavioral change. In studies of interventions to modify behaviors, a widely used psychosocial model is based on the transtheoretical model that often has more than three states (representing stages of change) and conceptually permits all possible instantaneous transitions. Very little attention is given to the study of the relationships between a CTMC model and associated covariates under the framework of transtheoretical model. We developed a Bayesian approach to evaluate the covariate effects on a CTMC model through a log-linear regression link. A simulation study of this approach showed that model parameters were accurately and precisely estimated. We analyzed an existing data set on stages of change in dietary intake from the Next Step Trial using the proposed method and the generalized multinomial logit model. We found that the generalized multinomial logit model was not suitable for these data because it ignores the unbalanced data structure and temporal correlation between successive measurements. Our analysis not only confirms that the nutrition intervention was effective but also provides information on how the intervention affected the transitions among the stages of change. We found that, compared with the control group, subjects in the intervention group, on average, spent substantively less time in the precontemplation stage and were more/less likely to move from an unhealthy/healthy state to a healthy/unhealthy state. PMID:26123093
19. Markov chains-cellular automata modeling and multicriteria analysis of land cover change in the Lower Nhecolândia subregion of the Brazilian Pantanal wetland
Bacani, Vitor Matheus; Sakamoto, Arnaldo Yoso; Quénol, Hervé; Vannier, Clémence; Corgne, Samuel
2016-01-01
The dynamics of land use/land cover change in the Lower Nhecolândia wetland are marked by deforestation for pasture expansion, resulting in a real threat to the ecological stability. The aim of our work was to analyze the spatial distribution of land cover changes in the Lower Nhecolândia from 1985 to 2013 and to predict changes in trends for 2040. The mapping of land cover changes was developed using Landsat satellite images of 1985, 1999, 2007, and 2013, based on geographic object-based image analysis approach. This study uses integrated Markov chains and cellular automata modeling and multicriteria evaluation techniques to produce transition probability maps and describe the trajectory analysis methodology to construct a continuity of spatial and temporal changes for the wetland. The results of the multitemporal change detection classification show that, from 1985 to 2013, the forest woodland decreased by 6.89% and the grassland class increased by 18.29%. On the other hand, all water bodies showed a reducing trend, while the bare soil class increased compared to 1985, but did not present a regular trend of increase or decrease. From the present day, the trend for the future is a reduction of almost 6.4% by 2040. We found that deforestation actions will be concentrated in the areas with the highest concentration of saline lakes, constituting a serious threat to the natural functioning of this environmental system.
20. A Markov chain analysis of the movements of juvenile salmonids, including sockeye salmon, in the forebay of McNary Dam, Washington and Oregon, 2006-09
USGS Publications Warehouse
Adams, Noah S.; Hatton, Tyson W.
2012-01-01
Passage and survival data were collected at McNary Dam between 2006 and 2009. These data have provided critical information for resource managers to implement structural and operational changes designed to improve the survival of juvenile salmonids as they migrate past the dam. Much of the valuable information collected at McNary Dam was in the form of three-dimensional (hereafter referred to as 3-D) tracks of fish movements in the forebay. These data depicted the behavior of multiple species (in three dimensions) during different diel periods, spill conditions, powerhouse operations, and testing of the surface bypass structures (temporary spillway weirs; TSWs). One of the challenges in reporting 3-D results is presenting the information in a manner that allows interested parties to summarize the behavior of many fish over many different conditions across multiple years. To accomplish this, we used a Markov chain analysis to characterize fish movement patterns in the forebay of McNary Dam. The Markov chain analysis allowed us to numerically summarize the behavior of fish in the forebay. This report is the second report published in 2012 that uses this analytical method. The first report included only fish released as part of the annual studies conducted at McNary Dam. This second report includes sockeye salmon that were released as part of studies conducted by the Chelan and Grant County Public Utility Districts at mid-Columbia River dams. The studies conducted in the mid-Columbia used the same transmitters as were used for McNary Dam studies, but transmitter pulse width was different between studies. Additionally, no passive integrated transponder tags were implanted in sockeye salmon. Differences in transmitter pulse width resulted in lower detection probabilities for sockeye salmon at McNary Dam. The absence of passive integrated transponder tags prevented us from determining if fish passed the powerhouse through the juvenile bypass system (JBS) or turbines. To
1. Decentralized learning in Markov games.
PubMed
Vrancx, Peter; Verbeeck, Katja; Nowé, Ann
2008-08-01
Learning automata (LA) were recently shown to be valuable tools for designing multiagent reinforcement learning algorithms. One of the principal contributions of the LA theory is that a set of decentralized independent LA is able to control a finite Markov chain with unknown transition probabilities and rewards. In this paper, we propose to extend this algorithm to Markov games--a straightforward extension of single-agent Markov decision problems to distributed multiagent decision problems. We show that under the same ergodic assumptions of the original theorem, the extended algorithm will converge to a pure equilibrium point between agent policies. PMID:18632387
2. Monte Carlo simulation and equation of state for flexible charged hard-sphere chain fluids: Polyampholyte and polyelectrolyte solutions
SciTech Connect
2014-11-07
The thermodynamic modeling of flexible charged hard-sphere chains representing polyampholyte or polyelectrolyte molecules in solution is considered. The excess Helmholtz energy and osmotic coefficients of solutions containing short polyampholyte and the osmotic coefficients of solutions containing short polyelectrolytes are determined by performing canonical and isobaric-isothermal Monte Carlo simulations. A new equation of state based on the thermodynamic perturbation theory is also proposed for flexible charged hard-sphere chains. For the modeling of such chains, the use of solely the structure information of monomer fluid for calculating the chain contribution is found to be insufficient and more detailed structure information must therefore be considered. Two approaches, i.e., the dimer and dimer-monomer approaches, are explored to obtain the contribution of the chain formation to the Helmholtz energy. By comparing with the simulation results, the equation of state with either the dimer or dimer-monomer approach accurately predicts the excess Helmholtz energy and osmotic coefficients of polyampholyte and polyelectrolyte solutions except at very low density. It also well captures the effect of temperature on the thermodynamic properties of these solutions.
3. Fused hard-sphere chain molecules: Comparison between Monte Carlo simulation for the bulk pressure and generalized Flory theories
SciTech Connect
Costa, L.A.; Zhou, Y.; Hall, C.K.; Carra, S.
1995-04-15
We report Monte Carlo simulation results for the bulk pressure of fused-hard-sphere (FHS) chain fluids with bond-length-to-bead-diameter ratios {approx} 0.4 at chain lengths {ital n}=4, 8 and 16. We also report density profiles for FHS chain fluids at a hard wall. The results for the compressibility factor are compared to results from extensions of the Generalized Flory (GF) and Generalized Flory Dimer (GFD) theories proposed by Yethiraj {ital et} {ital al}. and by us. Our new GF theory, GF-AB, significantly improves the prediction of the bulk pressure of fused-hard-sphere chains over the GFD theories proposed by Yethiraj {ital et} {ital al}. and by us although the GFD theories give slightly better low-density results. The GFD-A theory, the GFD-B theory and the new theories (GF-AB, GFD-AB, and GFD-AC) satisfy the exact zero-bonding-length limit. All theories considered recover the GF or GFD theories at the tangent hard-sphere chain limit.
4. Zipf exponent of trajectory distribution in the hidden Markov model
Bochkarev, V. V.; Lerner, E. Yu
2014-03-01
This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different.
5. Super-Resolution Using Hidden Markov Model and Bayesian Detection Estimation Framework
2006-12-01
This paper presents a new method for super-resolution (SR) reconstruction of a high-resolution (HR) image from several low-resolution (LR) images. The HR image is assumed to be composed of homogeneous regions. Thus, the a priori distribution of the pixels is modeled by a finite mixture model (FMM) and a Potts Markov model (PMM) for the labels. The whole a priori model is then a hierarchical Markov model. The LR images are assumed to be obtained from the HR image by lowpass filtering, arbitrarily translation, decimation, and finally corruption by a random noise. The problem is then put in a Bayesian detection and estimation framework, and appropriate algorithms are developed based on Markov chain Monte Carlo (MCMC) Gibbs sampling. At the end, we have not only an estimate of the HR image but also an estimate of the classification labels which leads to a segmentation result.
6. Fast Protein Loop Sampling and Structure Prediction Using Distance-Guided Sequential Chain-Growth Monte Carlo Method
PubMed Central
Tang, Ke; Zhang, Jinfeng; Liang, Jie
2014-01-01
Loops in proteins are flexible regions connecting regular secondary structures. They are often involved in protein functions through interacting with other molecules. The irregularity and flexibility of loops make their structures difficult to determine experimentally and challenging to model computationally. Conformation sampling and energy evaluation are the two key components in loop modeling. We have developed a new method for loop conformation sampling and prediction based on a chain growth sequential Monte Carlo sampling strategy, called Distance-guided Sequential chain-Growth Monte Carlo (DiSGro). With an energy function designed specifically for loops, our method can efficiently generate high quality loop conformations with low energy that are enriched with near-native loop structures. The average minimum global backbone RMSD for 1,000 conformations of 12-residue loops is Å, with a lowest energy RMSD of Å, and an average ensemble RMSD of Å. A novel geometric criterion is applied to speed up calculations. The computational cost of generating 1,000 conformations for each of the x loops in a benchmark dataset is only about cpu minutes for 12-residue loops, compared to ca cpu minutes using the FALCm method. Test results on benchmark datasets show that DiSGro performs comparably or better than previous successful methods, while requiring far less computing time. DiSGro is especially effective in modeling longer loops (– residues). PMID:24763317
7. Meta-heuristic ant colony optimization technique to forecast the amount of summer monsoon rainfall: skill comparison with Markov chain model
Chaudhuri, Sutapa; Goswami, Sayantika; Das, Debanjana; Middey, Anirban
2014-05-01
Forecasting summer monsoon rainfall with precision becomes crucial for the farmers to plan for harvesting in a country like India where the national economy is mostly based on regional agriculture. The forecast of monsoon rainfall based on artificial neural network is a well-researched problem. In the present study, the meta-heuristic ant colony optimization (ACO) technique is implemented to forecast the amount of summer monsoon rainfall for the next day over Kolkata (22.6°N, 88.4°E), India. The ACO technique belongs to swarm intelligence and simulates the decision-making processes of ant colony similar to other adaptive learning techniques. ACO technique takes inspiration from the foraging behaviour of some ant species. The ants deposit pheromone on the ground in order to mark a favourable path that should be followed by other members of the colony. A range of rainfall amount replicating the pheromone concentration is evaluated during the summer monsoon season. The maximum amount of rainfall during summer monsoon season (June—September) is observed to be within the range of 7.5-35 mm during the period from 1998 to 2007, which is in the range 4 category set by the India Meteorological Department (IMD). The result reveals that the accuracy in forecasting the amount of rainfall for the next day during the summer monsoon season using ACO technique is 95 % where as the forecast accuracy is 83 % with Markov chain model (MCM). The forecast through ACO and MCM are compared with other existing models and validated with IMD observations from 2008 to 2012.
8. Study of Disease Progression and Relevant Risk Factors in Diabetic Foot Patients Using a Multistate Continuous-Time Markov Chain Model
PubMed Central
Begun, Alexander; Morbach, Stephan; Rümenapf, Gerhard; Icks, Andrea
2016-01-01
The diabetic foot is a lifelong disease. The longer patients with diabetes and foot ulcers are observed, the higher the likelihood that they will develop comorbidities that adversely influence ulcer recurrence, amputation and survival (for example peripheral arterial disease, renal failure or ischaemic heart disease). The purpose of our study was to quantify person and limb-related disease progression and the time-dependent influence of any associated factors (present at baseline or appearing during observation) based on which effective prevention and/or treatment strategies could be developed. Using a nine-state continuous-time Markov chain model with time-dependent risk factors, all living patients were divided into eight groups based on their ulceration (previous or current) and previous amputation (none, minor or major) status. State nine is an absorbing state (death). If all transitions are fully observable, this model can be decomposed into eight submodels, which can be analyzed using the methods of survival analysis for competing risks. The dependencies of the risk factors (covariates) were included in the submodels using Cox-like regression. The transition intensities and relative risks for covariates were calculated from long-term data of patients with diabetic foot ulcers collected in a single specialized center in North-Rhine Westphalia (Germany). The detected estimates were in line with previously published, but scarce, data. Together with the interesting new results obtained, this indicates that the proposed model may be useful for studying disease progression in larger samples of patients with diabetic foot ulcers. PMID:26814723
9. Chain pooling to minimize prediction error in subset regression. [Monte Carlo studies using population models
NASA Technical Reports Server (NTRS)
Holms, A. G.
1974-01-01
Monte Carlo studies using population models intended to represent response surface applications are reported. Simulated experiments were generated by adding pseudo random normally distributed errors to population values to generate observations. Model equations were fitted to the observations and the decision procedure was used to delete terms. Comparison of values predicted by the reduced models with the true population values enabled the identification of deletion strategies that are approximately optimal for minimizing prediction errors.
10. Unmixing hyperspectral images using Markov random fields
SciTech Connect
Eches, Olivier; Dobigeon, Nicolas; Tourneret, Jean-Yves
2011-03-14
This paper proposes a new spectral unmixing strategy based on the normal compositional model that exploits the spatial correlations between the image pixels. The pure materials (referred to as endmembers) contained in the image are assumed to be available (they can be obtained by using an appropriate endmember extraction algorithm), while the corresponding fractions (referred to as abundances) are estimated by the proposed algorithm. Due to physical constraints, the abundances have to satisfy positivity and sum-to-one constraints. The image is divided into homogeneous distinct regions having the same statistical properties for the abundance coefficients. The spatial dependencies within each class are modeled thanks to Potts-Markov random fields. Within a Bayesian framework, prior distributions for the abundances and the associated hyperparameters are introduced. A reparametrization of the abundance coefficients is proposed to handle the physical constraints (positivity and sum-to-one) inherent to hyperspectral imagery. The parameters (abundances), hyperparameters (abundance mean and variance for each class) and the classification map indicating the classes of all pixels in the image are inferred from the resulting joint posterior distribution. To overcome the complexity of the joint posterior distribution, Markov chain Monte Carlo methods are used to generate samples asymptotically distributed according to the joint posterior of interest. Simulations conducted on synthetic and real data are presented to illustrate the performance of the proposed algorithm.
11. Markov reward processes
NASA Technical Reports Server (NTRS)
Smith, R. M.
1991-01-01
Numerous applications in the area of computer system analysis can be effectively studied with Markov reward models. These models describe the behavior of the system with a continuous-time Markov chain, where a reward rate is associated with each state. In a reliability/availability model, upstates may have reward rate 1 and down states may have reward rate zero associated with them. In a queueing model, the number of jobs of certain type in a given state may be the reward rate attached to that state. In a combined model of performance and reliability, the reward rate of a state may be the computational capacity, or a related performance measure. Expected steady-state reward rate and expected instantaneous reward rate are clearly useful measures of the Markov reward model. More generally, the distribution of accumulated reward or time-averaged reward over a finite time interval may be determined from the solution of the Markov reward model. This information is of great practical significance in situations where the workload can be well characterized (deterministically, or by continuous functions e.g., distributions). The design process in the development of a computer system is an expensive and long term endeavor. For aerospace applications the reliability of the computer system is essential, as is the ability to complete critical workloads in a well defined real time interval. Consequently, effective modeling of such systems must take into account both performance and reliability. This fact motivates our use of Markov reward models to aid in the development and evaluation of fault tolerant computer systems.
12. Building Simple Hidden Markov Models. Classroom Notes
ERIC Educational Resources Information Center
Ching, Wai-Ki; Ng, Michael K.
2004-01-01
Hidden Markov models (HMMs) are widely used in bioinformatics, speech recognition and many other areas. This note presents HMMs via the framework of classical Markov chain models. A simple example is given to illustrate the model. An estimation method for the transition probabilities of the hidden states is also discussed.
13. Indexed semi-Markov process for wind speed modeling.
Petroni, F.; D'Amico, G.; Prattico, F.
2012-04-01
-order Markov chain with different number of states, and Weibull distribution. All this model use Markov chains to generate synthetic wind speed time series but the search for a better model is still open. Approaching this issue, we applied new models which are generalization of Markov models. More precisely we applied semi-Markov models to generate synthetic wind speed time series. In a previous work we proposed different semi-Markov models, showing their ability to reproduce the autocorrelation structures of wind speed data. In that paper we showed also that the autocorrelation is higher with respect to the Markov model. Unfortunately this autocorrelation was still too small compared to the empirical one. In order to overcome the problem of low autocorrelation, in this paper we propose an indexed semi-Markov model. More precisely we assume that wind speed is described by a discrete time homogeneous semi-Markov process. We introduce a memory index which takes into account the periods of different wind activities. With this model the statistical characteristics of wind speed are faithfully reproduced. The wind is a very unstable phenomenon characterized by a sequence of lulls and sustained speeds, and a good wind generator must be able to reproduce such sequences. To check the validity of the predictive semi-Markovian model, the persistence of synthetic winds were calculated, then averaged and computed. The model is used to generate synthetic time series for wind speed by means of Monte Carlo simulations and the time lagged autocorrelation is used to compare statistical properties of the proposed models with those of real data and also with a time series generated though a simple Markov chain. [1] A. Shamshad, M.A. Bawadi, W.M.W. Wan Hussin, T.A. Majid, S.A.M. Sanusi, First and second order Markov chain models for synthetic generation of wind speed time series, Energy 30 (2005) 693-708. [2] H. Nfaoui, H. Essiarab, A.A.M. Sayigh, A stochastic Markov chain model for simulating
14. Chain formation and aging process in biocompatible polydisperse ferrofluids: experimental investigation and Monte Carlo simulations.
PubMed
Bakuzis, Andris Figueiroa; Branquinho, Luis César; e Castro, Leonardo Luiz; e Eloi, Marcos Tiago de Amaral; Miotto, Ronei
2013-05-01
We review the use of Monte Carlo simulations in the description of magnetic nanoparticles dispersed in a liquid carrier. Our main focus is the use of theory and simulation as tools for the description of the properties of ferrofluids. In particular, we report on the influence of polydispersity and short-range interaction on the self-organization of nanoparticles. Such contributions are shown to be extremely important for systems characterized by particles with diameters smaller than 10nm. A new 3D polydisperse Monte Carlo implementation for biocompatible magnetic colloids is proposed. As an example, theoretical and simulation results for an ionic-surfacted ferrofluid dispersed in a NaCl solution are directly compared to experimental data (transmission electron microscopy - TEM, magneto-transmissivity, and electron magnetic resonance - EMR). Our combined theoretical and experimental results suggest that during the aging process two possible mechanisms are likely to be observed: the nanoparticle's grafting decreases due to aggregate formation and the Hamaker constant increases due to oxidation. In addition, we also briefly discuss theoretical agglomerate formation models and compare them to experimental data. PMID:23360743
15. Nonlinear Markov processes
Frank, T. D.
2008-06-01
Some elementary properties and examples of Markov processes are reviewed. It is shown that the definition of the Markov property naturally leads to a classification of Markov processes into linear and nonlinear ones.
16. A compositional framework for Markov processes
Baez, John C.; Fong, Brendan; Pollard, Blake S.
2016-03-01
We define the concept of an "open" Markov process, or more precisely, continuous-time Markov chain, which is one where probability can flow in or out of certain states called "inputs" and "outputs." One can build up a Markov process from smaller open pieces. This process is formalized by making open Markov processes into the morphisms of a dagger compact category. We show that the behavior of a detailed balanced open Markov process is determined by a principle of minimum dissipation, closely related to Prigogine's principle of minimum entropy production. Using this fact, we set up a functor mapping open detailed balanced Markov processes to open circuits made of linear resistors. We also describe how to "black box" an open Markov process, obtaining the linear relation between input and output data that holds in any steady state, including nonequilibrium steady states with a nonzero flow of probability through the system. We prove that black boxing gives a symmetric monoidal dagger functor sending open detailed balanced Markov processes to Lagrangian relations between symplectic vector spaces. This allows us to compute the steady state behavior of an open detailed balanced Markov process from the behaviors of smaller pieces from which it is built. We relate this black box functor to a previously constructed black box functor for circuits.
17. Bayesian comparison of Markov models of molecular dynamics with detailed balance constraint
Bacallado, Sergio; Chodera, John D.; Pande, Vijay
2009-07-01
Discrete-space Markov models are a convenient way of describing the kinetics of biomolecules. The most common strategies used to validate these models employ statistics from simulation data, such as the eigenvalue spectrum of the inferred rate matrix, which are often associated with large uncertainties. Here, we propose a Bayesian approach, which makes it possible to differentiate between models at a fixed lag time making use of short trajectories. The hierarchical definition of the models allows one to compare instances with any number of states. We apply a conjugate prior for reversible Markov chains, which was recently introduced in the statistics literature. The method is tested in two different systems, a Monte Carlo dynamics simulation of a two-dimensional model system and molecular dynamics simulations of the terminally blocked alanine dipeptide.
18. Bayesian Clustering Using Hidden Markov Random Fields in Spatial Population Genetics
PubMed Central
François, Olivier; Ancelet, Sophie; Guillot, Gilles
2006-01-01
We introduce a new Bayesian clustering algorithm for studying population structure using individually geo-referenced multilocus data sets. The algorithm is based on the concept of hidden Markov random field, which models the spatial dependencies at the cluster membership level. We argue that (i) a Markov chain Monte Carlo procedure can implement the algorithm efficiently, (ii) it can detect significant geographical discontinuities in allele frequencies and regulate the number of clusters, (iii) it can check whether the clusters obtained without the use of spatial priors are robust to the hypothesis of discontinuous geographical variation in allele frequencies, and (iv) it can reduce the number of loci required to obtain accurate assignments. We illustrate and discuss the implementation issues with the Scandinavian brown bear and the human CEPH diversity panel data set. PMID:16888334
19. Forest cover change prediction using hybrid methodology of geoinformatics and Markov chain model: A case study on sub-Himalayan town Gangtok, India
Mukhopadhyay, Anirban; Mondal, Arun; Mukherjee, Sandip; Khatua, Dipam; Ghosh, Subhajit; Mitra, Debasish; Ghosh, Tuhin
2014-08-01
In the Himalayan states of India, with increasing population and activities, large areas of forested land are being converted into other land-use features. There is a definite cause and effect relationship between changing practice for development and changes in land use. So, an estimation of land use dynamics and a futuristic trend pattern is essential. A combination of geospatial and statistical techniques were applied to assess the present and future land use/land cover scenario of Gangtok, the subHimalayan capital of Sikkim. Multi-temporal satellite imageries of the Landsat series were used to map the changes in land use of Gangtok from 1990 to 2010. Only three major land use classes (built-up area and bare land, step cultivated area, and forest) were considered as the most dynamic land use practices of Gangtok. The conventional supervised classification, and spectral indices-based thresholding using NDVI (Normalized Difference Vegetation Index) and SAVI (Soil Adjusted Vegetation Index) were applied along with the accuracy assessments. Markov modelling was applied for prediction of land use/land cover change and was validated. SAVI provides the most accurate estimate, i.e., the difference between predicted and actual data is minimal. Finally, a combination of Markov modelling and SAVI was used to predict the probable land-use scenario in Gangtok in 2020 AD, which indicted that more forest areas will be converted for step cultivation by the year 2020.
20. Compressible generalized hybrid Monte Carlo
Fang, Youhan; Sanz-Serna, J. M.; Skeel, Robert D.
2014-05-01
One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a Markov chain Monte Carlo method, which converges only in the limit to the prescribed distribution. Such methods typically inch through configuration space step by step, with acceptance of a step based on a Metropolis(-Hastings) criterion. An acceptance rate of 100% is possible in principle by embedding configuration space in a higher dimensional phase space and using ordinary differential equations. In practice, numerical integrators must be used, lowering the acceptance rate. This is the essence of hybrid Monte Carlo methods. Presented is a general framework for constructing such methods under relaxed conditions: the only geometric property needed is (weakened) reversibility; volume preservation is not needed. The possibilities are illustrated by deriving a couple of explicit hybrid Monte Carlo methods, one based on barrier-lowering variable-metric dynamics and another based on isokinetic dynamics.
1. On multitarget pairwise-Markov models
Mahler, Ronald
2015-05-01
Single- and multi-target tracking are both typically based on strong independence assumptions regarding both the target states and sensor measurements. In particular, both are theoretically based on the hidden Markov chain (HMC) model. That is, the target process is a Markov chain that is observed by an independent observation process. Since HMC assumptions are invalid in many practical applications, the pairwise Markov chain (PMC) model has been proposed as a way to weaken those assumptions. In this paper it is shown that the PMC model can be directly generalized to multitarget problems. Since the resulting tracking filters are computationally intractable, the paper investigates generalizations of the cardinalized probability hypothesis density (CPHD) filter to applications with PMC models.
2. A Markov Chain Monte Carlo Software Package to Constrain the Evolution of Luminosity Functions, Test SED Models, and Simulate Future Surveys
Kurinsky, Noah; Sajina, Anna
2014-06-01
We present a novel simulation and fitting program which employs MCMC to constrain the spectral energy distribution makeup and luminosity function evolution required to produce a given mutli-wavelength survey. This tool employs a multidimensional color-color diagnostic to determine goodness of fit, and simulates observational sources of error such as flux-limits and instrumental noise. Our goals in designing this tool were to a) use it to study Infrared surveys and test SED template models, and b) create it in such a way as to make it usable in any electromagnetic regime for any class of sources to which any luminosity functional form can be prescribed.I will discuss our specific use of the program to characterize a survey from the Herschel SPIRE HerMES catalog, including implications for our luminosity function and SED models. I will also briefly discuss the ways we envision using it for simulation and application to other surveys, and I will demonstrate the degree to which its reusability can serve to enrich a wide range of analyses.
3. On the applicability of surrogate-based Markov chain Monte Carlo-Bayesian inversion to the Community Land Model: Case studies at flux tower sites
Huang, Maoyi; Ray, Jaideep; Hou, Zhangshuan; Ren, Huiying; Liu, Ying; Swiler, Laura
2016-07-01
The Community Land Model (CLM) has been widely used in climate and Earth system modeling. Accurate estimation of model parameters is needed for reliable model simulations and predictions under current and future conditions, respectively. In our previous work, a subset of hydrological parameters has been identified to have significant impact on surface energy fluxes at selected flux tower sites based on parameter screening and sensitivity analysis, which indicate that the parameters could potentially be estimated from surface flux observations at the towers. To date, such estimates do not exist. In this paper, we assess the feasibility of applying a Bayesian model calibration technique to estimate CLM parameters at selected flux tower sites under various site conditions. The parameters are estimated as a joint probability density function (PDF) that provides estimates of uncertainty of the parameters being inverted, conditional on climatologically average latent heat fluxes derived from observations. We find that the simulated mean latent heat fluxes from CLM using the calibrated parameters are generally improved at all sites when compared to those obtained with CLM simulations using default parameter sets. Further, our calibration method also results in credibility bounds around the simulated mean fluxes which bracket the measured data. The modes (or maximum a posteriori values) and 95% credibility intervals of the site-specific posterior PDFs are tabulated as suggested parameter values for each site. Analysis of relationships between the posterior PDFs and site conditions suggests that the parameter values are likely correlated with the plant functional type, which needs to be confirmed in future studies by extending the approach to more sites.
4. From Bray-Curtis ordination to Markov Chain Monte Carlo simulation: assessing anthropogenically-induced and/or climatically-induced changes in arboreal ecosystems
Mapping forest resources is useful for identifying threat patterns and monitoring changes associated with landscapes. Remote Sensing and Geographic Information Science techniques are effective tools used to identify and forecast forest resource threats such as exotic plant invasion, vulnerability to climate change, and land-use/cover change. This research focused on mapping abundance and distribution of Russian-olive using soil and land-use/cover data, evaluating historic land-use/cover change using mappable water-related indices addressing the primary loss of riparian arboreal ecosystems, and detecting year-to-year land-cover changes on forest conversion processes. Digital image processing techniques were used to detect the changes of arboreal ecosystems using ArcGIS ArcInfoRTM 9.3, ENVIRTM, and ENVIRTM EX platforms. Research results showed that Russian-olive at the inundated habitats of the Missouri River is abundant compared to terrestrial habitats in the Bismarck-Mandan Wildland Urban Interface. This could be a consequence of habitat quality of the floodplain, such as its silt loam and silty clay soil type, which favors Russian-olive regeneration. Russian-olive has close assemblage with cottonwood (Populus deltoides) and buffaloberry (Shepherdia argentea) trees at the lower elevations. In addition, the Russian-olive-cottonwood association correlated with low nitrogen, low pH, and high Fe, while Russian-olive- buffaloberry association occurred in highly eroded areas. The Devils Lake sub-watershed was selected to demonstrate how both land-use/cover modification and climatic variability have caused the vulnerability of arboreal ecosystems on the fringe to such changes. Land-cover change showed that the forest acreage declined from 9% to 1%, water extent increased from 13% to 25%, and cropland extent increased from 34% to 39% between 1992 and 2006. In addition, stochastic modeling was adapted to simulate how land-use/cover change influenced forest conversion to non-forested lands at the urban-wildland fringes in Cass County. The analysis yielded two distinct statistical groups of transition probabilities for forest to non-forest, with high transition probability of unchanged forest (0.54≤ Pff ≤ 0.68) from 2006 to 2011. Generally, the land-uses, such as row crops, showed an increasing trend, while grains, hay, seeds, and other crops showed a declining trend. This information is vital to forest managers for implementing restoration and conservation practices in arboreal ecosystems.
5. Efficient posterior exploration of a high-dimensional groundwater model from two-stage Markov chain Monte Carlo simulation and polynomial chaos expansion
Laloy, Eric; Rogiers, Bart; Vrugt, Jasper A.; Mallants, Dirk; Jacques, Diederik
2013-05-01
This study reports on two strategies for accelerating posterior inference of a highly parameterized and CPU-demanding groundwater flow model. Our method builds on previous stochastic collocation approaches, e.g., Marzouk and Xiu (2009) and Marzouk and Najm (2009), and uses generalized polynomial chaos (gPC) theory and dimensionality reduction to emulate the output of a large-scale groundwater flow model. The resulting surrogate model is CPU efficient and serves to explore the posterior distribution at a much lower computational cost using two-stage MCMC simulation. The case study reported in this paper demonstrates a two to five times speed-up in sampling efficiency.
6. A new approach to simulating stream isotope dynamics using Markov switching autoregressive models
Birkel, Christian; Paroli, Roberta; Spezia, Luigi; Dunn, Sarah M.; Tetzlaff, Doerthe; Soulsby, Chris
2012-09-01
In this study we applied Markov switching autoregressive models (MSARMs) as a proof-of-concept to analyze the temporal dynamics and statistical characteristics of the time series of two conservative water isotopes, deuterium (δ2H) and oxygen-18 (δ18O), in daily stream water samples over two years in a small catchment in eastern Scotland. MSARMs enabled us to explicitly account for the identified non-linear, non-Normal and non-stationary isotope dynamics of both time series. The hidden states of the Markov chain could also be associated with meteorological and hydrological drivers identifying the short (event) and longer-term (inter-event) transport mechanisms for both isotopes. Inference was based on the Bayesian approach performed through Markov Chain Monte Carlo algorithms, which also allowed us to deal with a high rate of missing values (17%). Although it is usually assumed that both isotopes are conservative and exhibit similar dynamics, δ18O showed somewhat different time series characteristics. Both isotopes were best modelled with two hidden states, but δ18O demanded autoregressions of the first order, whereas δ2H of the second. Moreover, both the dynamics of observations and the hidden states of the two isotopes were explained by two different sets of covariates. Consequently use of the two tracers for transit time modelling and hydrograph separation may result in different interpretations on the functioning of a catchment system.
7. On Monte Carlo Methods and Applications in Geoscience
Zhang, Z.; Blais, J.
2009-05-01
Monte Carlo methods are designed to study various deterministic problems using probabilistic approaches, and with computer simulations to explore much wider possibilities for the different algorithms. Pseudo- Random Number Generators (PRNGs) are based on linear congruences of some large prime numbers, while Quasi-Random Number Generators (QRNGs) provide low discrepancy sequences, both of which giving uniformly distributed numbers in (0,1). Chaotic Random Number Generators (CRNGs) give sequences of 'random numbers' satisfying some prescribed probabilistic density, often denser around the two corners of interval (0,1), but transforming this type of density to a uniform one is usually possible. Markov Chain Monte Carlo (MCMC), as indicated by its name, is associated with Markov Chain simulations. Basic descriptions of these random number generators will be given, and a comparative analysis of these four methods will be included based on their efficiencies and other characteristics. Some applications in geoscience using Monte Carlo simulations will be described, and a comparison of these algorithms will also be included with some concluding remarks.
8. A Hamiltonian Monte-Carlo method for Bayesian inference of supermassive black hole binaries
Porter, Edward K.; Carré, Jérôme
2014-07-01
We investigate the use of a Hamiltonian Monte-Carlo to map out the posterior density function for supermassive black hole binaries. While previous Markov Chain Monte-Carlo (MCMC) methods, such as Metropolis-Hastings MCMC, have been successfully employed for a number of different gravitational wave sources, these methods are essentially random walk algorithms. The Hamiltonian Monte-Carlo treats the inverse likelihood surface as a ‘gravitational potential’ and by introducing canonical positions and momenta, dynamically evolves the Markov chain by solving Hamilton's equations of motion. This method is not as widely used as other MCMC algorithms due to the necessity of calculating gradients of the log-likelihood, which for most applications results in a bottleneck that makes the algorithm computationally prohibitive. We circumvent this problem by using accepted initial phase-space trajectory points to analytically fit for each of the individual gradients. Eliminating the waveform generation needed for the numerical derivatives reduces the total number of required templates for a {{10}^{6}} iteration chain from \\sim {{10}^{9}} to \\sim {{10}^{6}}. The result is in an implementation of the Hamiltonian Monte-Carlo that is faster, and more efficient by a factor of approximately the dimension of the parameter space, than a Hessian MCMC.
9. Metrics for Diagnosing Undersampling in Monte Carlo Tally Estimates
SciTech Connect
Perfetti, Christopher M.; Rearden, Bradley T.
2015-01-01
This study explored the potential of using Markov chain convergence diagnostics to predict the prevalence and magnitude of biases due to undersampling in Monte Carlo eigenvalue and flux tally estimates. Five metrics were applied to two models of pressurized water reactor fuel assemblies and their potential for identifying undersampling biases was evaluated by comparing the calculated test metrics with known biases in the tallies. Three of the five undersampling metrics showed the potential to accurately predict the behavior of undersampling biases in the responses examined in this study.
10. Wormhole Hamiltonian Monte Carlo
PubMed Central
Lan, Shiwei; Streets, Jeffrey; Shahbaba, Babak
2015-01-01
In machine learning and statistics, probabilistic inference involving multimodal distributions is quite difficult. This is especially true in high dimensional problems, where most existing algorithms cannot easily move from one mode to another. To address this issue, we propose a novel Bayesian inference approach based on Markov Chain Monte Carlo. Our method can effectively sample from multimodal distributions, especially when the dimension is high and the modes are isolated. To this end, it exploits and modifies the Riemannian geometric properties of the target distribution to create wormholes connecting modes in order to facilitate moving between them. Further, our proposed method uses the regeneration technique in order to adapt the algorithm by identifying new modes and updating the network of wormholes without affecting the stationary distribution. To find new modes, as opposed to redis-covering those previously identified, we employ a novel mode searching algorithm that explores a residual energy function obtained by subtracting an approximate Gaussian mixture density (based on previously discovered modes) from the target density function. PMID:25861551
11. Neutrino oscillation parameter sampling with MonteCUBES
Blennow, Mattias; Fernandez-Martinez, Enrique
2010-01-01
We present MonteCUBES ("Monte Carlo Utility Based Experiment Simulator"), a software package designed to sample the neutrino oscillation parameter space through Markov Chain Monte Carlo algorithms. MonteCUBES makes use of the GLoBES software so that the existing experiment definitions for GLoBES, describing long baseline and reactor experiments, can be used with MonteCUBES. MonteCUBES consists of two main parts: The first is a C library, written as a plug-in for GLoBES, implementing the Markov Chain Monte Carlo algorithm to sample the parameter space. The second part is a user-friendly graphical Matlab interface to easily read, analyze, plot and export the results of the parameter space sampling. Program summaryProgram title: MonteCUBES (Monte Carlo Utility Based Experiment Simulator) Catalogue identifier: AEFJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFJ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence No. of lines in distributed program, including test data, etc.: 69 634 No. of bytes in distributed program, including test data, etc.: 3 980 776 Distribution format: tar.gz Programming language: C Computer: MonteCUBES builds and installs on 32 bit and 64 bit Linux systems where GLoBES is installed Operating system: 32 bit and 64 bit Linux RAM: Typically a few MBs Classification: 11.1 External routines: GLoBES [1,2] and routines/libraries used by GLoBES Subprograms used:Cat Id ADZI_v1_0, Title GLoBES, Reference CPC 177 (2007) 439 Nature of problem: Since neutrino masses do not appear in the standard model of particle physics, many models of neutrino masses also induce other types of new physics, which could affect the outcome of neutrino oscillation experiments. In general, these new physics imply high-dimensional parameter spaces that are difficult to explore using classical methods such as multi-dimensional projections and minimizations, such as those
12. Semi-Markov Arnason-Schwarz models.
PubMed
King, Ruth; Langrock, Roland
2016-06-01
We consider multi-state capture-recapture-recovery data where observed individuals are recorded in a set of possible discrete states. Traditionally, the Arnason-Schwarz model has been fitted to such data where the state process is modeled as a first-order Markov chain, though second-order models have also been proposed and fitted to data. However, low-order Markov models may not accurately represent the underlying biology. For example, specifying a (time-independent) first-order Markov process involves the assumption that the dwell time in each state (i.e., the duration of a stay in a given state) has a geometric distribution, and hence that the modal dwell time is one. Specifying time-dependent or higher-order processes provides additional flexibility, but at the expense of a potentially significant number of additional model parameters. We extend the Arnason-Schwarz model by specifying a semi-Markov model for the state process, where the dwell-time distribution is specified more generally, using, for example, a shifted Poisson or negative binomial distribution. A state expansion technique is applied in order to represent the resulting semi-Markov Arnason-Schwarz model in terms of a simpler and computationally tractable hidden Markov model. Semi-Markov Arnason-Schwarz models come with only a very modest increase in the number of parameters, yet permit a significantly more flexible state process. Model selection can be performed using standard procedures, and in particular via the use of information criteria. The semi-Markov approach allows for important biological inference to be drawn on the underlying state process, for example, on the times spent in the different states. The feasibility of the approach is demonstrated in a simulation study, before being applied to real data corresponding to house finches where the states correspond to the presence or absence of conjunctivitis. PMID:26584064
13. A reward semi-Markov process with memory for wind speed modeling
Petroni, F.; D'Amico, G.; Prattico, F.
2012-04-01
-order Markov chain with different number of states, and Weibull distribution. All this model use Markov chains to generate synthetic wind speed time series but the search for a better model is still open. Approaching this issue, we applied new models which are generalization of Markov models. More precisely we applied semi-Markov models to generate synthetic wind speed time series. The primary goal of this analysis is the study of the time history of the wind in order to assess its reliability as a source of power and to determine the associated storage levels required. In order to assess this issue we use a probabilistic model based on indexed semi-Markov process [4] to which a reward structure is attached. Our model is used to calculate the expected energy produced by a given turbine and its variability expressed by the variance of the process. Our results can be used to compare different wind farms based on their reward and also on the risk of missed production due to the intrinsic variability of the wind speed process. The model is used to generate synthetic time series for wind speed by means of Monte Carlo simulations and backtesting procedure is used to compare results on first and second oder moments of rewards between real and synthetic data. [1] A. Shamshad, M.A. Bawadi, W.M.W. Wan Hussin, T.A. Majid, S.A.M. Sanusi, First and second order Markov chain models for synthetic gen- eration of wind speed time series, Energy 30 (2005) 693-708. [2] H. Nfaoui, H. Essiarab, A.A.M. Sayigh, A stochastic Markov chain model for simulating wind speed time series at Tangiers, Morocco, Re- newable Energy 29 (2004) 1407-1418. [3] F. Youcef Ettoumi, H. Sauvageot, A.-E.-H. Adane, Statistical bivariate modeling of wind using first-order Markov chain and Weibull distribu- tion, Renewable Energy 28 (2003) 1787-1802. [4]F. Petroni, G. D'Amico, F. Prattico, Indexed semi-Markov process for wind speed modeling. To be submitted.
14. Advanced interacting sequential Monte Carlo sampling for inverse scattering
Giraud, F.; Minvielle, P.; Del Moral, P.
2013-09-01
The following electromagnetism (EM) inverse problem is addressed. It consists in estimating the local radioelectric properties of materials recovering an object from global EM scattering measurements, at various incidences and wave frequencies. This large scale ill-posed inverse problem is explored by an intensive exploitation of an efficient 2D Maxwell solver, distributed on high performance computing machines. Applied to a large training data set, a statistical analysis reduces the problem to a simpler probabilistic metamodel, from which Bayesian inference can be performed. Considering the radioelectric properties as a hidden dynamic stochastic process that evolves according to the frequency, it is shown how advanced Markov chain Monte Carlo methods—called sequential Monte Carlo or interacting particles—can take benefit of the structure and provide local EM property estimates.
15. Magnetization dynamics of mixed Co-Au chains on Cu(110) substrate: Combined ab initio and kinetic Monte Carlo study
M. Tsysar, K.; V. Kolesnikov, S.; M. Saletsky, A.
2015-09-01
We present an investigation of the one-dimensional ferromagnetism in Au-Co nanowires deposited on the Cu(110) surface. By using the density functional theory, the influence of the nonmagnetic copper substrate Cu(110) on the magnetic properties of the bimetallic Au-Co nanowires is studied. The results show the emergence of magnetic anisotropy in the supported Au-Co nanowires. The magnetic anisotropy energy has the same order of magnitude as the exchange interaction energy between Co atoms in the wire. Our electronic structure calculation reveals the emergence of new hybridized bands between Au and Co atoms and surface Cu atoms. The Curie temperature of the Au-Co wires is calculated by means of kinetic Monte Carlo simulation. The strong size effect of the Curie temperature is demonstrated. Project supported by the Russian Foundation of Basic Researches.
16. A methodology to monitor the changing trends in health status of an elderly person by developing a markov model.
PubMed
Kaushik, Alka; Celler, B G; Ambikairajah, E
2005-01-01
In this paper we are proposing a statistical testing methodology to monitor changing trends in the health status of elderly people. The occupancy pattern of elderly people can be modeled using a Markov chain, estimating transition probabilities of the chain and test hypotheses about them. The profile of the person for a given period can be stored as a transition matrix of a discrete, regular, ergodic Markov chain. The observation of the occupancy pattern for a given test period can be established as a test Markov chain using information from sensors such as infrared sensors, magnetic switches etc. In the absence of real time data, we have used uniformly distributed transition probabilities to define the profile of the Markov chain and then generated test Markov chain based on this model. The transition probabilities are extracted for the test and profile Markov chain using Maximum Likelihood Estimates (MLE). The statistical testing of occupancy monitoring establishes a basis for statistical inference about the system performance without generating any real time statistics for the occupancy pattern. Chi square test and likelihood ratio tests ensure that the sequences generated from the two Markov chains are statistically same. Any difference in profile Markov chain and test Markov chain could indicate a changed health status of the elderly person. PMID:17282661
17. Efficient chain moves for Monte Carlo simulations of a wormlike DNA model: Excluded volume, supercoils, site juxtapositions, knots, and comparisons with random-flight and lattice models
Liu, Zhirong; Chan, Hue Sun
2008-04-01
We develop two classes of Monte Carlo moves for efficient sampling of wormlike DNA chains that can have significant degrees of supercoiling, a conformational feature that is key to many aspects of biological function including replication, transcription, and recombination. One class of moves entails reversing the coordinates of a segment of the chain along one, two, or three axes of an appropriately chosen local frame of reference. These transformations may be viewed as a generalization, to the continuum, of the Madras-Orlitsky-Shepp algorithm for cubic lattices. Another class of moves, termed T±2, allows for interconversions between chains with different lengths by adding or subtracting two beads (monomer units) to or from the chain. Length-changing moves are generally useful for conformational sampling with a given site juxtaposition, as has been shown in previous lattice studies. Here, the continuum T±2 moves are designed to enhance their acceptance rate in supercoiled conformations. We apply these moves to a wormlike model in which excluded volume is accounted for by a bond-bond repulsion term. The computed autocorrelation functions for the relaxation of bond length, bond angle, writhe, and branch number indicate that the new moves lead to significantly more efficient sampling than conventional bead displacements and crankshaft rotations. A close correspondence is found in the equilibrium ensemble between the map of writhe computed for pair of chain segments and the map of site juxtapositions or self-contacts. To evaluate the more coarse-grained freely jointed chain (random-flight) and cubic lattice models that are commonly used in DNA investigations, twisting (torsional) potentials are introduced into these models. Conformational properties for a given superhelical density σ may then be sampled by computing the writhe and using White's formula to relate the degree of twisting to writhe and σ. Extensive comparisons of contact patterns and knot probabilities
18. Efficient chain moves for Monte Carlo simulations of a wormlike DNA model: excluded volume, supercoils, site juxtapositions, knots, and comparisons with random-flight and lattice models.
PubMed
Liu, Zhirong; Chan, Hue Sun
2008-04-14
We develop two classes of Monte Carlo moves for efficient sampling of wormlike DNA chains that can have significant degrees of supercoiling, a conformational feature that is key to many aspects of biological function including replication, transcription, and recombination. One class of moves entails reversing the coordinates of a segment of the chain along one, two, or three axes of an appropriately chosen local frame of reference. These transformations may be viewed as a generalization, to the continuum, of the Madras-Orlitsky-Shepp algorithm for cubic lattices. Another class of moves, termed T+/-2, allows for interconversions between chains with different lengths by adding or subtracting two beads (monomer units) to or from the chain. Length-changing moves are generally useful for conformational sampling with a given site juxtaposition, as has been shown in previous lattice studies. Here, the continuum T+/-2 moves are designed to enhance their acceptance rate in supercoiled conformations. We apply these moves to a wormlike model in which excluded volume is accounted for by a bond-bond repulsion term. The computed autocorrelation functions for the relaxation of bond length, bond angle, writhe, and branch number indicate that the new moves lead to significantly more efficient sampling than conventional bead displacements and crankshaft rotations. A close correspondence is found in the equilibrium ensemble between the map of writhe computed for pair of chain segments and the map of site juxtapositions or self-contacts. To evaluate the more coarse-grained freely jointed chain (random-flight) and cubic lattice models that are commonly used in DNA investigations, twisting (torsional) potentials are introduced into these models. Conformational properties for a given superhelical density sigma may then be sampled by computing the writhe and using White's formula to relate the degree of twisting to writhe and sigma. Extensive comparisons of contact patterns and knot
19. Benchmarking of a Markov multizone model of contaminant transport.
PubMed
Jones, Rachael M; Nicas, Mark
2014-10-01
A Markov chain model previously applied to the simulation of advection and diffusion process of gaseous contaminants is extended to three-dimensional transport of particulates in indoor environments. The model framework and assumptions are described. The performance of the Markov model is benchmarked against simple conventional models of contaminant transport. The Markov model is able to replicate elutriation predictions of particle deposition with distance from a point source, and the stirred settling of respirable particles. Comparisons with turbulent eddy diffusion models indicate that the Markov model exhibits numerical diffusion in the first seconds after release, but over time accurately predicts mean lateral dispersion. The Markov model exhibits some instability with grid length aspect when turbulence is incorporated by way of the turbulent diffusion coefficient, and advection is present. However, the magnitude of prediction error may be tolerable for some applications and can be avoided by incorporating turbulence by way of fluctuating velocity (e.g. turbulence intensity). PMID:25143517
20. Mixed Markov models
PubMed Central
Fridman, Arthur
2003-01-01
Markov random fields can encode complex probabilistic relationships involving multiple variables and admit efficient procedures for probabilistic inference. However, from a knowledge engineering point of view, these models suffer from a serious limitation. The graph of a Markov field must connect all pairs of variables that are conditionally dependent even for a single choice of values of the other variables. This makes it hard to encode interactions that occur only in a certain context and are absent in all others. Furthermore, the requirement that two variables be connected unless always conditionally independent may lead to excessively dense graphs, obscuring the independencies present among the variables and leading to computationally prohibitive inference algorithms. Mumford [Mumford, D. (1996) in ICIAM 95, eds. Kirchgassner, K., Marenholtz, O. & Mennicken, R. (Akademie Verlag, Berlin), pp. 233–256] proposed an alternative modeling framework where the graph need not be rigid and completely determined a priori. Mixed Markov models contain node-valued random variables that, when instantiated, augment the graph by a set of transient edges. A single joint probability distribution relates the values of regular and node-valued variables. In this article, we study the analytical and computational properties of mixed Markov models. In particular, we show that positive mixed models have a local Markov property that is equivalent to their global factorization. We also describe a computationally efficient procedure for answering probabilistic queries in mixed Markov models. PMID:12829802
1. Performability analysis using semi-Markov reward processes
NASA Technical Reports Server (NTRS)
Ciardo, Gianfranco; Marie, Raymond A.; Sericola, Bruno; Trivedi, Kishor S.
1990-01-01
Beaudry (1978) proposed a simple method of computing the distribution of performability in a Markov reward process. Two extensions of Beaudry's approach are presented. The method is generalized to a semi-Markov reward process by removing the restriction requiring the association of zero reward to absorbing states only. The algorithm proceeds by replacing zero-reward nonabsorbing states by a probabilistic switch; it is therefore related to the elimination of vanishing states from the reachability graph of a generalized stochastic Petri net and to the elimination of fast transient states in a decomposition approach to stiff Markov chains. The use of the approach is illustrated with three applications.
2. Universal recovery map for approximate Markov chains
PubMed Central
Sutter, David; Fawzi, Omar; Renner, Renato
2016-01-01
A central question in quantum information theory is to determine how well lost information can be reconstructed. Crucially, the corresponding recovery operation should perform well without knowing the information to be reconstructed. In this work, we show that the quantum conditional mutual information measures the performance of such recovery operations. More precisely, we prove that the conditional mutual information I(A:C|B) of a tripartite quantum state ρABC can be bounded from below by its distance to the closest recovered state RB→BC(ρAB), where the C-part is reconstructed from the B-part only and the recovery map RB→BC merely depends on ρBC. One particular application of this result implies the equivalence between two different approaches to define topological order in quantum systems. PMID:27118889
3. Crime Specialization, Seriousness Progression, and Markov Chains.
ERIC Educational Resources Information Center
Holland, Terrill R.; McGarvey, Bill
1984-01-01
Subjected sequences of violent and nonviolent offenses to log-linear analyses of the stabilities and magnitudes of their transition probabilities. Results were seen to support previous research in which nonviolent criminality emerged as more fundamental than violence in potential for pattern development. (LLL)
4. Multihistogram reweighting for nonequilibrium Markov processes using sequential importance sampling methods.
PubMed
Bojesen, Troels Arnfred
2013-04-01
We present a multihistogram reweighting technique for nonequilibrium Markov chains with discrete energies. The method generalizes the single-histogram method of Yin et al. [Phys. Rev. E 72, 036122 (2005)], making it possible to calculate the time evolution of observables at a posteriori chosen couplings based on a set of simulations performed at other couplings. In the same way as multihistogram reweighting in an equilibrium setting improves the practical reweighting range as well as use of available data compared to single-histogram reweighting, the method generalizes the multihistogram advantages to nonequilibrium simulations. We demonstrate the procedure for the Ising model with Metropolis dynamics, but stress that the method is generally applicable to a range of models and Monte Carlo update schemes. PMID:23679555
5. 0.234: The Myth of a Universal Acceptance Ratio for Monte Carlo Simulations
Potter, Christopher C. J.; Swendsen, Robert H.
Two well-known papers by Gelman, Roberts, and Gilks have proposed the application of the results of an interesting mathematical proof to practical optimizations of Markov Chain Monte Carlo computer simulations. In particular, they advocated tuning the simulation parameters to select an acceptance ratio of 0.234. In this paper, we point out that although the proof is valid, its significance is questionable, and its application to practical computations is not advisable. The simulation algorithm considered in the proof is very inefficient and produces poor results under all circumstances.
6. A novel framework to simulating non-stationary, non-linear, non-Normal hydrological time series using Markov Switching Autoregressive Models
Birkel, C.; Paroli, R.; Spezia, L.; Tetzlaff, D.; Soulsby, C.
2012-12-01
In this paper we present a novel model framework using the class of Markov Switching Autoregressive Models (MSARMs) to examine catchments as complex stochastic systems that exhibit non-stationary, non-linear and non-Normal rainfall-runoff and solute dynamics. Hereby, MSARMs are pairs of stochastic processes, one observed and one unobserved, or hidden. We model the unobserved process as a finite state Markov chain and assume that the observed process, given the hidden Markov chain, is conditionally autoregressive, which means that the current observation depends on its recent past (system memory). The model is fully embedded in a Bayesian analysis based on Markov Chain Monte Carlo (MCMC) algorithms for model selection and uncertainty assessment. Hereby, the autoregressive order and the dimension of the hidden Markov chain state-space are essentially self-selected. The hidden states of the Markov chain represent unobserved levels of variability in the observed process that may result from complex interactions of hydroclimatic variability on the one hand and catchment characteristics affecting water and solute storage on the other. To deal with non-stationarity, additional meteorological and hydrological time series along with a periodic component can be included in the MSARMs as covariates. This extension allows identification of potential underlying drivers of temporal rainfall-runoff and solute dynamics. We applied the MSAR model framework to streamflow and conservative tracer (deuterium and oxygen-18) time series from an intensively monitored 2.3 km2 experimental catchment in eastern Scotland. Statistical time series analysis, in the form of MSARMs, suggested that the streamflow and isotope tracer time series are not controlled by simple linear rules. MSARMs showed that the dependence of current observations on past inputs observed by transport models often in form of the long-tailing of travel time and residence time distributions can be efficiently explained by
7. Likelihood free inference for Markov processes: a comparison.
PubMed
Owen, Jamie; Wilkinson, Darren J; Gillespie, Colin S
2015-04-01
Approaches to Bayesian inference for problems with intractable likelihoods have become increasingly important in recent years. Approximate Bayesian computation (ABC) and "likelihood free" Markov chain Monte Carlo techniques are popular methods for tackling inference in these scenarios but such techniques are computationally expensive. In this paper we compare the two approaches to inference, with a particular focus on parameter inference for stochastic kinetic models, widely used in systems biology. Discrete time transition kernels for models of this type are intractable for all but the most trivial systems yet forward simulation is usually straightforward. We discuss the relative merits and drawbacks of each approach whilst considering the computational cost implications and efficiency of these techniques. In order to explore the properties of each approach we examine a range of observation regimes using two example models. We use a Lotka-Volterra predator-prey model to explore the impact of full or partial species observations using various time course observations under the assumption of known and unknown measurement error. Further investigation into the impact of observation error is then made using a Schlögl system, a test case which exhibits bi-modal state stability in some regions of parameter space. PMID:25720092
8. A Markov model for NASA's Ground Communications Facility
NASA Technical Reports Server (NTRS)
1974-01-01
A 'natural' way of constructing finite-state Markov chains (FSMC) is presented for those noise burst channels that can be modeled by them. In particular, a five-state Markov chain is given as a model of errors occurring at the Ground Communications Facility (GCF). A maximum likelihood procedure applicable to any FSMC is developed for estimating all the model parameters starting from the data of error runs. A few of the statistics important for estimating the performance of error control strategies on the channel are provided.
9. Hidden Markov Model Analysis of Multichromophore Photobleaching
PubMed Central
Messina, Troy C.; Kim, Hiyun; Giurleo, Jason T.; Talaga, David S.
2007-01-01
The interpretation of single-molecule measurements is greatly complicated by the presence of multiple fluorescent labels. However, many molecular systems of interest consist of multiple interacting components. We investigate this issue using multiply labeled dextran polymers that we intentionally photobleach to the background on a single-molecule basis. Hidden Markov models allow for unsupervised analysis of the data to determine the number of fluorescent subunits involved in the fluorescence intermittency of the 6-carboxy-tetramethylrhodamine labels by counting the discrete steps in fluorescence intensity. The Bayes information criterion allows us to distinguish between hidden Markov models that differ by the number of states, that is, the number of fluorescent molecules. We determine information-theoretical limits and show via Monte Carlo simulations that the hidden Markov model analysis approaches these theoretical limits. This technique has resolving power of one fluorescing unit up to as many as 30 fluorescent dyes with the appropriate choice of dye and adequate detection capability. We discuss the general utility of this method for determining aggregation-state distributions as could appear in many biologically important systems and its adaptability to general photometric experiments. PMID:16913765
10. A semi-Markov model for price returns
D'Amico, Guglielmo; Petroni, Filippo
2012-10-01
We study the high frequency price dynamics of traded stocks by a model of returns using a semi-Markov approach. More precisely we assume that the intraday returns are described by a discrete time homogeneous semi-Markov process and the overnight returns are modeled by a Markov chain. Based on this assumptions we derived the equations for the first passage time distribution and the volatility autocorrelation function. Theoretical results have been compared with empirical findings from real data. In particular we analyzed high frequency data from the Italian stock market from 1 January 2007 until the end of December 2010. The semi-Markov hypothesis is also tested through a nonparametric test of hypothesis.
11. Local Autoencoding for Parameter Estimation in a Hidden Potts-Markov Random Field.
PubMed
Song, Sanming; Si, Bailu; Herrmann, J Michael; Feng, Xisheng
2016-05-01
A local-autoencoding (LAE) method is proposed for the parameter estimation in a Hidden Potts-Markov random field model. Due to sampling cost, Markov chain Monte Carlo methods are rarely used in real-time applications. Like other heuristic methods, LAE is based on a conditional independence assumption. It adapts, however, the parameters in a block-by-block style with a simple Hebbian learning rule. Experiments with given label fields show that the LAE is able to converge in far less time than required for a scan. It is also possible to derive an estimate for LAE based on a Cramer–Rao bound that is similar to the classical maximum pseudolikelihood method. As a general algorithm, LAE can be used to estimate the parameters in anisotropic label fields. Furthermore, LAE is not limited to the classical Potts model and can be applied to other types of Potts models by simple label field transformations and straightforward learning rule extensions. Experimental results on image segmentations demonstrate the efficiency and generality of the LAE algorithm. PMID:27019491
12. Assessment of optimized Markov models in protein fold classification.
PubMed
Lampros, Christos; Simos, Thomas; Exarchos, Themis P; Exarchos, Konstantinos P; Papaloukas, Costas; Fotiadis, Dimitrios I
2014-08-01
Protein fold classification is a challenging task strongly associated with the determination of proteins' structure. In this work, we tested an optimization strategy on a Markov chain and a recently introduced Hidden Markov Model (HMM) with reduced state-space topology. The proteins with unknown structure were scored against both these models. Then the derived scores were optimized following a local optimization method. The Protein Data Bank (PDB) and the annotation of the Structural Classification of Proteins (SCOP) database were used for the evaluation of the proposed methodology. The results demonstrated that the fold classification accuracy of the optimized HMM was substantially higher compared to that of the Markov chain or the reduced state-space HMM approaches. The proposed methodology achieved an accuracy of 41.4% on fold classification, while Sequence Alignment and Modeling (SAM), which was used for comparison, reached an accuracy of 38%. PMID:25152041
13. Emulation of higher-order tensors in manifold Monte Carlo methods for Bayesian Inverse Problems
Lan, Shiwei; Bui-Thanh, Tan; Christie, Mike; Girolami, Mark
2016-03-01
The Bayesian approach to Inverse Problems relies predominantly on Markov Chain Monte Carlo methods for posterior inference. The typical nonlinear concentration of posterior measure observed in many such Inverse Problems presents severe challenges to existing simulation based inference methods. Motivated by these challenges the exploitation of local geometric information in the form of covariant gradients, metric tensors, Levi-Civita connections, and local geodesic flows have been introduced to more effectively locally explore the configuration space of the posterior measure. However, obtaining such geometric quantities usually requires extensive computational effort and despite their effectiveness affects the applicability of these geometrically-based Monte Carlo methods. In this paper we explore one way to address this issue by the construction of an emulator of the model from which all geometric objects can be obtained in a much more computationally feasible manner. The main concept is to approximate the geometric quantities using a Gaussian Process emulator which is conditioned on a carefully chosen design set of configuration points, which also determines the quality of the emulator. To this end we propose the use of statistical experiment design methods to refine a potentially arbitrarily initialized design online without destroying the convergence of the resulting Markov chain to the desired invariant measure. The practical examples considered in this paper provide a demonstration of the significant improvement possible in terms of computational loading suggesting this is a promising avenue of further development.
14. Monte Carlo Study of Real Time Dynamics on the Lattice.
PubMed
Alexandru, Andrei; Başar, Gökçe; Bedaque, Paulo F; Vartak, Sohan; Warrington, Neill C
2016-08-19
Monte Carlo studies involving real time dynamics are severely restricted by the sign problem that emerges from a highly oscillatory phase of the path integral. In this Letter, we present a new method to compute real time quantities on the lattice using the Schwinger-Keldysh formalism via Monte Carlo simulations. The key idea is to deform the path integration domain to a complex manifold where the phase oscillations are mild and the sign problem is manageable. We use the previously introduced "contraction algorithm" to create a Markov chain on this alternative manifold. We substantiate our approach by analyzing the quantum mechanical anharmonic oscillator. Our results are in agreement with the exact ones obtained by diagonalization of the Hamiltonian. The method we introduce is generic and, in principle, applicable to quantum field theory albeit very slow. We discuss some possible improvements that should speed up the algorithm. PMID:27588844
15. Empirical Analysis of Stochastic Volatility Model by Hybrid Monte Carlo Algorithm
Takaishi, Tetsuya
2013-04-01
The stochastic volatility model is one of volatility models which infer latent volatility of asset returns. The Bayesian inference of the stochastic volatility (SV) model is performed by the hybrid Monte Carlo (HMC) algorithm which is superior to other Markov Chain Monte Carlo methods in sampling volatility variables. We perform the HMC simulations of the SV model for two liquid stock returns traded on the Tokyo Stock Exchange and measure the volatilities of those stock returns. Then we calculate the accuracy of the volatility measurement using the realized volatility as a proxy of the true volatility and compare the SV model with the GARCH model which is one of other volatility models. Using the accuracy calculated with the realized volatility we find that empirically the SV model performs better than the GARCH model.
16. Precise estimation of pressure-temperature paths from zoned minerals using Markov random field modeling: theory and synthetic inversion
Kuwatani, Tatsu; Nagata, Kenji; Okada, Masato; Toriumi, Mitsuhiro
2012-03-01
The chemical zoning profile in metamorphic minerals is often used to deduce the pressure-temperature ( P- T) history of rock. However, it remains difficult to restore detailed paths from zoned minerals because thermobarometric evaluation of metamorphic conditions involves several uncertainties, including measurement errors and geological noise. We propose a new stochastic framework for estimating precise P- T paths from a chemical zoning structure using the Markov random field (MRF) model, which is a type of Bayesian stochastic method that is often applied to image analysis. The continuity of pressure and temperature during mineral growth is incorporated by Gaussian Markov chains as prior probabilities in order to apply the MRF model to the P- T path inversion. The most probable P- T path can be obtained by maximizing the posterior probability of the sequential set of P and T given the observed compositions of zoned minerals. Synthetic P- T inversion tests were conducted in order to investigate the effectiveness and validity of the proposed model from zoned Mg-Fe-Ca garnet in the divariant KNCFMASH system. In the present study, the steepest descent method was implemented in order to maximize the posterior probability using the Markov chain Monte Carlo algorithm. The proposed method successfully reproduced the detailed shape of the synthetic P- T path by eliminating appropriately the statistical compositional noises without operator's subjectivity and prior knowledge. It was also used to simultaneously evaluate the uncertainty of pressure, temperature, and mineral compositions for all measurement points. The MRF method may have potential to deal with several geological uncertainties, which cause cumbersome systematic errors, by its Bayesian approach and flexible formalism, so that it comprises potentially powerful tools for various inverse problems in petrology.
17. Variance reduction in Monte Carlo analysis of rarefied gas diffusion.
NASA Technical Reports Server (NTRS)
Perlmutter, M.
1972-01-01
The problem of rarefied diffusion between parallel walls is solved using the Monte Carlo method. The diffusing molecules are evaporated or emitted from one of the two parallel walls and diffuse through another molecular species. The Monte Carlo analysis treats the diffusing molecule as undergoing a Markov random walk, and the local macroscopic properties are found as the expected value of the random variable, the random walk payoff. By biasing the transition probabilities and changing the collision payoffs, the expected Markov walk payoff is retained but its variance is reduced so that the Monte Carlo result has a much smaller error.
18. Class-specific weighting for Markov random field estimation: application to medical image segmentation.
PubMed
2012-12-01
Many estimation tasks require Bayesian classifiers capable of adjusting their performance (e.g. sensitivity/specificity). In situations where the optimal classification decision can be identified by an exhaustive search over all possible classes, means for adjusting classifier performance, such as probability thresholding or weighting the a posteriori probabilities, are well established. Unfortunately, analogous methods compatible with Markov random fields (i.e. large collections of dependent random variables) are noticeably absent from the literature. Consequently, most Markov random field (MRF) based classification systems typically restrict their performance to a single, static operating point (i.e. a paired sensitivity/specificity). To address this deficiency, we previously introduced an extension of maximum posterior marginals (MPM) estimation that allows certain classes to be weighted more heavily than others, thus providing a means for varying classifier performance. However, this extension is not appropriate for the more popular maximum a posteriori (MAP) estimation. Thus, a strategy for varying the performance of MAP estimators is still needed. Such a strategy is essential for several reasons: (1) the MAP cost function may be more appropriate in certain classification tasks than the MPM cost function, (2) the literature provides a surfeit of MAP estimation implementations, several of which are considerably faster than the typical Markov Chain Monte Carlo methods used for MPM, and (3) MAP estimation is used far more often than MPM. Consequently, in this paper we introduce multiplicative weighted MAP (MWMAP) estimation-achieved via the incorporation of multiplicative weights into the MAP cost function-which allows certain classes to be preferred over others. This creates a natural bias for specific classes, and consequently a means for adjusting classifier performance. Similarly, we show how this multiplicative weighting strategy can be applied to the MPM
19. Sunspots and ENSO relationship using Markov method
Hassan, Danish; Iqbal, Asif; Ahmad Hassan, Syed; Abbas, Shaheen; Ansari, Muhammad Rashid Kamal
2016-01-01
The various techniques have been used to confer the existence of significant relations between the number of Sunspots and different terrestrial climate parameters such as rainfall, temperature, dewdrops, aerosol and ENSO etc. Improved understanding and modelling of Sunspots variations can explore the information about the related variables. This study uses a Markov chain method to find the relations between monthly Sunspots and ENSO data of two epochs (1996-2009 and 1950-2014). Corresponding transition matrices of both data sets appear similar and it is qualitatively evaluated by high values of 2-dimensional correlation found between transition matrices of ENSO and Sunspots. The associated transition diagrams show that each state communicates with the others. Presence of stronger self-communication (between same states) confirms periodic behaviour among the states. Moreover, closeness found in the expected number of visits from one state to the other show the existence of a possible relation between Sunspots and ENSO data. Moreover, perfect validation of dependency and stationary tests endorses the applicability of the Markov chain analyses on Sunspots and ENSO data. This shows that a significant relation between Sunspots and ENSO data exists. Improved understanding and modelling of Sunspots variations can help to explore the information about the related variables. This study can be useful to explore the influence of ENSO related local climatic variability.
20. Markov sequential pattern recognition : dependency and the unknown class.
SciTech Connect
Malone, Kevin Thomas; Haschke, Greg Benjamin; Koch, Mark William
2004-10-01
The sequential probability ratio test (SPRT) minimizes the expected number of observations to a decision and can solve problems in sequential pattern recognition. Some problems have dependencies between the observations, and Markov chains can model dependencies where the state occupancy probability is geometric. For a non-geometric process we show how to use the effective amount of independent information to modify the decision process, so that we can account for the remaining dependencies. Along with dependencies between observations, a successful system needs to handle the unknown class in unconstrained environments. For example, in an acoustic pattern recognition problem any sound source not belonging to the target set is in the unknown class. We show how to incorporate goodness of fit (GOF) classifiers into the Markov SPRT, and determine the worse case nontarget model. We also develop a multiclass Markov SPRT using the GOF concept.
1. Nonparametric identification and maximum likelihood estimation for hidden Markov models
PubMed Central
Alexandrovich, G.; Holzmann, H.; Leister, A.
2016-01-01
Nonparametric identification and maximum likelihood estimation for finite-state hidden Markov models are investigated. We obtain identification of the parameters as well as the order of the Markov chain if the transition probability matrices have full-rank and are ergodic, and if the state-dependent distributions are all distinct, but not necessarily linearly independent. Based on this identification result, we develop a nonparametric maximum likelihood estimation theory. First, we show that the asymptotic contrast, the Kullback–Leibler divergence of the hidden Markov model, also identifies the true parameter vector nonparametrically. Second, for classes of state-dependent densities which are arbitrary mixtures of a parametric family, we establish the consistency of the nonparametric maximum likelihood estimator. Here, identification of the mixing distributions need not be assumed. Numerical properties of the estimates and of nonparametric goodness of fit tests are investigated in a simulation study.
2. Using model-based proposals for fast parameter inference on discrete state space, continuous-time Markov processes.
PubMed
Pooley, C M; Bishop, S C; Marion, G
2015-06-01
Bayesian statistics provides a framework for the integration of dynamic models with incomplete data to enable inference of model parameters and unobserved aspects of the system under study. An important class of dynamic models is discrete state space, continuous-time Markov processes (DCTMPs). Simulated via the Doob-Gillespie algorithm, these have been used to model systems ranging from chemistry to ecology to epidemiology. A new type of proposal, termed 'model-based proposal' (MBP), is developed for the efficient implementation of Bayesian inference in DCTMPs using Markov chain Monte Carlo (MCMC). This new method, which in principle can be applied to any DCTMP, is compared (using simple epidemiological SIS and SIR models as easy to follow exemplars) to a standard MCMC approach and a recently proposed particle MCMC (PMCMC) technique. When measurements are made on a single-state variable (e.g. the number of infected individuals in a population during an epidemic), model-based proposal MCMC (MBP-MCMC) is marginally faster than PMCMC (by a factor of 2-8 for the tests performed), and significantly faster than the standard MCMC scheme (by a factor of 400 at least). However, when model complexity increases and measurements are made on more than one state variable (e.g. simultaneously on the number of infected individuals in spatially separated subpopulations), MBP-MCMC is significantly faster than PMCMC (more than 100-fold for just four subpopulations) and this difference becomes increasingly large. PMID:25994297
3. Using model-based proposals for fast parameter inference on discrete state space, continuous-time Markov processes
PubMed Central
Pooley, C. M.; Bishop, S. C.; Marion, G.
2015-01-01
Bayesian statistics provides a framework for the integration of dynamic models with incomplete data to enable inference of model parameters and unobserved aspects of the system under study. An important class of dynamic models is discrete state space, continuous-time Markov processes (DCTMPs). Simulated via the Doob–Gillespie algorithm, these have been used to model systems ranging from chemistry to ecology to epidemiology. A new type of proposal, termed ‘model-based proposal’ (MBP), is developed for the efficient implementation of Bayesian inference in DCTMPs using Markov chain Monte Carlo (MCMC). This new method, which in principle can be applied to any DCTMP, is compared (using simple epidemiological SIS and SIR models as easy to follow exemplars) to a standard MCMC approach and a recently proposed particle MCMC (PMCMC) technique. When measurements are made on a single-state variable (e.g. the number of infected individuals in a population during an epidemic), model-based proposal MCMC (MBP-MCMC) is marginally faster than PMCMC (by a factor of 2–8 for the tests performed), and significantly faster than the standard MCMC scheme (by a factor of 400 at least). However, when model complexity increases and measurements are made on more than one state variable (e.g. simultaneously on the number of infected individuals in spatially separated subpopulations), MBP-MCMC is significantly faster than PMCMC (more than 100-fold for just four subpopulations) and this difference becomes increasingly large. PMID:25994297
4. Rank-Driven Markov Processes
Grinfeld, Michael; Knight, Philip A.; Wade, Andrew R.
2012-01-01
We study a class of Markovian systems of N elements taking values in [0,1] that evolve in discrete time t via randomized replacement rules based on the ranks of the elements. These rank-driven processes are inspired by variants of the Bak-Sneppen model of evolution, in which the system represents an evolutionary fitness landscape' and which is famous as a simple model displaying self-organized criticality. Our main results are concerned with long-time large- N asymptotics for the general model in which, at each time step, K randomly chosen elements are discarded and replaced by independent U[0,1] variables, where the ranks of the elements to be replaced are chosen, independently at each time step, according to a distribution κ N on {1,2,…, N} K . Our main results are that, under appropriate conditions on κ N , the system exhibits threshold behavior at s ∗∈[0,1], where s ∗ is a function of κ N , and the marginal distribution of a randomly selected element converges to U[ s ∗,1] as t→∞ and N→∞. Of this class of models, results in the literature have previously been given for special cases only, namely the mean-field' or `random neighbor' Bak-Sneppen model. Our proofs avoid the heuristic arguments of some of the previous work and use Foster-Lyapunov ideas. Our results extend existing results and establish their natural, more general context. We derive some more specialized results for the particular case where K=2. One of our technical tools is a result on convergence of stationary distributions for families of uniformly ergodic Markov chains on increasing state-spaces, which may be of independent interest.
5. Generator estimation of Markov jump processes
Metzner, P.; Dittmer, E.; Jahnke, T.; Schütte, Ch.
2007-11-01
Estimating the generator of a continuous-time Markov jump process based on incomplete data is a problem which arises in various applications ranging from machine learning to molecular dynamics. Several methods have been devised for this purpose: a quadratic programming approach (cf. [D.T. Crommelin, E. Vanden-Eijnden, Fitting timeseries by continuous-time Markov chains: a quadratic programming approach, J. Comp. Phys. 217 (2006) 782-805]), a resolvent method (cf. [T. Müller, Modellierung von Proteinevolution, PhD thesis, Heidelberg, 2001]), and various implementations of an expectation-maximization algorithm ([S. Asmussen, O. Nerman, M. Olsson, Fitting phase-type distributions via the EM algorithm, Scand. J. Stat. 23 (1996) 419-441; I. Holmes, G.M. Rubin, An expectation maximization algorithm for training hidden substitution models, J. Mol. Biol. 317 (2002) 753-764; U. Nodelman, C.R. Shelton, D. Koller, Expectation maximization and complex duration distributions for continuous time Bayesian networks, in: Proceedings of the twenty-first conference on uncertainty in AI (UAI), 2005, pp. 421-430; M. Bladt, M. Sørensen, Statistical inference for discretely observed Markov jump processes, J.R. Statist. Soc. B 67 (2005) 395-410]). Some of these methods, however, seem to be known only in a particular research community, and have later been reinvented in a different context. The purpose of this paper is to compile a catalogue of existing approaches, to compare the strengths and weaknesses, and to test their performance in a series of numerical examples. These examples include carefully chosen model problems and an application to a time series from molecular dynamics.
6. A configuration space Monte Carlo algorithm for solving the nuclear pairing problem
Lingle, Mark
Nuclear pairing correlations using Quantum Monte Carlo are studied in this dissertation. We start by defining the nuclear pairing problem and discussing several historical methods developed to solve this problem, paying special attention to the applicability of such methods. A numerical example discussing pairing correlations in several calcium isotopes using the BCS and Exact Pairing solutions are presented. The ground state energies, correlation energies, and occupation numbers are compared to determine the applicability of each approach to realistic cases. Next we discuss some generalities related to the theory of Markov Chains and Quantum Monte Carlo in regards to nuclear structure. Finally we present our configuration space Monte Carlo algorithm starting from a discussion of a path integral approach by the authors. Some general features of the Pairing Hamiltonian that boost the effectiveness of a configuration space Monte Carlo approach are mentioned. The full details of our method are presented and special attention is paid to convergence and error control. We present a series of examples illustrating the effectiveness of our approach. These include situations with non-constant pairing strengths, limits when pairing correlations are weak, the computation of excited states, and problems when the relevant configuration space is large. We conclude with a chapter examining some of the effects of continuum states in 24O.
7. Characterising the Transmission Dynamics of Acinetobacter baumannii in Intensive Care Units Using Hidden Markov Models.
PubMed
Doan, Tan N; Kong, David C M; Marshall, Caroline; Kirkpatrick, Carl M J; McBryde, Emma S
2015-01-01
Little is known about the transmission dynamics of Acinetobacter baumannii in hospitals, despite such information being critical for designing effective infection control measures. In the absence of comprehensive epidemiological data, mathematical modelling is an attractive approach to understanding transmission process. The statistical challenge in estimating transmission parameters from infection data arises from the fact that most patients are colonised asymptomatically and therefore the transmission process is not fully observed. Hidden Markov models (HMMs) can overcome this problem. We developed a continuous-time structured HMM to characterise the transmission dynamics, and to quantify the relative importance of different acquisition sources of A. baumannii in intensive care units (ICUs) in three hospitals in Melbourne, Australia. The hidden states were the total number of patients colonised with A. baumannii (both detected and undetected). The model input was monthly incidence data of the number of detected colonised patients (observations). A Bayesian framework with Markov chain Monte Carlo algorithm was used for parameter estimations. We estimated that 96-98% of acquisition in Hospital 1 and 3 was due to cross-transmission between patients; whereas most colonisation in Hospital 2 was due to other sources (sporadic acquisition). On average, it takes 20 and 31 days for each susceptible individual in Hospital 1 and Hospital 3 to become colonised as a result of cross-transmission, respectively; whereas it takes 17 days to observe one new colonisation from sporadic acquisition in Hospital 2. The basic reproduction ratio (R0) for Hospital 1, 2 and 3 was 1.5, 0.02 and 1.6, respectively. Our study is the first to characterise the transmission dynamics of A. baumannii using mathematical modelling. We showed that HMMs can be applied to sparse hospital infection data to estimate transmission parameters despite unobserved events and imperfect detection of the organism
8. Using self-consistent fields to bias Monte Carlo methods with applications to designing and sampling protein sequences
Zou, Jinming; Saven, Jeffery G.
2003-02-01
For complex multidimensional systems, Monte Carlo methods are useful for sampling probable regions of a configuration space and, in the context of annealing, for determining "low energy" or "high scoring" configurations. Such methods have been used in protein design as means to identify amino acid sequences that are energetically compatible with a particular backbone structure. As with many other applications of Monte Carlo methods, such searches can be inefficient if trial configurations (protein sequences) in the Markov chain are chosen randomly. Here a mean-field biased Monte Carlo method (MFBMC) is presented and applied to designing and sampling protein sequences. The MFBMC method uses predetermined sequence identity probabilities wi(α) to bias the sequence selection. The wi(α) are calculated using a self-consistent, mean-field theory that can estimate the number and composition of sequences having predetermined values of energetically related foldability criteria. The MFBMC method is applied to both a simple protein model, the 27-mer lattice model, and an all-atom protein model. Compared to conventional Monte Carlo (MC) and configurational bias Monte Carlo (BMC), the MFBMC method converges faster to low energy sequences and samples such sequences more efficiently. The MFBMC method also tolerates faster cooling rates than the MC and BMC methods. The MFBMC method can be applied not only to protein sequence search, but also to a wide variety of polymeric and condensed phase systems.
9. A Markov model of the Indus script
PubMed Central
2009-01-01
Although no historical information exists about the Indus civilization (flourished ca. 2600–1900 B.C.), archaeologists have uncovered about 3,800 short samples of a script that was used throughout the civilization. The script remains undeciphered, despite a large number of attempts and claimed decipherments over the past 80 years. Here, we propose the use of probabilistic models to analyze the structure of the Indus script. The goal is to reveal, through probabilistic analysis, syntactic patterns that could point the way to eventual decipherment. We illustrate the approach using a simple Markov chain model to capture sequential dependencies between signs in the Indus script. The trained model allows new sample texts to be generated, revealing recurring patterns of signs that could potentially form functional subunits of a possible underlying language. The model also provides a quantitative way of testing whether a particular string belongs to the putative language as captured by the Markov model. Application of this test to Indus seals found in Mesopotamia and other sites in West Asia reveals that the script may have been used to express different content in these regions. Finally, we show how missing, ambiguous, or unreadable signs on damaged objects can be filled in with most likely predictions from the model. Taken together, our results indicate that the Indus script exhibits rich synactic structure and the ability to represent diverse content. both of which are suggestive of a linguistic writing system rather than a nonlinguistic symbol system. PMID:19666571
10. A Markov model of the Indus script.
PubMed
2009-08-18
Although no historical information exists about the Indus civilization (flourished ca. 2600-1900 B.C.), archaeologists have uncovered about 3,800 short samples of a script that was used throughout the civilization. The script remains undeciphered, despite a large number of attempts and claimed decipherments over the past 80 years. Here, we propose the use of probabilistic models to analyze the structure of the Indus script. The goal is to reveal, through probabilistic analysis, syntactic patterns that could point the way to eventual decipherment. We illustrate the approach using a simple Markov chain model to capture sequential dependencies between signs in the Indus script. The trained model allows new sample texts to be generated, revealing recurring patterns of signs that could potentially form functional subunits of a possible underlying language. The model also provides a quantitative way of testing whether a particular string belongs to the putative language as captured by the Markov model. Application of this test to Indus seals found in Mesopotamia and other sites in West Asia reveals that the script may have been used to express different content in these regions. Finally, we show how missing, ambiguous, or unreadable signs on damaged objects can be filled in with most likely predictions from the model. Taken together, our results indicate that the Indus script exhibits rich synactic structure and the ability to represent diverse content. both of which are suggestive of a linguistic writing system rather than a nonlinguistic symbol system. PMID:19666571
11. Stripes in a three-chain Hubbard ladder: A comparison of density-matrix renormalization group and constrained-path Monte Carlo results
SciTech Connect
Bonca, J.; Gubernatis, J. E.; Guerrero, M.; Jeckelmann, Eric; White, Steven R.
2000-02-01
Using both the density-matrix renormalization group method and the constrained-path quantum Monte Carlo method, we studied the ground-state energies and the spin and hole densities of a 12x3 Hubbard model with open boundary conditions and six holes doped away from half-filling. Results obtained with these two methods agree well in the small and intermediate U regimes. For U/t{>=}6 we find a ground-state with charge inhomogeneities consistent with stripes. (c) 2000 The American Physical Society.
12. On Markov parameters in system identification
NASA Technical Reports Server (NTRS)
Phan, Minh; Juang, Jer-Nan; Longman, Richard W.
1991-01-01
A detailed discussion of Markov parameters in system identification is given. Different forms of input-output representation of linear discrete-time systems are reviewed and discussed. Interpretation of sampled response data as Markov parameters is presented. Relations between the state-space model and particular linear difference models via the Markov parameters are formulated. A generalization of Markov parameters to observer and Kalman filter Markov parameters for system identification is explained. These extended Markov parameters play an important role in providing not only a state-space realization, but also an observer/Kalman filter for the system of interest.
13. Infinite Factorial Unbounded-State Hidden Markov Model.
PubMed
Valera, Isabel; Ruiz, Francisco J R; Perez-Cruz, Fernando
2016-09-01
There are many scenarios in artificial intelligence, signal processing or medicine, in which a temporal sequence consists of several unknown overlapping independent causes, and we are interested in accurately recovering those canonical causes. Factorial hidden Markov models (FHMMs) present the versatility to provide a good fit to these scenarios. However, in some scenarios, the number of causes or the number of states of the FHMM cannot be known or limited a priori. In this paper, we propose an infinite factorial unbounded-state hidden Markov model (IFUHMM), in which the number of parallel hidden Markovmodels (HMMs) and states in each HMM are potentially unbounded. We rely on a Bayesian nonparametric (BNP) prior over integer-valued matrices, in which the columns represent the Markov chains, the rows the time indexes, and the integers the state for each chain and time instant. First, we extend the existent infinite factorial binary-state HMM to allow for any number of states. Then, we modify this model to allow for an unbounded number of states and derive an MCMC-based inference algorithm that properly deals with the trade-off between the unbounded number of states and chains. We illustrate the performance of our proposed models in the power disaggregation problem. PMID:26571511
14. Markov Analysis of Sleep Dynamics
Kim, J. W.; Lee, J.-S.; Robinson, P. A.; Jeong, D.-U.
2009-05-01
A new approach, based on a Markov transition matrix, is proposed to explain frequent sleep and wake transitions during sleep. The matrix is determined by analyzing hypnograms of 113 obstructive sleep apnea patients. Our approach shows that the statistics of sleep can be constructed via a single Markov process and that durations of all states have modified exponential distributions, in contrast to recent reports of a scale-free form for the wake stage and an exponential form for the sleep stage. Hypnograms of the same subjects, but treated with Continuous Positive Airway Pressure, are analyzed and compared quantitatively with the pretreatment ones, suggesting potential clinical applications.
15. Probability of adsorption of peptide (CR3-1, S2) chains on clay minerals by coarse-grained Monte Carlo simulation
Pandey, Ras B.; Heinz, Hendrik; Farmer, Barry L.; Jones, Sharon; Drummy, Lawrence F.; Naik, Rajesh R.
2009-03-01
A coarse-grained description is used to study the structure and dynamics of peptide chains (CR3-1, S2) in presence of a clay surface on a cubic lattice. A peptide chain is represented by the specific sequence of amino acids. Specificity of residues is captured via an interaction matrix based on the insight gained from the atomistic simulation, i.e., each residue interacts with surrounding residues, solvent, and the clay surface with a unique interaction potential. We use a standard LJ potential with its coefficient controlled by the interaction matrix. Simulations are performed with a number of peptide chains. Along with the global energy and dynamics of peptides, we keep track of mobility, energy (total and adsorption), and correlation with the local structure from the density profiles of each residue. Based on the analysis of local and global quantities, we are able to assess the probability of adsorption of peptides to clay surface in agreement with experiment. The probability of adsorption of S2 is found to be much higher than that of CR3-1 in which S2 is anchored by Lysine. The procedure is complementary to biopanning experiments since it allows screening a large number of peptides (more than 10E+5) on the surface to estimate their binding potential.
16. A Bayesian method for inferring transmission chains in a partially observed epidemic.
SciTech Connect
Marzouk, Youssef M.; Ray, Jaideep
2008-10-01
We present a Bayesian approach for estimating transmission chains and rates in the Abakaliki smallpox epidemic of 1967. The epidemic affected 30 individuals in a community of 74; only the dates of appearance of symptoms were recorded. Our model assumes stochastic transmission of the infections over a social network. Distinct binomial random graphs model intra- and inter-compound social connections, while disease transmission over each link is treated as a Poisson process. Link probabilities and rate parameters are objects of inference. Dates of infection and recovery comprise the remaining unknowns. Distributions for smallpox incubation and recovery periods are obtained from historical data. Using Markov chain Monte Carlo, we explore the joint posterior distribution of the scalar parameters and provide an expected connectivity pattern for the social graph and infection pathway.
17. Improved inference in Bayesian segmentation using Monte Carlo sampling: application to hippocampal subfield volumetry.
PubMed
Iglesias, Juan Eugenio; Sabuncu, Mert Rory; Van Leemput, Koen
2013-10-01
Many segmentation algorithms in medical image analysis use Bayesian modeling to augment local image appearance with prior anatomical knowledge. Such methods often contain a large number of free parameters that are first estimated and then kept fixed during the actual segmentation process. However, a faithful Bayesian analysis would marginalize over such parameters, accounting for their uncertainty by considering all possible values they may take. Here we propose to incorporate this uncertainty into Bayesian segmentation methods in order to improve the inference process. In particular, we approximate the required marginalization over model parameters using computationally efficient Markov chain Monte Carlo techniques. We illustrate the proposed approach using a recently developed Bayesian method for the segmentation of hippocampal subfields in brain MRI scans, showing a significant improvement in an Alzheimer's disease classification task. As an additional benefit, the technique also allows one to compute informative "error bars" on the volume estimates of individual structures. PMID:23773521
18. Monte Carlo methods for localization of cones given multielectrode retinal ganglion cell recordings.
PubMed
Sadeghi, K; Gauthier, J L; Field, G D; Greschner, M; Agne, M; Chichilnisky, E J; Paninski, L
2013-01-01
It has recently become possible to identify cone photoreceptors in primate retina from multi-electrode recordings of ganglion cell spiking driven by visual stimuli of sufficiently high spatial resolution. In this paper we present a statistical approach to the problem of identifying the number, locations, and color types of the cones observed in this type of experiment. We develop an adaptive Markov Chain Monte Carlo (MCMC) method that explores the space of cone configurations, using a Linear-Nonlinear-Poisson (LNP) encoding model of ganglion cell spiking output, while analytically integrating out the functional weights between cones and ganglion cells. This method provides information about our posterior certainty about the inferred cone properties, and additionally leads to improvements in both the speed and quality of the inferred cone maps, compared to earlier "greedy" computational approaches. PMID:23194406
19. Improved Inference in Bayesian Segmentation Using Monte Carlo Sampling: Application to Hippocampal Subfield Volumetry
PubMed Central
Iglesias, Juan Eugenio; Sabuncu, Mert Rory; Leemput, Koen Van
2013-01-01
Many segmentation algorithms in medical image analysis use Bayesian modeling to augment local image appearance with prior anatomical knowledge. Such methods often contain a large number of free parameters that are first estimated and then kept fixed during the actual segmentation process. However, a faithful Bayesian analysis would marginalize over such parameters, accounting for their uncertainty by considering all possible values they may take. Here we propose to incorporate this uncertainty into Bayesian segmentation methods in order to improve the inference process. In particular, we approximate the required marginalization over model parameters using computationally efficient Markov chain Monte Carlo techniques. We illustrate the proposed approach using a recently developed Bayesian method for the segmentation of hippocampal subfields in brain MRI scans, showing a significant improvement in an Alzheimer’s disease classification task. As an additional benefit, the technique also allows one to compute informative “error bars” on the volume estimates of individual structures. PMID:23773521
20. Application of stochastic approach based on Monte Carlo (MC) simulation for life cycle inventory (LCI) to the steel process chain: case study.
PubMed
Bieda, Bogusław
2014-05-15
The purpose of the paper is to present the results of application of stochastic approach based on Monte Carlo (MC) simulation for life cycle inventory (LCI) data of Mittal Steel Poland (MSP) complex in Kraków, Poland. In order to assess the uncertainty, the software CrystalBall® (CB), which is associated with Microsoft® Excel spreadsheet model, is used. The framework of the study was originally carried out for 2005. The total production of steel, coke, pig iron, sinter, slabs from continuous steel casting (CSC), sheets from hot rolling mill (HRM) and blast furnace gas, collected in 2005 from MSP was analyzed and used for MC simulation of the LCI model. In order to describe random nature of all main products used in this study, normal distribution has been applied. The results of the simulation (10,000 trials) performed with the use of CB consist of frequency charts and statistical reports. The results of this study can be used as the first step in performing a full LCA analysis in the steel industry. Further, it is concluded that the stochastic approach is a powerful method for quantifying parameter uncertainty in LCA/LCI studies and it can be applied to any steel industry. The results obtained from this study can help practitioners and decision-makers in the steel production management. PMID:24290145
1. Non-Arrhenius temperature dependence of the island density of one-dimensional Al chains on Si(100): A kinetic Monte Carlo study
SciTech Connect
Albia, Jason R.; Albao, Marvin A.
2015-03-15
Classical nucleation theory predicts that the evolution of mean island density with temperature during growth in one-dimensional systems obeys the Arrhenius relation. In this study, kinetic Monte Carlo simulations of a suitable atomistic lattice-gas model were performed to investigate the experimentally observed non-Arrhenius scaling behavior of island density in the case of one-dimensional Al islands grown on Si(100). Previously, it was proposed that adatom desorption resulted in a transition temperature signaling the departure from classical predictions. Here, the authors demonstrate that desorption above the transition temperature is not possible. Instead, the authors posit that the existence of a transition temperature is due to a combination of factors such as reversibility of island growth, presence of C-defects, adatom diffusion rates, as well as detachment rates at island ends. In addition, the authors show that the anomalous non-Arrhenius behavior vanishes when adatom binds irreversibly with C-defects as observed in In on Si(100) studies.
2. Entropic effects in large-scale Monte Carlo simulations.
PubMed
Predescu, Cristian
2007-07-01
The efficiency of Monte Carlo samplers is dictated not only by energetic effects, such as large barriers, but also by entropic effects that are due to the sheer volume that is sampled. The latter effects appear in the form of an entropic mismatch or divergence between the direct and reverse trial moves. We provide lower and upper bounds for the average acceptance probability in terms of the Rényi divergence of order 1/2 . We show that the asymptotic finitude of the entropic divergence is the necessary and sufficient condition for nonvanishing acceptance probabilities in the limit of large dimension. Furthermore, we demonstrate that the upper bound is reasonably tight by showing that the exponent is asymptotically exact for systems made up of a large number of independent and identically distributed subsystems. For the last statement, we provide an alternative proof that relies on the reformulation of the acceptance probability as a large deviation problem. The reformulation also leads to a class of low-variance estimators for strongly asymmetric distributions. We show that the entropy divergence causes a decay in the average displacements with the number of dimensions n that are simultaneously updated. For systems that have a well-defined thermodynamic limit, the decay is demonstrated to be n(-1/2) for random-walk Monte Carlo and n(-1/6) for smart Monte Carlo (SMC). Numerical simulations of the Lennard-Jones 38 (LJ(38)) cluster show that SMC is virtually as efficient as the Markov chain implementation of the Gibbs sampler, which is normally utilized for Lennard-Jones clusters. An application of the entropic inequalities to the parallel tempering method demonstrates that the number of replicas increases as the square root of the heat capacity of the system. PMID:17677591
3. A comparison of the Monte Carlo and the flux gradient method for atmospheric diffusion
SciTech Connect
Lange, R.
1990-05-01
In order to model the dispersal of atmospheric pollutants in the planetary boundary layer, various methods of parameterizing turbulent diffusion have been employed. The purpose of this paper is to use a three-dimensional particle-in-cell transport and diffusion model to compare the Markov chain (Monte Carlo) method of statistical particle diffusion with the deterministic flux gradient (K-theory) method. The two methods are heavily used in the study of atmospheric diffusion under complex conditions, with the Monte Carlo method gaining in popularity partly because of its more direct application of turbulence parameters. The basis of comparison is a data set from night-time drainage flow tracer experiments performed by the US Department of Energy Atmospheric Studies in Complex Terrain (ASCOT) program at the Geysers geothermal region in northern California. The Atmospheric Diffusion Particle-In-Cell (ADPIC) model used is the main model in the Lawrence Livermore National Laboratory emergency response program: Atmospheric Release Advisory Capability (ARAC). As a particle model, it can simulate diffusion in both the flux gradient and Monte Carlo modes. 9 refs., 6 figs.
4. The Metropolis Monte Carlo method with CUDA enabled Graphic Processing Units
SciTech Connect
Hall, Clifford; Ji, Weixiao; Blaisten-Barojas, Estela
2014-02-01
We present a CPU–GPU system for runtime acceleration of large molecular simulations using GPU computation and memory swaps. The memory architecture of the GPU can be used both as container for simulation data stored on the graphics card and as floating-point code target, providing an effective means for the manipulation of atomistic or molecular data on the GPU. To fully take advantage of this mechanism, efficient GPU realizations of algorithms used to perform atomistic and molecular simulations are essential. Our system implements a versatile molecular engine, including inter-molecule interactions and orientational variables for performing the Metropolis Monte Carlo (MMC) algorithm, which is one type of Markov chain Monte Carlo. By combining memory objects with floating-point code fragments we have implemented an MMC parallel engine that entirely avoids the communication time of molecular data at runtime. Our runtime acceleration system is a forerunner of a new class of CPU–GPU algorithms exploiting memory concepts combined with threading for avoiding bus bandwidth and communication. The testbed molecular system used here is a condensed phase system of oligopyrrole chains. A benchmark shows a size scaling speedup of 60 for systems with 210,000 pyrrole monomers. Our implementation can easily be combined with MPI to connect in parallel several CPU–GPU duets. -- Highlights: •We parallelize the Metropolis Monte Carlo (MMC) algorithm on one CPU—GPU duet. •The Adaptive Tempering Monte Carlo employs MMC and profits from this CPU—GPU implementation. •Our benchmark shows a size scaling-up speedup of 62 for systems with 225,000 particles. •The testbed involves a polymeric system of oligopyrroles in the condensed phase. •The CPU—GPU parallelization includes dipole—dipole and Mie—Jones classic potentials.
5. On Factor Maps that Send Markov Measures to Gibbs Measures
Yoo, Jisang
2010-12-01
Let X and Y be mixing shifts of finite type. Let π be a factor map from X to Y that is fiber-mixing, i.e., given x,bar{x}in X with π(x)=π(bar{x})=yin Y, there is z∈ π -1( y) that is left asymptotic to x and right asymptotic to bar{x}. We show that any Markov measure on X projects to a Gibbs measure on Y under π (for a Hölder continuous potential). In other words, all hidden Markov chains (i.e. sofic measures) realized by π are Gibbs measures. In 2003, Chazottes and Ugalde gave a sufficient condition for a sofic measure to be a Gibbs measure. Our sufficient condition generalizes their condition and is invariant under conjugacy and time reversal. We provide examples demonstrating our result.
6. Multiple testing for neuroimaging via hidden Markov random field.
PubMed
Shu, Hai; Nan, Bin; Koeppe, Robert
2015-09-01
Traditional voxel-level multiple testing procedures in neuroimaging, mostly p-value based, often ignore the spatial correlations among neighboring voxels and thus suffer from substantial loss of power. We extend the local-significance-index based procedure originally developed for the hidden Markov chain models, which aims to minimize the false nondiscovery rate subject to a constraint on the false discovery rate, to three-dimensional neuroimaging data using a hidden Markov random field model. A generalized expectation-maximization algorithm for maximizing the penalized likelihood is proposed for estimating the model parameters. Extensive simulations show that the proposed approach is more powerful than conventional false discovery rate procedures. We apply the method to the comparison between mild cognitive impairment, a disease status with increased risk of developing Alzheimer's or another dementia, and normal controls in the FDG-PET imaging study of the Alzheimer's Disease Neuroimaging Initiative. PMID:26012881
7. Stochastic algorithms for Markov models estimation with intermittent missing data.
PubMed
Deltour, I; Richardson, S; Le Hesran, J Y
1999-06-01
Multistate Markov models are frequently used to characterize disease processes, but their estimation from longitudinal data is often hampered by complex patterns of incompleteness. Two algorithms for estimating Markov chain models in the case of intermittent missing data in longitudinal studies, a stochastic EM algorithm and the Gibbs sampler, are described. The first can be viewed as a random perturbation of the EM algorithm and is appropriate when the M step is straightforward but the E step is computationally burdensome. It leads to a good approximation of the maximum likelihood estimates. The Gibbs sampler is used for a full Bayesian inference. The performances of the two algorithms are illustrated on two simulated data sets. A motivating example concerned with the modelling of the evolution of parasitemia by Plasmodium falciparum (malaria) in a cohort of 105 young children in Cameroon is described and briefly analyzed. PMID:11318215
8. Markov reliability models for digital flight control systems
NASA Technical Reports Server (NTRS)
Mcgough, John; Reibman, Andrew; Trivedi, Kishor
1989-01-01
The reliability of digital flight control systems can often be accurately predicted using Markov chain models. The cost of numerical solution depends on a model's size and stiffness. Acyclic Markov models, a useful special case, are particularly amenable to efficient numerical solution. Even in the general case, instantaneous coverage approximation allows the reduction of some cyclic models to more readily solvable acyclic models. After considering the solution of single-phase models, the discussion is extended to phased-mission models. Phased-mission reliability models are classified based on the state restoration behavior that occurs between mission phases. As an economical approach for the solution of such models, the mean failure rate solution method is introduced. A numerical example is used to show the influence of fault-model parameters and interphase behavior on system unreliability.
9. The Metropolis Monte Carlo method with CUDA enabled Graphic Processing Units
Hall, Clifford; Ji, Weixiao; Blaisten-Barojas, Estela
2014-02-01
We present a CPU-GPU system for runtime acceleration of large molecular simulations using GPU computation and memory swaps. The memory architecture of the GPU can be used both as container for simulation data stored on the graphics card and as floating-point code target, providing an effective means for the manipulation of atomistic or molecular data on the GPU. To fully take advantage of this mechanism, efficient GPU realizations of algorithms used to perform atomistic and molecular simulations are essential. Our system implements a versatile molecular engine, including inter-molecule interactions and orientational variables for performing the Metropolis Monte Carlo (MMC) algorithm, which is one type of Markov chain Monte Carlo. By combining memory objects with floating-point code fragments we have implemented an MMC parallel engine that entirely avoids the communication time of molecular data at runtime. Our runtime acceleration system is a forerunner of a new class of CPU-GPU algorithms exploiting memory concepts combined with threading for avoiding bus bandwidth and communication. The testbed molecular system used here is a condensed phase system of oligopyrrole chains. A benchmark shows a size scaling speedup of 60 for systems with 210,000 pyrrole monomers. Our implementation can easily be combined with MPI to connect in parallel several CPU-GPU duets.
10. Markov Tracking for Agent Coordination
NASA Technical Reports Server (NTRS)
Washington, Richard; Lau, Sonie (Technical Monitor)
1998-01-01
Partially observable Markov decision processes (POMDPs) axe an attractive representation for representing agent behavior, since they capture uncertainty in both the agent's state and its actions. However, finding an optimal policy for POMDPs in general is computationally difficult. In this paper we present Markov Tracking, a restricted problem of coordinating actions with an agent or process represented as a POMDP Because the actions coordinate with the agent rather than influence its behavior, the optimal solution to this problem can be computed locally and quickly. We also demonstrate the use of the technique on sequential POMDPs, which can be used to model a behavior that follows a linear, acyclic trajectory through a series of states. By imposing a "windowing" restriction that restricts the number of possible alternatives considered at any moment to a fixed size, a coordinating action can be calculated in constant time, making this amenable to coordination with complex agents.
11. COCIS: Markov processes in single molecule fluorescence
PubMed Central
Talaga, David S.
2009-01-01
This article examines the current status of Markov processes in single molecule fluorescence. For molecular dynamics to be described by a Markov process, the Markov process must include all states involved in the dynamics and the FPT distributions out of those states must be describable by a simple exponential law. The observation of non-exponential first-passage time distributions or other evidence of non-Markovian dynamics is common in single molecule studies and offers an opportunity to expand the Markov model to include new dynamics or states that improve understanding of the system. PMID:19543444
12. A Test of the Need Hierarchy Concept by a Markov Model of Change in Need Strength.
ERIC Educational Resources Information Center
Rauschenberger, John; And Others
1980-01-01
In this study of 547 high school graduates, Alderfer's and Maslow's need hierarchy theories were expressed in Markov chain form and were subjected to empirical test. Both models were disconfirmed. Corroborative multiwave correlational analysis also failed to support the need hierarchy concept. (Author/IRT)
13. A path-independent method for barrier option pricing in hidden Markov models
Rashidi Ranjbar, Hedieh; Seifi, Abbas
2015-12-01
This paper presents a method for barrier option pricing under a Black-Scholes model with Markov switching. We extend the option pricing method of Buffington and Elliott to price continuously monitored barrier options under a Black-Scholes model with regime switching. We use a regime switching random Esscher transform in order to determine an equivalent martingale pricing measure, and then solve the resulting multidimensional integral for pricing barrier options. We have calculated prices for down-and-out call options under a two-state hidden Markov model using two different Monte-Carlo simulation approaches and the proposed method. A comparison of the results shows that our method is faster than Monte-Carlo simulation methods.
14. A Markov switching model for annual hydrologic time series
Akıntuǧ, B.; Rasmussen, P. F.
2005-09-01
This paper investigates the properties of Markov switching (MS) models (also known as hidden Markov models) for generating annual time series. This type of model has been used in a number of recent studies in the water resources literature. The model considered here assumes that climate is switching between M states and that the state sequence can be described by a Markov chain. Observations are assumed to be drawn from a normal distribution whose parameters depend on the state variable. We present the stochastic properties of this class of models along with procedures for model identification and parameter estimation. Although, at a first glance, MS models appear to be quite different from ARMA models, we show that it is possible to find an ARMA model that has the same autocorrelation function and the same marginal distribution as any given MS model. Hence, despite the difference in model structure, there are strong similarities between MS and ARMA models. MS and ARMA models are applied to the time series of mean annual discharge of the Niagara River. Although it is difficult to draw any general conclusion from a single case study, it appears that MS models (and ARMA models derived from MS models) generally have stronger autocorrelation at higher lags than ARMA models estimated by conventional maximum likelihood. This may be an important property if the purpose of the study is the analysis of multiyear droughts.
15. Analysis of Quantum Monte Carlo Dynamics in Infinite-Range Ising Spin Systems:. Theory and its Possible Applications
Inoue, Jun-Ichi
2013-09-01
In terms of the stochastic process of a quantum-mechanical variant of Markov chain Monte Carlo method based on the Suzuki-Trotter decomposition, we analytically derive deterministic flows of order parameters such as magnetization in infinite-range (a mean-field like) quantum spin systems. Under the static approximation, differential equations with respect to order parameters are explicitly obtained from the Master equation that describes the microscopic-law in the corresponding classical system. We discuss several possible applications of our approach to several research topics, say, image processing and neural networks. This paper is written as a self-review of two papers1,2 for Symposium on Interface between Quantum Information and Statistical Physics at Kinki University in Osaka, Japan.
16. Markov constant and quantum instabilities
Pelantová, Edita; Starosta, Štěpán; Znojil, Miloslav
2016-04-01
For a qualitative analysis of spectra of certain two-dimensional rectangular-well quantum systems several rigorous methods of number theory are shown productive and useful. These methods (and, in particular, a generalization of the concept of Markov constant known in Diophantine approximation theory) are shown to provide a new mathematical insight in the phenomenologically relevant occurrence of anomalies in the spectra. Our results may inspire methodical innovations ranging from the description of the stability properties of metamaterials and of certain hiddenly unitary quantum evolution models up to the clarification of the mechanisms of occurrence of ghosts in quantum cosmology.
17. The Full Monte Carlo: A Live Performance with Stars
Meng, Xiao-Li
2014-06-01
Markov chain Monte Carlo (MCMC) is being applied increasingly often in modern Astrostatistics. It is indeed incredibly powerful, but also very dangerous. It is popular because of its apparent generality (from simple to highly complex problems) and simplicity (the availability of out-of-the-box recipes). It is dangerous because it always produces something but there is no surefire way to verify or even diagnosis that the “something” is remotely close to what the MCMC theory predicts or one hopes. Using very simple models (e.g., conditionally Gaussian), this talk starts with a tutorial of the two most popular MCMC algorithms, namely, the Gibbs Sampler and the Metropolis-Hasting Algorithm, and illustratestheir good, bad, and ugly implementations via live demonstration. The talk ends with a story of how a recent advance, the Ancillary-Sufficient Interweaving Strategy (ASIS) (Yu and Meng, 2011, http://www.stat.harvard.edu/Faculty_Content/meng/jcgs.2011-article.pdf)reduces the danger. It was discovered almost by accident during a Ph.D. student’s (Yaming Yu) struggle with fitting a Cox process model for detecting changes in source intensity of photon counts observed by the Chandra X-ray telescope from a (candidate) neutron/quark star.
18. Diagnosing Undersampling in Monte Carlo Eigenvalue and Flux Tally Estimates
SciTech Connect
Perfetti, Christopher M; Rearden, Bradley T
2015-01-01
This study explored the impact of undersampling on the accuracy of tally estimates in Monte Carlo (MC) calculations. Steady-state MC simulations were performed for models of several critical systems with varying degrees of spatial and isotopic complexity, and the impact of undersampling on eigenvalue and fuel pin flux/fission estimates was examined. This study observed biases in MC eigenvalue estimates as large as several percent and biases in fuel pin flux/fission tally estimates that exceeded tens, and in some cases hundreds, of percent. This study also investigated five statistical metrics for predicting the occurrence of undersampling biases in MC simulations. Three of the metrics (the Heidelberger-Welch RHW, the Geweke Z-Score, and the Gelman-Rubin diagnostics) are commonly used for diagnosing the convergence of Markov chains, and two of the methods (the Contributing Particles per Generation and Tally Entropy) are new convergence metrics developed in the course of this study. These metrics were implemented in the KENO MC code within the SCALE code system and were evaluated for their reliability at predicting the onset and magnitude of undersampling biases in MC eigenvalue and flux tally estimates in two of the critical models. Of the five methods investigated, the Heidelberger-Welch RHW, the Gelman-Rubin diagnostics, and Tally Entropy produced test metrics that correlated strongly to the size of the observed undersampling biases, indicating their potential to effectively predict the size and prevalence of undersampling biases in MC simulations.
19. An efficient approach to ab initio Monte Carlo simulation
SciTech Connect
Leiding, Jeff; Coe, Joshua D.
2014-01-21
We present a Nested Markov chain Monte Carlo (NMC) scheme for building equilibrium averages based on accurate potentials such as density functional theory. Metropolis sampling of a reference system, defined by an inexpensive but approximate potential, was used to substantially decorrelate configurations at which the potential of interest was evaluated, thereby dramatically reducing the number needed to build ensemble averages at a given level of precision. The efficiency of this procedure was maximized on-the-fly through variation of the reference system thermodynamic state (characterized here by its inverse temperature β{sup 0}), which was otherwise unconstrained. Local density approximation results are presented for shocked states of argon at pressures from 4 to 60 GPa, where—depending on the quality of the reference system potential—acceptance probabilities were enhanced by factors of 1.2–28 relative to unoptimized NMC. The optimization procedure compensated strongly for reference potential shortcomings, as evidenced by significantly higher speedups when using a reference potential of lower quality. The efficiency of optimized NMC is shown to be competitive with that of standard ab initio molecular dynamics in the canonical ensemble.
20. A Hidden Markov Approach to Modeling Interevent Earthquake Times
Chambers, D.; Ebel, J. E.; Kafka, A. L.; Baglivo, J.
2003-12-01
A hidden Markov process, in which the interevent time distribution is a mixture of exponential distributions with different rates, is explored as a model for seismicity that does not follow a Poisson process. In a general hidden Markov model, one assumes that a system can be in any of a finite number k of states and there is a random variable of interest whose distribution depends on the state in which the system resides. The system moves probabilistically among the states according to a Markov chain; that is, given the history of visited states up to the present, the conditional probability that the next state is a specified one depends only on the present state. Thus the transition probabilities are specified by a k by k stochastic matrix. Furthermore, it is assumed that the actual states are unobserved (hidden) and that only the values of the random variable are seen. From these values, one wishes to estimate the sequence of states, the transition probability matrix, and any parameters used in the state-specific distributions. The hidden Markov process was applied to a data set of 110 interevent times for earthquakes in New England from 1975 to 2000. Using the Baum-Welch method (Baum et al., Ann. Math. Statist. 41, 164-171), we estimate the transition probabilities, find the most likely sequence of states, and estimate the k means of the exponential distributions. Using k=2 states, we found the data were fit well by a mixture of two exponential distributions, with means of approximately 5 days and 95 days. The steady state model indicates that after approximately one fourth of the earthquakes, the waiting time until the next event had the first exponential distribution and three fourths of the time it had the second. Three and four state models were also fit to the data; the data were inconsistent with a three state model but were well fit by a four state model.
1. Quasi-Monte Carlo methods for lattice systems: A first look
Jansen, K.; Leovey, H.; Ammon, A.; Griewank, A.; Müller-Preussker, M.
2014-03-01
We investigate the applicability of quasi-Monte Carlo methods to Euclidean lattice systems for quantum mechanics in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable calculated by averaging over random observations generated from an ordinary Markov chain Monte Carlo simulation behaves like N, where N is the number of observations. By means of quasi-Monte Carlo methods it is possible to improve this behavior for certain problems to N-1, or even further if the problems are regular enough. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling. Catalogue identifier: AERJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERJ_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence version 3 No. of lines in distributed program, including test data, etc.: 67759 No. of bytes in distributed program, including test data, etc.: 2165365 Distribution format: tar.gz Programming language: C and C++. Computer: PC. Operating system: Tested on GNU/Linux, should be portable to other operating systems with minimal efforts. Has the code been vectorized or parallelized?: No RAM: The memory usage directly scales with the number of samples and dimensions: Bytes used = “number of samples” × “number of dimensions” × 8 Bytes (double precision). Classification: 4.13, 11.5, 23. External routines: FFTW 3 library (http://www.fftw.org) Nature of problem: Certain physical models formulated as a quantum field theory through the Feynman path integral, such as quantum chromodynamics, require a non-perturbative treatment of the path integral. The only known approach that achieves this is the lattice regularization. In this formulation the path integral is discretized to a finite, but very high dimensional integral. So far only Monte
2. Maximal Parrondo's Paradox for Classical and Quantum Markov Chains
Grünbaum, F. Alberto; Pejic, Michael
2016-02-01
Parrondo's paradox refers to the situation where two, multi-round games with a fixed winning criteria, both with probability greater than one-half for one player to win, are combined. Using a possibly biased coin to determine the rule to employ for each round, paradoxically, the previously losing player now wins the combined game with probability greater than one-half. In this paper, we will analyze classical observed, classical hidden, and quantum versions of a game that displays this paradox. The game we have utilized is simpler than games for which this behavior has been previously noted in the classical and quantum cases. We will show that in certain situations the paradox can occur to a greater degree in the quantum version than is possible in the classical versions.
3. Discovering Student Web Usage Profiles Using Markov Chains
ERIC Educational Resources Information Center
Marques, Alice; Belo, Orlando
2011-01-01
Nowadays, Web based platforms are quite common in any university, supporting a very diversified set of applications and services. Ranging from personal management to student evaluation processes, Web based platforms are doing a great job providing a very flexible way of working, promote student enrolment, and making access to academic information…
4. Predicting Precipitation in Darwin: An Experiment with Markov Chains
ERIC Educational Resources Information Center
Boncek, John; Harden, Sig
2009-01-01
As teachers of first-year college mathematics and science students, the authors are constantly on the lookout for simple classroom exercises that improve their students' analytical and computational skills. In this article, the authors outline a project entitled "Predicting Precipitation in Darwin." In this project, students: (1) analyze and…
5. A Markov Chain Approach to Probabilistic Swarm Guidance
NASA Technical Reports Server (NTRS)
Acikmese, Behcet; Bayard, David S.
2012-01-01
This paper introduces a probabilistic guidance approach for the coordination of swarms of autonomous agents. The main idea is to drive the swarm to a prescribed density distribution in a prescribed region of the configuration space. In its simplest form, the probabilistic approach is completely decentralized and does not require communication or collabo- ration between agents. Agents make statistically independent probabilistic decisions based solely on their own state, that ultimately guides the swarm to the desired density distribution in the configuration space. In addition to being completely decentralized, the probabilistic guidance approach has a novel autonomous self-repair property: Once the desired swarm density distribution is attained, the agents automatically repair any damage to the distribution without collaborating and without any knowledge about the damage.
6. Markov Chain Estimation of Avian Seasonal Fecundity, Presentation
EPA Science Inventory
Avian seasonal fecundity is of interest from evolutionary, ecological, and conservation perspectives. However, direct estimation of seasonal fecundity is difficult, especially with multibrooded birds, and models representing the renesting and quitting processes are usually requi...
7. Generators of quantum Markov semigroups
Androulakis, George; Ziemke, Matthew
2015-08-01
Quantum Markov Semigroups (QMSs) originally arose in the study of the evolutions of irreversible open quantum systems. Mathematically, they are a generalization of classical Markov semigroups where the underlying function space is replaced by a non-commutative operator algebra. In the case when the QMS is uniformly continuous, theorems due to the works of Lindblad [Commun. Math. Phys. 48, 119-130 (1976)], Stinespring [Proc. Am. Math. Soc. 6, 211-216 (1955)], and Kraus [Ann. Phys. 64, 311-335 (1970)] imply that the generator of the semigroup has the form L ( A ) = ∑ n = 1 ∞ Vn ∗ A V n + G A + A G ∗ , where Vn and G are elements of the underlying operator algebra. In the present paper, we investigate the form of the generators of QMSs which are not necessarily uniformly continuous and act on the bounded operators of a Hilbert space. We prove that the generators of such semigroups have forms that reflect the results of Lindblad and Stinespring. We also make some progress towards forms reflecting Kraus' result. Finally, we look at several examples to clarify our findings and verify that some of the unbounded operators we are using have dense domains.
8. Testing the Markov hypothesis in fluid flows
Meyer, Daniel W.; Saggini, Frédéric
2016-05-01
Stochastic Markov processes are used very frequently to model, for example, processes in turbulence and subsurface flow and transport. Based on the weak Chapman-Kolmogorov equation and the strong Markov condition, we present methods to test the Markov hypothesis that is at the heart of these models. We demonstrate the capabilities of our methodology by testing the Markov hypothesis for fluid and inertial particles in turbulence, and fluid particles in the heterogeneous subsurface. In the context of subsurface macrodispersion, we find that depending on the heterogeneity level, Markov models work well above a certain scale of interest for media with different log-conductivity correlation structures. Moreover, we find surprising similarities in the velocity dynamics of the different media considered.
9. A reverse Monte Carlo method for deriving optical constants of solids from reflection electron energy-loss spectroscopy spectra
SciTech Connect
Da, B.; Sun, Y.; Ding, Z. J.; Mao, S. F.; Zhang, Z. M.; Jin, H.; Yoshikawa, H.; Tanuma, S.
2013-06-07
A reverse Monte Carlo (RMC) method is developed to obtain the energy loss function (ELF) and optical constants from a measured reflection electron energy-loss spectroscopy (REELS) spectrum by an iterative Monte Carlo (MC) simulation procedure. The method combines the simulated annealing method, i.e., a Markov chain Monte Carlo (MCMC) sampling of oscillator parameters, surface and bulk excitation weighting factors, and band gap energy, with a conventional MC simulation of electron interaction with solids, which acts as a single step of MCMC sampling in this RMC method. To examine the reliability of this method, we have verified that the output data of the dielectric function are essentially independent of the initial values of the trial parameters, which is a basic property of a MCMC method. The optical constants derived for SiO{sub 2} in the energy loss range of 8-90 eV are in good agreement with other available data, and relevant bulk ELFs are checked by oscillator strength-sum and perfect-screening-sum rules. Our results show that the dielectric function can be obtained by the RMC method even with a wide range of initial trial parameters. The RMC method is thus a general and effective method for determining the optical properties of solids from REELS measurements.
10. A Measure-Theoretic Proof of the Markov Property for Hybrid Systems with Markovian Inputs
NASA Technical Reports Server (NTRS)
Tejada, Arturo; Gonzalez, Oscar R.; Gray, W. Steven
2006-01-01
The behavior of a general hybrid system in discrete time can be represented by a non-linear difference equation x(k+1) = Fk(x(k), theta(k)), where theta(k) is assumed to be a finite state Markov chain. An important step in the stability analysis of these systems is to establish the Markov property of (x(k), theta(k)). There are, however, no complete proofs of this property which are simple to understand. This paper aims to correct this problem by presenting a complete and explicit proof, which uses only basic measure-theoretical concepts.
11. On the Markov Property for Nonlinear Discrete-Time Systems with Markovian Inputs
NASA Technical Reports Server (NTRS)
Tejada, Arturo; Gonzalez, Oscar R.; Gray, W. Steven
2006-01-01
The behavior of a general hybrid system in discrete-time can be represented by a non-linear difference equation x(k + 1) = Fk(x(k), theta(k)), where theta(k) is assumed to be a finite-state Markov chain. An important step in the stability analysis of these systems is to establish the Markov property of (x(k), theta(k)). There are, however, no complete proofs of this property which are simple to understand. This paper aims to correct this problem by presenting a complete and explicit proof, which uses only fundamental measure-theoretical concepts.
12. Variance reduction in Monte Carlo analysis of rarefied gas diffusion
NASA Technical Reports Server (NTRS)
Perlmutter, M.
1972-01-01
The present analysis uses the Monte Carlo method to solve the problem of rarefied diffusion between parallel walls. The diffusing molecules are evaporated or emitted from one of two parallel walls and diffused through another molecular species. The analysis treats the diffusing molecule as undergoing a Markov random walk and the local macroscopic properties are found as the expected value of the random variable, the random walk payoff. By biasing the transition probabilities and changing the collision payoffs the expected Markov walk payoff is retained but its variance is reduced so that the M. C. result has a much smaller error.
13. Using Markov models to simulate electron spin resonance spectra from molecular dynamics trajectories.
PubMed
Sezer, Deniz; Freed, Jack H; Roux, Benoit
2008-09-01
Simulating electron spin resonance (ESR) spectra directly from molecular dynamics simulations of a spin-labeled protein necessitates a large number (hundreds or thousands) of relatively long (hundreds of nanoseconds) trajectories. To meet this challenge, we explore the possibility of constructing accurate stochastic models of the spin label dynamics from atomistic trajectories. A systematic, two-step procedure, based on the probabilistic framework of hidden Markov models, is developed to build a discrete-time Markov chain process that faithfully captures the internal spin label dynamics on time scales longer than about 150 ps. The constructed Markov model is used both to gain insight into the long-lived conformations of the spin label and to generate the stochastic trajectories required for the simulation of ESR spectra. The methodology is illustrated with an application to the case of a spin-labeled poly alanine alpha helix in explicit solvent. PMID:18698714
14. Translocation of reptating chains
Żurek, S.; Drzewiński, A.; van Leeuwen, J. M. J.
2011-05-01
Voltage-driven translocation is modeled with the Rubinstein-Duke rules for hopping reptons in one- and two-dimensional lattices. The chain is driven through the pore by a bias potential promoting the transition of stored length in one direction. Coupling states give a semi-periodicity of the process that enables us to relate the properties to the stationary state of the master equation. The exact solution for short chains and Monte Carlo simulations for longer chains are used to calculate displacements, velocities and the translocation time.
15. Algorithms for Discovery of Multiple Markov Boundaries
PubMed Central
Statnikov, Alexander; Lytkin, Nikita I.; Lemeire, Jan; Aliferis, Constantin F.
2013-01-01
Algorithms for Markov boundary discovery from data constitute an important recent development in machine learning, primarily because they offer a principled solution to the variable/feature selection problem and give insight on local causal structure. Over the last decade many sound algorithms have been proposed to identify a single Markov boundary of the response variable. Even though faithful distributions and, more broadly, distributions that satisfy the intersection property always have a single Markov boundary, other distributions/data sets may have multiple Markov boundaries of the response variable. The latter distributions/data sets are common in practical data-analytic applications, and there are several reasons why it is important to induce multiple Markov boundaries from such data. However, there are currently no sound and efficient algorithms that can accomplish this task. This paper describes a family of algorithms TIE* that can discover all Markov boundaries in a distribution. The broad applicability as well as efficiency of the new algorithmic family is demonstrated in an extensive benchmarking study that involved comparison with 26 state-of-the-art algorithms/variants in 15 data sets from a diversity of application domains. PMID:25285052
16. Transitive reasoning distorts induction in causal chains.
PubMed
von Sydow, Momme; Hagmayer, York; Meder, Björn
2016-04-01
A probabilistic causal chain A→B→C may intuitively appear to be transitive: If A probabilistically causes B, and B probabilistically causes C, A probabilistically causes C. However, probabilistic causal relations can only guaranteed to be transitive if the so-called Markov condition holds. In two experiments, we examined how people make probabilistic judgments about indirect relationships A→C in causal chains A→B→C that violate the Markov condition. We hypothesized that participants would make transitive inferences in accordance with the Markov condition although they were presented with counterevidence showing intransitive data. For instance, participants were successively presented with data entailing positive dependencies A→B and B→C. At the same time, the data entailed that A and C were statistically independent. The results of two experiments show that transitive reasoning via a mediating event B influenced and distorted the induction of the indirect relation between A and C. Participants' judgments were affected by an interaction of transitive, causal-model-based inferences and the observed data. Our findings support the idea that people tend to chain individual causal relations into mental causal chains that obey the Markov condition and thus allow for transitive reasoning, even if the observed data entail that such inferences are not warranted. PMID:26620811
17. Monte Carlo portal dosimetry
SciTech Connect
Chin, P.W. . E-mail: mary.chin@physics.org
2005-10-15
This project developed a solution for verifying external photon beam radiotherapy. The solution is based on a calibration chain for deriving portal dose maps from acquired portal images, and a calculation framework for predicting portal dose maps. Quantitative comparison between acquired and predicted portal dose maps accomplishes both geometric (patient positioning with respect to the beam) and dosimetric (two-dimensional fluence distribution of the beam) verifications. A disagreement would indicate that beam delivery had not been according to plan. The solution addresses the clinical need for verifying radiotherapy both pretreatment (without the patient in the beam) and on treatment (with the patient in the beam). Medical linear accelerators mounted with electronic portal imaging devices (EPIDs) were used to acquire portal images. Two types of EPIDs were investigated: the amorphous silicon (a-Si) and the scanning liquid ion chamber (SLIC). The EGSnrc family of Monte Carlo codes were used to predict portal dose maps by computer simulation of radiation transport in the beam-phantom-EPID configuration. Monte Carlo simulations have been implemented on several levels of high throughput computing (HTC), including the grid, to reduce computation time. The solution has been tested across the entire clinical range of gantry angle, beam size (5 cmx5 cm to 20 cmx20 cm), and beam-patient and patient-EPID separations (4 to 38 cm). In these tests of known beam-phantom-EPID configurations, agreement between acquired and predicted portal dose profiles was consistently within 2% of the central axis value. This Monte Carlo portal dosimetry solution therefore achieved combined versatility, accuracy, and speed not readily achievable by other techniques.
18. Entropy, complexity, and Markov diagrams for random walk cancer models
PubMed Central
Newton, Paul K.; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter
2014-01-01
The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential. PMID:25523357
19. Self-Organizing Hidden Markov Model Map (SOHMMM).
PubMed
Ferles, Christos; Stafylopatis, Andreas
2013-12-01
A hybrid approach combining the Self-Organizing Map (SOM) and the Hidden Markov Model (HMM) is presented. The Self-Organizing Hidden Markov Model Map (SOHMMM) establishes a cross-section between the theoretic foundations and algorithmic realizations of its constituents. The respective architectures and learning methodologies are fused in an attempt to meet the increasing requirements imposed by the properties of deoxyribonucleic acid (DNA), ribonucleic acid (RNA), and protein chain molecules. The fusion and synergy of the SOM unsupervised training and the HMM dynamic programming algorithms bring forth a novel on-line gradient descent unsupervised learning algorithm, which is fully integrated into the SOHMMM. Since the SOHMMM carries out probabilistic sequence analysis with little or no prior knowledge, it can have a variety of applications in clustering, dimensionality reduction and visualization of large-scale sequence spaces, and also, in sequence discrimination, search and classification. Two series of experiments based on artificial sequence data and splice junction gene sequences demonstrate the SOHMMM's characteristics and capabilities. PMID:24001407
20. Entropy, complexity, and Markov diagrams for random walk cancer models
| 136,698
| 677,452
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.640625
| 3
|
CC-MAIN-2016-50
|
latest
|
en
| 0.89303
|
https://pharmpk.com/PK05/PK2005581.html
| 1,643,262,666,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-05/segments/1642320305141.20/warc/CC-MAIN-20220127042833-20220127072833-00555.warc.gz
| 485,973,978
| 2,461
|
# PharmPK Discussion - Unequal washouts during BE studies
PharmPK Discussion List Archive Index page
• On 20 Sep 2005 at 22:52:18, "Rhishikesh Mandke" (mandke.rhishikesh.aaa.gmail.com) sent the message
`Dear Group,Recently during one of our 3-way BE studies, 2 volunteers from agroup of 18 were absent for second period. However, these volunteersagreed to participate in the study further and the study wascontinued. Now the problem is as follows.16 Volunteers: Washout between period 1 and 2: (x) days. Washout between period 2 and 3: (x) daysRest 2 Volunteers: Washout between period 1 and 2: (x + 7) days Washout between period 2 and 3: (x) daysMy first question is that, will this kind of unequal washout affectthe PK parameters measured during the study?My second question is that how this kind of situations treatedstatistically? (What I wanted to know is whether any specialstatistical treatment has to be given during such situations)Thanks and best regards,Rhishikesh MANDKE`
Back to the Top
• On 21 Sep 2005 at 04:40:34, Priti Pandey (priti_pandey.-a-.yahoo.com) sent the message
`Hello Rhishikesh,There are two methods to do statistical analysis in this case. Eitheryou eliminate those two subjects who were absent during period II oranalyse all the 18 subject subjects. In the first case, you arereducing power of your study. In second case your power will be morebut you are using missing value for two subjects in statisticalanalysis. It is upto you how you want to go ahead.Statistial purpose to give equal wash out period between each periodis to test: "Is there significant difference between carry over ornot if it exist?"So unequal wash-out period won't affect much if you have given enoughwashout period between each period in case of bioequivalence. ifthere is any carry over then you will come to know in pre dosesampling time point. if this situation is out of question then youcan go ahead with unequal wash-out period for statistical analysis.All the bestPriti PandeyRanbaxy, India`
Back to the Top
• On 21 Sep 2005 at 07:18:39, manish issar (issarmanish.aaa.yahoo.com) sent the message
`HiI would like to add in addition to what preeti just mentioned.Before the study is initiated there has to be a mention in theprotocol how incomplete data (like missing samples or subjects notcompleting the perioid) is going to be handled in the PK statistics.One cannot make decisions after the study has been executed. Alsorejection of data cannot be according to ones wish.hope this helpsManish Issar, Ph.DSandoz4700 Eon DriveWilson, NC-27893`
Back to the Top
• On 21 Sep 2005 at 13:37:05, Prah.James.at.epamail.epa.gov sent the message
`The following message was posted to: PharmPKDear Manish,In addition one would want to define in the protocol how an outlier isdefined rather than doing it post hoc.JimJames D. Prah, PhDUS EPAHuman Studies Division MD (58B)Research Triangle Park, NC, 27711919 966 6244919 966 6367 FAX`
Back to the Top
Want to post a follow-up message on this topic? If this link does not work with your browser send a follow-up message to PharmPK@boomer.org with "Unequal washouts during BE studies" as the subject
Copyright 1995-2010 David W. A. Bourne (david@boomer.org)
| 829
| 3,263
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.53125
| 3
|
CC-MAIN-2022-05
|
latest
|
en
| 0.927869
|
http://betterlesson.com/lesson/resource/2315616/four-square-poster-standard-verbal-visual-and-real-life-problem
| 1,488,219,963,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-09/segments/1487501173405.40/warc/CC-MAIN-20170219104613-00210-ip-10-171-10-108.ec2.internal.warc.gz
| 25,770,364
| 24,009
|
## FOUR Square Poster: Standard, Verbal, Visual and Real Life problem - Section 5: Work It Out
FOUR Square Poster: Standard, Verbal, Visual and Real Life problem
# Everything In Its Place: Place Value
Unit 1: Working with Whole Numbers
Lesson 6 of 10
## Big Idea: Recognizing and connecting number values, expressed in a standard form and as a numeral.
Print Lesson
13 teachers like this lesson
Standards:
Subject(s):
Math, Place Value, Number Sense and Operations, Integers, number, whole numbers, standard form, word form, expanded form, game
80 minutes
### James Ewing
##### Similar Lessons
###### Show what you know + Equivalency
6th Grade Math » The College Project - Working with Decimals
Big Idea: What do students understand? What gaps do they have in their understanding? How are fractions, decimals, and percents connected?
Favorites(13)
Resources(23)
Somerville, MA
Environment: Urban
###### Place Value Review
5th Grade Math » Operations with Decimals and Whole Numbers
Big Idea: Attention: Value found in starting with Place.
Favorites(91)
Resources(9)
Grand Rapids, MI
Environment: Urban
###### Playing With Place Value - Manipulatives
5th Grade Math » The Value of a Whole Number - Place Value
Big Idea: Seeing is believing - especially in place value.
Favorites(19)
Resources(20)
Scottsdale, AZ
Environment: Urban
| 312
| 1,339
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.484375
| 3
|
CC-MAIN-2017-09
|
latest
|
en
| 0.807554
|
https://www.convert-measurement-units.com/convert+Kilosiemens+to+Nanosiemens.php
| 1,712,920,013,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-18/segments/1712296815919.75/warc/CC-MAIN-20240412101354-20240412131354-00541.warc.gz
| 648,479,715
| 13,398
|
Convert kS to nS (Kilosiemens to Nanosiemens)
## Kilosiemens into Nanosiemens
numbers in scientific notation
https://www.convert-measurement-units.com/convert+Kilosiemens+to+Nanosiemens.php
# Convert Kilosiemens to Nanosiemens (kS to nS):
1. Choose the right category from the selection list, in this case 'Electric conductance'.
2. Next enter the value you want to convert. The basic operations of arithmetic: addition (+), subtraction (-), multiplication (*, x), division (/, :, ÷), exponent (^), square root (√), brackets and π (pi) are all permitted at this point.
3. From the selection list, choose the unit that corresponds to the value you want to convert, in this case 'Kilosiemens [kS]'.
4. Finally choose the unit you want the value to be converted to, in this case 'Nanosiemens [nS]'.
5. Then, when the result appears, there is still the possibility of rounding it to a specific number of decimal places, whenever it makes sense to do so.
With this calculator, it is possible to enter the value to be converted together with the original measurement unit; for example, '482 Kilosiemens'. In so doing, either the full name of the unit or its abbreviation can be usedas an example, either 'Kilosiemens' or 'kS'. Then, the calculator determines the category of the measurement unit of measure that is to be converted, in this case 'Electric conductance'. After that, it converts the entered value into all of the appropriate units known to it. In the resulting list, you will be sure also to find the conversion you originally sought. Alternatively, the value to be converted can be entered as follows: '64 kS to nS' or '1 kS into nS' or '41 Kilosiemens -> Nanosiemens' or '81 kS = nS' or '31 Kilosiemens to nS' or '28 kS to Nanosiemens' or '80 Kilosiemens into Nanosiemens'. For this alternative, the calculator also figures out immediately into which unit the original value is specifically to be converted. Regardless which of these possibilities one uses, it saves one the cumbersome search for the appropriate listing in long selection lists with myriad categories and countless supported units. All of that is taken over for us by the calculator and it gets the job done in a fraction of a second.
Furthermore, the calculator makes it possible to use mathematical expressions. As a result, not only can numbers be reckoned with one another, such as, for example, '(13 * 9) kS'. But different units of measurement can also be coupled with one another directly in the conversion. That could, for example, look like this: '482 Kilosiemens + 1446 Nanosiemens' or '69mm x 77cm x 56dm = ? cm^3'. The units of measure combined in this way naturally have to fit together and make sense in the combination in question.
The mathematical functions sin, cos, tan and sqrt can also be used. Example: sin(π/2), cos(pi/2), tan(90°), sin(90) or sqrt(4).
If a check mark has been placed next to 'Numbers in scientific notation', the answer will appear as an exponential. For example, 4.742 716 006 224 ×1023. For this form of presentation, the number will be segmented into an exponent, here 23, and the actual number, here 4.742 716 006 224. For devices on which the possibilities for displaying numbers are limited, such as for example, pocket calculators, one also finds the way of writing numbers as 4.742 716 006 224 E+23. In particular, this makes very large and very small numbers easier to read. If a check mark has not been placed at this spot, then the result is given in the customary way of writing numbers. For the above example, it would then look like this: 474 271 600 622 400 000 000 000. Independent of the presentation of the results, the maximum precision of this calculator is 14 places. That should be precise enough for most applications.
| 919
| 3,769
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.203125
| 3
|
CC-MAIN-2024-18
|
latest
|
en
| 0.801116
|
https://community.khronos.org/t/how-can-we-draw-a-cylinder-using-two-points-in-3d-space/28689
| 1,718,675,240,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-26/segments/1718198861746.4/warc/CC-MAIN-20240618011430-20240618041430-00346.warc.gz
| 160,943,065
| 5,503
|
# How can we draw a cylinder using two points in 3D space
Hi,
I was wonderring how we can draw a cylinder using any two points in 3D space?
I tried using glu cylinder but I can only translate to 1 point but what about the other point, is there a way I can draw a cylinder between two points in 3D space?
A_Newbie
You need to translate the cylinder to the first point and rotate it towards the other point. The height of the cylinder is equal to the distance between the two points.
The problem is to find the proper rotation matrix, but I think you can use gluLookAt in some way to build the required transformation matrix.
You can first translate to the first point then
let the second vector be
v2 = (30,30,30)
calculate the angle on the x and y plane using
v2 = (30, 30, 0) and unit along x axis = 1,0,0
i.e. theta1 = angle bw v2 and unitX;
similarly find angle on x and z plane as theta2 with v2 = (30,0,30) then
glRotatef(theta1,1,0,0);
glrotatef(90-theta2,0,1,0);
drawcylinder().
[This message has been edited by Fastian (edited 03-29-2001).]
Hello,
I tried this but it did not work. Here is the code that I used. I have pos1 and pos2 which are structures with x, y, and z members. dx, dy, and dz are the deltas between pos1.y and pos2.x, and .z. dxSquared is dx*dx, etc.
glPushMatrix ();
glTranslatef (pos1->x, pos1->y, pos1->z);
``````// rotate about x axis
opp = pos2->y - pos1->y;
theta = 360 * (theta / (2*3.1415926));
glRotatef (-theta, 1.0, 0.0, 0.0);
opp = pos2->x - pos1->x;
theta = 360 * (theta / (2*3.1415926));
glRotatef (90-(-theta), 0.0, 1.0, 0.0);
``````
glPopMatrix ();
Can someone tell me what I am doing wrong? I think it has something to do with the non-communicative nature of rotational transformations (i.e., the order of the rotation matters – the first rotation changes the angle required by the second).
Somewhere, someone must have actual working code that draws a cylindar (including the end disks!) when given two points in cartesian coordinate space. Help!
Originally posted by Fastian:
[b]You can first translate to the first point then
let the second vector be
v2 = (30,30,30)
calculate the angle on the x and y plane using
v2 = (30, 30, 0) and unit along x axis = 1,0,0
i.e. theta1 = angle bw v2 and unitX;
similarly find angle on x and z plane as theta2 with v2 = (30,0,30) then
glRotatef(theta1,1,0,0);
glrotatef(90-theta2,0,1,0);
drawcylinder().
[This message has been edited by Fastian (edited 03-29-2001).][/b]
void CGraphics: rawCylinder(const RGFW3f *startPoint, float angleXY, float angleXZ, float length, float baseRadius, float topRadius, RGFW4f *StartColor, RGFW4f *EndColor)
{
glPushMatrix();
// move to the starting position of the pipe
glTranslatef(startPoint->x, startPoint->y, startPoint->z);
// orient the pipe to be perpendicular to the screen
glRotatef(90, 0, 1, 0);
// rotate on the xy plane i.e. around the z axis. since pipe is already rotated
// by 90 degree therefore our z has become the x axis in this case.
glRotatef(angleXY, 1, 0, 0);
// rotate on the xz plane i.e. around the Y axis.
glRotatef(angleXZ, 0, 1, 0);
// draw the pipe
| 948
| 3,139
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.34375
| 3
|
CC-MAIN-2024-26
|
latest
|
en
| 0.888654
|
https://mathexamination.com/lab/line-bundle.php
| 1,623,832,014,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-25/segments/1623487622234.42/warc/CC-MAIN-20210616063154-20210616093154-00288.warc.gz
| 327,728,941
| 8,595
|
## Do My Line Bundle Lab
As discussed over, I utilized to compose a basic and also uncomplicated mathematics lab with only Line Bundle Nonetheless, the less complex you make your lab, the less complicated it becomes to get stuck at completion of it, then at the start. This can be very irritating, and all this can occur to you due to the fact that you are making use of Line Bundle and/or Modular Equations incorrectly.
With Modular Formulas, you are currently making use of the wrong equation when you obtain stuck at the beginning, if not, then you are most likely in a dead end, as well as there is no feasible escape. This will just become worse as the trouble ends up being extra complicated, however then there is the concern of how to wage the problem. There is no other way to effectively set about resolving this sort of mathematics issue without being able to instantly see what is taking place.
It is clear that Line Bundle and Modular Formulas are challenging to learn, and it does take method to develop your very own feeling of intuition. Yet when you intend to solve a math problem, you need to use a tool, and also the tools for learning are utilized when you are stuck, and also they are not utilized when you make the incorrect action. This is where lab Assist Solution can be found in.
As an example, what is wrong with the inquiry is incorrect ideas, such as obtaining a partial value when you do not have enough functioning parts to complete the entire work. There is a great factor that this was wrong, and also it refers reasoning, not intuition. Logic enables you to comply with a detailed treatment that makes sense, and also when you make an incorrect action, you are normally compelled to either try to go forward as well as remedy the mistake, or attempt to step as well as do an in reverse step.
Another instance is when the pupil does not understand a step of a process. These are both logical failings, and also there is no way around them. Also when you are stuck in a location that does not permit you to make any kind of move, such as a triangular, it is still important to understand why you are stuck, to make sure that you can make a much better step as well as go from the step you are stuck at to the following location.
With this in mind, the most effective way to address a stuck scenario is to merely take the step forward, rather than attempting to step. Both procedures are different in their technique, but they have some standard similarities. Nevertheless, when they are attempted with each other, you can quickly tell which one is much better at resolving the trouble, as well as you can likewise inform which one is extra powerful.
Let's discuss the first instance, which relates to the Line Bundle math lab. This is not too complicated, so let's very first go over how to start. Take the following procedure of affixing a part to a panel to be made use of as a body. This would require three measurements, as well as would be something you would certainly require to affix as part of the panel.
Now, you would certainly have an extra dimension, however that does not indicate that you can just keep that dimension as well as go from there. When you made your very first step, you can conveniently ignore the measurement, and after that you would certainly need to go back and backtrack your actions.
Nonetheless, instead of remembering the added measurement, you can utilize what is called a "mental shortcut" to help you remember that extra measurement. As you make your very first step, imagine yourself taking the dimension as well as attaching it to the component you want to attach to, and then see how that makes you feel when you duplicate the process.
Visualisation is an extremely powerful technique, as well as is something that you should not miss over. Visualize what it would certainly feel like to in fact attach the component and be able to go from there, without the measurement.
Currently, allow's take a look at the 2nd example. Let's take the very same procedure as in the past, today the student needs to keep in mind that they are mosting likely to move back one step. If you tell them that they need to move back one action, but then you remove the suggestion of needing to move back one action, then they will not know just how to wage the issue, they won't understand where to seek that action, and the procedure will certainly be a mess.
Instead, make use of a mental shortcut like the mental diagram to mentally show them that they are mosting likely to move back one action. and also put them in a placement where they can move on from there. without needing to think about the missing out on a step.
## Pay Me To Do Your Line Bundle Lab
" Line Bundle - Required Assist With a Mathematics lab?" However, many trainees have actually had a trouble realizing the principles of direct Line Bundle. Luckily, there is a brand-new style for linear Line Bundle that can be used to educate linear Line Bundle to students that struggle with this principle. Trainees can make use of the lab Assist Solution to help them discover new strategies in direct Line Bundle without facing a mountain of problems as well as without having to take an examination on their concepts.
The lab Aid Service was developed in order to assist struggling students as they relocate from university and also high school to the university as well as task market. Many students are not able to handle the stress and anxiety of the knowing procedure and also can have extremely little success in realizing the concepts of direct Line Bundle.
The lab Help Solution was developed by the Educational Screening Solution, that provides a selection of various online examinations that trainees can take and also exercise. The Examination Help Solution has actually aided several trainees enhance their ratings and can assist you improve your ratings also. As students relocate from college and high school to the university and work market, the TTS will aid make your students' change much easier.
There are a couple of different ways that you can benefit from the lab Help Solution. The primary manner in which trainees use the lab Aid Service is via the Solution Managers, which can assist pupils find out strategies in straight Line Bundle, which they can use to help them succeed in their training courses.
There are a number of issues that trainees experience when they initially use the lab Assist Service. Students are frequently overwhelmed as well as do not recognize just how much time they will certainly require to devote to the Service. The Solution Supervisors can assist the students review their principle understanding as well as help them to review all of the material that they have actually already learned in order to be gotten ready for their next training course work.
The lab Help Solution works similarly that a professor carries out in terms of assisting pupils comprehend the principles of direct Line Bundle. By offering your pupils with the devices that they require to find out the crucial concepts of linear Line Bundle, you can make your trainees much more successful throughout their studies. As a matter of fact, the lab Aid Solution is so efficient that many students have actually switched over from traditional math class to the lab Assist Service.
The Task Supervisor is created to aid trainees handle their research. The Task Manager can be established to arrange how much time the student has readily available to finish their appointed homework. You can likewise establish a personalized amount of time, which is a wonderful function for trainees who have a hectic timetable or a really busy secondary school. This attribute can assist students stay clear of feeling overwhelmed with mathematics tasks.
Another useful attribute of the lab Help Solution is the Trainee Assistant. The Student Assistant helps pupils handle their work as well as gives them an area to publish their homework. The Trainee Aide is useful for students who don't want to obtain bewildered with responding to numerous concerns.
As students obtain more comfortable with their jobs, they are encouraged to connect with the Job Manager and also the Pupil Aide to obtain an on the internet support group. The on the internet support group can help students keep their focus as they answer their projects.
All of the assignments for the lab Aid Service are consisted of in the bundle. Trainees can login as well as complete their assigned job while having the trainee aid readily available in the background to help them. The lab Help Service can be a terrific help for your trainees as they start to navigate the difficult college admissions as well as job hunting waters.
Trainees need to be prepared to obtain used to their jobs as rapidly as feasible in order to reach their main objective of entering the university. They have to strive sufficient to see results that will certainly permit them to stroll on at the following degree of their research studies. Obtaining utilized to the process of finishing their projects is extremely crucial.
Trainees have the ability to discover various ways to help them learn exactly how to utilize the lab Help Service. Understanding how to use the lab Assist Service is important to pupils' success in university and also job application.
## Hire Someone To Take My Line Bundle Lab
Line Bundle is used in a lot of colleges. Some instructors, nevertheless, do not utilize it really successfully or use it incorrectly. This can have an unfavorable influence on the pupil's discovering.
So, when assigning assignments, utilize an excellent Line Bundle assistance solution to assist you with each lab. These solutions provide a variety of valuable services, consisting of:
Projects might need a great deal of examining and also browsing on the computer. This is when utilizing an assistance service can be a wonderful advantage. It allows you to obtain more job done, raise your comprehension, and avoid a lot of stress and anxiety.
These kinds of homework solutions are a fantastic method to begin working with the best sort of aid for your requirements. Line Bundle is just one of the most difficult subjects to understand for students. Dealing with a service, you can ensure that your needs are fulfilled, you are educated properly, and you understand the material appropriately.
There are a lot of ways that you can show on your own to work well with the course as well as achieve success. Make use of an appropriate Line Bundle help solution to guide you and obtain the job done. Line Bundle is just one of the hardest classes to find out yet it can be conveniently understood with the appropriate aid.
Having a homework service also assists to improve the pupil's grades. It permits you to include additional credit report as well as boost your GPA. Getting extra credit scores is often a huge advantage in numerous colleges.
Pupils that don't make the most of their Line Bundle class will certainly wind up continuing of the remainder of the class. Fortunately is that you can do it with a fast and simple service. So, if you want to continue in your course, make use of a great aid service. Something to keep in mind is that if you truly want to raise your quality degree, your program job needs to get done. As high as feasible, you need to understand as well as work with all your issues. You can do this with a great assistance solution.
One benefit of having a research solution is that you can assist on your own. If you do not feel great in your capacity to do so, then an excellent tutor will certainly have the ability to aid you. They will have the ability to resolve the problems you face as well as assist you comprehend them so as to get a much better quality.
When you graduate from secondary school as well as go into college, you will certainly need to strive in order to remain ahead of the other trainees. That means that you will certainly require to strive on your research. Utilizing an Line Bundle service can assist you get it done.
Maintaining your grades up can be tough since you typically require to examine a whole lot as well as take a lot of tests. You don't have time to work with your grades alone. Having an excellent tutor can be a fantastic help since they can assist you as well as your research out.
A help service can make it simpler for you to handle your Line Bundle course. In addition, you can discover more about on your own as well as assist you be successful. Find the most effective tutoring service as well as you will be able to take your research skills to the next degree.
| 2,465
| 12,654
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.90625
| 3
|
CC-MAIN-2021-25
|
latest
|
en
| 0.977047
|
https://scienceoxygen.com/how-do-you-calculate-the-concentration-of-naoh-in-a-titration/
| 1,675,292,299,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-06/segments/1674764499953.47/warc/CC-MAIN-20230201211725-20230202001725-00344.warc.gz
| 525,271,139
| 24,557
|
# How do you calculate the concentration of NaOH in a titration?
1. Amount of solute in mol = concentration in mol/dm 3 × volume in dm 3
2. Amount of sodium hydroxide = 0.100 × 0.0250.
3. = 0.00250 mol.
4. The balanced equation is: NaOH(aq) + HCl(aq) → NaCl(aq) + H 2O(l)
5. So the mole ratio NaOH:HCl is 1:1.
## How do you perform a titration step by step?
Record the pH value in the data table as “pH initial.” Place the flask under the NaOH burette and add the base slowly, drop by drop while swirling the solution. Watch the solution carefully, when the last drop added causes the solution to change color the titration is close to completion.
## How do you calculate pH from titration?
For a Strong Acid-Strong Base titration, there are three possibilities: If there is excess HA at the end of the reaction, calculate its new molarity. Then, use p H = − log [ H 3 O + ] to solve for pH. If there is excess OH – at the end of the reaction, calculate its new molarity.
## What are the 4 types of titration?
• Acid-base Titrations.
• Redox Titrations.
• Precipitation Titrations.
• Complexometric Titrations.
## How do you calculate titration factor?
1. The equation for Titration Formula is articulated as:
2. Where,
3. 1000 = factor relating mg to grams.
4. W = mass of the sample.
5. N = normality of titrant.
6. V = volume of titrant.
7. Eq.wt = equivalent weight of acid.
## How do you calculate titration in a level?
2. Step 1: Find the number of moles of acid. moles of acid = concentration x volume in dm3
3. Step 2: Deduce the number of moles of alkali. The equation for the reaction shows the mole ratio is 1:1.
4. Step 3: Work out the concentration of the alkali. concentration = moles/volume in dm3
## Why is titration done 3 times?
Since you know how much standard you have used and its concentration you can work out the concentration of the unknown sample. Remember you should always repeat whole process at least 3 times to ensure you have an accurate result, as there is the potential for both random and systematic errors to affect your results.
## How do you prepare a sample for a titration?
1. Place the titration beaker on the balance and tare.
2. Weigh the substance under investigation into the beaker.
3. Add the solvent to the desired quantity e.g. 50 mL.
## How do you write a titration experiment?
1. Use a pipette and pipette filler to add 25 cm 3 of alkali solution to a clean conical flask.
2. Add a few drops of a suitable indicator and put the conical flask on a white tile.
3. Fill the burette with dilute acid.
4. Slowly add the acid from the burette to the conical flask, swirling to mix.
## How do you find the unknown acid in a titration?
Your unknown solid is an acid. You will dissolve it in water, add some phenolphthalein indicator and then titrate to the end point with your standard NaOH solution. The unknown acid is monoprotic; it has only one acidic hydrogen per molecule.
## How do I calculate the concentration of a solution?
Divide the mass of the solute by the total volume of the solution. Write out the equation C = m/V, where m is the mass of the solute and V is the total volume of the solution. Plug in the values you found for the mass and volume, and divide them to find the concentration of your solution.
## How do you calculate H+ concentration from titration?
Convert the number of moles of H+ to the concentration of H+ by taking the number of moles of H+ and dividing by the volume (in liters) of unknown that you originally had. This gives you the concentration of H+ in the unknown solution.
## Is NaOH an acid or base?
NaOH is an Arrhenius base because it dissociates in water to give the hydroxide (OH-) and sodium (Na+) ions. An Arrhenius acid is therefore any substance that ionizes when it dissolves in water to give the H+, or hydrogen, ion.
## What is end point of titration?
indicator colour change is the end point of the titration. The end point is used as an approximation of the equivalence point and is employed, with the known concentration of the titrant, to calculate the amount or concentration of the analyte.
## Where is EDTA used in titration?
The most common indicators in complexometric titrations are organic dyes which function by forming a colored complex with the metal ion being titrated. During the reaction, EDTA replaces the indicator to form a more stable complex with metal and when the reaction is completed the change for the color is observed.
## What is titration give example?
The indicator used depends on the type of reaction. For example: phenolphthalein or methyl orange can be used for titrations involving acids and bases. The indicators indicate the endpoint by changing their colours at the endpoint, sometimes one of the reactants itself can act as an indicator.
## Why indicator is used in titration?
The common application of indicators is the detection of end points of titrations. The colour of an indicator alters when the acidity or the oxidizing strength of the solution, or the concentration of a certain chemical species, reaches a critical range of values.
## Why is a burette used in titration?
Answer and Explanation: The reason why it is preferred to use burette in titration because it can be used to dispense accurate volumes of liquid and it can contain enough amount of reagents for titration. It has graduation marks used to read the volume delivered and it reads from top to bottom starting zero.
## Why do you repeat titration without indicator?
A universal indicator will only give you relatively slow gradual colour changes, that are not precise enough to determine an end point accurately. Industry has long moved away from indicator end points in titration, where possible, and tends to favour potentiometric detection via automated instruments.
## Why acid is taken in burette?
Suppose if there is any leaking in burette due to lid or tighter, acid may flow to our hand fingers resulting in erossion of our skin….. In case of base in burette solution, it less reactable due to high pH and doesn’t cause more problems… This is the reason to take acid in an conical flask and base in an burette.
| 1,452
| 6,173
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.859375
| 4
|
CC-MAIN-2023-06
|
latest
|
en
| 0.873396
|
https://ask.learncbse.in/t/a-spiral-is-made-up-of-successive-semicircles-with-centres-alternately-at-a-and-b/41651
| 1,701,378,637,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-50/segments/1700679100232.63/warc/CC-MAIN-20231130193829-20231130223829-00180.warc.gz
| 134,356,829
| 3,758
|
# A spiral is made up of successive semicircles, with centres alternately at A and B,
A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm,… as shown in figure. What is the total length of such a spiral made up of thirteen consecutive semicircles?
(Take π = 22/7)
[ Hint: Length of successive semicircles is l1, l2, l3, l4, … with centres at A, B, respectively.]
| 139
| 461
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.921875
| 3
|
CC-MAIN-2023-50
|
latest
|
en
| 0.946953
|
http://gmatclub.com/forum/statement-of-a-united-states-copper-mining-company-import-63589.html?sort_by_oldest=true
| 1,485,128,201,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-04/segments/1484560281649.59/warc/CC-MAIN-20170116095121-00166-ip-10-171-10-70.ec2.internal.warc.gz
| 114,974,983
| 56,036
|
Statement of a United States copper mining company: Import : GMAT Critical Reasoning (CR)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack
It is currently 22 Jan 2017, 15:36
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# Events & Promotions
###### Events & Promotions in June
Open Detailed Calendar
# Statement of a United States copper mining company: Import
Author Message
TAGS:
### Hide Tags
Director
Joined: 06 Jan 2008
Posts: 555
Followers: 2
Kudos [?]: 353 [0], given: 2
Statement of a United States copper mining company: Import [#permalink]
### Show Tags
07 May 2008, 09:58
00:00
Difficulty:
(N/A)
Question Stats:
0% (00:00) correct 0% (00:00) wrong based on 2 sessions
### HideShow timer Statistics
Statement of a United States copper mining company: Import quotas should be imposed on the less expensive copper mined outside the country to maintain the price of copper in this country; otherwise, our companies will not be able to stay in business.
Response of a United States copper wire manufacturer: United States wire and cable manufacturers purchase about 70 percent of the copper mined in the United States. If the copper prices we pay are not at the international level, our sales will drop, and then the demand for United States copper will go down.
If the factual information presented by both companies is accurate, the best assessment of the logical relationship between the two arguments is that the wire manufacturers argument
(A) is self-serving and irrelevant to the proposal of the mining company
(B) is circular, presupposing what it seeks to prove about the proposal of the mining company
(C) shows that the proposal of the mining company would have a negative effect on the mining companys own business
(D) fails to give a reason why the proposal of the mining company should not be put into effect to alleviate the concern of the mining company for staying in business
(E) establishes that even the mining companys business will prosper if the mining companys proposal is rejected
If you have any questions
New!
Senior Manager
Joined: 26 Mar 2008
Posts: 337
Location: Washington DC
Followers: 2
Kudos [?]: 76 [1] , given: 4
Re: CR - copper mining [#permalink]
### Show Tags
07 May 2008, 10:45
1
KUDOS
Straight C.
Director
Joined: 26 Jul 2007
Posts: 541
Schools: Stern, McCombs, Marshall, Wharton
Followers: 7
Kudos [?]: 158 [1] , given: 0
Re: CR - copper mining [#permalink]
### Show Tags
07 May 2008, 10:48
1
KUDOS
I go with C on this one.
Statement of a United States copper mining company: Import quotas should be imposed on the less expensive copper mined outside the country to maintain the price of copper in this country; otherwise, our companies will not be able to stay in business.
The mining companies wants to restrict the amount less expensive copper mined outside the U.S. so that they can keep their prices high and stay in business.
Response of a United States copper wire manufacturer: United States wire and cable manufacturers purchase about 70 percent of the copper mined in the United States. If the copper prices we pay are not at the international level, our sales will drop, and then the demand for United States copper will go down.
The manufacturers are saying that if the U.S. prices are not the same as the cheaper international prices then copper demand will go down. In other words if the U.S. manfactures put their plan in place and keep U.S. prices high, then demand drops.
(C) shows that the proposal of the mining company would have a negative effect on the mining companys own business
Manager
Joined: 04 Jun 2007
Posts: 59
Location: United Kingdom
Followers: 1
Kudos [?]: 4 [1] , given: 0
Re: CR - copper mining [#permalink]
### Show Tags
07 May 2008, 10:49
1
KUDOS
No doubt C .
Intern
Joined: 17 Mar 2008
Posts: 18
Followers: 0
Kudos [?]: 3 [1] , given: 0
Re: CR - copper mining [#permalink]
### Show Tags
07 May 2008, 18:48
1
KUDOS
Although i agree with 'C'. Can anyone please explain me why "E" is wrong?
SVP
Joined: 11 Mar 2008
Posts: 1634
Location: Southern California
Schools: Chicago (dinged), Tuck (November), Columbia (RD)
Followers: 9
Kudos [?]: 201 [1] , given: 0
Re: CR - copper mining [#permalink]
### Show Tags
07 May 2008, 20:55
1
KUDOS
C
_________________
Check out the new Career Forum
http://gmatclub.com/forum/133
SVP
Joined: 11 Mar 2008
Posts: 1634
Location: Southern California
Schools: Chicago (dinged), Tuck (November), Columbia (RD)
Followers: 9
Kudos [?]: 201 [0], given: 0
Re: CR - copper mining [#permalink]
### Show Tags
07 May 2008, 20:56
mbamogul wrote:
Although i agree with 'C'. Can anyone please explain me why "E" is wrong?
It directly stated that if the proposal is accepted, the demand for copper will go down. However, it did not directly state that if the proposal is rejected, that demand will go up. You can not make this assumption.
_________________
Check out the new Career Forum
http://gmatclub.com/forum/133
Director
Joined: 06 Jan 2008
Posts: 555
Followers: 2
Kudos [?]: 353 [0], given: 2
Re: CR - copper mining [#permalink]
### Show Tags
08 May 2008, 05:37
OA:C Thanks
Re: CR - copper mining [#permalink] 08 May 2008, 05:37
Similar topics Replies Last post
Similar
Topics:
Statement of a United States copper mining company: Import 4 24 Mar 2011, 15:38
Statement of a United States copper mining company: Import 11 17 Aug 2009, 07:07
1 Statement of a United States copper mining company: Import 2 27 Jun 2009, 07:52
Statement of a United States copper mining company: Import 4 04 Aug 2008, 10:29
Statement of a United States copper mining company: Import 5 06 Aug 2007, 04:25
Display posts from previous: Sort by
| 1,617
| 6,177
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.046875
| 3
|
CC-MAIN-2017-04
|
latest
|
en
| 0.893386
|
http://forums.wolfram.com/mathgroup/archive/2012/Mar/msg00130.html
| 1,590,418,152,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-24/segments/1590347388758.12/warc/CC-MAIN-20200525130036-20200525160036-00427.warc.gz
| 49,295,420
| 8,178
|
Re: much power to mathematica
• To: mathgroup at smc.vnet.net
• Subject: [mg125355] Re: much power to mathematica
• From: "djmpark" <djmpark at comcast.net>
• Date: Fri, 9 Mar 2012 06:07:32 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <jj4qn7\$ifa\$1@smc.vnet.net> <15040062.90100.1331201203073.JavaMail.root@m06>
```David,
There is a case where parallel processing will give a gain much greater than
the number of cores used! This is when breaking a complicated graphic, say a
contour or density plot, into multiple pieces.
If you have to use 200 x 200 PlotPoints for a regular plot, then you can
break it into four 100 x 100 plots for the same resolution. You obtain the
approximate factor of 4 but also much faster execution because you are using
only 1/4 the PlotPoints for each plot. There might also be some improvement
with MaxRecursion, because each plot is simpler.
I've found that the easiest way to understand and use parallel processing is
to learn about and use ParallelSubmit and WaitAll.
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/index.html
From: David Bailey [mailto:dave at removedbailey.co.uk]
On 06/03/2012 10:59, Bill Rowe wrote:
> On 3/5/12 at 1:03 AM, aleks.post at gmail.com (Alexey Kornetov) wrote:
>
>> Hmm.. You are right. I'm new in mathematica if there is the way to
>> allocate evolution between the cores to gain much speed?
>
> To allocate processing between cores you need to write your code to
> make use of functions such as ParallelTable. That is, your code needs
> to take advantage of parallel processing. Note, parallel processing
> can and will speed up some things but not all things.
>
>
Alexey,
Since you say you are a newcomer to Mathematica, I would be very wary about
plunging into parallel constructs unless you are sure your code cannot be
speeded up in other ways, such as:
Use of functional constructs.
Ensuring all arrays are 'packed'.
etc.
Remember that the maximum possible gain from parallelisation is given by the
number of cores on your machine, whereas other speedup tricks can often
achieve larger savings.
David Bailey
http://www.dbaileyconsultancy.co.uk
```
• Prev by Date: Re: graph
• Next by Date: Re: new functional operator
• Previous by thread: Re: much power to mathematica
• Next by thread: Re: much power to mathematica
| 624
| 2,363
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.671875
| 3
|
CC-MAIN-2020-24
|
longest
|
en
| 0.891892
|
https://www.bryanshalloway.com/2023/11/03/odds-are-you-re-using-probabilities-to-describe-event-outcomes/
| 1,718,221,613,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-26/segments/1718198861183.54/warc/CC-MAIN-20240612171727-20240612201727-00760.warc.gz
| 622,814,126
| 10,490
|
# Odds Are You're Using Probabilities to Describe Event Outcomes
We grow up learning proportions, percentages, risks, probabilities. You encounter them when a teacher gives a grade on a test or a doctor describes the risk of an illness. On the other hand, we rarely interact with odds and when we do it’s often in contexts like:
So that in our modern cultural consciousness ‘odds’ are relegated to the shady domains of gambling, sports betting1, and dystopian murder games.
However human understanding of odds predates our formal understanding of probability. You can find references to odds dating back to Shakespeare:
Knew that we ventured on such dangerous seas
That if we wrought out life ’twas ten to one;
- Shakespeare’s Henry IV, Part II, 1597
Yet, in most common settings, modern society has largely supplanted odds for probabilities. You can imagine if Shakespeare were writing today the line might end “’twas ten out of eleven2.
Beyond betting and dramatic playwriting, ‘odds’ remain a useful method for conceptualizing event distributions. My hope is you leave this post with some intuitions on when communicating with odds may be useful and an understanding of how the ‘odds way’ of framing a problem can be convenient for comparing event outcomes across circumstances3.
Note that if you are completely new to odds, you should first start here: Ratios and fractions of events or find a short primer online.
You make a glass of chocolate milk for your nephew and add 1 part chocolate for every 9 parts milk. He takes a sip and says, “Please make it three times as chocolatey.” The most obvious way to satisfy his request would be to triple the amount of chocolate in the cup4, i.e. the ratio of chocolate to milk should go from 1 : 9 to 3 : 9. To go from one part chocolate to three parts chocolate you simply add two more parts chocolate, bringing the beverage to the correct 3 to 9 chocolate to milk ratio (simplified: 1 to 3). If instead you took his comment as him wanting the cup to be composed of $$\frac{3}{10}$$ chocolate rather than the current $$\frac{1}{10}$$ chocolate, your calculations (without starting over on the drink) would be more complicated5.
In a similar way that it can be easier to think of parts of recipes in terms of ratios rather than fractions out of a whole, it can sometimes be easier to think of event distributions in terms of odds rather than probabilities.
• the outcome of interest is essentially arbitrary or symmetric (e.g. you could frame the problem in terms of parts milk or parts chocolate)
• you want to compare your ratio of outcomes across different contexts (e.g. how does the distribution of milk to chocolate in my cup relate to the distribution in some other cup?) or solve for relationships in a way that uses multiplication
## Ratio of odds (odds ratio)
Let’s change examples to sports and substitute parts chocolate to milk for parts winning to losing when playing on one’s home court. Say in professional basketball the odds of the home team winning are 3 to 2, i.e. for every 3 home team wins the away team wins 2. Equivalently there is a $$\frac{3}{5}$$ chance (60% probability) of the home team winning. Maybe you want to compare this ‘home court advantage’ between professional and college basketball. Odds ratios are a useful method for describing such relationships as they are easy to calculate and manipulate and allow flexibility in problem formulation.
Perhaps you have a friend who says “College players get rattled easily. The impact of home court advantage in college is twice what it is at the professional level.” This type of comparison could be viewed as an odds ratio. You have two sets of odds each concerning winning to losing on home court, one for college and one for the pros, and you are taking the ratio of the odds to characterize the relationship of home court advantage depending on the league of play6. Pretend your friend next asks, “Given my statement above and what you know about home court advantage at the professional level, what would be the relationship between winning and losing at home in college7?”
Taking an odds approach, you might formalize the problem your friend gave you as:
• Already known: Odds of winning at home in the pros is 3 to 2.
• New information from friend: The ratio of home wins to losses in the pros vs college (i.e. the odds ratio) is 2 to 1.
• Question friend is asking: What are the odds of winning at home in college?”
$\frac{??}{3/2} = 2/1$
To solve for the odds of winning at home in college you simply double the ratio of winning at home in the pros and you now have a meaningful answer for your friend: the odds of the home team winning at the college level are 3 to 1!
You could have framed this problem in terms of losses and come to an equivalent conclusion. E.g. let’s invert our example:
$\frac{??}{2/3} = 1/2$
Solving for this, our odds of losing at home in college simplifies to 1 to 3. This is the reciprocal of our 3 to 1 odds of winning at home. Whether we frame the problem in terms of ‘winning at home’ or ‘losing at home’, the odds are reciprocally related, demonstrating a consistent relationship.
It is less clear how you might formalize the problem in terms of probabilities; also the reciprocal nature of your solutions would not be preserved under multiplication. Doubling the probability of winning from $$\frac{3}{5}$$ would produce a meaningless answer of $$\frac{6}{5}$$. You could attempt to flip the problem and instead first frame it as ‘What is the chance of losing at home in college.’ Chance of losing at home is $$\frac{2}{5}$$, halved becomes $$\frac{1}{5}$$, entailing the chance of winning would be $$\frac{4}{5}$$. While you arrived at an answer for “chance of home team winning in college: $$\frac{4}{5}$$,” your solution was dependent on whether you started out from a “chance of winning” or a “chance of losing” perspective.
Another Example:
To reiterate this lack of symmetry when manipulating a probability and its complement, let’s say your friend instead says, “Home court advantage is only a third more important in college than in the pros.” We can think of ‘a third more’ as a relationship of 4 to 3.
For odds this becomes:
$\frac{??}{3/2} = 4/3$
This simplifies to a 2:1 odds of winning at home in college or, if you inverted the problem, you would calculate a 1:2 odds of losing – again, these solutions are consistent with one another.
For probability, if we start at a $$\frac{3}{5}$$ chance of winning at home in the pros and multiply this by $$\frac{4}{3}$$ we get an 80% chance of winning at home in college. However say you invert the problem to calculate it from the perspective of losing: $$\frac{2}{5}*\frac{3}{4} = \frac{3}{10}$$ this 30% home loss rate equates to a 70% home win rate. Hence, depending on whether you set-up the initial calculation in terms of home winning or home losing, you get a college home win rate of either 80% or 70% respectively. This lack of conformity of results when manipulating8 the relationship between event outcomes and their complements can make probabilities less wieldly compared to constructing problems as odds9.
# Communicating odds
An advantage of probabilities over odds is that people are accustomed to probabilities. If you want to communicate odds to someone who is new to the concept, a helpful heuristic is to frame it in the template “for every ___ , there are ___.” E.g. “For every 3 home wins, there are 2 home losses”, or the odds of winning at home are 3 to 2. If you want to communicate a relationship between odds with an odds ratio you could tweak this structure slightly, e.g. “The ratio of home wins to home losses is twice as high in college compared to in the pros.” Keeping the context of the problem central to the explanation is central to being understood. The payoff of using odds is the ability to clearly articulate multiplicative relationships and comparisons between event outcomes which may be cumbersome or unclear when confined to the language of probability alone.
With a little help, we can stop acting like Han Solo.
Who, in the end, could not beat the odds.
# Appendix
## Ratios and fractions of events
Imagine a bag with 5 red marbles and 2 blue marbles that has been mixed thoroughly.
library(dplyr)
library(ggplot2)
library(DiagrammeR)
create_graph() %>%
label = "I am red!!",
node_aes = node_aes(fillcolor = "red",
fontsize = 5)) %>%
label = "I am blue :-(",
node_aes = node_aes(fillcolor = "blue",
fontsize = 5)) %>%
render_graph()
Odds could be used to represent the ratio between red and blue marbles. Probability could represent the fraction of all marbles that are red10.
$O(R) = \frac{R}{B}$
$P(R) = \frac{R}{B+R}$
Ratio for odds11:
tibble(color = c(rep("red", 5), rep("blue", 2)),
y = c(rep(.5, 5), rep(-.5, 2)),
x = c(1:5, 2.5, 3.5)) %>%
ggplot(aes(x = x, y = y, colour = color, size = 10))+
geom_hline(yintercept = 0, size = 3, colour = "black")+
geom_point()+
theme_void()+
guides(size = "none", colour = "none")+
scale_colour_manual(values = c(blue = "blue", red = "red"))
Fraction for probability12:
tibble(color = c(rep("red", 5), rep("red", 5), rep("blue", 2)),
y = c(rep(.5, 5), rep(-.5, 7)),
x = c(1:5, seq(0, 6, length.out = 7))) %>%
ggplot(aes(x = x, y = y, colour = color, size = 10))+
geom_hline(yintercept = 0, size = 3, colour = "black")+
geom_point()+
theme_void()+
guides(size = "none", colour = "none")+
scale_colour_manual(values = c(blue = "blue", red = "red"))
For odds (when there are only two possible outcomes13) each outcome could be thought of as existing either in the numerator or in the denominator. For probabilities, the class of interest (e.g. red marbles) influences both sides14.
You can switch between odds and probabilities using the function below:
$O = \frac{P}{1-P}$
Odds emphasizes the relationship between the frequencies of possible events whereas probabilities emphasizes the relative frequency of a particular event. Some problems lend themselves more naturally to probability and others to odds15.
## Many variables
There are other factors that might affect the relationship between winning or losing at home other than college/professional level (e.g. ‘quality of coach’, ‘distance away team traveled’, etc.). Understanding odds and ratios of odds is important when using methods like Logistic Regression that can relate the association of multiple variables to an event outcome16.
### Other problems
We’ve shown how ratios of odds are helpful for comparing the impacts of variables when the target outcome falls into categories such as win/loss, red/blue, etc. Problems like these are often modeled in relation to multiple variables using methods like logistic regression, which are well-suited for considering odds and odds ratios. However, ratios of odds are not the only, or always the best, way to formalize all types of problems involving discrete events. In many medical environments (e.g., cohort studies), it is common to speak in terms of ‘relative risk’, which relates to a ratio of probabilities17. When the goal is to model the frequency of an event’s occurrence, Poisson regression is often the method of choice18. Poisson regression models the probability of a given number of events occurring within a fixed period or space and therefore interpretation of the parts of the model is more aligned with considerations of probability. Another example where probability is commonly preferred over odds is in Bayes’ theorem. One of the most important functions in statistics, Bayes’ theorem is typically presented and, I believe easier to follow, in its probability formulation:
Bayes’ function, probability:
$P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)}$
For comparison, here’s a common formulation of Bayes’ theorem in terms of odds:
$O(A|B) = O(A) \cdot \frac{P(B|A)}{P(B|\neg A)}$
These examples highlight that while formulating problems in terms of odds is helpful in certain contexts involving discrete outcomes, in other scenarios, probability is indeed the more appropriate formulation.
1. I will not be explaining American betting or the meaning of -100, +200…↩︎
2. Which, to me, doesn’t capture the doom of that moment with quite the same import. I’m also assuming today’s Shakespeare still prefers antiquated phrasings like ”’twas.”↩︎
3. The inspiration for this post came from my old graduate school classmate, Will Burton. Will argued that describing anything in terms of ‘odds’ to business stakeholders adds confusion. Wherever possible he translates statistical measures on event outcomes to be in terms of probability. Due to our modern conditioning, Will may be right, however in this post I describe some simple examples where an ‘odds’ way of describing the problem may feel more natural.↩︎
4. The size of his sip is being approximated to a size of 0 parts.↩︎
5. If you go through the hassle, you would realize you’d need to add $$\frac{20}{7}$$ more parts of chocolate to the beverage.↩︎
6. Because odds themselves are a kind of ratio, odds ratios are just a particular kind of ratio of ratios.↩︎
7. You try and interrogate them for additional details but they remain silent, leaving you with a vague problem statement.↩︎
8. Specifically, when multiplying…↩︎
9. In the examples, ‘twice’ or a ‘third bigger’ of ‘an effect on home winning’ is an intentionally vague, contrived phrasing; you should work-out with stakeholders precisely what is being asked in order to determine an appropriate approach. For these cases I largely leaned on the problems of multiplication manipulations of probabilities. For a more rigorous discussion of how to try and formalize a similar comment, check-out this Stack Exchange thread: https://math.stackexchange.com/questions/761504/what-does-twice-as-likely-mean.↩︎
10. Note that while probability is limited to the domain of 0 to 1, odds can take any positive rational number.↩︎
11. You could say there are 5 to 2 (5:2) odds of selecting a red marble at random from the bag or, if you ran this exercise many times, you’d expect to select 2.5 times as many red marbles as blue marbles.↩︎
12. You’d say there is a $$\frac{5}{7}$$ chance of selecting a red marble, or that you would select a red marble ~71% of the time.↩︎
13. I’ll only be discussing problems with two possible outcomes.↩︎
14. Sidenote: It might be fun to think of odds as being more egalitarian because, in the case of a binary outcome, both possible outcomes get their own side of the ratio/fraction. Probabilities are ‘outcome of interest’ centric in that the selected outcome affects both sides. Hence, if you believe in things like equality and freedom you should be a fan of odds and odds ratios!↩︎
15. I briefly reference some of these differences in Other problems. However for the remainder of the post I’ll focus on where odds suggest an intuitive and consistent framework – after all odds are the ones that need PR help.↩︎
16. A more simple example (or at least better in-line with a reader’s expectations) for odds may have been to start with the odds of an individual team winning and then compare their odds of winning at home or away as the example for odds ratios. Instead I took ‘home winning’ as my starting point and went from there to concoct a perhaps stretched example of comparisons of home winning between leagues.↩︎
17. However odds are also commonly used in medical contexts.↩︎
18. e.g., “How many times will the mascot start dancing during the game?” Relevant variables might include the weight of the costume, whether it’s a game against a rival, etc.↩︎
| 3,683
| 15,599
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.1875
| 4
|
CC-MAIN-2024-26
|
latest
|
en
| 0.929428
|
http://de.metamath.org/mpeuni/reseq2i.html
| 1,718,874,281,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-26/segments/1718198861916.26/warc/CC-MAIN-20240620074431-20240620104431-00519.warc.gz
| 7,315,119
| 4,587
|
Metamath Proof Explorer < Previous Next > Nearby theorems Mirrors > Home > MPE Home > Th. List > reseq2i Structured version Visualization version GIF version
Theorem reseq2i 5314
Description: Equality inference for restrictions. (Contributed by Paul Chapman, 22-Jun-2011.)
Hypothesis
Ref Expression
reseqi.1 𝐴 = 𝐵
Assertion
Ref Expression
reseq2i (𝐶𝐴) = (𝐶𝐵)
Proof of Theorem reseq2i
StepHypRef Expression
1 reseqi.1 . 2 𝐴 = 𝐵
2 reseq2 5312 . 2 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))
31, 2ax-mp 5 1 (𝐶𝐴) = (𝐶𝐵)
Colors of variables: wff setvar class Syntax hints: = wceq 1475 ↾ cres 5040 This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-v 3175 df-in 3547 df-opab 4644 df-xp 5044 df-res 5050 This theorem is referenced by: reseq12i 5315 rescom 5343 resdmdfsn 5365 rescnvcnv 5515 resdm2 5542 funcnvres 5881 resasplit 5987 fresaunres2 5989 fresaunres1 5990 resdif 6070 resin 6071 funcocnv2 6074 fvn0ssdmfun 6258 residpr 6315 wfrlem5 7306 domss2 8004 ordtypelem1 8306 ackbij2lem3 8946 facnn 12924 fac0 12925 hashresfn 12990 relexpcnv 13623 divcnvshft 14426 ruclem4 14802 fsets 15723 setsid 15742 meet0 16960 join0 16961 symgfixelsi 17678 psgnsn 17763 dprd2da 18264 ply1plusgfvi 19433 uptx 21238 txcn 21239 ressxms 22140 ressms 22141 iscmet3lem3 22896 volres 23103 dvlip 23560 dvne0 23578 lhop 23583 dflog2 24111 dfrelog 24116 dvlog 24197 wilthlem2 24595 0pth 26100 2pthlem1 26125 df1stres 28864 df2ndres 28865 ffsrn 28892 resf1o 28893 fpwrelmapffs 28897 sitmcl 29740 eulerpartlemn 29770 bnj1326 30348 divcnvlin 30871 frrlem5 31028 poimirlem9 32588 zrdivrng 32922 isdrngo1 32925 eldioph4b 36393 diophren 36395 rclexi 36941 rtrclex 36943 cnvrcl0 36951 dfrtrcl5 36955 dfrcl2 36985 relexpiidm 37015 relexp01min 37024 relexpaddss 37029 seff 37530 sblpnf 37531 radcnvrat 37535 hashnzfzclim 37543 dvresioo 38811 fourierdlem72 39071 fourierdlem80 39079 fourierdlem94 39093 fourierdlem103 39102 fourierdlem104 39103 fourierdlem113 39112 fouriersw 39124 sge0split 39302 0grsubgr 40502 0pth-av 41293 1pthdlem1 41302 eupth2lemb 41405 rngcidALTV 41783 ringcidALTV 41846
Copyright terms: Public domain W3C validator
| 1,371
| 2,601
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.390625
| 3
|
CC-MAIN-2024-26
|
latest
|
en
| 0.09941
|
https://issuu.com/eribaudo/docs/20100505book2
| 1,506,438,962,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-39/segments/1505818696182.97/warc/CC-MAIN-20170926141625-20170926161625-00421.warc.gz
| 688,826,098
| 18,236
|
Mathematics Test Book 2
6
May 5–7, 2010 Name_ __________________________________ 21653
Developed and published by CTB/McGraw-Hill LLC, a subsidiary of The McGraw-Hill Companies, Inc., 20 Ryan Ranch Road, Monterey, California 93940-5703. Copyright Š 2010 by the New York State Education Department. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the New York State Education Department.
Book 2 Tips for taking the test Here are some suggestions to help you do your best:
This picture means that you will use your ruler.
Secure material
Do not reproduce. Do not discuss contents until end of designated makeup schedule.
Book 2
Page
26
What is the value of n in the equation below? 66 1 n 5 226 Show your work.
Go On Secure material
Do not reproduce. Do not discuss contents until end of designated makeup schedule.
Book 2
Page
27
The diagram below shows a box in a warehouse. The box is in the shape of a rectangular prism.
8 ft
2 ft 4 ft
[not drawn to scale] What is the volume, in cubic feet, of the box? V 5 lwh
Page
cubic feet
Book 2
Secure material
Do not reproduce. Do not discuss contents until end of designated makeup schedule.
28
The ratio of the number of bananas to the number of apples at a fruit stand is 3:5. Moe says that the ratio is equivalent to 12:25. In the space below, use words, numbers, or symbols to show why Moe’s statement is incorrect. Be sure to provide a ratio equivalent to 3:5 in your answer.
Go On Secure material
Do not reproduce. Do not discuss contents until end of designated makeup schedule.
Book 2
Page
29
Matthew plans to plot point A at (2, 3). y
6 5 4 3 2 1 0
1
2
3
4
5
6
x
Plot and label point A on the coordinate plane using Matthew’s coordinates.
On the lines below, explain how you determined where to plot the coordinates.
Page
Book 2
Secure material
Do not reproduce. Do not discuss contents until end of designated makeup schedule.
30
Patty has 123 CDs in her music collection. Of the 123 CDs, 27 are country music. Estimate the percent of Patty’s CDs that are country music CDs. Estimation
%
On the lines below, explain how you determined your estimation.
Go On Secure material
Do not reproduce. Do not discuss contents until end of designated makeup schedule.
Book 2
Page
31
At a bakery, there are 16 packages of hamburger buns for sale. The baker placed 8 hamburger buns in each package. He uses the equation below to calculate the total number of hamburger buns, b, for sale. b ďż˝ 16 8 What is the total number of hamburger buns for sale at the bakery? Show your work.
Page
hamburger buns
Book 2
Secure material
Do not reproduce. Do not discuss contents until end of designated makeup schedule.
32
The temperature in Buffalo, New York, one Saturday was 68째F. The temperature the following Monday was 80째F. Write an equation that shows the change in temperature when x represents the number of degrees the temperature increased. Equation
How many degrees did the temperature increase? Show your work.
degrees
Go On Secure material
Do not reproduce. Do not discuss contents until end of designated makeup schedule.
Book 2
Page
33
What fraction can be used to create a proportion with 4  ? 12 Answer
4 5 12
Page
10
Book 2
Secure material
Do not reproduce. Do not discuss contents until end of designated makeup schedule.
34
The table below shows the prices of different sandwiches.
Price
Small Tuna Sandwich
\$6.00
Small Chicken Sandwich
\$6.50
Large Tuna Sandwich
\$7.00
Large Chicken Sandwich
\$8.00
Leota orders 3 small tuna sandwiches and 3 large chicken sandwiches. What is the total amount Leota will pay for the sandwiches she orders? Answer \$
In the space below, show how Leota can use the distributive property to calculate the total amount.
Go On Secure material
Do not reproduce. Do not discuss contents until end of designated makeup schedule.
Book 2
Page
11
35
The pictograph below shows the number of trees for sale at five different nurseries.
TREES FOR SALE KEY
= 4 trees
Nursery
Number of Trees
Wilson Bryant Klein Randolph Smiley
How many trees are for sale at the Wilson nursery? Answer
trees
What is the total number of trees for sale at the Bryant nursery, the Klein nursery, and the Smiley nursery? Show your work.
trees
STOP Page
12
Book 2
Secure material
Do not reproduce. Do not discuss contents until end of designated makeup schedule.
Place Student Label Here
| 1,165
| 4,704
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.40625
| 3
|
CC-MAIN-2017-39
|
latest
|
en
| 0.842769
|
http://salesianipinerolo.it/pvvj/math-3-unit-1-practice-test.html
| 1,591,375,939,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-24/segments/1590348502097.77/warc/CC-MAIN-20200605143036-20200605173036-00332.warc.gz
| 100,909,778
| 19,506
|
Tracing Basic Shapes. For instance, in 5 3 X 3 2 we simply have to do the math the long way. Math 9 Unit 2 ***PRACTICE*** Exam (Property Of Rockridge Math Department) 3 Write each expression as a power, with no negative exponents (6 marks) 7 7− −6 2÷. asked by Birdie on March 1, 2018; Algebra. Solve absolute value equations. Leave any comments or questions below. Thus, the following equation may be written: 76 = 2(22) + 2 w , which simplifies to 76 = 44 + 2 w , where w = 16. Account Settings. HOME ABOUT Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6. Math Readiness Test 2 (MRT 2) is recommended for students who took advanced high school math courses. Set students up for success in 3rd grade and beyond! Explore the entire 3rd grade math curriculum: multiplication, division, fractions, and more. Large Print Paper Practice Tests can also be printed on 11" x 17" paper with a print size of less than 150% of the standard print. Math 30-1 Function Operations Practice Test ID: B 1 Math 30-1 Function Operations *ANSWER KEY is at the end of this document* 1. Which number is Ronnie thinking of? A. Tell whether the number is odd or even. In Mathematics II, students learned about the trigonometric ratios sine, cosine, and tangent. MASSACHUSETTS COMPREHENSIVE ASSESSMENT SYSTEM. 1 Skills Pages. Try it free!. INTRODUCTION: In seventh and eighth grade, students learned about functions generally and about linear functions specifically. A van that is driven 107 miles costs $97. PARCC Assessment: Grade 5 Mathematics Online Practice Test - Answer and Alignment Document 4 1. #N#Math Worksheet. Skill Practice INV 2. 12 to 15 5. 4 Partial-Quotients Algorithm Strategies Lesson 4. 7th Grade Math UNIT 7B NOTES. Each of the 3 tests mirrors the format of the actual assessment. R 12 MAY 2016 - 8. eps C Common. These online tests are designed to work on computers, laptops, iPads, and other tablets. Computer-Based Practice Test Unit 1. It is very helpful if you are using the Florida Math Standards (MAFS) adaptation of the Common Core. Leave the answer blank and study the solution later. Exam 1 Practice Problems. Understand unit fractions with a numerator of 1, rectangular area and analyzing shapes. Another teacher’s FOM 12 page – with review packages and lots of extra practice. Affirm: Eureka Math Digital Assessments. 3 Pythagorean Theorem and SOHCAHTOA M 16 MAY 2016 - 8. Worksheet 3. a) driving 180 km in 3 hours b) 54 hot dogs for 18 people c) 160 words typed in 4 m inutes d)$27. Full-length practice tests like this one offer a wealth of individualization opportunities, especially when they includes a number of open-response questions. Counting tens and units - up to 30. 3rd Grade Math Test Prep. Rectangular prism Square pyramid. Math 30-1: Transformations Review Practice Test: Name: _____ /25 Part A: Multiple Choice: Place the letter corresponding to the best answer in the blank next to the number of the question. Secondary Math 1. Test tomorrow! March 7th Warm-up: Milestone Practice Packet Unit 1 #7-9 Mini assessment! 10 questions total. 5 Unit Rate Story Questions. Unit One Std 4 - Displaying top 8 worksheets found for this concept. Math I Unit 3 Geometry Math 1 Unit 3 Acquisition Lesson Concept 4. 3 Asymptotes. org website. Math 3 Unit 1 Practice, Functions and Inverses Essay 8. Use a diagram, symbols , and words. Math: 6-1 : Place Value to the Trillions: Math: 6-2 : The Symbols Greater Than or Equal To and Less Than or Equal To: Math: 6-3 : Place Value to the Hundred Thousandths: Math: 6-4 : Problem Solving! Math: 6-5 : Place Value to Trillions, Greater & Less Than, & Thousandths: Math: 6-6 : Commutative Property of Multiplication: Math: 6-7. 1 - How well can you measure? Lesson 1. Skip-counting by 4. Welcome to McDougal Littell's Test Practice site. Then, follow the directions to answer each question. Peoples Education STAAR Practice Test 2 239 STAAR Grade 8 Mathematics Practice Test 2 33 A segment has its endpoints at (2, 1) and (3, 4). 12 Progress Check 3 (Test on Unit 3) Study Guide for Unit 3 Unit 4: Decimals and Their Uses Lesson 4. 1st Grade CCSS Math Practice The common core standards for grade 1 focus on: addition and subtraction within 20, whole number relationships and place value, measuring lengths, and composing and. Worksheet 1-3: Unit Rates- Comparisons 1. Math 1 Unit 4 Practice Test. #N#Multiplying decimals. There are five levels of difficulty. Unit 1 - Algebra Review. Then check your work by choosing the the appropriate "answer" link. Free student math practice. This Performance Based Assessment Practice Test (Grade 8 Math) Assessment is suitable for 8th Grade. Counting tens and units - up to 30. 1-5: Dividing Rational Numbers 29. Convert Place Values Practice converting between place values (example: 3 thousands = ___ ones). 3 Solve a problem involving the cosine law that requires the manipulation of a formula. Powered by Create your own unique website with customizable templates. Three pounds of peaches cost 1. Refer to my shop for units 6-19. TUTORING SCHEDULE. Final Exam Review: Booklet 1 - Measurement & Trigonometry Book 1 KEY; Booklet 2 - Real Numbers, Radical + Exponents & Polynomials. 4 15 5 6 22. -Class Notes - Day 1 - Translating and solving one-step/two-step equations-Class Notes - Day 2 - Multi-Step Equations-Class Notes - Day 3 - Literal Equations and Word Problems-Lab Rubric - Using Your Head page 191-Class Notes - Day 5 - Inequalities-Lab Rubric - Using Your Head, More or Less page 194-Worksheet - Unit 2 Test Review -Worksheet - Fantasy Football. Chapter 11. Given the function graphed, state the domain and range of its inverse. These include mental math routines, practice with fact triangles (flash cards of fact families), daily sets of review problems called Math Boxes, homework, timed tests and a wide variety of math games. The module begins with solving one- and two-step word problems based on a variety of topics studied throughout the year. (1 mark each) 1) Which equation represents the graph of y f x () after it is reflected about the x-axis and then translated. Select one of the links below to get started. #N#Form 4-Digit Numbers. Displaying Practice Math 7 Unit 2 test. Answer Key (HARD COPY) for4 full length practice tests that are aligned with the NEW Common Core Standards of 6th Grade Math. Learn vocabulary, terms, and more with flashcards, games, and other study tools. MrTestPreparation. 3; Homework 3. Practice Tests > Math 1. 2 Classroom Set Solutions. Express 71/1000 as a decimal. Taking a full-length SAT practice test is one of the best ways to simulate test day. National Curriculum. PARCC Assessment: Grade 5 Mathematics Online Practice Test – Answer and Alignment Document 4 1. Click the button for 100% free full practice test. Next, look at the titles of the sessions and notes in the unit to remind yourself in more detail what is. Practice Math 7 Unit 2 test. Evaluating expressions. Math 30-1: Transformations Review Practice Test: Name: _____ /25 Part A: Multiple Choice: Place the letter corresponding to the best answer in the blank next to the number of the question. Solving Equations to Define a Unit - Lesson 1. Math 2 Notes. By appointment (Thursdays 2:15-3:15) There will be a Google sign up form sent the Monday prior to the tutoring session. Also given to middle school students as a Talent Search test. Mathematics PRACTICE TEST. Solve absolute value equations. −1 1 4 and 3 4. 6 Decimals in Money Lesson 4. 6 Remember to hand in the Grade 9 review sheet tomorrow if you did not complete it in class. 1- Modling Data with. Romeo High School. Math I Unit 3 Geometry Math 1 Unit 3 Acquisition Lesson Concept 4. M6:estimate and measure the passage of time in five-minute intervals, and in days, weeks, months, and years. For some questions, you will mark your answers by filling in the circles in your. The test is divided into two parts: First part: 5 test questions. Smart-Kids Practice test Mathematics Grade 1. 4 Estimating with Decimals Lesson 4. Unlimited Online Practice. specialists will have available to them a unit plan in an eighth grade mathematics classroom. centimeter MATHEMATICS PRACTICE TEST NEG4MathPTPaper 7 Go on to the next page. Then check your work by choosing the the appropriate "answer" link. Do not make any pencil marks outside of the. Do not use print scaling or fit-to-page in your printer settings. Class Notes. While individuals may use calculators and conversion tables to help with the problems on the assessment, math skills are still needed to think them through. These sites may not be within. 1 Points, Lines, Angles, and Planes: Students understand the relationship between geometric ideas and their representation. (8, 1) -6 -4 -2 2 4 6 8 10 12 14 16 x 2. 4: Shifting, Reflecting, and Stretching Graphs Section 1. Mathematics Third Grade Unit OneGSE Third Grade Unit 1: Number and Operations in Base Ten Richard Woods, State School Superintendent July 2019 Page 2 of 122. UNIT 1 - Transformations in the Coordinate Plane; UNIT 2 - Similarity Congruence, Proofs; UNIT 3 - Right Triangle Trigonometry; UNIT 4 - Circles & Volume; UNIT 5 - Geometric & Algebraic Connections; UNIT 6 - Applications of Probability; EOC Prep; GSE Algebra II. SAT Math Test Prep Online Crash Course Algebra & Geometry Study Guide Review, Functions,Youtube - Duration: 2:28:48. Scores ranges to 36, average score (2006) is 21. The actual height of the clock tower is 315 2/3 feet. Math 1 Unit 4 Practice Test. 5 Unit Rate Story Questions. ACE Inv 3 Questions. Refer to Figure 1. 1/2 ~ aaaaa 0; 2. Sample Question. g_unit_3_review_complete. Mark your answers to these questions in the spaces provided on pages 4 and 5 of your Practice Test Answer Document. Practice Test Answers:. April 28-May 3: Work on Unit 5 Assignment due at 3:30. Practice Tests > Math 1. 12 14 56 42 x 20. Showing 76 of 369. Benchmark Test : Grade 4 Math ©1999-2011 Progress Testing Page 1 Name Date Class/Grade Benchmark: MA. 2) Translating Trigonometric Graphs - Module 19. Bring the Math Teacher Home with the free Math6. • Chapter 3 Practice Test A. You can better prepare for this important test by using this site to strengthen. Rice’s full course notes. Ships from and sold by Amazon. Test Practice. UNIT 1 - Transformations in the Coordinate Plane; UNIT 2 - Similarity Congruence, Proofs; UNIT 3 - Right Triangle Trigonometry; UNIT 4 - Circles & Volume; UNIT 5 - Geometric & Algebraic Connections; UNIT 6 - Applications of Probability; EOC Prep; GSE Algebra II. Here is the Unit 3 Cover Page to help you keep everything organized. Six of the practice tests have even previously been given as actual SAT exams. Ratio, Rate and Proportions Unit Test Math 8 Write each ratio as a fraction in simplest form. #N#Estimating and rounding. Free WorkKeys Practice Tests (2020 Update) Use our Free WorkKeys Practice Tests (updated for 2020) to pass your exam. 3 Mathematics - Unit Test (Real numbers, sets, Pohynomials) Class: X Max Marks: 25 Time: 45 min Instructions: · The question paper consists of three sections. - Guided Examples and Practice all 3 HW - Watch and take notes on Adding and Subtracting Rational Expressions 3/8/16 Test on Unit 3 - Polynomials HW - Watch and take notes Simplify Rational Expressions Multiply Rational Expressions Divide Rational Expressions Watch all three and write a little of each - they are very similar, but not the same. Some of the worksheets for this concept are Bridges in mathematics grade 4 teachers guide, Bridges in mathematics grade 5 unit 4 module 2, Table of contents grade 4 module 2, Grade 4 mathematics practice test, Second edition teachers guide 2, Grade 4 english language arts. 40 for 4 hours of work e)12. Grade 6 Math Practice Test actual grade 6 transitional math assessment is like. Video Tutorials – by MathScienceX (look for Foundations 12 obviously) Mr. The AP Calculus AB Exam site: Has past exams and sample problems for AP calculus exam. ∡ q o r is a(n) 4. 1: Lines in the Plane Section 1. Access study guides, math practice questions, and answers, bundled into mini-tests, all available online for an unlimited number of attempts. Want to improve your mathematics? Try these pages. Choose "Unit 1, 2, or 3 Computer-Based Test" Experience Georgia Milestone Testing! Education Galaxy. Practice Test: 3-Digit Addition & Subtraction. Math 3 Unit 1 Practice, Functions and Inverses Essay 8. Grade 3 Math Pearson Unit 14. Give a practical interpretation of D 320200. 1 Math 9 Unit 9 Probability and Statistics Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. Intro to exponential functions. Of these 20 questions, 15 are multiple choice and 5 are grid-ins, in which you enter your answer in a grid. For example: 4! = 4 ∗ 3 ∗ 2 ∗ 1 = 24. explain my thinking clearly when I write so a reader can understand my math thinking; Tap/click the following links to print math tests from Unit 1: 1. Here's how to do basic multiplication of exponents. Which of t hese numbers is a perfect square? How do you know? a) 14 b. 1 thousand and 6 hundreds D. PLACE VALUE IN WHOLE NUMBERS AND DECIMALS. Understand unit fractions with a numerator of 1, rectangular area and analyzing shapes. Bringetto Math 1 and 2. Unit 7 Practice Test. Whether you are studying for a school math exam or just looking to challenge your math skills, this test will help you assess your skill level. 1) Before a student is given the chance to retest, she must complete the following: 1) all assigned homework and classwork that was assigned to prepare students for the assessment during that unit of study; 2) any assigned reteaching or relearning activities, including tutorials, test corrections or study guides. Book 2 KEY; Booklet 3 - Relations + Functions, Slope + Linear Equations, Systems of Linear Equations. Which is the most appropriate metric unit for measuring the length of a spoon? A. Free New York State Test practice and sample questions for Math and English Language Arts(ELA). Tell whether the number is odd or even. Chapter 10 Ch. Name the coordinates of the points A, B, C, and D. Use your calculator wisely. When taking quizzes or tests, be sure to use your time wisely. If such a zero has been measured, or is the first estimated digit, it is significant. Robert Leitzel. 3 Drawing Lines with X and Y intercepts. Unit 1 Practice Test Questions (Algebra) Unit 3 Exam Math Quiz 3. ) C Numbers & Operations 4 2 3 Multiple-choice (1 pt. Cycles in the Environment. 226-227 #1-11. Some of the worksheets displayed are Parcc eoy assessment grade 3 mathematics, Common core state standards for mathematics, Practice test answer and alignment document, Pearson scott foresman envision math grade 1, Unit b homework helper answer key, Ixl skill alignment, Homework practice and. If you had an item with the answer 3__ 6, it could be entered as 3__ 6 or simplified into either __1 2 or 0. 4 Solutions: 7: U3D7_S Unit Rate Story Questions. It is very helpful if you are using the Florida Math Standards (MAFS) adaptation of the Common Core. Edugain Advantage membership. 1 thousand and 6 hundreds D. The length of a triangular prism is 5 cm. lesson plan medium to large size of mon core math worksheets algebra them and try via goodfaucet. Solving Equations Tuesday, Sept. Use your notes and/or goals sheet if needed. Illuminate Itembank™ Continue: Turn to the next page. This session contains 8 questions. i) Tasks do not have a context. • Chapter 3 Practice Test B. #N#Math Worksheet. There is no need to download any app for these activities. 12 to 15 5. Read each question carefully and then answer it as well as you can. Given the function graphed, state the domain and range of its inverse. Practice Tests. Assists teachers and improves students standardized test performance. 5 Estimating Graphs. Danielle Hart. 360 miles in 6 hours 8. 25 per kg then find the profit/loss percent incurred by shopkeeper. R 12 MAY 2016 - 8. Michael is measuring fabric for the costumes of a school play. eps C Common. Topic 1: Operations with Rational Numbers. Practice Test Answers:. Unlimited Online Practice. In Class Assignment: Topics 1-3. INV 3 Additional Practice. It is designed to take 1 hour (assuming. It is just for practice. Goals: Solve linear equations using multiplication and division and use linear equations to solve real-life problems. Sign up today, FREE!!. The online math tests and quizzes about arithmetic and geometric series. If they need a quick review, there's an example at the top of the page showing the process for three. Home › Grade1 › School Syllabus. Unit 2: Linear Functions. Lesson 7 Equivalent Ratios Have the Same Unit Rates. Solve the problem. 6 Graphs of Other Trigonometric Functions 4. Unit 5 Test: L: Topic 1- Exponent laws: May 6-10: Topic 2- Evaluating Powers with Integer Exponents : Topic 3- Evaluating Powers with rational Exponents. Free student math practice. Mathematics Readiness Tests The Mathematics Readiness Test 1 (MRT 1) is required of all incoming students without an ACT/SAT score or college-level math credit. • Chapter 3 Practice Test B. Give a practical interpretation of D 320200. Given the function graphed, state the domain and range of its inverse. 1 Skills Pages. Free SAT Maths Level 2 Subject Test Practice Questions with Answers - Sample 1. 3 Pythagorean Theorem and SOHCAHTOA M 16 MAY 2016 - 8. Around d world architecture. Exam 1 Practice Problems. 3 Drawing Lines with X and Y intercepts. Find y such that the point A is on the. COLLEGE LEVEL MATHEMATICS PRETEST This pretest is designed to give you the opportunity to practice the types of problems that appear on the college-level mathematics placement test. Grade 12- Financial Mathematics Online Test 1. Try it free!. Point b is 1 unit further away from c than a is. Showing top 8 worksheets in the category - Grade 3 Math Pearson Unit 14. Mathematics I – Unit 1: Function Families. UNIT 1 - Function Families; UNIT 2 - Algebra Investigations; UNIT 3 - Geometry; UNIT 4 - The Chance of. Kelly has nine pieces of ribbon. Mathematics 3 GO TASC Mathematics Test Practice Items Using Gridded-Response Item Blocks (cont. Which number is the same as 1,670? A. Chapter 11: Networks and decision mathematics: Revision Unit 3 Topic 3: Revision Unit 4 Topic 3: Practice assessment 1 Problem solving and modelling task Unit 3: Practice assessment 3 Unit 4 examination: Topic 4: Earth geometry and time zones: Practice assessment 4 Units 3 and 4 examination: Chapter 6: Earth geometry and time zones: Revision. Level 3 is the least complex, and Level 7 is the. When taking quizzes or tests, be sure to use your time wisely. How many more yards of fabric does he need? 14968 1 3 0000000 1111111 2222222 3333333 4444444 5555555 6666666 7777777 8888888 9999999 aaaaaaa 1 0 / 3 4. For example: 4! = 4 ∗ 3 ∗ 2 ∗ 1 = 24. Scores ranges to 36, average score (2006) is 21. Six of the practice tests have even previously been given as actual SAT exams. Mathematics Third Grade Unit OneGSE Third Grade Unit 1: Number and Operations in Base Ten Richard Woods, State School Superintendent July 2019 Page 2 of 122. Which is the equivalent decimal number for forty nine thousandths? Decimal Tips Tricks and Shortcuts. Sample Question. Unit 2: Linear Functions. Solving Equations Tuesday, Sept. Math Sense provides instruction and practice for the range of math skills that adults need to succeed in life, at work, and on high school equivalency tests. Free New York State Test practice and sample questions for Math and English Language Arts(ELA). 4 Partial-Quotients Algorithm Strategies Lesson 4. document will give teachers an understanding of the features of TestNav 8 prior to working with students. The segment is reflected across the y-axis. Here the class can really get some hands-on experience wrestling with the open-ended response problems, along with the tricks for. Competitive Exams. 3) Browse a printable teacher resource book that helps third-grade students review graphs, time, money, and the concepts of "likely" and "unlikely. books 82 via engageny. 5 Quiz and Area of Oblique Triangles. Ships from and sold by Amazon. Which number is the same as 1,670? A. 6 Remember to hand in the Grade 9 review sheet tomorrow if you did not complete it in class. The module begins with solving one- and two-step word problems based on a variety of topics studied throughout the year. lesson plan medium to large size of mon core math worksheets algebra them and try via goodfaucet. For Students/Parents. Drug Dosage Calculations NCLEX Exam 1 (20 Items) NOTE: The rationales and computation solutions for this quiz are available in the. HANDOUTS: Unit 1. The Practice Test may be used at home or at school for students to become familiar with the iLEAP test they will take in spring 2013. 1 Math 9 Unit 5 Polynomials Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 3 B with support. The TestNav app needs to be restarted due to network connectivity issues. Home 7th Math Algebra Extra Practice cas_practice_test. 1/2 ~` aaaaa 0; 2. Math 1 Unit 2 Practice Test. It will cover handouts, lecture notes, and examples from class, homework assignments 1 through 6, and material from sections 1. Answer keys are optional if the Teacher's Guides are purchased. The sample item sets in the CMAS Practice Resources are not intended to be representative of a complete unit or test. 4 up ____ 2. Grade 3 Module 7: Geometry and Measurement Word Problems. His fi gure • is a parallelogram, and • has four right angles. He gave up a position as a researcher at Montana State University (working with NASA, among other projects) to become a full-time maths tutor, helping adults and GCSE, A-level, and university students overcome their fear of maths – a position he finds 'far more enjoyable than real. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. Chapter 5. Use “Unit 1 Review Practice” and “Unit 2 – Review Practice for Test 3” to see which review topics might be on Test 3. The Teacher's Guides give teaching tips, extra practice, solutions, LightUnit answers, and alternate LightUnit tests. Find the number. asked by Birdie on March 1, 2018; Algebra. For example, if you divide the space between 0 and 1 on a number line into three equal parts, then each part has size 1/3 and the first endpoint represents the point 1/3. Chapter 2: Numeration. 2 Graphing Sine and Cosine F 13 MAY 2016 - 8. Free Printable Math Worksheets for Grade 3 This is a comprehensive collection of math worksheets for grade 3, organized by topics such as addition, subtraction, mental math, regrouping, place value, multiplication, division, clock, money, measuring, and geometry. Practice your computation skills and you will be the smartest kid in class Perimeter, Area and Volume- Practice Test. Answer all the questions. A shopkeeper mixes two variants of wheat in the ratio 3:1. Choose from 500 different sets of test unit 3 math 1 flashcards on Quizlet. Unit 2 Challenge 12. Lesson #1 - Order of. SAT Math Test Prep Online Crash Course Algebra & Geometry Study Guide Review, Functions,Youtube - Duration: 2:28:48. For Grade K–8+, discover core programs, Sadlier Math and Progress in Mathematics, and supplemental programs include instruction, practice, preparation for assessments, and rich digital resources such as virtual manipulatives to help students develop the deep conceptual understanding they need to be successful. Extra practice: Worksheet 3. · All questions are compulsory. You are to choose the answer that you think is better. Features & Components: Each chapter comprises Test A and Test B. Exam 1 Practice Problems. 8 Extra Practice. Home › Grade1 › School Syllabus. Welcome to the Virginia State Standards of Learning Practice Tests! All of the questions on this site come from test materials released by the Virginia Department of Education and are used here with permission. 2 (Pouches and Coins) Homework 3. The number is 20 more than 40. Unit Test Answer Keys. Math 8: Unit 3 Test-Angle Measurements Review Practice Test Assessment ID: ib. Browse or search thousands of free teacher resources for all grade levels and subjects. −1 1 4 and 3 4. Patterns on a Hundred Chart Use the hundred chart. In Class Assignment: Topics 1-3. Contact me if you have any questions - [email protected] 3b Strategies for Multiplying • Unit 1. The TestNav app needs to be restarted due to network connectivity issues. For example, if you divide the space between 0 and 1 on a number line into three equal parts, then each part has size 1/3 and the first endpoint represents the point 1/3. Vocabulary. 6 Order of Operations with Integers Part 1 • Unit 1. 5 Solutions: 8: Unit 3 Review. 2 Applications. Timed tests are available, as well as printable math worksheets. Test Review KEY. The division practice test offers a variety of division questions involving single-digit division, 2-digit, 3-digit and 4-digit numbers divided by single-digit numbers, 4 digit by 2-digit division and much more. As the nationwide leader in credentialing exam preparation, Teachers Test Prep is proud to serve over 250,000 individual account holders as well as top universities, schools, and teachers’ organizations. 28 Use the hundred chart. Mathematics Practice Test for Ninth Graders Answer Key Question No. pdf: File Size: 69 kb: File Type: pdf: Download File. dilations practice and answers 2nd page also includes doing a composition when given an Algebraic rule. You will not be able to use a calculator. If the mixed wheat is sold at the price of 20. Test Practice. Do not use print scaling or fit-to-page in your printer settings. Showing top 8 worksheets in the category - Grade 3 Math Pearson Unit 14. #N#TABLE OF CONTENTS. Math 3 Unit 1 Practice, Functions and Inverses Multiple Choice (Calculator Inactive) Identify the choice that best completes the statement or answers the question. Prentice Hall Mathematics: Course 1 Day 1: Ratios (Date: January 18th) Lesson 6-1 (pages 269-272) Vocabulary: ratio, equal ratio Chapter 6 Overview – In Class Homework: Practice 6-1, Vocabulary CU 1-3, GPS 6-1 Day 2: Unit Rates (Date: January 19th). April 28-May 3: Work on Unit 5 Assignment due at 3:30. 4 Number Story Questions Extra Practice. #N#Chapter 5 - Number Theory and the Real Numbers. To help you better prepare for the exam, the Paragraph Comprehension section of the ASVAB practice test has passages of similar length and style to those on the actual ASVAB test. Please ensure that you have all practice papers! Speed, Accuracy and Precision! Grading of all R 2 S MCQ practice tests is computerized using any of 2 input options: Form A - Test-coded answer sheets. Year 8 Revision Test 4. Math 1 Unit 3 Practice Test. Learn vocabulary, terms, and more with flashcards, games, and other study tools. The number is 20 more than 40. Showing top 8 worksheets in the category - Grade 3 Math Pearson Unit 14. It is very helpful if you are using the Florida Math Standards (MAFS) adaptation of the Common Core. 5: Combinations of Functions Section 1. Week of January 3, 2011 7-8 (Mon), Chapter 7 Test, Form 2A (Tues), Chapter 7 Test, Form 2B (Wed), TBA (Thurs), 8-1 (Fri) Core Math Lessons Monday: Lesson 7-8 Tuesday: Chapter 7 Study Guide and Review Wednesday: Chapter 7 Practice Test (from the textbook) Thursday: Chapter 7 Final Friday: Lesson 8-1. MATHEMATICS TEST 5 PRACTICE BOOK 007624-72506 • GRE Math Practice Book • Hel, Neu, New Aster • indd CS2 MAC • Draft01 04/18/08 ljg • edits dr01 04/21/08 ljg • edits dr01 04/42/08 ljg • dr02 051108 ljg • prefl ight 052708 ljg Additional Topics—25% ˜ Introductory real analysis: sequences and. Numerical Response Answer Keys. Algebra 1 Test Practice. MPM1D Unit 4 – Modelling With Graphs. Figure 1 1. #1-4 (ac of each), 6, 8-11, 16, 19, 20. On Core Mathematics Algebra 1 Unit 3: Systems of Equations and Inequalities Chapter Exam Instructions. To practice, choose the appropriate test and complete. Help students gain the full range of math skills needed for high school equivalency test success. WHOM - What's the Difference? - English Grammar - When to Use Who or Whom - Duration: 14:53. This practice test for the General Curriculum mathematics subtest is a sample test consisting of 45 multiple- choice questions and 1 open-response item assignment. Quiz 3: 6 questions Practice what you've learned, and level up on the 5 questions Practice what you've learned, and level up on the above skills. 2: Divisibility by 3 and 9; Lesson 1. Unit 2 Challenge 12. Online tests and testing for certification, practice tests, test making tools, medical testing and more. Help your child practice his math skills with this printable worksheet, which will help him count up to 100. Set students up for success in Algebra 1 and beyond! Explore the entire Algebra 1 curriculum: quadratic equations, exponents, and more. #N#Form 4-Digit Numbers. Unit 8: Rags to Riches! The Word within the Word Vol. Are you looking for a 6th grade math test that you can take online? The following links provide free access to different tests and quizzes suitable for 6th grade students. t m s ã is a(n) 5. 1 Lesson 6 - Combinations Pt. made people stand in one place C. PLACE VALUE IN WHOLE NUMBERS AND DECIMALS. The ultimate goal of this unit plan is to develop an effective unit plan for teaching Scientific Notation to 8th grade mathematics students. MATHEMATICS TEST 5 PRACTICE BOOK 007624-72506 • GRE Math Practice Book • Hel, Neu, New Aster • indd CS2 MAC • Draft01 04/18/08 ljg • edits dr01 04/21/08 ljg • edits dr01 04/42/08 ljg • dr02 051108 ljg • prefl ight 052708 ljg Additional Topics—25% ˜ Introductory real analysis: sequences and. 1-4: Multiplying Rational Numbers 23. #1-4 (ac of each), 6, 8-11, 16, 19, 20. Edugain Advantage membership. Fast and easy to use. Ships from and sold by Amazon. - Unit 5 Test (Chapter 6 &7) Today but will finish it tomorrow - look over study guide! - Math Final Exam on Wednesday 12/18/13 - every chapter since the beginning of the year (Chapters 1 through 7) Friday: (12/13/13): Finish the Unit 5 Study Guide- attached if you need it again - Unit 5 Test (Chapter 6 &7) on Monday 12/16/13. 2 Practice B (Answers) 3. Account Settings. Select one of the links below to get started. 4th Grade Unit 4 Module 1 Session - Displaying top 8 worksheets found for this concept. 2) Translating Trigonometric Graphs - Module 19. Unlimited Online Practice. 4: Shifting, Reflecting, and Stretching Graphs Section 1. Automatic spacing. Math 1 Unit 3. Competitive Exams. Title: Math 3 Unit 1 Practice Test Last modified by: NBHS Teacher Created Date: 8/31/2015 10:11:00 AM Other titles: Math 3 Unit 1 Practice Test. Sample Question. Which number is Ronnie thinking of? A. It is 138 miles from Concord, NH, to Colebrook, NH. 5 km in 30 minutes. (A) 0 (B) 3 1 (C) 1 (D) 3 (E) None of the above 30. Counting forward and backward. Essential Question:. Unit One Std 4 - Displaying top 8 worksheets found for this concept. 9th class Mathematics Chapter 3 (Urdu Medium) Here you can prepare 9th Mathematics chapter 3 online MCQ test with answers (Unit 3 Logarithms). Varsity Tutors’ Learning Tools also offer dozens of Full-Length Math Practice Tests. Use a diagram, symbols , and words. 3 - Polystrip and quadrilaterals; Investigation 3. Showing 76 of 369. Find the surface area of the triangular prism. asked by Arrow Moore on April 3, 2020; Math. Do not use print scaling or fit-to-page in your printer settings. Solving for a. Unit Cost - Sample Math Practice Problems The math problems below can be generated by MathScore. Computer-Based Practice Test Unit 1. Math 11 Foundations is an academic course that prepares students for Math 12 Foundations. Page 2 | 19. The molecular formula of a compound is a representation of the number and type of elements present in one molecular unit of the compound. 2 Trigonometric Functions: The Unit Circle 4. Here you can download a copy of the unit circle. \$5 12 h h × 2. 2 (Part 1) Writing Equations of Transformed Tangents - Mod 19. AIMS (Arizona) revised 2006 - [41 pages] Reading and Mathematics multiple-choice questions (answers provided), the Writing test asks for pre-writing, rough draft, and final copy, no answer key provided for the Writing section. 7th Grade Math. The division practice test offers a variety of division questions involving single-digit division, 2-digit, 3-digit and 4-digit numbers divided by single-digit numbers, 4 digit by 2-digit division and much more. Lesson #1 - Order of. Take the Lab Safety Practice Test. Read each question carefully and then answer it as well as you can. 6/5 Delta Math Teacher Code: 957441. Learn unit 3 test math equations with free interactive flashcards. Practice taking math sentences and creating mathematical expressions to represent the scenario in more difficult situations. An angle in standard form with a measure of 215^\circ lies in what quadrant? An angle in standard form with a measure of -320^\circ lies in what quadrant? An angle in standard form with a measure of 500^\circ lies in what quadrant? The point A\left (\frac12, \frac {\sqrt2}2\right) is on the unit circle. Read each question. In which direction must the graph of be shifted to produce the graph of ? a. 1 Mathematics—Session 1 (Non-Calculator) Answer questions 1 through 4 on page 2. Features & Components: Each chapter comprises Test A and Test B. Some of the worksheets displayed are Parcc eoy assessment grade 3 mathematics, Common core state standards for mathematics, Practice test answer and alignment document, Pearson scott foresman envision math grade 1, Unit b homework helper answer key, Ixl skill alignment, Homework practice and. Study Guide for the Middle School Mathematics Test 3 How to Use This Study Guide This study guide gives you instruction, practice, and test-taking tips to help you prepare for the Middle School Mathematics test. Lesson 1 - The Fundamental Counting Principle Lesson 2 - Factorial Notation and Permutations Lesson 3 - Permutations with Restrictions Lesson 4 - Permutations with Repetitions Lesson 5 - Combinations Pt. 1 Skills Pages. Quiz 3: 6 questions Practice what you've learned, and level up on the 5 questions Practice what you've learned, and level up on the above skills. Bringetto Math 1 and 2. Six of the practice tests have even previously been given as actual SAT exams. Math: 6-1 : Place Value to the Trillions: Math: 6-2 : The Symbols Greater Than or Equal To and Less Than or Equal To: Math: 6-3 : Place Value to the Hundred Thousandths: Math: 6-4 : Problem Solving! Math: 6-5 : Place Value to Trillions, Greater & Less Than, & Thousandths: Math: 6-6 : Commutative Property of Multiplication: Math: 6-7. 2 Grade,Angle and Distance. 1) Before a student is given the chance to retest, she must complete the following: 1) all assigned homework and classwork that was assigned to prepare students for the assessment during that unit of study; 2) any assigned reteaching or relearning activities, including tutorials, test corrections or study guides. Assessment covering verbs. #N#Numbers on Abacus. 1 Skills Pages. Math 3 Unit 1 Practice, Functions and Inverses Multiple Choice (Calculator Inactive) Identify the choice that best completes the statement or answers the question. Section 4 allows a calculator, and consists of 38 questions which must be. That's why we created our ALEKS Math test prep course - to offer the perfect balance of affordability and effectiveness that has always been missing for students preparing for the ALEKS Math test. Help your child practice his math skills with this printable worksheet, which will help him count up to 100. Here is the graph of y = f(x). Natural disasters. Math tests can be daunting, especially if you don't consider math your best subject. a_unit_1_review_video. Solve the problem. Support Resources. 12 14 56 42 x 20. Unit One Std 4 - Displaying top 8 worksheets found for this concept. Year 8 Revision Test 4. Express the area of each part as a unit fraction of the whole. Chapter 5: Measuring Length, Time, and Temperature. Investigation 3. Parents and teachers can use these tests to check how well your 1st Grade (er) is progressing through the Math curriculum. It can help students feel more relaxed when they take the actual test. Match the names with there pictures. HOME ABOUT Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6. Session 1 FSA Mathematics Practice Test Answer Key 3. Powered by Create your own unique website with customizable templates. Group achievement test, with sections in English, math, reading, science, and writing (optional). ) A Geometry & Measurement 1 2 2 Multiple-choice (1 pt. a square D. Everyday Math Practice Sheets (Gr. (1 mark each) 1) Which equation represents the graph of y f x () after it is reflected about the x-axis and then translated. Showing top 8 worksheets in the category - Grade 3 Math Pearson Unit 14. Support Resources. Write the polynomial represented by this set of algebra tiles. 08 Solve problems using prime factorization, common factors, and common multiples. Khan Academy Support Videos. Worksheet 3. This site offers multiple interactive quizzes and tests to improve your test-taking skills. Which number correctly completes the subtraction sentence 5. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape. Help students gain the full range of math skills needed for high school equivalency test success. 1 Decimal Place Value Lesson 4. Then, follow the directions to answer each question. Definitions were derived from student generated meanings. Please have a look. 3-2 Solving Systems by Graphing and Substitution Unit 3 Graphing Practice ANSWERS. Unit 5 Test: L: Topic 1- Exponent laws: May 6-10: Topic 2- Evaluating Powers with Integer Exponents : Topic 3- Evaluating Powers with rational Exponents. For example, if you divide the space between 0 and 1 on a number line into three equal parts, then each part has size 1/3 and the first endpoint represents the point 1/3. 3 2MC excerpted test items 10/2016 from PARCC Online Practice Tests 47. Do not make any pencil marks outside of the. You can also search a book's contents by keyword. He needs 47 feet of fabric. Contact me if you have any questions - [email protected] This practice test for the General Curriculum mathematics subtest is a sample test consisting of 45 multiple- choice questions and 1 open-response item assignment. This session contains 8 questions. Prepare your students for success with meticulously researched ELA, math, and science practice for grades 5-8. Page 1 of 4. Each unit concludes with Cumulative Tests A and B. Content Standards. Each of the 3 tests mirrors the format of the actual assessment. Want to improve your mathematics? Try these pages. Grade 4 • Unit 4 • Week 3 Selection Test /BNF Writing on the Wall " Fill in the bubble next to the best answer. 2: Divisibility by 3 and 9; Lesson 1. com, a math practice program for schools and individual families. Some of the worksheets displayed are Parcc eoy assessment grade 3 mathematics, Common core state standards for mathematics, Practice test answer and alignment document, Pearson scott foresman envision math grade 1, Unit b homework helper answer key, Ixl skill alignment, Homework practice and. As the nationwide leader in credentialing exam preparation, Teachers Test Prep is proud to serve over 250,000 individual account holders as well as top universities, schools, and teachers’ organizations. • Every question in the practice exam has already been covered in the Math 30-1 workbook. 4 up ____ 2. 000 000 000 mm has 10 sig figs. Math Sense provides instruction and practice for the range of math skills that adults need to succeed in life, at work, and on high school equivalency tests. Software for math teachers that creates exactly the worksheets you need in a matter of minutes. Start studying Math Practice Test Unit 1. Test A consists of free response questions and assesses comprehension of key concepts and problem solving skills. The PARCC Mathematics Exam. Grade 5 Practice Tests - Triumph Learning. Lesson 4 Converting Units. #N#Nelson Education > School > Mathematics K-8 > Mathematics 3 > Student Centre > Try It Out. section II includes a record – primarily based question and a protracted essay question. Because the English language arts and math tests are new, there are a smaller number of sample test items available until the item development process is completed and practice tests can be released. High School Replace your patchwork of digital curriculum and bring the world's most comprehensive practice resources to all subjects and grade levels. Essential Question:. The Great Wall of Los Angeleslinked people together. Fun, Interactive Practice and Assignments for any Classroom or Home User. Mathematics Unit 1 Unit 1 Directions: Today, you will take Unit 1 of the Grade 5 Mathematics Practice Test. Find the number. Test 1 Test 2 Test 3 Test 4 Test 5 Test 6: Test-out 1 Test-out 2; Part 4: Contents of Part 1 - 3, and 4 4. 1 hundred and 67 tens C. Directions. Do not use print scaling or fit-to-page in your printer settings. Algebra 1 Unit 3 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. Interactive Games & Exercises for Classrooms - From ESL Games World. HANDOUTS: Unit 1. Which number is the same as 1,670? A. Video Lessons by Unit & Level. #N#Estimating and rounding. To find the percent of boys, divide 8 by 25: 8 ÷ 25 = 0. Lesson 6 Interpreting Rates. Warm-up: Milestone Practice Packet Unit 1 #10 Finish Mini assessment! 10 questions total. The comprehensive lesson plans outlined below provide a detailed list of the Time4Learning. #N#TABLE OF CONTENTS. You may not use a calculator for session 1, but you may use a calculator for sessions 2 and 3. Leave all answers exact or rounded to three significant figures. Refer to my shop for units 6-19. These include mental math routines, practice with fact triangles (flash cards of fact families), daily sets of review problems called Math Boxes, homework, timed tests and a wide variety of math games. Unlimited Online Practice. HANDOUTS: Unit 1. About the Book Author Colin Beveridge, PhD, holds a doctorate in mathematics from the University of St Andrews. Browse or search thousands of free teacher resources for all grade levels and subjects.
qgj46za5pjvnkjo, ddy8g46upa0u, ayxh3j1qw466ji, 8q39729w2h0, zhbil0j46fk3p, h2eduo2yl7t, auvht483ik66m, 5nvrwxlici71, hb00nf76gm6171, j2k5gpdmdxa37o1, f2f4q6uq99a4sij, ehtn12n7vy6, r3v6i2xgfwe, jamgxbqqhk, x5ou3z67b7cotpp, vcgy4uva5ff6d2f, tiijhxjydmx, g0n6283qutcq57j, gc2834k7fyalro, 79z7oh0ha7o8, 5ew0kwv569, 42rlg4zilklwb7p, i0t0vkltf1v3z, m2xcxnhgru, wnxcp86lr4, aaegammrv25, tjuhls9vjb8h
| 10,648
| 42,945
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.53125
| 4
|
CC-MAIN-2020-24
|
latest
|
en
| 0.860474
|
https://mathematica.stackexchange.com/questions/161186/how-to-visualize-elastic-collision-among-particles-confined-in-a-square-2d-conta
| 1,713,807,038,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-18/segments/1712296818312.80/warc/CC-MAIN-20240422144517-20240422174517-00038.warc.gz
| 343,841,567
| 37,927
|
# How to visualize elastic collision among particles confined in a square 2D container?
I've already simulate two particle confined in a square 2D container, but I don't know how to simulate the elastic collision between them. Currently, they just pass through each other without any collision.
Further, I want to carry this to multiple identical particles system, where many elastic collision will happen.
What's the most effective way to simulate the elastic collision in this multiple identical particles system?
Here's my code.
(*Given two spheres in the square 2D container: initial position and initial velocity*)
ball = {{{0.5, 0.5}, {Cos[\[Pi]/6], Sin[\[Pi]/6]}}, {{0.3, 0.3}, {Cos[1], Sin[1]}}};
Graphics[{PointSize[0.05],
(*Draw the container*)
Line[{{-1, -1}, {1, -1}, {1, 1}, {-1, 1}, {-1, -1}}],
Point[
Dynamic[
(*balls moving*)
ball = Map[{#[[1]] + #[[2]]*0.009, #[[2]]} &, ball];
(*reflection from the container walls*)
ball = Map[If[Abs[#[[1, 2]]] > 1, {{#[[1, 1]], 2*Sign[#[[1, 2]]] - #[[1, 2]]}, {1, -1} #[[2]]}, #] &, ball];
ball = Map[If[Abs[#[[1, 1]]] > 1, {{2*Sign[#[[1, 1]]] - #[[1, 1]], #[[1, 2]]}, {-1, 1} #[[2]]}, #] &, ball];
Map[First, ball]
]]},
PlotRange -> {{-1.025, 1.025}, {-1.025, 1.025}},
ImageSize -> {250, 250}]
• Have a look a the bouncy bubbles question. Dec 2, 2017 at 19:41
Simple fix will be adding this code inside your loop (assuming d is a diameter of your ball):
r = ball[[1, 1]] - ball[[2, 1]];
| 490
| 1,451
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.1875
| 3
|
CC-MAIN-2024-18
|
latest
|
en
| 0.741088
|
https://au.mathworks.com/matlabcentral/profile/authors/16301808
| 1,632,816,405,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-39/segments/1631780060538.11/warc/CC-MAIN-20210928062408-20210928092408-00065.warc.gz
| 164,276,430
| 19,692
|
Community Profile
# ruke xiong
Last seen: 6 months ago Active since 2020
#### Content Feed
View by
Solved
Insert zeros into vector
Insert zeros after each elements in the vector. Number of zeros is specified as the input parameter. For example: x = [1 ...
6 months ago
Solved
Change the sign of even index entries of the reversed vector
change the signs of the even index entries of the reversed vector example 1 vec = [4 -1 -2 9] ans = [9 2 -1 -4] example2...
6 months ago
Solved
Create a vector whose elements depend on the previous element
The idea is to create a vector A whose elements depend on the previous element : *A(i+1) = 2*A(i)+1* *2 Inputs*: - A : The...
7 months ago
Solved
Unique values without using UNIQUE function
You must return unique values in a vector in *stable* mode without using the unique function. About stable order flag: ...
7 months ago
Solved
Set a diagonal
Given a matrix M, row vector v of appropriate length, and diagonal index d (where 0 indicates the main diagonal and off-diagonal...
7 months ago
Solved
Max index of 3D array
Given a three dimensional array M(m,n,p) write a code that finds the three coordinates x,y,z of the Maximum value. Example ...
7 months ago
Solved
Finding peaks
Find the peak values in the signal. The peak value is defined as the local maxima. For example, x= [1 12 3 2 7 0 3 1 19 7]; ...
11 months ago
Solved
Find nth maximum
Find nth maximum in a vector of integer numbers. Return NaN if no such number exists. x = [2 6 4 9 -10 3 1 5 -10]; So ...
11 months ago
Solved
Create an index-powered vector
Given a input vector x, return y as index-powered vector as shown below. Example x = [2 3 6 9] then y should be [...
11 months ago
Solved
Oh Zero Zero Zero!!!
Hello all, So you have to find the largest section of zeros in a vector and then find the length of those zeros and there start...
11 months ago
Solved
Find last zero for each column
Given a numeric array of arbitrary size, return the row index of the last zero for each column. If a column contains all nonzero...
11 months ago
Solved
Count consecutive 0's in between values of 1
So you have some vector that contains 1's and 0's, and the goal is to return a vector that gives the number of 0's between each ...
11 months ago
Solved
Calculate the Number of Sign Changes in a Row Vector (No Element Is Zero)
For a row vector: V=[7 1 2 -3] there is one sign change (from 2 to -3). So, the function you write must return N=1. F...
11 months ago
Solved
Symmetry of vector
Determine whether the vector is symmetric or not (vector could be even or odd in length). For example: x = [1 2 3 3 2 1] ...
11 months ago
Solved
Create an n-by-n null matrix and fill with ones certain positions
The positions will be indicated by a z-by-2 matrix. Each row in this z-by-2 matrix will have the row and column in which a 1 has...
11 months ago
Solved
Implement a bubble sort technique and output the number of swaps required
A bubble sort technique compares adjacent items and swaps them if they are in the wrong order. This is done recursively until al...
11 months ago
Solved
"Look and say" sequence
What's the next number in this sequence? * [0] * [1 0] * [1 1 1 0] * [3 1 1 0] * [1 3 2 1 1 0] This a variant on the w...
12 months ago
Solved
Find the stride of the longest skip sequence
We define a _skip sequence_ as a regularly-spaced list of integers such as might be generated by MATLAB's <http://www.mathworks....
12 months ago
Solved
Sum of first n terms of a harmonic progression
Given inputs a, d and n, return the sum of the first n terms of the harmonic progression a, a/(1+d), a/(1+2d), a/(1+3d),....
12 months ago
Solved
How to subtract?
*± ± ± ± ± ± ± ± ± ± ±* * Imagine you need to subtract one...
12 months ago
Solved
The Hitchhiker's Guide to MATLAB
Output logical "true" if the input is the answer to life, the universe and everything. Otherwise, output logical "false".
12 months ago
Solved
Approximation of Pi
Pi (divided by 4) can be approximated by the following infinite series: pi/4 = 1 - 1/3 + 1/5 - 1/7 + ... For a given numbe...
12 months ago
Solved
Volume Pillar
Calculate the volume of a pillar with radius l and heigth ar.
12 months ago
Solved
Given input in radians, output to degrees
12 months ago
Solved
Perimeter of a semicircle
Given the diameter d, find the perimeter of a semicircle
12 months ago
Solved
Return fibonacci sequence do not use loop and condition
Calculate the nth Fibonacci number. Given n, return f where f = fib(n) and f(1) = 1, f(2) = 1, f(3) = 2, ... Examples: ...
12 months ago
Solved
Find the next Fibonacci number
In the sequence of Fibonacci numbers, every number is the sum of the two preceding ones: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...
12 months ago
Solved
Integer Sequence - II : New Fibonacci
Crack the following Integer Sequence. (Hints : It has been obtained from original Fibonacci Sequence and all the terms are also ...
12 months ago
Solved
Return the Fibonacci Sequence
Write a code which returns the Fibonacci Sequence such that the largest value in the sequence is less than the input integer N. ...
1 year ago
Solved
Given a square and a circle, please decide whether the square covers more area.
You know the side of a square and the diameter of a circle, please decide whether the square covers more area.
1 year ago
| 1,462
| 5,460
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.34375
| 3
|
CC-MAIN-2021-39
|
latest
|
en
| 0.716258
|
https://sks23cu.net/dwqa-question/show-y-23ex-e-2x
| 1,719,140,666,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-26/segments/1718198862466.81/warc/CC-MAIN-20240623100101-20240623130101-00560.warc.gz
| 460,546,169
| 11,126
|
## Show that y = 2/3e^(x) + e^(-2x)
Differential equationsShow that y = 2/3e^(x) + e^(-2x)
3 years ago
Show that y = 2/3e^(x) + e^(-2x) is a solution of the differential equation y’ + 2y = 2e^(x)
| 86
| 196
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.15625
| 3
|
CC-MAIN-2024-26
|
latest
|
en
| 0.58439
|
https://homework.zookal.com/questions-and-answers/the-electrical-potential-due-to-a-point-load-of-60-916824878
| 1,618,144,704,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-17/segments/1618038062492.5/warc/CC-MAIN-20210411115126-20210411145126-00261.warc.gz
| 405,886,610
| 25,951
|
1. Science
2. Physics
3. the electrical potential due to a point load of 60...
# Question: the electrical potential due to a point load of 60...
###### Question details
The electrical potential due to a point load of 6.0 μC at a point A is measured as 2.1 x 104 V. The distance that the load is from point A is:
a.2.6 m
b. 3.5 m
c. 3.1 m
d. 1.8 m
| 114
| 353
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.5625
| 3
|
CC-MAIN-2021-17
|
latest
|
en
| 0.860569
|
https://www.smore.com/42h01
| 1,552,919,816,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-13/segments/1552912201329.40/warc/CC-MAIN-20190318132220-20190318154220-00416.warc.gz
| 890,984,857
| 12,082
|
Polynomials
Intro to Polynomials
What is a Polynomial?
A Polynomial is an extension of Quadratics with Complex Numbers.
Polynomials Vocabulary
• polynomial- a monomial or a sum of difference of monomials
• polynomial function- a function whose rule is a polynomial
• factor by grouping- to factor a polynomial with four terms by grouping, factor common monomials from pairs of terms, and then look for common binomial factors
• factor by grouping- pairs of terms that have a common monomial factor
• synthetic division- a shorthand method of dividing by a linear binomial of the form (x-a) by writing only the coefficients of the polynomial
Multiplying Polynomials
multiply a polynomial by a monomial
multiply binomial by a binomial (using FOIL)
binomial by a trinomial
Synthetic Division
normal synthetic division
quotient is factorable (trial and error)
quotient is factorable (difference of two squares)
zeros in the quotient (trial and error)
zeros in the quotient (factor by grouping)
Citations
"10.1 - Introduction to Polynomials." 10.1 - Introduction to Polynomials. N.p., n.d. Web. 19 Jan. 2016.
"HRW: High School Math - Multilingual Glossary." HRW: High School Math - Multilingual Glossary. N.p., n.d. Web. 19 Jan. 2016.
"Multiply Polynomial By Monomial." . Examples, Practice Problems Explained Step by Step. All You Have to Do Is.. N.p., n.d. Web. 20 Jan. 2016.
"Simplifying Using the FOIL Method Lessons -- Algebra.Help." Simplifying Using the FOIL Method Lessons -- Algebra.Help. N.p., n.d. Web. 20 Jan. 2016. <http://www.algebrahelp.com/lessons/simplifying/foilmethod/pg2.htm>.
| 400
| 1,605
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.953125
| 4
|
CC-MAIN-2019-13
|
latest
|
en
| 0.809403
|
https://de.scribd.com/document/90126541/Liquidity-Ratios
| 1,558,583,448,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-22/segments/1558232257002.33/warc/CC-MAIN-20190523023545-20190523045545-00528.warc.gz
| 434,255,595
| 50,596
|
You are on page 1of 4
# Liquidity Ratios Efficiency Ratios Profitability Ratios
Liquidity Ratios:
Liquidity Ratios are ratios that come off the the Balance Sheet and hence measure the liquidity of the company as on a particular day i.e the day that the Balance Sheet was prepared. These ratios are important in measuring the ability of a company to meet both its short term and long term obligations.
## FIRST LIQUIDITY RATIO
Current Ratio: This ratio is obtained by dividing the 'Total Current Assets' of a company by its 'Total Current Liabilities'.
The ratio is regarded as a test of liquidity for a company. It expresses the 'working capital' relationship of current assets available to meet the company's current obligations.
The formula:
Current Ratio = Total Current Assets/ Total Current Liabilities
## An example from our Balance sheet:
Current Ratio = \$261,050 / \$176,522 Current Ratio = 1.48
The Interpretation:
Lumber & Building Supply Company has \$1.48 of Current Assets to meet \$1.00 of its Current Liability Review the Industry same industry.
Norms and Ratios for this ratio to compare and see if they are above below or equal to the others in the
## SECOND LIQUIDITY RATIO
Quick Ratio: This ratio is obtained by dividing the 'Total Quick Assets' of a company by its 'Total Current Liabilities'.
Sometimes a company could be carrying heavy inventory as part of its current assets, which might be obsolete or slow moving. Thus eliminating inventory from current assets and then doing the liquidity test is measured by this ratio. The ratio is regarded as an acid test of liquidity for a company. It expresses the true 'working capital' relationship of its cash, accounts receivables, prepaids and notes receivables available to meet the company's current obligations.
The formula:
Quick Ratio = Total Quick Assets/ Total Current Liabilities Quick Assets = Total Current Assets (minus) Inventory
## An example from our Balance sheet:
Quick Ratio = \$261,050- \$156,822 / \$176,522 Quick Ratio = \$104,228 / \$176,522 Quick Ratio = 0.59
The Interpretation:
Lumber & Building Supply Company has \$0.59 cents of Quick Assets to meet \$1.00 of its Current Liability Review the Industry same industry.
Norms and Ratios for this ratio to compare and see if they are above below or equal to the others in the
## THIRD LIQUIDITY RATIO
Debt to Equity Ratio: This ratio is obtained by dividing the 'Total Liability or Debt ' of a company by its 'Owners Equity
a.k.a Net Worth'. The ratio measures how the company is leveraging its debt against the capital employed by its owners. If the liabilities exceed the net worth then in that case the creditors have more stake than the shareowners.
The formula:
Debt to Equity Ratio = Total Liabilities / Owners Equity or Net Worth
## An example from our Balance sheet:
Debt to Equity Ratio = \$186,522 / \$133,522 Debt to Equity Ratio = 1.40
The Interpretation:
Lumber & Building Supply Company has \$1.40 cents of Debt and only \$1.00 in Equity to meet this obligation. Review the Industry Norms in the same industry.
and Ratios for this ratio to compare and see if they are above below or equal to the others
iency ratios are ratios that come off the the Balance Sheet and the Income Statement and therefore incorporate one dynamic statement, the income statement and one static statement , the balance sheet. These ratios are important in measuring the efficiency of a company in either turning their inventory, sales, assets, accounts receivables or payables. It also ties into the ability of a company to meet both its short term and long term obligations. This is because if they do not get paid on time how will you get paid paid on time. You may have perhaps heard the excuse 'I will pay you when I get paid' or 'My customers have not paid me!'
## FIRST EFFICIENCY RATIO
DSO (Days Sales Outstanding): The Days Sales Outstanding ratio shows both the average time it takes to turn the
receivables into cash and the age, in terms of days, of a company's accounts receivable. The ratio is regarded as a test of Efficiency for a company. The effectiveness with which it converts its receivables into cash. This ratio is of particular importance to credit and collection associates. Best Possible DSO yields insight into delinquencies since it uses only the current portion of receivables. As a measurement, the closer the regular DSO is to the Best Possible DSO, the closer the receivables are to the optimal level. Best Possible DSO requires three pieces of information for calculation:
Formula:
Current Receivables Total credit sales for the period analyzed The Number of days in the period analyzed
## Best Possible DSO = Current Receivables/Total Credit Sales X Number of Days
The formula:
Regular DSO = (Total Accounts Receivables/Total Credit Sales) x Number of Days in the period that is being analyzed
## An example from our Balance sheet and Income Statement:
Total Accounts Receivables (from Total Credit Sales (from
## Income Statement) = \$727,116
Number of days in the period = 1 year = 360 days ( some take this number as 365 days) DSO = [ \$97,456 / \$727,116 ] x 360 = 48.25 days
The Interpretation:
Lumber & Building Supply Company takes approximately 48 days to convert its accounts receivables into cash. Compare this to their Terms of Net 30 days. This means at an average their customers take 18 days beyond terms to pay. Review the Industry same industry.
Norms and Ratios for this ratio to compare and see if they are above below or equal to the others in the
## SECOND EFFICIENCY RATIO
Inventory Turnover ratio: This ratio is obtained by dividing the 'Total Sales' of a company by its 'Total Inventory'. The
ratio is regarded as a test of Efficiency and indicates the rapiditity with which the company is able to move its merchandise.
The formula:
Inventory Turnover Ratio = Net Sales / Inventory
It could also be calculated as: Inventory Turnover Ratio = Cost of Goods Sold / Inventory An example from our Balance sheet and Income Statement:
Net Sales = \$727,116 (from
## Inventory Turnover Ratio = \$727,116/ \$156,822 Inventory Turnover = 4.6 times
The Interpretation:
Lumber & Building Supply Company is able to rotate its inventory in sales 4.6 times in one fiscal year. Review the Industry Norms others in the same industry.
and Ratios for this ratio to compare their efficiency and see if they are above, below or equal to the
## THIRD EFFICIENCY RATIO
Accounts Payable to Sales (%): This ratio is obtained by dividing the 'Accounts Payables' of a company by its 'Annual
Net Sales'. This ratio gives you an indication as to how much of their suppliers money does this company use in order to fund its Sales. Higher the ratio means that the company is using its suppliers as a source of cheap financing. The working capital of such companies could be funded by their suppliers..
The formula:
Accounts Payables to Sales Ratio = [Accounts Payables / Net Sales ] x 100
## An example from our Balance sheet and Income Statement:
Accounts Payables = \$152,240 (from Balance sheet ) Net Sales = \$727,116 (from Income Statement) Accounts Payables to Sales Ratio = [\$152,240 / \$727,116] x 100 Accounts Payables to Sales Ratio = 20.9%
The Interpretation:
21% of Lumber & Building Supply Company's Sales is being funded by its suppliers. Review the Industry Norms in the same industry.
and Ratios for this ratio to compare and see if they are above below or equal to the others
| 1,668
| 7,503
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.171875
| 3
|
CC-MAIN-2019-22
|
latest
|
en
| 0.931041
|
https://www.physicsforums.com/threads/is-it-possible-to-calculate-the-unknowns-in-these-equations.848007/
| 1,532,308,286,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-30/segments/1531676594675.66/warc/CC-MAIN-20180722233159-20180723013159-00215.warc.gz
| 967,351,446
| 15,941
|
# Is it possible to calculate the unknowns in these equations?
Tags:
1. Dec 13, 2015
### jonjacson
Well folks,
I am a bit confused with this apparently "simple" system of equations.
pa=Probability player A wins a point when he is on serve
qa=1-pa=Probability player A loses a point when he is on serve
pb, and qb are the same for player B when he is on his own serve
I have calculated the probability of winning a Tie Break when they are tied at 6,6:
Probability player A wins a Tie Break from score PA(6,6)=(pa*qb)/(1-pa*pb-qa*qb) equation 1
Probability player B wins a Tie Break from score PB(6,6)=(pb*qa)/(1-pa*pb-qa*qb) equation 2
PA(6,6)+PB(6,6)=1 equation 3
If I know pa and pb I can easily calculate PA and PB, let's say pa=0.6 and pb=0.6, then we get:
PA(6,6)= 0.6*0.4/(1-0.6*0.6-0.4*0.4)=0.5
PB(6,6)=0.6*0.4/0.48=0.5
For pa=0.9 and pb=0.5 I get PA=0.9 and PB=0.1 so player A will win the Tie Break 90% of the time and player B only 10%.
Now the problem is the input data is PA and PB, so let's say player A wins 80% of the Tie Breaks and player B wins only 20%. Can I calculate probabilities pa and pb?
Apparently I have only two unkowns pa, and pb, and I have enough equations to solve it. But when I try to do it I find an absurd result.
I guess the equations are not independent, so they mean the same and it is not possible to calculate pa and pb.
Because for every value of pa, I can choose a pb that satisfies the values of PA and PB.
Am I correct? Is it impossible to calculate pa and pb? Or is there any way to get those values?
2. Dec 13, 2015
### PeroK
You've almost got the answer yourself, which I've underlined. What you could do is choose a value for $p_a$ and find the value for $p_b$ that makes $PA = 0.8$.
It won't work for every $p_a$, e.g. with $p_a = 0$ you can never get $PA = 0.8$.
You could also try to find the general formula for $p_b$ in terms of $p_a$ and $PA$.
Can you work out how likely it is that the players hold serve? That's an interesting probability problem.
3. Dec 13, 2015
### jonjacson
Well, I can use "trial an error" but I guess I could be in trouble because what I want is calculate pa and pb when the tennis match starts and then project that value for different scores. And I maybe there are two pair of values that work for the start of the match, let's say pa=0,6 and pb=0.55 and pa=0.70 and pb=0.65, but then after some points are played those pairs entail different match winning probabilities.
Well, I could try to do it going to head to head statistics and using those quantities. Let's say that for the last 5 matches one player won 250/400 points on his serve and the other 200/400, I could use that to calculate pa and pb, the problem is that the criteria used to calculate pa and pb is a bit subjective right?
Why do I chose the last 5 matches and not the last 10? And what happens if they have never played agains each other?
4. Dec 13, 2015
### PeroK
There's a big difference between modelling a single tennis match or tie-break by assuming a fixed probablity for each point (based on who's serving) and statisticaly analysing tennis match results. The former is a simple probability question. The latter is full-on statistical analysis of data.
Players play better or worse from one day to the next. They may be in-form or out-of-form or neither and/or recovering from injury. They play on different surfaces etc. A data analysis of tennis results would have to consider at least these factors.
5. Dec 13, 2015
### jonjacson
Yes, I agree.
What I mean is, for sure if you order to 10 PhysicsForums users to perform that analysis I am sure they will get 10 different values for pa and pb because they will interpret and choose differently the data.
6. Dec 13, 2015
### PeroK
I'd say $p_a$ and $p_b$ don't exist. In the sense that there are no single values that would model all matches beween two players. Any values would, for example, give Nadal the same chance of winning against player X on any surface. You cannot statistically model men's tennis with a single value.
If, however, you are watching a specific match between two players, you might be able to model it based on something as simple as a single $p_a$ and $p_b$.
To illustrate the point, you have already used two values, depending on who's serving. An even simpler model would have a single probability for each point. That might even be valid in some women's tennis, but not men's tennis.
7. Dec 13, 2015
### jonjacson
I agree with you that modelling a tennis match is something very complex and maybe using the model with pa and pb constants is not reallistic. But I was curious about betting odds, I wanted to know if during a real tennis match the odds behave like pa and pb are constant or not. That is my goal, to know if that model works or if the odds behave like they were changing all the time.
| 1,304
| 4,878
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.953125
| 4
|
CC-MAIN-2018-30
|
latest
|
en
| 0.94255
|
http://www.sawaal.com/calendar-questions-and-answers/what-was-the-day-of-the-week-on-16th-july-1776_4602
| 1,521,900,718,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-13/segments/1521257650685.77/warc/CC-MAIN-20180324132337-20180324152337-00738.warc.gz
| 463,976,456
| 17,726
|
123
Q:
# What was the day of the week on, 16th July, 1776?
A) Tuesday B) Wednesday C) Monday D) Saturday
Explanation:
16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776)
Counting of odd days :
1600 years have 0 odd day.
100 years have 5 odd days.
75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days
1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day.
Jan Feb Mar Apr May Jun Jul
31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 2 days)
Total number of odd days = (0 + 2) = 2.
Required day was 'Tuesday'.
Q:
What is two weeks from today?
A) same day B) previous day C) next day D) None
Explanation:
We know that the day repeats every 7 days, 14 days, 21 days,...
So if today is Monday, after 7 days it is again Monday, after 14 days again it is Monday.
Hence, after 2 weeks i.e, 14 days the day repeats and is the same day.
1 350
Q:
How old are you if you are born in 1995?
A) 22 B) 23 C) 24 D) 25
Explanation:
Calculating Age has 2 conditions. Let your Birthday is on January 1st.
1. If the month in which you are born is completed in the present year i.e, your birthday, then
Your Age = Present year - Year you are born
As of now, present year = 2018
i.e, Age = 2018 - 1995 = 23 years.
2. If the month in which you are born is not completed in the present year i.e, your birthday, then
Your Age = Last year - Year you are born
As of now, present year = 2018
i.e, Age = 2017 - 1995 = 22 years.
2 284
Q:
The day before yesterday, I was 25 years old, and next year I will turn 28. How is it possible?
On carefully inspecting this question, one can understand that there are two days which are important and these are:
A. My Birthday.
B. The day when I am making this statement.
If you think for a while, you will understand that such statements can be made only around the year’s end. So, if my birthday is on 31 December, then I will be making this statement on 1 January.
I will further explain using the following example:
1. Consider that today is 01 January 2017.
2. Then, the day before yesterday was 30 December 2016 and according to the question I was 25 then.
3. Yesterday was 31 December 2016, which happens to be my birthday too (Woohoo!), and my age increases by one to become 26.
4. I will turn 27 on my birthday this year (31 December 2017).
5. I will turn 28 on my birthday next year (31 December 2018).
Now, if you read the question again, it will make more sense:
The day before yesterday(30 December 2016), I was 25 years old and next year(31 December 2018) I will be 28.
301
Q:
The calendar for the year 2018 will be the same for the year
A) 2023 B) 2027 C) 2029 D) 2022
Explanation:
How to find the years which have the same Calendars :
Leap year calendar repeats every 28 years.
Here 28 is distributed as 6 + 11 + 11.
Rules:
a) If given year is at 1st position after Leap year then next repeated calendar year is Givenyear+6.
b) If given year is at 2nd position after Leap year then next repeated calendar year is Givenyear+11.
c) If given year is at 3rd position after Leap year then next repeated calendar year is Givenyear+11.
Now, the given year is 2018
We know that 2016 is a Leap year.
2016 2017 2018 2019 2020
Lp Y 1st 2nd 3rd Lp Y
Here 2018 is at 2 nd position after the Leap year.
According to rule b) the calendar of 2018 is repeated for the year is 2018 + 11 = 2029.
5 646
Q:
How many days in 4 years?
A) 1460 B) 1461 C) 1462 D) 1459
Explanation:
Days in 4 years =>
Let the first year is Normal year i.e, its not Leap year. A Leap Years occurs once for every 4 years.
4 years => 365 + 365 + 365 + 366(Leap year)
4 years => 730 + 731 = 1461
Therefore, Number of Days in 4 Years = 1461 Days.
6 613
Q:
How many weekends in a year?
A) 52 B) 53 C) 103 D) 104
Explanation:
In normal we have 104 Weekend Days.
We know that a Each normal year has 365 days or 52 weeks plus one day, and each week has two weekend days, which means there are approximately 104 weekend days each year.
Whereas in a leap year we have 366 days it adds one more day to the year. And what makes the change is the starting day of the year.
9 594
Q:
What is 90 days from today?
Hints : Today is 20th January 2017, Sunday
A) 18th April, Friday B) 20th April, Saturday C) 21th April, Sunday D) 19th April, Saturday
Explanation:
Given Today is 20th January 2017, Sunday
In january, we have 31 days
February - 28 days (Non leap year)
March - 31 days
April - 30 days
=> Remaining days => 31 - 20 = 11 in Jan
+ 28 in Feb + 31 in Mar = 11 + 28 + 31 = 70 days
More 20 days to complete 90 days => upto 20th April
Therefore, after 90 days from today i.e, 20th Jan 2017 is 20th Apr 2017.
Now, the day of the week will be
90/7 => Remainder '6'
As the day starts with '0' on sunday
6 => Saturday.
Required day is 20th April, Saturday.
6 1027
Q:
The calendar for the year 1988 is same as which upcoming year ?
A) 2012 B) 2014 C) 2016 D) 2010
| 1,578
| 5,075
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.21875
| 4
|
CC-MAIN-2018-13
|
longest
|
en
| 0.958874
|
http://skill-guru.com/151/gre-math-practice-test/questions
| 1,600,445,128,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-40/segments/1600400188049.8/warc/CC-MAIN-20200918155203-20200918185203-00240.warc.gz
| 109,994,132
| 12,673
|
### Questions of Test: GRE Math Practice Test
1 ```1. Lines l1, l2, and l3 are parallel; the diagonal line is straight. Column A: a + d Column B: c – b + 180``` 2 ``` All lines are straight and intersect as shown. Column A: c Column B: a + b``` 3 ``` Given: The large circle has its center at point N. The medium circle has its center at M and is tangent to the large circle. The small circle has its center at point P, intersects point N, and is tangent to the large circle. NP is 8 units long. NM is 6 units long and is perpendicular to NP. Column A: area of the shaded portion Column B: 2.5 times the area of the small circle``` 4 ``` Column A: November sales Column B: December sales``` 5 ```(Refer to chart “Gasoline Sales”) Column A: The percent change in premium sales from February to March Column B: The percent change in total sales January to February``` 6 ```Given line m is parallel to line n. The measure of angle a° is A 35 B 45 C 65 D Not possible to calculate from the information given``` 7 ``` The values for a and b are: A 32, 58 B 36, 54 C 36, 68 D 54, 32``` 8 ``` The ratio of the measures of the two complementary angles shown is 2:3. Angle a is A 30 B 36 C 54 D 60 E 72``` 9 ``` A garden store sells fall bulbs. There were twice as many lily bulbs as amaryllis bulbs sold. If 700 bulbs total were sold, how many lily bulbs were sold? A 56 B 84 C 112 D 168 E 532```
| 433
| 1,732
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4
| 4
|
CC-MAIN-2020-40
|
latest
|
en
| 0.888505
|
https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327-260.html?kudos=1
| 1,495,703,303,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-22/segments/1495463608058.13/warc/CC-MAIN-20170525083009-20170525103009-00326.warc.gz
| 762,542,709
| 66,922
|
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack
It is currently 25 May 2017, 02:08
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# Events & Promotions
###### Events & Promotions in June
Open Detailed Calendar
# How to get 6.0 AWA....my guide
Author Message
Senior Manager
Joined: 24 Feb 2008
Posts: 348
Schools: UCSD ($) , UCLA, USC ($), Stanford
Followers: 191
Kudos [?]: 3142 [1523] , given: 2
How to get 6.0 AWA....my guide [#permalink]
### Show Tags
22 May 2008, 06:56
1523
KUDOS
1706
This post was
BOOKMARKED
Guide to Perfect 6.0 AWA GMAT Score
Related AWA Resources:
I took the GMAT twice and scored 6.0 each time. I did put a lot of time in it the first time....too much actually. Being a non-native speaker and having not written a damn essay (of any kind) in many many years, I was very scared of the AWA. So, I went through every guide that I could find and wrote nearly 25-30 essays. Even had a friend grade them for me.....Pathetic, huh?
Anyway, for my second time, I just looked over my templates I created and wrote one of each the day before test just to refresh my memory on faster typing without making too many typos......
So, here it is....Enjoy, and please do not blame me if the 6.0 percentile goes down to 80 soon
AWA GUIDE
by Chineseburned
1. General Structure
Intro - Restate argument, point out flaws or state intention to discuss them below
1st Para - First,...
3rd Para - Third/Finally,...
Conclusion - The argument is flawed/weak/unconvincing because of the above -mentioned...Ultimately, the argument can be strengthened if/by...
2. Structural Word (should be all over the essays)
1. Supporting examples - for example, to illustrate, for instance, because, specifically
2. Additional support - furthermore, in addition, similarly, just as, also, as a result, moreover
3. Importance - surely, truly, undoubtedly, clearly, in fact, most importantly
4. Contrast - on the contrary, yet, despite, rather, instead, however, although, while
5. Decide against - one cannot deny that, it could be argued that, granted, admittedly
6. Ying-yang - on the one hand/on the other hand
7. Concluding - therefore, in summary, consequently, hence, in conclusion, ultimately, in closing
3. Templates
Intro:
The argument claims that ....(restate)
Stated in this way the argument:
a) manipulates facts and conveys a distorted view of the situation
b) reveals examples of leap of faith, poor reasoning and ill-defined terminology
c) fails to mention several key factors, on the basis of which it could be evaluated
The conclusion of the argument relies on assumptions for which there is no clear evidence. Hence, the argument is weak/unconvincing and has several flaws.
1st Para:
First, the argument readily assumes that......
This statement is a stretch....
For example,...
Clearly,...
The argument could have been much clearer if it explicitly stated that...
2nd Para:
Second, the argument claims that....
This is again a very weak and unsupported claim as the argument does not demonstrate any correlation between....and...
To illustrate,...
While,...
However,....indeed....
In fact, it is not at all clear...rather....
If the argument had provided evidence that.....then the argument would have been a lot more convincing.
3rd Para:
Finally,...
(pose some questions for the argument).....Without convincing answers to these questions, one is left with the impression that the claim is more of a wishful thinking rather than substantive evidence.
Conclusion:
In conclusion, the argument is flawed for the above-mentioned reasons and is therefore unconvincing. It could be considerably strengthened if the author clearly mentioned all the relevant facts....
In order to assess the merits of a certain situation/decision, it is essential to have full knowledge of all contributing factors. In this particular case....
Without this information, the argument remains unsubstantiated and open to debate.
4. Going from the templates to full-fledged essays
ESSAY QUESTION:
The following appeared in the editorial section of a national news magazine:[/b]
"The rating system for electronic games is similar to the movie rating system in that it provides consumers with a quick reference so that they can determine if the subject matter and contents are appropriate. This electronic game rating system is not working because it is self regulated and the fines for violating the rating system are nominal. As a result an independent body should oversee the game industry and companies that knowingly violate the rating system should be prohibited from releasing a game for two years."
Discuss how well reasoned you find this argument. Point out flaws in the argument's logic and analyze the argument's underlying assumptions. In addition, evaluate how supporting evidence is used and what evidence might counter the argument's conclusion. You may also discuss what additional evidence could be used to strengthen the argument or what changes would make the argument more logically sound.
Quote:
The argument claims that the electronic games rating system, although similar to the movie rating system, is not working because it is self regulated and violation fines are nominal, Hence, the gaming rating system should be overseen by an independent body. Stated in this way the argument fails to mention several key factors, on the basis of which it could be evaluated. The conclusion relies on assumptions, for which there is no clear evidence. Therefore, the argument is rather weak, unconvincing, and has several flaws.
First, the argument readily assumes that because the electronic game rating system is self regulated, it is not working well. This statement is a stretch and not substantiated in any way. There are numerous examples in other areas of business or commerce, where the entities are self regulated and rather successful. For instance, FIA, the Formula1 racing organization is self regulated. Yet, the sport is very popular and successful, drawing millions of spectators around the world each year. Tickets are rather expensive, races are shown on pay-per-view, and nearly all drivers are paid very well. Another example is the paralleled movie rating system that the argument mentions. The author fails to clarify whether it is working well, but it is clear that the movie rating system is pretty well received by people, who often base their decisions to go see a movie with kids or not on the movie rating. It has never been a case when someone would feel cheated by the movie rating and express disappointment afterwards. Since the movie rating system is also self regulated, it follows that this regulatory method is working pretty well and it is not obvious how it can be the reason for the poor electronic game rating system. The argument would have been much clearer if it explicitly gave examples of how the self regulatory system led to bad ratings and customer dissatisfaction.
Second, the argument claims that any violation fees for bad electronic game ratings are nominal. It thus suggests that this is yet another reason for the rating system not working. This is again a very weak and unsupported claim as the argument does not demonstrate any correlation between the monetary amount of the fines and the quality of the electronic game rating system. In fact, the argument does not even draw a parallel with the mentioned movie rating system and its violation fines. If any such correlation had been shown for the movie rating system, which supposedly works well, then the author would have sounded a bit more convincing. In addition, if the argument provided evidence that low violation fines lead to electronic game manufacturers to ignore any regulations with respect to the game rating system, the argument could have been strengthened even further.
Finally, the argument concludes that an independent body should oversee the game industry and companies that violate the rating system, should be punished. From this statement again, it is not at all clear how an independent regulatory body can do a better job than a self regulated one. Without supporting evidence and examples from other businesses where independent regulatory bodies have done a great job, one is left with the impression that the claim is more of a wishful thinking rather than substantive evidence. As a result, this conclusion has no legs to stand on.
In summary, the argument is flawed and therefore unconvincing. It could be considerably strengthened if the author clearly mentioned all the relevant facts. In order to assess the merits of a certain situation, it is essential to have full knowledge of all contributing factors.
5. Final tips
• During the tutorial type in a few sentences in the mock essay window to get used to the keyboard.
• Again during the tutorial, jot down on your notebook the basic structure of your essays or the opening sentences in case you get too nervous and forget them when the clock starts ticking.
• Write as much as you can. Try to write at least 500 words per essay.
• Always have the e-rater in mind as your potential reviewer. Remember that the human rater will make every effort to grade just like the e-rater. In that sense, keep your structure and volume in mind over actual quality/content.
• Be careful of spelling mistakes. Double check words that you normally know you misspell (e.g. exercise). Try to finish 2-3 minutes before time is up so you can slowly re-read your essay for the purposes of spell checking. Do not reorganize/delete sentences/paragraphs with less than 2 min left.
• No matter how great you thought your essays went, try to stay humble and focused - remember this was just a warm-up and the real stuff hasn't started yet!
Good luck!
_________________
Best AWA guide here: http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html
Last edited by carcass on 26 Aug 2014, 11:26, edited 9 times in total.
Intern
Joined: 07 Jul 2012
Posts: 14
Followers: 0
Kudos [?]: 1 [0], given: 1
Re: How to get 6.0 AWA....my guide [#permalink]
### Show Tags
09 Oct 2012, 21:34
I got a 5.5 using this template. Hopefully I can get a 6.0 on my next test.
Intern
Joined: 24 Jul 2012
Posts: 6
GMAT 1: 710 Q48 V40
Followers: 0
Kudos [?]: 4 [0], given: 0
Re: How to get 6.0 AWA....my guide [#permalink]
### Show Tags
16 Oct 2012, 06:26
Great post, really helped me on the test!
Jordan
Manager
Joined: 08 Sep 2012
Posts: 79
Concentration: Entrepreneurship, Other
GMAT 1: 700 Q49 V36
GMAT 2: 760 Q50 V41
Followers: 0
Kudos [?]: 23 [0], given: 87
Re: How to get 6.0 AWA....my guide [#permalink]
### Show Tags
20 Oct 2012, 07:58
I used this(spent only 30 mins) and received a score of 6!
Thanks a lot!
Intern
Joined: 29 Jun 2012
Posts: 15
Location: India
WE: Information Technology (Computer Software)
Followers: 2
Kudos [?]: 10 [0], given: 48
Re: How to get 6.0 AWA....my guide [#permalink]
### Show Tags
21 Oct 2012, 00:02
Many thanks mate!! You are a star!
_________________
Rgds,
Mudit
------------------------------------------------------------------------
'Take risks and conquer your fears!'
Intern
Joined: 22 Sep 2012
Posts: 3
Followers: 0
Kudos [?]: 0 [0], given: 0
Re: How to get 6.0 AWA....my guide [#permalink]
### Show Tags
25 Oct 2012, 13:18
Does anyone know where I can find more example of AWA questions and responsed essays?
Thank you,
Intern
Joined: 05 Nov 2012
Posts: 2
Followers: 0
Kudos [?]: 0 [0], given: 2
Re: How to get 6.0 AWA....my guide [#permalink]
### Show Tags
05 Nov 2012, 00:21
HAHA you must be Chinese 楼主，CD上下的作文资料吧 哈哈 我很开心的下载下来发现就是CD上的。。。 ~~
Intern
Joined: 02 Apr 2012
Posts: 29
GPA: 3.65
Followers: 3
Kudos [?]: 19 [0], given: 23
Re: How to get 6.0 AWA....my guide [#permalink]
### Show Tags
02 Dec 2012, 05:14
awesome post.thanks a lot
Intern
Joined: 23 Jan 2012
Posts: 28
Location: United States
Concentration: Technology, General Management
GMAT 1: 690 Q49 V34
GPA: 3.92
WE: Information Technology (Computer Software)
Followers: 1
Kudos [?]: 10 [0], given: 1
Re: How to get 6.0 AWA....my guide [#permalink]
### Show Tags
05 Dec 2012, 13:41
How is everyone handling AWA these days? Does Chineseburned still rocks?
_________________
Regards
BUZZZ
http://www.gmatexecmba.blogspot.com
Intern
Joined: 23 Jan 2012
Posts: 28
Location: United States
Concentration: Technology, General Management
GMAT 1: 690 Q49 V34
GPA: 3.92
WE: Information Technology (Computer Software)
Followers: 1
Kudos [?]: 10 [0], given: 1
Re: How to get 6.0 AWA....my guide [#permalink]
### Show Tags
05 Dec 2012, 13:42
Forgot to add, he helped me get a 6.0
_________________
Regards
BUZZZ
http://www.gmatexecmba.blogspot.com
Intern
Status: Destination Sales and Guest Relations Manager for Russia, CIS & Eastern Europe
Affiliations: Starwood Hotels: The Grand Mauritian & Le Meridien
Joined: 09 Nov 2012
Posts: 10
Location: Mauritius
Olga: Kovshanova, MBA, MA
Concentration: General Management, Marketing
GMAT Date: 02-20-2013
GPA: 3.9
WE: Sales (Hospitality and Tourism)
Followers: 0
Kudos [?]: 5 [0], given: 3
Re: How to get 6.0 AWA....my guide [#permalink]
### Show Tags
15 Dec 2012, 00:00
Merci -- very great help!
_________________
Olga Kovshanova, MBA, MA
Hotel Professional Extraordinaire
Destination Sales and Guest Relations Manager for Russia, CIS & Eastern Europe
Starwood Hotels: The Grand Mauritian & Le Meridien
M: +230-717-5790 evenings
Intern
Joined: 11 Apr 2012
Posts: 39
Followers: 0
Kudos [?]: 69 [0], given: 93
Re: How to get 6.0 AWA....my guide [#permalink]
### Show Tags
18 Dec 2012, 04:54
Dear Chineseburned-Where ever you are,God bless you! I truly owe my fab 6.0 score to your guide here.
Cheers!
BSchool Forum Moderator
Joined: 27 Aug 2012
Posts: 1194
Followers: 134
Kudos [?]: 1617 [0], given: 145
Re: How to get 6.0 AWA....my guide [#permalink]
### Show Tags
23 Dec 2012, 11:47
Hi chineseburned,
Hats Off for putting this much of effort for the entire community...Outstanding contribtuion man..!! Kudos a ton...
w.r.t. the current GMAT Test pattern,as the Analysis of an Issue is replaced by interesting IR-do you really think that this replaced part should be present in this article any more ? Instead, if we zero down on the Analysis of an Argument then don't you think that would be better off.That said,could you please let us know if there is any change in the approach of Analysis of an Argument section or it remains exactly same as before ?
BTW,Happy Holidays...Cheers
_________________
Manager
Joined: 09 Nov 2012
Posts: 169
GMAT 1: 700 Q43 V42
Followers: 5
Kudos [?]: 67 [0], given: 29
Re: How to get 6.0 AWA....my guide [#permalink]
### Show Tags
30 Dec 2012, 07:18
I used this guide and practice wrote five essays from this thread to get a feel for it. I scored a 5.5 on the real GMAT.
_________________
If my post helped you, please consider giving me kudos.
BSchool Forum Moderator
Joined: 27 Aug 2012
Posts: 1194
Followers: 134
Kudos [?]: 1617 [0], given: 145
Re: How to get 6.0 AWA....my guide [#permalink]
### Show Tags
30 Dec 2012, 09:39
debayan222 wrote:
Hi chineseburned,
Hats Off for putting this much of effort for the entire community...Outstanding contribtuion man..!! Kudos a ton...
w.r.t. the current GMAT Test pattern,as the Analysis of an Issue is replaced by interesting IR-do you really think that this replaced part should be present in this article any more ? Instead, if we zero down on the Analysis of an Argument then don't you think that would be better off.That said,could you please let us know if there is any change in the approach of Analysis of an Argument section or it remains exactly same as before ?
BTW,Happy Holidays...Cheers
Hi chineseburned.
Any update on this ?
_________________
Manager
Joined: 13 Oct 2012
Posts: 70
Schools: IE '15 (A)
GMAT 1: 760 Q49 V46
Followers: 1
Kudos [?]: -11 [0], given: 0
Re: How to get 6.0 AWA....my guide [#permalink]
### Show Tags
03 Jan 2013, 16:19
Thank you for the guidelines
Manager
Joined: 13 Oct 2012
Posts: 70
Schools: IE '15 (A)
GMAT 1: 760 Q49 V46
Followers: 1
Kudos [?]: -11 [0], given: 0
Re: How to get 6.0 AWA....my guide [#permalink]
### Show Tags
03 Jan 2013, 16:32
Thnx for the tips!! As per Manhattan GMAT guide, 300+ words are sufficient to get a 6.0 score if it is well written.
Do you feel that is too less?
Intern
Joined: 25 Nov 2012
Posts: 3
Followers: 0
Kudos [?]: 0 [0], given: 2
Re: How to get 6.0 AWA....my guide [#permalink]
### Show Tags
12 Jan 2013, 05:55
Hi ,
Thanks for the tips.
Does anybody know if there is a way to get the essay rated online?
I am really scared of this AWA section of GMAT.
k
Intern
Joined: 02 Jul 2012
Posts: 36
GPA: 3.86
Followers: 0
Kudos [?]: 1 [0], given: 0
Re: How to get 6.0 AWA....my guide [#permalink]
### Show Tags
16 Jan 2013, 08:55
This is a great guide. The only resource needed for AWA.
BSchool Forum Moderator
Joined: 27 Aug 2012
Posts: 1194
Followers: 134
Kudos [?]: 1617 [0], given: 145
Re: How to get 6.0 AWA....my guide [#permalink]
### Show Tags
29 Jan 2013, 09:08
[Reveal] Spoiler:
chineseburned wrote:
Guide to Perfect 6.0 AWA GMAT Score
Related AWA Resources:
I took the GMAT twice and scored 6.0 each time. I did put a lot of time in it the first time....too much actually. Being a non-native speaker and having not written a damn essay (of any kind) in many many years, I was very scared of the AWA. So, I went through every guide that I could find and wrote nearly 25-30 essays. Even had a friend grade them for me.....Pathetic, huh?
Anyway, for my second time, I just looked over my templates I created and wrote one of each the day before test just to refresh my memory on faster typing without making too many typos......
So, here it is....Enjoy, and please do not blame me if the 6.0 percentile goes down to 80 soon
AWA GUIDE
by Chineseburned
1. General Structure
Intro - Restate argument, point out flaws or state intention to discuss them below
1st Para - First,...
3rd Para - Third/Finally,...
Conclusion - The argument is flawed/weak/unconvincing because of the above -mentioned...Ultimately, the argument can be strengthened if/by...
2. Structural Word (should be all over the essays)
1. Supporting examples - for example, to illustrate, for instance, because, specifically
2. Additional support - furthermore, in addition, similarly, just as, also, as a result, moreover
3. Importance - surely, truly, undoubtedly, clearly, in fact, most importantly
4. Contrast - on the contrary, yet, despite, rather, instead, however, although, while
5. Decide against - one cannot deny that, it could be argued that, granted, admittedly
6. Ying-yang - on the one hand/on the other hand
7. Concluding - therefore, in summary, consequently, hence, in conclusion, ultimately, in closing
3. Templates
Intro:
The argument claims that ....(restate)
Stated in this way the argument:
a) manipulates facts and conveys a distorted view of the situation
b) reveals examples of leap of faith, poor reasoning and ill-defined terminology
c) fails to mention several key factors, on the basis of which it could be evaluated
The conclusion of the argument relies on assumptions for which there is no clear evidence. Hence, the argument is weak/unconvincing and has several flaws.
1st Para:
First, the argument readily assumes that......
This statement is a stretch....
For example,...
Clearly,...
The argument could have been much clearer if it explicitly stated that...
2nd Para:
Second, the argument claims that....
This is again a very weak and unsupported claim as the argument does not demonstrate any correlation between....and...
To illustrate,...
While,...
However,....indeed....
In fact, it is not at all clear...rather....
If the argument had provided evidence that.....then the argument would have been a lot more convincing.
3rd Para:
Finally,...
(pose some questions for the argument).....Without convincing answers to these questions, one is left with the impression that the claim is more of a wishful thinking rather than substantive evidence.
Conclusion:
In conclusion, the argument is flawed for the above-mentioned reasons and is therefore unconvincing. It could be considerably strengthened if the author clearly mentioned all the relevant facts....
In order to assess the merits of a certain situation/decision, it is essential to have full knowledge of all contributing factors. In this particular case....
Without this information, the argument remains unsubstantiated and open to debate.
4. Going from the templates to full-fledged essays
ESSAY QUESTION:
The following appeared in the editorial section of a national news magazine:[/b]
"The rating system for electronic games is similar to the movie rating system in that it provides consumers with a quick reference so that they can determine if the subject matter and contents are appropriate. This electronic game rating system is not working because it is self regulated and the fines for violating the rating system are nominal. As a result an independent body should oversee the game industry and companies that knowingly violate the rating system should be prohibited from releasing a game for two years."
Discuss how well reasoned you find this argument. Point out flaws in the argument's logic and analyze the argument's underlying assumptions. In addition, evaluate how supporting evidence is used and what evidence might counter the argument's conclusion. You may also discuss what additional evidence could be used to strengthen the argument or what changes would make the argument more logically sound.
Quote:
The argument claims that the electronic games rating system, although similar to the movie rating system, is not working because it is self regulated and violation fines are nominal, Hence, the gaming rating system should be overseen by an independent body. Stated in this way the argument fails to mention several key factors, on the basis of which it could be evaluated. The conclusion relies on assumptions, for which there is no clear evidence. Therefore, the argument is rather weak, unconvincing, and has several flaws.
First, the argument readily assumes that because the electronic game rating system is self regulated, it is not working well. This statement is a stretch and not substantiated in any way. There are numerous examples in other areas of business or commerce, where the entities are self regulated and rather successful. For instance, FIA, the Formula1 racing organization is self regulated. Yet, the sport is very popular and successful, drawing millions of spectators around the world each year. Tickets are rather expensive, races are shown on pay-per-view, and nearly all drivers are paid very well. Another example is the paralleled movie rating system that the argument mentions. The author fails to clarify whether it is working well, but it is clear that the movie rating system is pretty well received by people, who often base their decisions to go see a movie with kids or not on the movie rating. It has never been a case when someone would feel cheated by the movie rating and express disappointment afterwards. Since the movie rating system is also self regulated, it follows that this regulatory method is working pretty well and it is not obvious how it can be the reason for the poor electronic game rating system. The argument would have been much clearer if it explicitly gave examples of how the self regulatory system led to bad ratings and customer dissatisfaction.
Second, the argument claims that any violation fees for bad electronic game ratings are nominal. It thus suggests that this is yet another reason for the rating system not working. This is again a very weak and unsupported claim as the argument does not demonstrate any correlation between the monetary amount of the fines and the quality of the electronic game rating system. In fact, the argument does not even draw a parallel with the mentioned movie rating system and its violation fines. If any such correlation had been shown for the movie rating system, which supposedly works well, then the author would have sounded a bit more convincing. In addition, if the argument provided evidence that low violation fines lead to electronic game manufacturers to ignore any regulations with respect to the game rating system, the argument could have been strengthened even further.
Finally, the argument concludes that an independent body should oversee the game industry and companies that violate the rating system, should be punished. From this statement again, it is not at all clear how an independent regulatory body can do a better job than a self regulated one. Without supporting evidence and examples from other businesses where independent regulatory bodies have done a great job, one is left with the impression that the claim is more of a wishful thinking rather than substantive evidence. As a result, this conclusion has no legs to stand on.
In summary, the argument is flawed and therefore unconvincing. It could be considerably strengthened if the author clearly mentioned all the relevant facts. In order to assess the merits of a certain situation, it is essential to have full knowledge of all contributing factors.
5. Final tips
• During the tutorial type in a few sentences in the mock essay window to get used to the keyboard.
• Again during the tutorial, jot down on your notebook the basic structure of your essays or the opening sentences in case you get too nervous and forget them when the clock starts ticking.
• Write as much as you can. Try to write at least 500 words per essay.
• Always have the e-rater in mind as your potential reviewer. Remember that the human rater will make every effort to grade just like the e-rater. In that sense, keep your structure and volume in mind over actual quality/content.
• Be careful of spelling mistakes. Double check words that you normally know you misspell (e.g. exercise). Try to finish 2-3 minutes before time is up so you can slowly re-read your essay for the purposes of spell checking. Do not reorganize/delete sentences/paragraphs with less than 2 min left.
• No matter how great you thought your essays went, try to stay humble and focused - remember this was just a warm-up and the real stuff hasn't started yet!
Good luck!
Hi Vercules,
Great job for making this superb thread filtered by removing the 'Issue' part..
_________________
Manager
Joined: 05 Sep 2012
Posts: 79
Followers: 2
Kudos [?]: 10 [0], given: 17
Re: How to get 6.0 AWA....my guide [#permalink]
### Show Tags
02 Feb 2013, 07:06
Can anyone tell me if spelling or grammar mistakes are marked negatively in AWA?
I made 8 spelling mistakes nd 4 grammatical mistakes in my AWA essay. Yet the gmatawa site gave me a 6 score.
My word count was 416. I usually reserved the last 5 min for catching the spelling mistakes.
I will refrain from doing it in case if it is not important and focus on increasing sentences.
Re: How to get 6.0 AWA....my guide [#permalink] 02 Feb 2013, 07:06
Go to page Previous 1 ... 10 11 12 13 14 15 16 17 ... 21 Next [ 419 posts ]
Similar topics Replies Last post
Similar
Topics:
Aiming at 5.0 - 6.0. How do you find my awa? 0 20 Jul 2015, 08:25
How to move from 5.0 to 6.0 0 15 Sep 2014, 02:55
9 GMAT: How to score a 6.0 on your AWA. 7 18 Feb 2017, 09:35
4 Please Review my AWA.My first and non native.Thank you :) 6 29 Feb 2016, 08:32
HELP -- How can I get me essays reviewed and scored???? 0 02 May 2012, 13:41
Display posts from previous: Sort by
| 6,862
| 28,054
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.453125
| 3
|
CC-MAIN-2017-22
|
longest
|
en
| 0.933696
|
https://macscripter.net/viewtopic.php?id=46453&action=new
| 1,560,881,506,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-26/segments/1560627998808.17/warc/CC-MAIN-20190618163443-20190618185443-00333.warc.gz
| 502,144,186
| 4,887
|
Tuesday, June 18, 2019
You are not logged in.
• Index
• » Code Exchange
• » Exploring all the ways ONE and ZERO can interact as text or as numbers
## #1 2018-09-13 10:01:38 am
Mr. Science
Member
From:: Satellite Beach, Florida
Registered: 2015-08-13
Posts: 43
Website
### Exploring all the ways ONE and ZERO can interact as text or as numbers
This is an idea I played with from another project. It was used to generate a quick set of truths that could be used for other things. One really useful part of this was it's ability to produce and run a ''virtual-script'' using the ''run script'' command.
Basically, it uses 1 and 0 as examples (which could be any number such as pi), then runs them thru a sieve of operators to produce a list of possible interactions and results.
Obviously ''all'' the ways would require a bigger internet. For example, it might generate some unexpected patterns if each character was converted into it's hexadecimal or binary version prior to running the gauntlet.
If it is useful to you, let me know. If you find an interesting way to modify it, I'd be interested in that too!
#### Applescript:
set OPRTRS to {"<", "≤", "=", "≠", "≥", ">", "^", "*", "÷", "+", "-", "&", " mod ", " div ", "/", " & ", " and ", " or ", " not ", "is", "contains"}
#GENERATE A STRING FOR EACH POSSIBLE EQUATION of ONE and ZERO
set rprt to return
set vals to {0, 1}
repeat with n1 in vals
repeat with n2 in vals
repeat with op in OPRTRS
set strng to "(" & n1 & " " & op & " " & n2 & ")"
set rslt to my runSCRPT(strng)
set rprt to rprt & strng & "=" & rslt & return
end repeat
end repeat
end repeat
return rprt --show all results
# RUN STRING AS A SCRIPT, GET RESULT
on runSCRPT(strng)
try
set rslt to run script strng
on error err
return "err"
end try
return rslt
end runSCRPT
(* set SAMPLE_RESULT to "
(0 < 0)=false
(0 ≤ 0)=true
(0 = 0)=true
(0 ≠ 0)=false
(0 ≥ 0)=true
(0 > 0)=false
(0 ^ 0)=1.0
(0 * 0)=0
(0 ÷ 0)=err
(0 + 0)=0
(0 - 0)=0
(0 & 0)=00
(0 mod 0)=err
(0 div 0)=err
(0 / 0)=err
(0 & 0)=00
(0 and 0)=err
(0 or 0)=err
(0 not 0)=err
(0 is 0)=true
(0 contains 0)=true
(0 < 1)=true
(0 ≤ 1)=true
(0 = 1)=false
(0 ≠ 1)=true
(0 ≥ 1)=false
(0 > 1)=false
(0 ^ 1)=0.0
(0 * 1)=0
(0 ÷ 1)=0.0
(0 + 1)=1
(0 - 1)=-1
(0 & 1)=01
(0 mod 1)=0
(0 div 1)=0
(0 / 1)=0.0
(0 & 1)=01
(0 and 1)=err
(0 or 1)=err
(0 not 1)=err
(0 is 1)=false
(0 contains 1)=false
(1 < 0)=false
(1 ≤ 0)=false
(1 = 0)=false
(1 ≠ 0)=true
(1 ≥ 0)=true
(1 > 0)=true
(1 ^ 0)=1.0
(1 * 0)=0
(1 ÷ 0)=err
(1 + 0)=1
(1 - 0)=1
(1 & 0)=10
(1 mod 0)=err
(1 div 0)=err
(1 / 0)=err
(1 & 0)=10
(1 and 0)=err
(1 or 0)=err
(1 not 0)=err
(1 is 0)=false
(1 contains 0)=false
(1 < 1)=false
(1 ≤ 1)=true
(1 = 1)=true
(1 ≠ 1)=false
(1 ≥ 1)=true
(1 > 1)=false
(1 ^ 1)=1.0
(1 * 1)=1
(1 ÷ 1)=1.0
(1 + 1)=2
(1 - 1)=0
(1 & 1)=11
(1 mod 1)=0
(1 div 1)=1
(1 / 1)=1.0
(1 & 1)=11
(1 and 1)=err
(1 or 1)=err
(1 not 1)=err
(1 is 1)=true
(1 contains 1)=true
"*)
Model: Mac Pro, Yosemite
AppleScript: 2.7
Browser: Safari 601.2.7
Operating System: Mac OS X (10.13 Developer Beta 3)
"Fail and fail until you fail to fail!" ~ http://www.theMrScienceShow.com
Offline
• Index
• » Code Exchange
• » Exploring all the ways ONE and ZERO can interact as text or as numbers
| 1,306
| 3,228
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.59375
| 3
|
CC-MAIN-2019-26
|
latest
|
en
| 0.855261
|
http://planning.cs.uiuc.edu/node605.html
| 1,513,449,685,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-51/segments/1512948588420.68/warc/CC-MAIN-20171216181940-20171216203940-00039.warc.gz
| 217,371,270
| 5,214
|
#### Solving the active localization problem
From the previous two examples, it should be clear how to compute nondeterministic I-states and therefore solve the passive localization problem on a grid. Now consider constructing a plan that solves the active localization problem. Imagine using a computer to help in this task. There are two general approaches:
Precomputed Plan: In this approach, a planning algorithm running on a computer accepts a map of the environment and computes an information-feedback plan that immediately indicates which action to take based on all possible I-states that could result (a derived I-space could be used). During execution, the actions are immediately determined from the stored, precomputed plan.
Lazy Plan: In this case the map is still given, but the appropriate action is computed just as it is needed during each stage of execution. The computer runs on-board of the robot and must compute which action to take based on the current I-state.
The issues are similar to those of the sampling-based roadmap in Section 5.6. If faster execution is desired, then the precomputed plan may be preferable. If it would consume too much time or space, then a lazy plan may be preferable.
Using either approach, it will be helpful to recall the formulation of Section 12.1.1, which considers as a new state space, , in which state feedback can be used. Even though there are no nature sensing actions, the observations are not predictable because the state is generally unknown. This means that is unknown, and future new states, , are unpredictable once and are given. A plan must therefore use feedback, which means that it needs information learned during execution to solve the problem. The state transition function on the new state space was illustrated for the localization problem in Examples 12.1 and 12.2. The initial state is the set of all original states. If there are no symmetries, the goal set is the set of all singleton subsets of ; otherwise, it is the set of all smallest possible I-states that are reachable (this does not need to be constructed in advance). If desired, cost terms can be defined to produce an optimal planning problem. For example, if a motion occurs, or otherwise.
Consider the approach of precomputing a plan. The methods of Section 12.1.2 can generally be applied to compute a plan, , that solves the localization problem from any initial nondeterministic I-state. The approach may be space-intensive because an action must be stored for every state in . If there are grid tiles, then . If the initial I-state is always , then it may be possible to restrict to a much smaller portion of . From any , a search based on backprojections can be conducted. If the initial I-state is added to , then the partial plan will reliably localize the robot. Parts of for which is not specified will never be reached and can therefore be ignored.
Now consider the lazy approach. An algorithm running on the robot can perform a kind of search by executing actions and seeing which I-states result. This leads to a directed graph over that is incrementally revealed through the robot's motions. The graph is directed because the information regarding the state generally improves. For example, once the robot knows its state (or symmetry class of states), it cannot return to an I-state that represents greater uncertainty. In many cases, the robot may get lucky during execution and localize itself using much less memory than would be required for a precomputed plan.
The robot needs to recognize that the same positions have been reached in different ways, to ensure a systematic search. Even though the robot does not necessarily know its position on the map, it can usually deduce whether it has been to some location previously. One way to achieve this is to assign coordinates to the positions already visited. It starts with assigned to the initial position. If is applied, then suppose that position is reached, assuming the robot moves to a new grid cell. If is applied, then is reached if the robot is not blocked. The point may be reachable by or . One way to interpret this is that a local coordinate frame in is attached to the robot's initial position. Let this be referred to as the odometric coordinates. The orientation between this coordinate frame and the map is not known in the beginning, but a transformation between the two can be computed if the robot is able to localize itself exactly.
A variety of search algorithms can now be defined by starting in the initial state and trying actions until a goal condition is satisfied (e.g., no smaller nondeterministic I-states are reachable). There is, however, a key difference between this search and the search conducted by the algorithms in Section 2.2.1. Previously, the search could continue from any state that has been explored previously without any additional cost. In the current setting, there are two issues:
1. [] Reroute paths: Most search algorithms enable new states to be expanded from any previously considered states at any time. For the lazy approach, the robot must move to a state and apply an action to determine whether a new state can be reached. The robot is capable of returning to any previously considered state by using its odometric coordinates. This induces a cost that does not exist in the previous search problem. Rather than being able to jump from place to place in a search tree, the search is instead a long, continuous path that is traversed by the robot. Let the jump be referred to as a reroute path. This will become important in Section 12.3.2.
2. [] Information improvement: The robot may not even be able to return to a previous nondeterministic I-state. For example, if the robot follows and then tries to return to the same state using , it will indeed know that it returned to the same state, but the state remains unknown. It might be the case, however, that after executing , it was able to narrow down the possibilities for its current state. Upon returning using , the nondeterministic I-state will be different.
The implication of these issues is that the search algorithm should take into account the cost of moving the robot and that the search graph is directed. The second issue is really not a problem because even though the I-state may be different when returning to the same position, it will always be at least as good as the previous one. This means that if and are the original and later history I-states from the same position, it will always be true that . Information always improves in this version of the localization problem. Thus, while trying to return to a previous I-state, the robot will find an improved I-state.
Steven M LaValle 2012-04-20
| 1,353
| 6,753
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3
| 3
|
CC-MAIN-2017-51
|
latest
|
en
| 0.943861
|
https://numberworld.info/2712600
| 1,624,193,511,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-25/segments/1623487662882.61/warc/CC-MAIN-20210620114611-20210620144611-00292.warc.gz
| 383,456,681
| 4,745
|
# Number 2712600
### Properties of number 2712600
Cross Sum:
Factorization:
2 * 2 * 2 * 3 * 3 * 5 * 5 * 11 * 137
Count of divisors:
Sum of divisors:
Prime number?
No
Fibonacci number?
No
Bell Number?
No
Catalan Number?
No
Base 2 (Binary):
Base 3 (Ternary):
Base 4 (Quaternary):
Base 5 (Quintal):
Base 8 (Octal):
Base 32:
2ip0o
sin(2712600)
-0.94836345000398
cos(2712600)
-0.31718569749681
tan(2712600)
2.9899313162237
ln(2712600)
14.813418142511
lg(2712600)
6.4333857574179
sqrt(2712600)
1646.9972677573
Square(2712600)
### Number Look Up
Look Up
2712600 which is pronounced (two million seven hundred twelve thousand six hundred) is a amazing figure. The cross sum of 2712600 is 18. If you factorisate the number 2712600 you will get these result 2 * 2 * 2 * 3 * 3 * 5 * 5 * 11 * 137. The number 2712600 has 144 divisors ( 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 18, 20, 22, 24, 25, 30, 33, 36, 40, 44, 45, 50, 55, 60, 66, 72, 75, 88, 90, 99, 100, 110, 120, 132, 137, 150, 165, 180, 198, 200, 220, 225, 264, 274, 275, 300, 330, 360, 396, 411, 440, 450, 495, 548, 550, 600, 660, 685, 792, 822, 825, 900, 990, 1096, 1100, 1233, 1320, 1370, 1507, 1644, 1650, 1800, 1980, 2055, 2200, 2466, 2475, 2740, 3014, 3288, 3300, 3425, 3960, 4110, 4521, 4932, 4950, 5480, 6028, 6165, 6600, 6850, 7535, 8220, 9042, 9864, 9900, 10275, 12056, 12330, 13563, 13700, 15070, 16440, 18084, 19800, 20550, 22605, 24660, 27126, 27400, 30140, 30825, 36168, 37675, 41100, 45210, 49320, 54252, 60280, 61650, 67815, 75350, 82200, 90420, 108504, 113025, 123300, 135630, 150700, 180840, 226050, 246600, 271260, 301400, 339075, 452100, 542520, 678150, 904200, 1356300, 2712600 ) whith a sum of 10010520. The figure 2712600 is not a prime number. The number 2712600 is not a fibonacci number. The number 2712600 is not a Bell Number. The number 2712600 is not a Catalan Number. The convertion of 2712600 to base 2 (Binary) is 1010010110010000011000. The convertion of 2712600 to base 3 (Ternary) is 12002210222200. The convertion of 2712600 to base 4 (Quaternary) is 22112100120. The convertion of 2712600 to base 5 (Quintal) is 1143300400. The convertion of 2712600 to base 8 (Octal) is 12262030. The convertion of 2712600 to base 16 (Hexadecimal) is 296418. The convertion of 2712600 to base 32 is 2ip0o. The sine of the figure 2712600 is -0.94836345000398. The cosine of the figure 2712600 is -0.31718569749681. The tangent of 2712600 is 2.9899313162237. The root of 2712600 is 1646.9972677573.
If you square 2712600 you will get the following result 7358198760000. The natural logarithm of 2712600 is 14.813418142511 and the decimal logarithm is 6.4333857574179. You should now know that 2712600 is very impressive number!
| 1,186
| 2,699
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.265625
| 3
|
CC-MAIN-2021-25
|
latest
|
en
| 0.587111
|
https://math.stackexchange.com/questions/1648186/does-a-map-between-topologies-determine-a-map-between-sets
| 1,722,793,218,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-33/segments/1722640408316.13/warc/CC-MAIN-20240804164455-20240804194455-00765.warc.gz
| 317,048,022
| 37,839
|
# Does a map between topologies determine a map between sets?
Let $(X,\mathcal{A})$ and $(Y,\mathcal{B})$ be Hausdorff spaces. Consider a function \begin{equation*} \phi:\mathcal{B}\rightarrow \mathcal{A} \end{equation*} which preserves inclusion, arbitrary unions, finite intersections, and satifies $\phi(\emptyset)=\emptyset, \phi(Y)=\phi(X)$.
Does there exist $f: X\rightarrow Y$ such that $\phi= f^{-1}$ ?
I know that if such an $f$ exists it is uniquely determined by $\displaystyle f^{-1}(y)=\bigcap_{O\in \mathcal{B},y\in O} \phi(O)$. I also know this gives an effective definition for $f$ satisfying $f^{-1}=\phi$ if \begin{equation*} \bigcup_{y\in O}\left(\bigcap_{O'\in \mathcal{B},y\in O'}\phi(O')\right)=\phi(O) \end{equation*} for all open sets $O\subset Y$. But I don't know if this is necesarily the case.
• If there is such an $f$, then for any $y$, the set of $X_y=X\setminus\phi(Y\setminus\{y\})$ is the set of values $x\in X$ such that $f(x)=y$. The the question is, is it possible for two $y_1\neq y_2$ to have $X_{y_1}\cap X_{y_2}\neq \emptyset$, or, alternatively, is it possible that sucn an $f$ is not continuous? Commented Feb 9, 2016 at 21:42
• +1, nice question. Where did you get this? :) Commented Feb 9, 2016 at 22:00
• @IvoTerek I made it up ! My motivations come from category theory which I'm studying at the moment. Commented Feb 10, 2016 at 0:13
• @ThomasAndrews Because $Y\setminus \{y_{1}\} \cup Y\setminus \{y_{2}\}=Y$ you have $X_{y_{1}}\cap X_{y_{2}}=\emptyset$. What seems more difficult to me is that $\bigcup X_{y}=X$ since I do not assume $\phi$ preserves arbitrary intersections. Commented Feb 10, 2016 at 0:16
• This might be related to the fact that $T_2$ spaces are sober, and the category of sober spaces is equivalent to that of spatial locales, that is, (the opposite of) lattices of open sets with maps as you defined. Check this Wikipedia article. Commented Feb 10, 2016 at 3:19
I'm going to answer my own question, and I'm madly delighted to say the answer is yes, there always is such an $f$.
Note that for all $x\in X$ the set $\displaystyle N(x)=\bigcup_{O\in \mathcal{B}, x\notin \phi(O)}O$ has the form $Y\setminus\{y\}$. Indeed
• Suppose that $N(x)$ is all of $Y$. Then we would have $X=\phi(Y)=\phi(N(x))=\bigcup_{O\in \mathcal{B}, x\notin \phi(O)}\phi(O)$ and $x\notin X$ which is absurd.
• Suppose there were distinct $y_{1},y_{2}$ not in $N(x)$. Then there are two disjoint sets $O_{1},O_{2}$ containing $y_{1}$ and $y_{2}$ respectively. The sets $\phi(O_{1})$ and $\phi(O_{2})$ are disjoint so they cannot both contain $x$. Without loss of generality $x\notin \phi(O_{1})$ so that $O_{1}\subset N(x)$ and $y_{1}\in N(x)$ which is again absurd.
Define $f$ by letting $f(x)$ be the only element of $Y\setminus N(x)$. We have \begin{align*} &x\in f^{-1}(U) \\ \iff &U \not\subset N(x) \\ \iff &x\in\phi(U) \end{align*} hence $f$ has the desired property.
| 995
| 2,922
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.21875
| 3
|
CC-MAIN-2024-33
|
latest
|
en
| 0.846777
|
https://socratic.org/questions/how-do-you-convert-7-12-into-a-decimal-and-percent
| 1,579,575,707,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-05/segments/1579250601241.42/warc/CC-MAIN-20200121014531-20200121043531-00102.warc.gz
| 655,585,481
| 6,774
|
# How do you convert 7/12 into a decimal and percent?
Jun 18, 2018
Decimal value - $0.583333333$
Percent value - 58.33%
#### Explanation:
So to convert $\frac{7}{12}$ into a decimal, you divide 7 by 12 which gives us $0.583333333$.
So to convert it to a percent, we can take the decimal value and convert it to a percentage but, we need to move the dot by 2 places which gives us: 58.33%
Jun 18, 2018
$\frac{58. \overline{33}}{100}$ & $0.58 \overline{33}$
#### Explanation:
To convert a fraction into a decimal/percent, it helps to make it have a denominator of $100$. We can essentially set up the following ratio:
$\frac{7}{12} = \frac{x}{100}$
We can cross multiply to get
$\frac{7 \cdot 100}{12}$
Which simplifies to $58. \overline{33}$
This means $\frac{7}{12}$ is equivalent to $\frac{58. \overline{33}}{100}$.
When we have a fraction with a denominator of $100$, the numerator gives us the percent, since the word "percent" literally means per $100$.
This means the fraction is 58.bar(33)%.
We can loop this value twice to the left (same as dividing by $100$) to find the decimal equivalent. We get
$0.58 \overline{33}$
Hope this helps!
Jun 18, 2018
Decimal = $0.583 \ldots$
Percetange = 58.33...%
#### Explanation:
Well, there are two ways to find it out:
Method one:
To find out the decimal of a fraction you must do $7 / 12$. So if you do $7$ divided by $12$.
This gives you: $0.5833 \ldots$ We can just make this $0.58$
So the answer would be $0.58$ for the decimal one.
Now for the percentage, you will just have to do 58%
(because that is $58$ hundredths and the highest is 100%
Hope this helped!
You can also just put a dot over the $3$ to show that it is reccuring.
| 516
| 1,709
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 30, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.5625
| 5
|
CC-MAIN-2020-05
|
latest
|
en
| 0.848263
|
http://forum.arduino.cc/index.php/topic,21785.0.html
| 1,408,818,890,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2014-35/segments/1408500826343.66/warc/CC-MAIN-20140820021346-00213-ip-10-180-136-8.ec2.internal.warc.gz
| 65,247,126
| 15,909
|
Pages: [1] Go Down
Author Topic: Really need help with acs712 and Arduino (Read 5553 times) 0 Members and 1 Guest are viewing this topic.
0
Offline
Newbie
Karma: 0
Posts: 4
Arduino rocks
« on: May 26, 2010, 10:03:00 am » Bigger Smaller Reset
Hi everyone,I have an acs712 working with arduino and everything is ok, its sends a 2.5 - 2.7v reading on the analog pin and so on, but i can´t find out how to caculate power (KW or KW//h) can someone help with this problem? I would realy apreciate it if anyone could post the equation if they´d allready done one of these. I´m in Europe so its sensing +/- 230VAC 15A.
Thanks,
Chris
Logged
0
Offline
Jr. Member
Karma: 0
Posts: 55
Arduino rocks
« Reply #1 on: May 28, 2010, 02:16:56 pm » Bigger Smaller Reset
this web site has information on the subject i think you can use the acs712 insted of the CT sensor
http://openenergymonitor.org/emon/
Logged
0
Offline
Newbie
Karma: 0
Posts: 3
Arduino rocks
« Reply #2 on: October 29, 2010, 10:06:18 am » Bigger Smaller Reset
The output from the ACS712 is ratiometric so you will have to come up with y=mx+b values to calculate your current.
For the 5A version, the output runs from 0amps,2.5v to 5amps,3.5v...or 0amps,512 analogcounts to 5amps,716 analog counts.
So.....the equation for the 5a version is y=.0245(analogcounts)-12.55
Here is the calc from my arduino sketch:
Logged
0
Offline
Newbie
Karma: 0
Posts: 5
Arduino rocks
« Reply #3 on: December 19, 2010, 02:40:08 am » Bigger Smaller Reset
Hello,
I am using ACS 712 with arduino to measure the current. I tried to do it as per the Sparkfun instructions. (Except I have connected 1 microfarad caps instead of 0.1 microfarad).
I am getting readings from 0 to 1024 on the serial monitor of Arduino IDE. Can anyone tell me how to calibrate the sensor(ACS 712) to get exact current values on serial monitor?
I mean if ACS 712 outputs the analog voltage, then why am I getting digital readings on the serial monitor?
Logged
nr Bundaberg, Australia
Offline
Tesla Member
Karma: 126
Posts: 8501
Scattered showers my arse -- Noah, 2348BC.
« Reply #4 on: December 19, 2010, 04:18:00 am » Bigger Smaller Reset
Quote
I mean if ACS 712 outputs the analog voltage, then why am I getting digital readings on the serial monitor?
Just guessing here, but I'd say it's got something to do with the fact that you're reading the analogue values via an ADC (Analogue to Digital Converter) and sending the digital value to the serial monitor.
Or was that a trick question?
PS, why don't they have a sarcasm smiley?
Sorry amitkc, as for calibrating, assuming the 712 is linear measure the current with a known accurate meter, compare that value against what you are reading from the 712, then multiply by a fudge factor and/or apply an offset to bring the ADC value into line. See Jeremy's post above.
______
Rob
« Last Edit: December 19, 2010, 04:41:42 am by graynomad » Logged
Rob Gray aka the GRAYnomad www.robgray.com
0
Offline
Newbie
Karma: 0
Posts: 5
Arduino rocks
« Reply #5 on: December 19, 2010, 05:04:07 pm » Bigger Smaller Reset
well, let's say even if you have a DMM, It measures RMS values and not the average. So, if the values are changing instantaneously. So, it really makes it difficult to measure average value of current.
And basically, the question is how to develope a formula which can convert those voltage readings into current ?
Logged
nr Bundaberg, Australia
Offline
Tesla Member
Karma: 126
Posts: 8501
Scattered showers my arse -- Noah, 2348BC.
« Reply #6 on: December 19, 2010, 08:11:39 pm » Bigger Smaller Reset
I gather that the thing you want to measure is constantly fluctuating and therefore you can't get a good reading with the DVM.
You can't calibrate form a moving target, so set up a known stable current with a steady PSU and a resistor. Get the 712 callibrated with that.
Quote
how to develope a formula which can convert those voltage readings into current ?
I think that's what Jeremy's formula does. But maybe you can used the map() function.
Let's say you're getting readings from 200 to 600 and you know these equate to currents in the range 1A to 5A. Then the call
x = map(reading, 200, 600, 1, 5);
should work except that map() deals with ints so the returned values could only 1, 2, 3, 4 or 5 which is a little course. The way around that is to work with mA instead of A
x = map(reading, 200, 600, 1000, 5000);
______
Rob
Logged
Rob Gray aka the GRAYnomad www.robgray.com
0
Offline
Newbie
Karma: 0
Posts: 5
Arduino rocks
« Reply #7 on: December 19, 2010, 08:34:43 pm » Bigger Smaller Reset
I will try the map function. I am assuming that I will have to call that map function in MS excel and not in Arduino IDE.
Also, I tried Jeremy's formula, but it gave me negative readings for those digital numbers. So, I thought I should calibrate for my sensor. (My previous experience with Sharp Long Range IR sensor tells me to do so.)
The digital readings on the serial monitor vary from around 480 to 1023 for motor speed of 50 rpm. I am using Mabuchi FA 130 motor.
If I increase the speed to 100 or 200 still the readings go as high as
1023. This tells me that the readings are varying or overshooting instantaneously because of the PWM technique, since they did not overshoot or fluctauate as much for a speed of 255; which is maximum.
So, in order to define that how much is average current for speed of 50, for speed of 100 and so on, first I will have to convert those digital numbers in voltage with the help of ADC resolution formula i.e.
Once I know that, I will also have to see that for what voltage, what current do I have for what rpm. I think the current might vary according to load condition and rpm , so u can not really say that there is a particular amount of current for corresponding digital number or voltage.
But all this process will not yield an equation between voltage and current which is applicable for all rpm (i.e. duty cycles) from 0 to 255.
The statement I made above has the challenge and question hidden in itself. Let me know if you can help me with that.
Thanks again,
Amit
Logged
nr Bundaberg, Australia
Offline
Tesla Member
Karma: 126
Posts: 8501
Scattered showers my arse -- Noah, 2348BC.
« Reply #8 on: December 20, 2010, 03:00:34 am » Bigger Smaller Reset
Quote
I am assuming that I will have to call that map function in MS excel and not in Arduino IDE.
AFAIK there is no map function in Excel, you'll have to do it in the Arduino.
The approach I suggested above is just for getting the instantaneous current with no thoughts about voltage or power factor etc. I was not aware of the other requirements until your last post. This however has no bearing on calibrating the 712, that can be done with a static setup.
I really don't know anything about power factors, I do know that the voltage being applied to the motor is easy to read, as is the RPM. How you combine that lot to get what you want I'm not sure.
One thing I find a little strange though is
Quote
The digital readings on the serial monitor vary from around 480 to 1023 for motor speed of 50 rpm.
Are you saying that you get this huge variation (in current?) with nothing changing?
______
Rob
« Last Edit: December 20, 2010, 03:01:36 am by graynomad » Logged
Rob Gray aka the GRAYnomad www.robgray.com
0
Offline
Newbie
Karma: 0
Posts: 5
Arduino rocks
« Reply #9 on: December 20, 2010, 03:39:35 am » Bigger Smaller Reset
Rob,
sorry for the "map" thing. I was not familiar with the function, so I just guessed since u did not mention the environment. Thank you for that .
Now, let me tell you what exactly I am trying to acheive.
I am trying to measure the current withdrawal from my battery. Its (9.6v, NiCd,700mAh).
At very first, I connected ACS 712 in series with just one motor .(since this is the major load in my rover. Motors are connected to Adafruit motorshield.) I was getting fluctuation in the DMM and ACS readings as well.
So, further I connected ACS 712 in series with battery and that in series with DMM,with that, the DMM readings are not fluctuating, but ACS readings are still fluctuating. I am sure this is because of the PWM technique Arduino uses. Now, one more thing here is, if I increase the Vref to 5v by rotating the Vref pot on ACS 712 at its max position and making the gain maximum, I constantly get the value 1023. No fluctuation. (which really does not make sense.) If I set this pot to min
the values are again constantly zeroes.(catches my nerves..!!!)
Further, I just tried to play with the sensor and kinda tuned the both pots just to get some sensible values on serial monitor. I got the values mentioned here for the constant current of 0.48A (current measured on DMM)
For 50 rpm,
0
0
121
219
189
204
220
0
0
141
198
216
191
193
0
0
Now, If I am correct, these values are representing the voltage and not the current since, the output of the ACS712 is analog voltage. I also know the current (bcoz of the DMM), but I do not know the voltage values, as I have tuned the pot (Vref and Gain) at some random position and now, I am not able to understand what is Gain value and what is Vref value!!! having said that , how do I calculate the voltage values from the digital numbers I am getting ?
If you think there is something wrong my set up or strategy to measure the current or if some of my concept is wrong let me know.
Hey, by the way, where did u get the power factor thing into this
..I am running a DC system.
Thanks again,
Amit
« Last Edit: December 20, 2010, 03:40:36 am by amitkc » Logged
nr Bundaberg, Australia
Offline
Tesla Member
Karma: 126
Posts: 8501
Scattered showers my arse -- Noah, 2348BC.
« Reply #10 on: December 20, 2010, 05:18:51 am » Bigger Smaller Reset
Quote
where did u get the power factor thing into this
No idea, senior moment maybe
Quote
if I increase the Vref to 5v by rotating the Vref pot on ACS 712 at its max position and making the gain maximum, I constantly get the value 1023. No fluctuation. (which really does not make sense.) If I set this pot to min
the values are again constantly zeroes.(catches my nerves..!!!)
Don't know without seeing the circuit, but it looks like it's being over driven and maxing out.
But let me get this right, you have
motor---712---DMM---PWM
Is that correct?
If so I think there's no way you'll get a good reading because of the PWM. The PWM will produce X amps or 0 amps, there are no values in between, it's the ratio between the two that counts. If you're reading the current as above you'll get X for some readings and 0 for others. Exactly how that pans out will depend on the sampling frequency but I imagine it would look very much like you are describing as the two frequencies (PWM and your sampling) beat.
It's possible that the DMM gets a different and stable reading because it samples in a different manner, maybe true RMS or something.
You say the DMM shows .48A, is this what the motor is spec'd at, my guess is that the specs say quite a lot more.
Anyway as I said I think there's no way to get a good reading if the setup is as I have drawn above, and if it is it's not immediately clear to me how one would get a proper reading.
Quote
Now, If I am correct, these values are representing the voltage and not the current since, the output of the ACS712 is analog voltage.
The readings are voltage, but proportional to the current, so affectively they are current values.
______
Rob
« Last Edit: December 20, 2010, 05:21:19 am by graynomad » Logged
Rob Gray aka the GRAYnomad www.robgray.com
0
Offline
Newbie
Karma: 0
Posts: 5
Arduino rocks
« Reply #11 on: December 20, 2010, 05:30:43 pm » Bigger Smaller Reset
Rob,
For last readings I sent you,
Battery---DMM---ACS 712---Adafruit Motorshield External Power Supply---H bridge (PWM) i.e. 1 L293Ds---2dc motors
When you say those readings are proportional to current and affectively represent current, do u mean following?
For a digital number of 1023 if Vref=5v
then,
Current or ADC or Voltage= 1023*Vref/2n
so for Vref=5v, Current=1023*5/1024=5A
or R u saying that current will increase as this Digital number increases and I will have to find the relation between them.
If I have to find the relation and evetually measure the values from DMM for the current, I wonder why they call it as a current sensor.
Logged
nr Bundaberg, Australia
Offline
Tesla Member
Karma: 126
Posts: 8501
Scattered showers my arse -- Noah, 2348BC.
« Reply #12 on: December 21, 2010, 04:03:24 am » Bigger Smaller Reset
Quote
R u saying that current will increase as this Digital number increases and I will have to find the relation between them.
yes but the other way around
The digital number increases as the current increases
And you do have to find the relationship between the two. The data sheet details what this relationship should be, but you may have to callibrate as well.
Quote
If I have to find the relation and evetually measure the values from DMM for the current, I wonder why they call it as a current sensor.
Well AFAIK you can't measure current directly, you measure the voltage it causes across a resistor, or in the case of the 712 the internal hall effect device does the same thing.
All sensors are the same, a light sensor varies in resistance according to the light and you read this as a varying voltage, a temp sensor produces a variable voltage, it doesn't produce a temperature.
Technically I suppose the 712 should be called a "current to voltage converter" or something.
As for your problem, I really can't see why you would be getting such varying results now that I see what you have connected. If the motor speed and load are stable the current should be pretty stable as well. How you can get values from 0 to 220 I don't know.
Thinking...forget that last paragraph, what I said before about trying to measure the current on a PWM line still holds true I think. You're measuring the shield's external power supply that's used for the motor, the current being drawn from your battery will be in pulses as I described in the last post.
I'm certain that's what you problem is, and equaly certain I don't know how to measure it without things getting a lot more complicated.
______
Rob
Logged
Rob Gray aka the GRAYnomad www.robgray.com
0
Offline
Jr. Member
Karma: 4
Posts: 65
Arduino rocks
« Reply #13 on: December 21, 2010, 07:45:16 am » Bigger Smaller Reset
I have looked at this sensor a bit because they are used in products built by my employer. Zero current will be 2.5V nominal. The volt (signal) output will go up with current but the sensitivity is relatively low. You need to look for the mV/A scale.
You may need to build a filter circuit and possibly an amplifier stage using an op-amp. Look for circuits such as inverting amplifier or non-inverting amplifer using an opamp. Look for RC circuits using a resistor and capacitor.
Logged
Pages: [1] Go Up
| 3,951
| 14,969
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.609375
| 3
|
CC-MAIN-2014-35
|
longest
|
en
| 0.818136
|
https://atariage.com/forums/topic/285639-multi-sprite-kernel-wall-detection/?tab=comments
| 1,618,746,286,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-17/segments/1618038476606.60/warc/CC-MAIN-20210418103545-20210418133545-00095.warc.gz
| 223,921,274
| 21,164
|
# Multi Sprite Kernel wall detection?
## Recommended Posts
I've seen this question in past posts but there doesn't seem to be a resolution to the problem.
The code I generally use doesn't work and I'm assuming because the playfield is flipped. This works pretty well for standard games but what would the Y calculation be for the multi sprite kernel?
if !joy0right then left
temp3 = (player0x - 14)/4 : temp4 = (player0y - 6)/8
temp3 = (player0x - 14)/4 : temp4 = (player0y - 1)/8
player0x = player0x + 1
left
if !joy0left then down
temp3 = (player0x - 18)/4 : temp4 = (player0y - 6)/8
temp3 = (player0x - 18)/4 : temp4 = (player0y - 1)/8
player0x = player0x - 1
down
if !joy0down then up
temp3 = (player0x - 17)/4 : temp4 = (player0y + 1)/8
temp3 = (player0x - 15)/4 : temp4 = (player0y + 1)/8
player0y = player0y + 1
up
if !joy0up then movedone
temp3 = (player0x - 17)/4 : temp4 = (player0y - 7)/8
temp3 = (player0x - 15)/4 : temp4 = (player0y - 7)/8
player0y = player0y - 1
movedone
any ideas?
##### Share on other sites
Not sure if the link below will help. RT and others have done some work, but from what I can gather it's because there is no pfpixel to use a reference point. Maybe someone else can help with more documentation as I'm still trying to figure something out as well.
Edited by Lewis2907
##### Share on other sites
I thought just reversing the Y calculation would work but it doesn't. Even though the playfield is flipped it seems the pfread doesn't flip. So if you have your Player0y at 80, to the Y pfread it thinks it at 2...I think., at least that's what it seems like it's doing.
I'll keep playing with it but it's starting to make me pull my hair out.
##### Share on other sites
Here is info on the official stuff:
Neither option has worked for me. My hunch is that smarted brains could get an example working with bogaxs code.
I've figured out how to use the ball as the collision object for the player0 sprite. I've provided a proof of concept that collides with walls without visible rebound and also slides against walls.
## Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.
× Pasted as rich text. Paste as plain text instead
Only 75 emoji are allowed.
× Your previous content has been restored. Clear editor
× You cannot paste images directly. Upload or insert images from URL.
| 692
| 2,410
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.875
| 3
|
CC-MAIN-2021-17
|
latest
|
en
| 0.960585
|
https://puzzling.stackexchange.com/questions/44925/a-long-overdue-riddle/45020
| 1,575,630,094,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-51/segments/1575540487789.39/warc/CC-MAIN-20191206095914-20191206123914-00071.warc.gz
| 519,467,157
| 38,708
|
# A long overdue riddle
(I am writing the riddle in third person)
For some who believe, it is a ghost
Depending on others, it may boast.
Its elder twin is quite selfish.
Even the dead feel bad, especially Elvis.
Today, its uses are vast.
One can decide its caste.
one uses it all the time.
Doesn't cost one a dime.
It's only 53. So, still a long way to go.
Begin to worry if one doesn't know.
After all, it's a masterpiece for a few..
No, it hasn't got anything with dew.
HINT 1:
There's a reason this riddle is written in third person.
• Is it a living being? You can skip to answer. – Techidiot Oct 25 '16 at 13:50
• Well, technically, YES! – Sid Oct 25 '16 at 13:50
• You're not 53 years old, Sid? – n00dles Oct 25 '16 at 14:46
• Is Elvis a dead person or some kind of metaphor? – Techidiot Oct 25 '16 at 16:07
• @Techidiot It rhymed pretty well and there is also a connection to the answer... – Sid Oct 25 '16 at 16:08
## 11 Answers
The answer is
I (the first-person pronoun)
But I'm having some trouble with the reasoning for almost all of the lines, so I'll make it a community wiki and maybe others can offer some insight.
For some who believe, it is a ghost.
In mathematics $i$ is the notation for an imaginary number.
Depending on others, it may boast.
Boastful statements might well contain the word "I".
Its elder twin is quite selfish.
Its elder twin is the Latin word "ego", a term which connotes selfishness.
Even the dead feel bad, especially Elvis.
Elvis had a song titled "I feel so bad".
Today, its uses are vast.
We use the word for all kinds of statements and speech acts.
One can decide its caste.
A play on "case". Letters can be lowercase or uppercase. Also, the first-person pronoun has different cases: subject ("I"), object ("me"), possessive ("my").
One uses it all the time.
It's probably the most frequently used pronoun.
Doesn't cost one a dime.
Speech is free.
It's only 53. So, still a long way to go.
"I" is the symbol for Iodine, which has atomic number 53
Begin to worry if one doesn't know.
If one doesn't know about the pronoun "I", it's unclear how one could express oneself, let alone understand others. This would be cause to worry (???). OP's edit: if you don't know about yourself, you are in trouble.
After all, it's a masterpiece for a few..
Our uses of "I" are kind of like tiny self-portraits (???). (OP's edit: use of i(the imaginary number) in Euler's famous equation.)
No, it hasn't got anything with dew.
A pun on "I do" and maybe also "deux" (since "i" is the Roman numeral for one).
Hint
There's a reason this riddle is written in third person.
-
Because otherwise you'd have written the answer ("I") all over the puzzle.
• Yep, that's it. You need to find the rest of the clues. It's only I and not iodine... – Sid Oct 26 '16 at 17:18
• Not sure if this was @Sid's intent, but a note of interest on the "caste" line: in Japanese, at least, there are different forms of the word "I" which should be used depending on the circumstance i.e. using a more colloquial term around friends (there are several of these depending on gender and dialect) vs. the standard formal for everyday non-familiar usage, including elders and those in a station above your own, and even a very humble form for use around those demanding great respect. – feelinferrety Jun 29 '17 at 17:31
Is it a...
Push Button Telephone
For some who believe, it is a ghost
Depending on others, it may boast.
For younger generation, the push button telephones are dead and gone. But for others it is proud possession.
Its elder twin is quite selfish.
Even the dead feel bad, especially Elvis.
If by elder twin you meant smart phones, they are selfish, as they are taking away more and more from other gadgets and making themselves better. Elvis feels bad because he did not get to use one.
Today, its uses are vast.
You can decide its caste.
Today we use smart phones for a lot of things. And they are 'caste-ized' as Android, iOS, Windows and more (you are welcome, BlackBerryOS)
You use it all the time.
Doesn't cost you a dime.
Literally, all the time.
It's only 53. So, still a long way to go.
Begin to worry if you don't know.
The push button telephone made available to general public in 1963, is 53 now. And has no signs of slowing down.
After all, it's a masterpiece for a few..
No, it hasn't got anything with dew.
From a humble beginning, it has revolutionized the way we communicate, learn, share and connect. Truly a masterpiece.
• Good one! Elder twin might be the updated smileys. Elvis might be anagram for evils pointing to the evil smileys – Techidiot Oct 25 '16 at 15:47
• Good idea, but no... You haven't explained all the lines... – Sid Oct 25 '16 at 17:52
• @Sid, I don't know if you intended this to be the answer, but a lot of the clues point to 'Andy Warhol'... And if this is on right tack then the answer would be his painting 'Eight Elvises' painted in 1963. – WeShall Oct 25 '16 at 19:49
• "Elder twin" would have preceded so "Elder twin" to "Push Button Telephone" might be "Rotary Dial Telephone". – Kevin Fegan Oct 26 '16 at 0:30
• @KevinFegan, i thought on those lines. But that could not figure out how a humble rotary phone would be selfish. – WeShall Oct 26 '16 at 0:34
Is it
Speech?
For some who believe, it is a ghost
Depending on others, it may boast.
For the mute, speech is a ghost. But braggers use it to boast
It's elder twin is quite selfish.
Even, The dead feel bad, especially Elvis.
The twin could be thoughts, which are kept private and are older as we learn to think before we learn to speak, and Elvis needed speech to sing
Today, it's uses are vast.
You can decide its caste.
You use speech for any things, and you decide what to say
You use it all the time.
doesn't cost you a dime
Some people use it too much.
It's only 53. So, still a long way to go
Begin to worry if you don't know.
Martin Luther King's speech 'I have a dream' was read out by him 53 years ago.
After all, it's a masterpiece for a few
No, it hasn't got anything with dew.
Some speeches are very memorable
• Lovely. Should be the answer I guess +1 – Techidiot Oct 25 '16 at 12:40
• @Techidiot I only got this because I looked up what happened 53 years ago, and MLK's speech was there. Rest fitted nicely – Beastly Gerbil Oct 25 '16 at 12:41
• Good try, but no. – Sid Oct 25 '16 at 12:48
This is pretty far fetched but I liked the idea :
FM Radio
For some who believe, it is a ghost
A voice without a physical person emitting it may seem like a ghost for people without the science.
Depending on others, it may boast.
It could be seen as an achievement to be heard on radio
It's elder twin is quite selfish.
Television has taken a bigger place than radio in our lives
Even, The dead feel bad, especially Elvis.
Radio still plays music from dead people like Elvis, earning them no money.
Today, it's uses are vast.
This technology is used for communications and other things everywhere.
You can decide its caste.
Some radio channels are aimed at a particular audience.
You use it all the time.
It's almost always on in your car.
doesn't cost you a dime
But listening to it doesn't cost money.
It's only 53. So, still a long way to go
Although it has been invented in 1933 (83 years ago), American car company introduce the use of FM band in 1963 (53 years ago). See : https://en.wikipedia.org/wiki/1963_in_radio
Begin to worry if you don't know. After all, it's a masterpiece for a few No, it hasn't got anything with dew.
Some musics broadcasted through the radio are masterpieces.
• Far from the right answer. – Sid Oct 25 '16 at 14:59
Could it be:
The Global Positioning System
Tearing it down line-by-line:
For some who believe, it is a ghost.
You can't really see the satellites by naked eye.
Depending on others, it may boast.
Some may see it as a power statement of US capabilities.
Its elder twin is quite selfish.
Its predecessor NAVSAT was mainly reserved for the US Navy. Alternatively, elder twin could refer to its even older land-based predecessor LORAN, which was also mainly reserved for military use.
Even the dead feel bad, especially Elvis.
It was conceived during the height of the Cold War, while also fighting in the Vietnam War (which Elvis also fought in), to be used within the military.
Today, its uses are vast.
Well, GPS is used for a vast array of things.
You can decide its caste.
Blank on this one.
You use it all the time.
We use our phones for navigation, location services.
Doesn't cost you a dime.
Using GPS on a compatible device doesn't incur any direct costs.
It's only 53. So, still a long way to go.
The concept of GPS was conceived 53 years ago, in 1963, as a result of a study on how space systems could be used in military applications.
Begin to worry if you don't know.
It would be worrying if GPS would be unfamiliar to someone on the internet.
After all, it's a masterpiece for a few.
Some may regard it as a masterful feat of engineering.
No, it hasn't got anything with dew.
Dew shouldn't appear in medium earth orbit.
Probably I'm wrong, but I guess it's
spirit
For some who believe, it is a ghost
Depending on others, it may boast.
The word "spirit" can mean a ghost, but also an alcoholic drink.
Its elder twin is quite selfish.
Even the dead feel bad, especially Elvis.
On that one I must pass.
Today, its uses are vast.
You can decide its caste.
It's very common to speak of the "spirit of something". And it is often not well defined what is meant, so you can decide for yourself.
You use it all the time.
Doesn't cost you a dime.
You use your (mental) spirit all the time, and you don't have to pay for it.
It's only 53. So, still a long way to go.
Begin to worry if you don't know.
OK, this is a bit weak, but maybe it refers to the Spirit of America, a jet-propelled car that set its first record in 1963, 53 years ago.
After all, it's a masterpiece for a few..
No, it hasn't got anything with dew.
OK, I'll have to pass on this again.
Is it -
Hypertext?
For some who believe, it is a ghost Depending on others, it may boast.
For the ones who know a little of programming, they know hypertext is not visible but does a lot of things. Which symbolizes to Ghost.
Its elder twin is quite selfish. Even the dead feel bad, especially Elvis.
HTML can be the elder brother who takes all the attention away. Elvis is a text editor which is not widely used. It might also symbolize that its not based on Elvis Presely's name who was well know for "Elvis". This editor comes with Hypertext help.
Today, its uses are vast. You can decide its caste.
Its widely used as we all know. And it has various types Axial, Arborescent, Networked, Layered
You use it all the time. Doesn't cost you a dime.
They are free to use and is being used all the time.
It's only 53. So, still a long way to go. Begin to worry if you don't know.
Ted Nelson coined this term in 1963 and hence 53 years old. Pity if you don't know what it is.
After all, it's a masterpiece for a few.. No, it hasn't got anything with dew.
Obviously!
If not this, I guess, 53 is not related to time line as all the inventions of 1963 have been taken off. :)
I'm fairly sure this is wrong but my first thought was
Rock and Roll
For some who believe, it is a ghost
Some say "Rock and Roll is dead"
Depending on others, it may boast.
Others claim "Rock and roll is here to stay"
It's elder twin is quite selfish.
it's mostly just called 'Rock' music now
Even, The dead feel bad, especially Elvis.
Elvis is known for Rock and Roll music
Today, it's uses are vast.
You can decide its caste.
Many different kinds of rock and people split it into subgenres
You use it all the time.
doesn't cost you a dime
You can listen to the radio for free, all the time
It's only 53. So, still a long way to go
This is where my argument falls apart, Rock is far older than 53.
Begin to worry if you don't know.
After all, it's a masterpiece for a few
Again, masterpiece made me think of music
No, it hasn't got anything with dew.
This part again I don't know, perhaps something to do with the idiom about 'a Rolling Stone gathers no moss' The Rolling Stones are 54 years old, so they might be a possible answer as well?
• Not even close,I am sorry.. – Sid Oct 25 '16 at 14:59
Ok, I'm going to have a try...
At first I thought of
Time, age
But they didn't really fit some lines.
So then I took a look at
Things that happened in 1963
and so came up with
Zip Codes & weight watchers (fat elvis) But weight watchers isn't used all the time, so... Zip Codes!
It seems to fit a lot of the riddle;
For some who believe, it is a ghost
Depending on others, it may boast.
Not sure of the first line. But you may boast if you live in an affluent zip code, or you may not have to because your zip code does all the boasting for you.
It's elder twin is quite selfish.
Even, The dead feel bad, especially Elvis.
Elder twin? Didn't elvis have his own zip code or something?
Today, it's uses are vast.
You can decide its caste.
well everyone has a zip code I think... and you relate zip codes to poor parts of a city.
You use it all the time.
doesn't cost you a dime
This fits nicely without explanation.
It's only 53. So, still a long way to go
Begin to worry if you don't know.
It is 53 years in use, and if you don't know where you are, you have something to worry about.
After all, it's a masterpiece for a few
No, it hasn't got anything with dew.
?
• Nowhere close to the intended answer. – Sid Oct 25 '16 at 16:05
• Well, I'm out then! – n00dles Oct 25 '16 at 16:17
It is
Smiley Face
For some who believe, it is a ghost Depending on others, it may boast.
Face without the body seems like a ghost
Its elder twin is quite selfish. Even the dead feel bad, especially Elvis.
Evil smiley looks bad
Today, its uses are vast. You can decide its caste.
Smileys are used all over the internet. Even local version of these smileys have arrived.
You use it all the time. Doesn't cost you a dime.
We use them whenever we chat or message someone. It doesn't cost us anything.
It's only 53. So, still a long way to go. Begin to worry if you don't know.
Smiley Face was invented in 1963.
After all, it's a masterpiece for a few.. No, it hasn't got anything with dew.
It is such a great thing. We can express our emotions with them.
• Unfortunately that answer's already been submitted and eliminated. You can't see it now because they've replaced it, but you can look at this answer and the comments to see the history. puzzling.stackexchange.com/a/44939/25802 – John Oct 26 '16 at 15:16
It is
Love
For some who believe, it is a ghost
Depending on others, it may boast.
It's not physical, some people in love boast?
Its elder twin is quite selfish.
Even the dead feel bad, especially Elvis.
Hate or (original) sin and heartbreak (hotel)
Today, its uses are vast.
You can decide its caste.
doesn't fit i know
You use it all the time.
Doesn't cost you a dime.
, it's free
It's only 53. So, still a long way to go.
Begin to worry if you don't know.
no clue
After all, it's a masterpiece for a few..
No, it hasn't got anything with dew.
some people find love?
Other things that fit a couple of lines, but not all:
time, sin, heart break, electricity
You said it was (technically) living:
fire
| 3,940
| 15,439
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.875
| 3
|
CC-MAIN-2019-51
|
latest
|
en
| 0.944773
|
http://forums.wolfram.com/mathgroup/archive/2001/Oct/msg00373.html
| 1,580,163,178,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-05/segments/1579251728207.68/warc/CC-MAIN-20200127205148-20200127235148-00460.warc.gz
| 64,045,728
| 8,243
|
Balls2
• To: mathgroup at smc.vnet.net
• Subject: [mg31366] Balls2
• From: "Juan Erfá" <erfa11 at hotmail.com>
• Date: Wed, 31 Oct 2001 03:30:56 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com
```Hello.
In my letter from yesterday there is a fail.
The function F2 shoud be:
F2[b_,x_]:=Sort[F[b,x],Greater], and not Sort[F1[b,x],Greater]
The function F, is define dawn in the page and it have to be in the
begining.
The all letter shoud be like that:
<< DiscreteMath`Combinatorica`
The problen is how to share b balls in x boxes.
There is 4 cases:
In[1]:= F[b_, x_] := (q = Table[0, {x}];
Table[r = Random[Integer, {1, x}]; q[[r]]++, {b}]; q)
1.The balls are equals, the boxes are diferent
In[2]:= F1[b_,x_]:=RandomComposition[b,x]
2.The balls are equals, the boxes are equals
In[3]:= F2[b_,x_]:=Sort[F[b,x],Greater]
3.The balls are diferents, the boxes are equals
In[4]:= F3[b_, x_] := (a3 = F2[b, x]; r3 = RandomTableau[a3];
4.The balls are diferents, the boxes are diferents
In[5]:= F4[b_, x_] := (a4 = F3[b, x]; r4 = RandomPermutation[x];
Map[a4[[#]] &, r4])
In[6]:= F1[11,7]
Out[6]= {0,2,0,3,5,1,0}
In[7]:= F2[11,7]
Out[7]= {5,2,2,1,1,0,0}
In[8]:= F3[11,7]
Out[8]= {{1,4,6,11},{2,5},{3,8},{7,9},{10},{},{}}
In[9]:= F4[11,7]
Out[9]= {{2,6},{3},{10},{},{1,4,5,7,9,11},{},{8}}
I have also calculate the probability to share b balls in x boxes, and n
balls at least in one box.
In[12]:= Prob[b_, x_, n_] := (t = Table[F[b, x], {200}];
c = Count[Map[MemberQ[#, n] &, t], True]; 0.005*c)
The birthday problem is:
In[13]:= Prob[23,365,2]
Out[18]= 0.515
I get this results:
In[14]:= Prob[90,365,3]
Out[14]= 0.515
In[15]:= Prob[190,365,4]
Out[20]= 0.505
The function BN[x_,n_,p_]= b,
(to get b, knowing x, n, and the probability p)
If n=2, then p=1-x!/((x-b)! x^b), and we can solve this ecuation for b
In[23]:= B2[x_,p_]:=FindRoot[1-x!/((x-b)!x^b)==p,{b,1,x}]
In[24]:= B2[365,.5]
Out[24]= {b->22.7677}
If n>2, then I don't know.
Salutes.Juan
PD.I don't know how to pas the programs I write in Mathematica to the
e-mail, so I have to copy and paste every sentens, an after to correct the
signs that can not be convert, and I get confuse.
_________________________________________________________________
Descargue GRATUITAMENTE MSN Explorer en http://explorer.msn.es/intl.asp
```
• Prev by Date: Re: commuting and non-commuting symbols
• Next by Date: RE: commuting and non-commuting symbols
• Previous by thread: Re: How big a problem can ConstrainedMax handle?
• Next by thread: RE: 2D to 3D graphics? and Thickness of Lines and Arcs
| 938
| 2,570
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.328125
| 3
|
CC-MAIN-2020-05
|
longest
|
en
| 0.651668
|
https://www.e-how.org/2020/10/how-to-do-battery-load-test.html
| 1,606,352,533,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-50/segments/1606141185851.16/warc/CC-MAIN-20201126001926-20201126031926-00210.warc.gz
| 653,425,409
| 39,158
|
# How to Do a Battery Load Test
Battery load testing involves measuring the amperes produced by a charged battery and is particularly relevant for vehicle batteries. The battery in a car or truck needs to produce high amperes to power the starter motor and turn the vehicle's engine. The term used to describe the battery's power is "cold cranking amps" or CCA. To do an accurate battery load test, you need to use a battery load tester.
Step 1 Charge your battery fully to get an accurate load test reading. Examine the label on the battery to ascertain the output voltage and then use a multimeter to check that the voltage reading is the same as that indicated on the battery label.
Step 2 Set the multimeter to "Voltage." Connect the red sensor from the meter to the positive battery terminal and attach the black sensor to the negative terminal. The battery terminals are labeled "+" and "-" for convenient identification. Read the meter. If the reading is more than 10 percent lower than the voltage on the battery label, you need to charge the battery before doing a load test.
Step 3 Remove the sensors from the battery terminals.
Step 4 Examine the battery label to determine its ampere rating. You will see "CCA" followed by a number that denotes the cold cranking amps. Divide this number by two on your calculator to arrive at the optimum figure for your load test. For example, if the battery label reads CCA 500, then divide 500 by 2 to get 250. Jot down the result of your calculation.
Step 5 Attach the load tester sensors to the battery terminals. Again, connect the red lead to the positive battery terminal and the black lead to the negative terminal as you did earlier.
Look at your watch or a timer. Leave the sensors connected to the battery posts for 15 seconds. Then, read the measurement on the load tester and compare it to the number that you calculated in Step 4. If the reading is more than 15 to 20 percent below that number, it indicates your battery is not able to produce the correct power and won't be able to get your engine running. Remove the sensors from the battery posts and replace the battery if necessary.
Items you will need: Multimeter, Calculator, Battery load tester
| 468
| 2,221
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.53125
| 3
|
CC-MAIN-2020-50
|
longest
|
en
| 0.921814
|
https://yuihuang.com/cf-463c/
| 1,718,712,798,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-26/segments/1718198861752.43/warc/CC-MAIN-20240618105506-20240618135506-00395.warc.gz
| 953,207,601
| 15,822
|
# 【題解】Codeforces 463C. Gargari and Bishops
```#include <bits/stdc++.h>
using namespace std;
long long n, g[2005][2005], l[4005], r[4005];
int main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
cin >> n;
for (int i = 1; i <= n; i++){
for (int j = 1; j <= n; j++){
cin >> g[i][j];
l[i-j+2000] += g[i][j];
r[i+j] += g[i][j];
}
}
long long tot[2] = {}, x[2] = {1, 1}, y[2] = {1, 2};
for (int i = 1; i <= n; i++){
for (int j = 1; j <= n; j++){
int tmp = (i+j)%2;
long long t = l[i-j+2000]+r[i+j]-g[i][j];
if (t > tot[tmp]){
tot[tmp] = t;
x[tmp] = i;
y[tmp] = j;
}
}
}
cout << tot[0]+tot[1] << "\n";
cout << x[0] << " " << y[0] << " " << x[1] << " " << y[1] << "\n";
}
```
| 300
| 668
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.5625
| 3
|
CC-MAIN-2024-26
|
latest
|
en
| 0.27333
|
https://math.stackexchange.com/questions/657850/generators-of-a-finite-cyclic-group
| 1,604,196,852,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-45/segments/1603107922746.99/warc/CC-MAIN-20201101001251-20201101031251-00521.warc.gz
| 409,493,926
| 34,790
|
# Generators of a finite cyclic group.
I have to find a single generator in the form G = for the finite cyclic group G = <13, 20>. I'm having trouble figuring out what the group <13,20> means and how to simplify this. I found this - (Generators of a cyclic group) as a related concept but am having trouble interpreting the results in the lemma there in the question I am given.
G is a subgroup of < Z, + >
Another clue I've figured out is the following line from the wikipedia page for Generating Set of a Group - "Different subsets of the same group can be generating subsets; for example, if p and q are integers with gcd(p, q) = 1, then {p, q} also generates the group of integers under addition (by Bézout's identity)." --- I'm again not sure how to interpret this in finding what the group itself is.
I'd appreciate clues to get me a step or two further, thanks!
• I don't understand what you mean by $\langle 13,20\rangle$. This doesn't inherently mean anything. Do you mean generated by an element of order $13$ and an element of order $20$? – Ian Coley Jan 30 '14 at 23:50
• What is the group operation? – David Jan 30 '14 at 23:51
• Well, what I mean by <13, 20> (as it is given in the book I am studying from) is that it is a cyclic subgroup of <Z, +> finitely generated by the set {13, 20}. I have not been able to get an understanding of what the meaning of the subgroup generated by a set of more than one element is, which is the root cause of my problem. – user125080 Jan 30 '14 at 23:57
• Sorry! As I put in my last comment, group operation is addition. I'll edit that into the question. – user125080 Jan 30 '14 at 23:57
Yes, Bezout's identity is useful here.
By the comments, it seems that you are looking for the finite-ly generated subgroup $\langle 13,20\rangle$ of the group $(\Bbb Z,+,-)$ which is also claimed to be cyclic.
So, if $13,20\in H$ for any subgroup $H$ of $\Bbb Z$, then also $7=20-13$ and $6=13-7$ and hence $1=7-6$ are all in $H$ as $H$ is closed under subtraction. But if $1\in H$ then every $n\in\Bbb Z$ is in $H$ (as $n=\pm(1+1+1+\dots)$), so $H=\langle 1\rangle=\Bbb Z$.
In particular, the generated subgroup $\langle 13,20\rangle$ can also be generated by $1$.
In general, by Bezout's identity, we have $$\langle a,b\rangle = \langle\gcd(a,b)\rangle$$ in $(\Bbb Z,+,-)$.
I think $\langle 13, 20 \rangle$ is the subgroup of $(\mathbb{Z},+)$ generated by $13$ and $20$. I.e., $$\langle 13, 20 \rangle=\{13a+20b:a,b \in \mathbb{Z}\}$$ under addition.
In this case, $\gcd(13,20)=1$, so using the claim mentioned in the question, $$\langle 13, 20 \rangle=\mathbb{Z}.$$
So, what's a generator of $\mathbb{Z}$?
Let $a\in \mathbb{Z}$. Note that $\mathbb{Z}$ is an additive group. The the subgroup of $\mathbb{Z}$ generated by $a$ is $$\langle a\rangle = a\mathbb{Z} = \{\dots,-3a, -2a, -a, 0 , a, 2a , 3a, \dots\}.$$ The group $H = \langle a,b\rangle$ is a group containing $a$ and $b$. This means that $H$ contains all numbers of the form $na + mb$ for any $n,m\in \mathbb{Z}$. This means that if you can find $n$ and $m$ such that $n13 + m20 = 1$, then $1\in \langle 13,20\rangle$. And if the group contains $1$, then ...
| 986
| 3,172
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.703125
| 4
|
CC-MAIN-2020-45
|
latest
|
en
| 0.949176
|
https://www.experts-exchange.com/questions/28378003/Python-byte-'s-Help-me-port-this-crucial-Java-byte-method.html
| 1,488,175,083,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-09/segments/1487501172447.23/warc/CC-MAIN-20170219104612-00077-ip-10-171-10-108.ec2.internal.warc.gz
| 831,898,598
| 31,488
|
Solved
# Python byte[]'s - Help me port this crucial Java byte[] method
Posted on 2014-03-01
384 Views
Hi
The following code is crucial, working code that I have been using in RTS projects that, now that I'm a Python convert, I need assistance in getting it right. It isn't obvious.
I might be suffering from lack of experience issues, even formatting.
This is the working Java code, below, that I'd like to convert to Python that converts byte arrays to integers, and the other way.
I cant yet do a simple porting, if this even is simple?
Does Python even do static methods, for easy use from anywhere, or must I re-paste this into other classes? Should I make bytearrays.py with all these methods?
Thanks
``````public static byte[] intToByteArray(int value) {
byte[] b = new byte[4];
for (int i = 0; i < 4; i++) {
int offset = (b.length - 1 - i) * 8;
b[i] = (byte) ((value >>> offset) & 0xFF);
}
return b;
}
``````
``````public static int byteArrayToInt(byte[] b, int offset) { #make offset 0 for beginning
int value = 0;
for (int i = 0; i < 4; i++) {
int shift = (4 - 1 - i) * 8;
value += (b[i + offset] & 0x000000FF) << shift;
}
return value;
}
``````
0
Question by:beavoid
• 5
• 4
LVL 28
Expert Comment
ID: 39900197
Try the following, but they are written as functions, not as methons. No need for methods here:
``````def intToBytes(n):
b = bytearray([0, 0, 0, 0]) # init
b[3] = n & 0xFF
n >>= 8
b[2] = n & 0xFF
n >>= 8
b[1] = n & 0xFF
n >>= 8
b[0] = n & 0xFF
# Return the result or as bytearray or as bytes (commented out)
##return bytes(b) # uncomment if you need
return b
def bytesToInt(b, offset):
n = (b[offset+0]<<24) + (b[offset+1]<<16) + (b[offset+2]<<8) + b[offset+3]
return n
``````
0
Author Comment
ID: 39900410
Thanks for those functions,
but, for some absurd reason, they are not visible from my run method, and I don't know why Python's visibility is non-intuitive?
In my code below, it complains that intToBytes is not visible, when it is the first thing defined!
What could I be doing wrong?
Thanks
``````import threading, socket
def intToBytes(n):
print ("_________intToBytes___________")
b = bytearray([0, 0, 0, 0]) # init
b[3] = n & 0xFF
n >>= 8
b[2] = n & 0xFF
n >>= 8
b[1] = n & 0xFF
n >>= 8
b[0] = n & 0xFF
# Return the result or as bytearray or as bytes (commented out)
##return bytes(b) # uncomment if you need
return b
def bytesToInt(b, offset):
n = (b[offset+0]<<24) + (b[offset+1]<<16) + (b[offset+2]<<8) + b[offset+3]
return n
def __init__(self, numclients):
print('Server constructor: ')
self.numClients=numclients
print(self.numClients, " clients")
def run(self):
print('Server run() . . . client join:')
B=intToBytes(150)
print(B[0])
print(" . ")
print([1])
print(" . ")
print([2])
print(" . ")
print([3])
print(" . ")
clientJoinMode=True
s = socket.socket(socket.AF_INET, socket.SOCK_DGRAM)
port = 1024
bufferSize = 1024
s.bind(("", port))
while clientJoinMode : # CLIENT JOIN LOOP
print ('JOIN waiting on port: ', port)
``````
0
LVL 28
Expert Comment
ID: 39900438
Or you place them as functions outside the class definition, or add self as the very first argument. In the later case, you also should prepend self. when calling the methods. It must be explicitly written in Python. This means that then your line 47 must look like B = self.intToBytes(150)
0
Author Comment
ID: 39900477
Thanks.
How would you make my run method look like to work? It isn't obvious. - Just a conversion, and a printing of the bytes.
Would you make an external .py file with all the byte[] conversion methods?
0
LVL 28
Accepted Solution
pepr earned 500 total points
ID: 39900514
Try
``````import threading, socket
def intToBytes(self, n):
print ("_________intToBytes___________")
b = bytearray([0, 0, 0, 0]) # init
b[3] = n & 0xFF
n >>= 8
b[2] = n & 0xFF
n >>= 8
b[1] = n & 0xFF
n >>= 8
b[0] = n & 0xFF
# Return the result or as bytearray
return b
def bytesToInt(self, b, offset):
n = (b[offset+0]<<24) + (b[offset+1]<<16) + (b[offset+2]<<8) + b[offset+3]
return n
def __init__(self, numclients):
print('Server constructor: ')
self.numClients=numclients
print(self.numClients, " clients")
def run(self):
print('Server run() . . . client join:')
B = self.intToBytes(150)
print(B[0])
print(" . ")
print(B[1])
print(" . ")
print(B[2])
print(" . ")
print(B[3])
print(" . ")
clientJoinMode=True
s = socket.socket(socket.AF_INET, socket.SOCK_DGRAM)
port = 1024
bufferSize = 1024
s.bind(("", port))
while clientJoinMode : # CLIENT JOIN LOOP
print ('JOIN waiting on port: ', port)
``````
It should print your 150 as four values in the bytes. Notice also the added B's in the print commands.
0
Author Closing Comment
ID: 39900590
Thanks
Why did I get visibility errors? I'd like to avoid that mistake again!
"self" must be first in the arguments declarations? Makes sense
0
Author Comment
ID: 39900637
Thanks again
One last thing,
if I convert -256 to bytes, and try to print it back at the end, I don't get -256,
I get 4294967040
it prints 255 255 255 0 as the four bytes
`````` B = self.intToBytes(-256)
print(B[0])
print(" . ")
print(B[1])
print(" . ")
print(B[2])
print(" . ")
print(B[3])
print(" . ")
print(self.bytesToInt(B,0))
``````
0
LVL 28
Expert Comment
ID: 39901777
This is because of how the negative numbers are expressed. Think about a single byte that has 8 bits. One can express 2^8 = 256 states using 8 bits. But you can decide how the states will be used for encoding numbers. The most natural (in some sense) is to use one byte for expressing numbers from zero to 255 (that is 256 states). If you need to express also negative values, then the most natural is to use half of the interval for positive numbers (here from zero to 127), and approximately the other half for the negative values (from minus one to -128). For negative values, the most significant bit of the number is set to one, and the shift to right puts one's to that bit. This is the reason why the all ones appeared. There is the agreement that the bytes and bytearray types interpret the values as small positive integers. This way the byte with all bits set to one is displayed as 255.
0
LVL 28
Expert Comment
ID: 39901804
For the self, yes. It must be explicitly declared in Python as the first argument. It could be given a different identifier but it is highly recommended to keep that convention.
0
## Featured Post
Question has a verified solution.
If you are experiencing a similar issue, please ask a related question
Flask is a microframework for Python based on Werkzeug and Jinja 2. This requires you to have a good understanding of Python 2.7. Lets install Flask! To install Flask you can use a python repository for libraries tool called pip. Download this f…
In this post we will learn how to connect and configure Android Device (Smartphone etc.) with Android Studio. After that we will run a simple Hello World Program.
| 2,020
| 6,924
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.546875
| 3
|
CC-MAIN-2017-09
|
longest
|
en
| 0.832329
|
http://www.physicsforums.com/showthread.php?t=467563
| 1,369,275,956,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2013-20/segments/1368702749808/warc/CC-MAIN-20130516111229-00033-ip-10-60-113-184.ec2.internal.warc.gz
| 638,685,783
| 8,101
|
## 1st order linear differential equation
1. The problem statement, all variables and given/known data
I'm trying to study for a quiz tomorrow by doing some practice problems. If someone could help me with the process of solving a 1st order linear diff. eq., that would be great.
(x+1)(dy/dx) + (x+2)y = 2xe-x
2. Relevant equations
3. The attempt at a solution
dy/dx + [(x+2)/(x+1)]y = 2xe-x/(x+1)
integrating factor: e∫(x+2)/(x+1)= exlx+1l
This is where I get confused. I should be able to use the product rule here:
(y(exlx+1l)'
so that I will be able to take the integral of (above) and {2xe-x/(x+1)]*[exlx+1l].
Once I take the integrals, then I can solve for c(not in this problem, though) and try to solve for y explicitly. Some help with the middle steps would be greatly appreciated.
Recognitions: Homework Help First divide throughout to obtain an equation of the form: $$\frac{dy}{dx}+P(x)y=Q(x)$$ Then multiply through by the integrating factor and the LHS will be a total derivative, in your case it should be: $$\left( e^{x}(1+x)y\right) '=2x$$
Where did the 2x come from?
Recognitions:
Gold Member
Staff Emeritus
## 1st order linear differential equation
The point was that the formula you used for the integrating factor requires that the coefficient of the derivative be 1. Here it is x+ 1 so you need to divide the entire equation by x+1:
$$\frac{dy}{dx}+ \frac{x+2}{x+1}y= \frac{2x}{x+1}e^{-x}$$.
(The first equality is from the product rule, the second from just multiplying the left side of the differential equation by u.)
Now, you are looking for a function, u(x), so that multiplying by it will make that left side a single derivative:
$$\frac{d(u(x)y)}{dx}= u(x)\frac{dy}{dx}+ \frac{du}{dx}y= u\frac{dy}{dx}+ \frac{x+2}{x+1}u y[/itex] That is, we must have [tex]\frac{du}{dx}= \frac{x+2}{x+1}u$$
or
$$\frac{du}{u}= \frac{x+2}{x+1}dx= (1+ \frac{1}{x+2})dx$$
Integrating both sides, $ln(u)= x+ ln(x+2)$ so that
$$u(x)= e^{x+ ln(x+2)}= (x+ 2)e^x$$
What do you get when you multiply both sides of your equation by that?
dy/dx + [(x+2)/(x+1)]y = 2xe-x/(x+1) y'(x+2)ex+[(x+2)2/(x+1)]y=2x Ok, now I see where the 2x comes from. Do I have the rest right? If so, then by the product rule I should have: (ex(x+2)y)'=2x Taking the integral of both sides: ex(x+2)y=x2+c y=(x2+c)/(ex(x+2)) Yes?
| 770
| 2,323
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.53125
| 5
|
CC-MAIN-2013-20
|
latest
|
en
| 0.898569
|
https://quantumcomputing.stackexchange.com/questions/25999/how-does-quantum-gate-teleportation-differ-from-state-teleportation
| 1,716,985,297,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-22/segments/1715971059239.72/warc/CC-MAIN-20240529103929-20240529133929-00745.warc.gz
| 397,674,894
| 41,048
|
# How does quantum gate teleportation differ from state teleportation?
As described e.g. in this post, quantum gate teleportation can be framed as a variation of quantum state teleportation where a gate is applied beforehand on the receiver, and this results in the final state being teleported being slightly different.
More precisely, if $$|\psi\rangle$$ is the state to send, $$|\Psi\rangle\equiv\sum_i |i,i\rangle$$ the shared maximally entangled state, then the standard state teleportation protocol can be seen as consequence of the fact that we can write (ignoring normalisation constants): $$|\psi\rangle|\Psi\rangle = \sum_a |\Psi_a\rangle\otimes (U_a^\dagger|\psi\rangle), \qquad |\Psi_a\rangle\equiv (U_a\otimes I)|\Psi\rangle,$$ where is a(ny) basis of unitary matrices, so that $$\operatorname{Tr}(U_a^\dagger U_b)=d\delta_{ab}$$, with $$d$$ dimension of the underlying space. This formulation is nicely described e.g. in this answer.
Similarly, for gate teleportation, we can write $$|\psi\rangle(I\otimes U)|\Psi\rangle = \sum_a |\Psi_a\rangle\otimes (UU_a^\dagger|\psi\rangle),$$ and we thus see how the "gate to teleport" $$U$$ is applied to the (corrected) teleported state. One can now go ahead and correct the teleported state as usual. Observing that $$UU_a^\dagger|\psi\rangle=(UU_a^\dagger U^\dagger) U|\psi\rangle$$, we see that to obtain $$U|\psi\rangle$$ we need to implement a correction of the form $$UU_a^\dagger U^\dagger$$ for some $$a$$.
The question is: if we assume to be able to implement local operations on the register containing $$|\psi\rangle$$, why not just apply directly $$U$$, either before or after performing standard state teleportation? After all, we are assuming to be able to apply $$U$$ to (a part of) $$|\Psi\rangle$$, so why not apply it to $$|\psi\rangle$$ itself? What's the context where this makes sense?
For example, if you were trying to implement a $$T$$ gate ($$\pi/8$$ phase gate), the corrections that you'd need would be $$I, Z$$ and $$(X\pm Y)/\sqrt{2}$$. All of these corrections are in the Clifford group. So, this is where something like magic state distillation comes in. Imagine you have an error correcting code (such as the Steane [[7,1,3]] code) where you can perform any Clifford gate transversally. To get universality, you need to add a $$T$$ gate. This cannot be performed transversally (by Eastin-Knill theorem). So, put lots of effort into preparing a state capable of teleporting the gate $$T$$. Any corrections you need to perform are in the set of available operations.
| 667
| 2,556
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 22, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.578125
| 3
|
CC-MAIN-2024-22
|
latest
|
en
| 0.835071
|
http://www.algebra.com/cgi-bin/show-question-source.mpl?solution=33025
| 1,369,224,495,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2013-20/segments/1368701670866/warc/CC-MAIN-20130516105430-00085-ip-10-60-113-184.ec2.internal.warc.gz
| 312,640,559
| 816
|
```Question 49781
{{{(sqrt(3)+5)(sqrt(3) -3)}}} [Use the FOIL method to multiply]
{{{(sqrt(3)(sqrt(3))+ (sqrt(3))(-3))+ ((5)(sqrt(3)) + ((5)(-3))))}}} [Simplify]
{{{(3)+ ((5-3sqrt(3))) + (-15)))}}} [Combine like-terms]
{{{(3)+ ((2sqrt(3))) + ((-15)))}}}
{{{(3)+ (-15) + (2sqrt(3)))}}}
{{{(-12) + (2sqrt(3)))}}}
| 137
| 310
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.609375
| 3
|
CC-MAIN-2013-20
|
latest
|
en
| 0.231925
|
https://listarchives.libreoffice.org/global/users/2012/msg02779.html
| 1,721,610,804,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-30/segments/1720763517805.92/warc/CC-MAIN-20240722003438-20240722033438-00322.warc.gz
| 308,191,237
| 3,456
|
2012 Archives by date, by thread · List index
# Re: [libreoffice-users] How do add percentage in Calc?
```2012/3/2 PDA1 <peace@aleksandrsolzhenitsyn.net>:
```
```I have no idea how to add a percentage to a number in Calc.
Example;
Cell A1 has the number 100
Cell A2 has a percentage- 2.9%
I want to add 2.9% to the number in A1 so that the answer is in cell A1.
That is- 100 +2.9%
(just for your reference- the percentage in A2 is always changing from my
input)
How in the world do I do it?
```
```
How do you mean?
1: A1=100, A2=2.9% → A1 changes to 102,9
2: You enter 3% in A2, A1 now changes to what? 103 or 105,987?
If 103, enter 100 in a hidden cell, let's say A3 and then let
A1=A3*(1+A2), or as a constant in A1, that is A1=100*(1+A2).
If you want A1 to change its value by Itself·(1+A2) every time you
enter a new value in A2, then you could use a macro for that, but how
ever you do it, you are very likely to shoot yourself in the foot.
Kind regards
Johnny Rosenberg
ジョニー・ローゼンバーグ
--
For unsubscribe instructions e-mail to: users+help@global.libreoffice.org
Problems? http://www.libreoffice.org/get-help/mailing-lists/how-to-unsubscribe/
Posting guidelines + more: http://wiki.documentfoundation.org/Netiquette
List archive: http://listarchives.libreoffice.org/global/users/
All messages sent to this list will be publicly archived and cannot be deleted
```
| 427
| 1,379
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.53125
| 3
|
CC-MAIN-2024-30
|
latest
|
en
| 0.800653
|
https://hirequalitywriter.com/results-and-discussion-sections-for-your-prior-work-observing-cricket-dominance-interactions/
| 1,656,771,533,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-27/segments/1656104141372.60/warc/CC-MAIN-20220702131941-20220702161941-00143.warc.gz
| 335,747,538
| 10,228
|
# Results and Discussion sections for your prior work observing cricket dominance interactions
500-800 words with word count on the top of the paper.Instructions: This final Peerceptiv assignment for the term gives you an opportunity to write the Results and Discussion sections for your prior work observing cricket dominance interactions.
One thing that you need to do in order to write your text for Peerceptiv Assignment 3 is to perform a statistical test on the combination of your data (you should have three “wins” from last week’s observations) and class data (shown below in Table 1). You will then interpret these results.
Table 1: Class Data
Observed wins Expected winsResidents 141+?________Intruders 64 +?________You will add your three observations (indicated by the “?” marks) to the data set in Table 1 and then calculate the expected value for wins. Because our null hypothesis is that there is no relationship between residency and the likelihood of winning fights, our expected values for residents and intruders should be 50:50. That’s the total count of observed wins for residents and intruders (class plus yours) divided by 2.
Data Analysis: Next you will go to GraphPad (Links to an external site.) and complete the following steps
Enter your data in Rows 1 & 2.Click the “Calculate Now” button.Document the following results of the Chi-square test. You will need to report both of these results in your Results section, as well as whether or not you could reject the null hypothesis.Chi-square value: This is the value calculated by the Chi-square equation based on your dataP-value: This is the probability that you would have observed this result if your null hypothesis were true (there is no relationship between residency and winning). By convention in biology, we reject the null hypothesis if our statistical test produces a p-value that is .05 or smaller.We have added a supplemental p-value explanation that hopefully will help you better grasp the concept.In the files below, you will find the p-value explanation sheet referred to and 2 example papers to help create a new, unplagiarized paper for this assignment. It will be screened through “TURN IT IT” plagiarize screener.
| 458
| 2,213
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.46875
| 3
|
CC-MAIN-2022-27
|
latest
|
en
| 0.920912
|
https://boards.fool.com/historical-calculators-34249423.aspx?sort=whole
| 1,568,626,016,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-39/segments/1568514572516.46/warc/CC-MAIN-20190916080044-20190916102044-00488.warc.gz
| 392,847,059
| 47,996
|
Message Font: Serif | Sans-Serif
No. of Recommendations: 1
Hi. Most retirement/investment calculators that I run across use either a "Monte Carlo" type system (Keep flipping the coin. Who knows what numbers they're using) or alternately will make you input what you think returns will be and what you think inflation will be, and things like that.
Are there any other calculators that work the same way FireCalc works? Straight-up, year-by-year success rates, using the numbers i.e. bonds, stocks, interest rates, inflation, as they actually happened, ripped from history's headlines?
No. of Recommendations: 7
You may not understand how Monte Carlo (at least the good ones) calculators work. They look at history and record the periodic changes. Next they rank order the changes by size. If the changes are daily for 100 years the number of changes is about 25,000.
At this point the Monte Carlo simulation for Trail #1 happens. The computer randomly picks a change for for the first time period (lets say a day). That random choice tells what happens for day #1 of trial #1. Next the computer picks a change for day #2. Note each pick to completely random. i.e. the change picked for the any day is not removed from the set of changes. This process continues until the first trial has been completed. Either the portfolio has money at the end or or does not.
Next another trial is run -- usually the number of trials is many thousands.
If portfolio plan "A" has 4% of its trials run out of money before 30 years some people will favor it over plan "B" which has a 10% incidence of running out of money. Clearly plans that don't run out of money have a residual and the residual size varies both based on the randomly selected daily changes and on the portfolio management plan.
Some individuals have taken their plans and run these against historical data. A well known example is the work of William Bengen who tested against various portfolios comprised of the S&P500 and the All Bond Index. Bengen's work showed the worst time to retire since the mid 1920s was not June 1929, but rather almost any time in 1968 or 1969. Unless you think the future market movements will mirror history, this approach may not be the best predictor.
No. of Recommendations: 0
Are there any other calculators that work the same way FireCalc works? Straight-up, year-by-year success rates, using the numbers i.e. bonds, stocks, interest rates, inflation, as they actually happened, ripped from history's headlines?
I recall Vanguard providing me with simulation results when I first started accounts with them several years ago. They didn't run full historical simulations, like fireCalc, but they did run historical simulations with start dates of several key years (starting years around 1929 and in the 70's). These are the years that establish worst case in historical simulators so the Vanguard simulations provided indications of whether your investment plan and spending would survive and for how long. It would be the equivalent of running FireCalc with only 8 to 10 start dates, but using only the start dates that tend to be worst case. When you run the entire historical simulation set like FireCalc, you get probability information (ie. historically 95% of the time this portfolio would survive 30 years) but if you think about it, that's not really a probability that matters to you at any given time. The fact that the US economy has had more years that would be good times to start retirement than bad is interesting, but that ratio of good years to total years is not really instructive or useful.
No. of Recommendations: 4
Note each pick to completely random. i.e. the change picked for the any day is not removed from the set of changes.
This is a critical weakness of using Monte Carlo analysis for investment performance.
First, if you look at the distribution of historical stock performance, bond performance and inflation, they are not nice gaussian distributions or easily described with analytical functions. This is important in how the random number generator converts its results to actual data.
It is not impossible to describe the actual historical distributions with a numerical function description and then convert the random number to an appropriate choice for rate, but I have yet to see a financial Monte Carlo simulator that actually does that.
Second, the performance of stocks this year is not a random event uncorrelated to bond performance, to inflation, or even to stock performance in previous years. Those correlations, however, are virtually impossible to quantify. I am aware of Monte Carlo simulators that attempt to include at least some of the correlations by only choosing stock, bond and inflation numbers that actually occurred in a single year sometime in history, yet randomly assemble the years. So the random number generator serves to identify which year to use, then selects another and another until 30 years worth have been listed. This still doesn't account for the correlations of performance this year to previous years. So you could simulate 1993 immediately following 1929, for example.
No. of Recommendations: 0
Who was it that said "Most of history is bunk"?
CNC
No. of Recommendations: 2
Second, the performance of stocks this year is not a random event uncorrelated to bond performance, to inflation, or even to stock performance in previous years. Those correlations, however, are virtually impossible to quantify. I am aware of Monte Carlo simulators that attempt to include at least some of the correlations by only choosing stock, bond and inflation numbers that actually occurred in a single year sometime in history, yet randomly assemble the years. So the random number generator serves to identify which year to use, then selects another and another until 30 years worth have been listed. This still doesn't account for the correlations of performance this year to previous years. So you could simulate 1993 immediately following 1929, for example.
This is what I meant about Monte Carlo calculators when I said "Keep flipping the coin. Who knows what numbers they're using...?" Yesterday's "random event" (if it really was random) is part of what makes today what it is and not one of an infinite number of other things it could have been. Monte Carlo calculators seem to just shake the bag and mix up the juxtapostioning. If they intervene with some tactic e.g. we've eliminated 1929 stock market performance from occurring at the same time as 1979's inflation" then it's not really random. And what about the 1,000 other "tweakings" that might have been better, more relevant, that they didn't think of?
Monte Carlo calcultors might be good as a sort of "stress test" beyond what previous reality has thus far whipped up
No. of Recommendations: 1
As regards FireCalc: I thought it was one of the more valuable tools (although certainly not the only one) when it came to answering, how close am I to having enough to retire reasonably safely?
(Anyone who’s asked that question knows that it’s a deceptively complex question, with data-driven opinions drawing almost every possible conclusion)(many of which rapidly approach There Is No Safety This Side Of The Grave)
But as regards FireCalc specifically, my most valuable takeaway was that with any reasonable set of starting parameters - those that gave the historical failure rates of say less than 5% - those 20- or 30-year failures were virtually always those portfolios with a miserable first three years or so.
This reinforces the importance that sequence of returns is one of the most valuable criteria, but from a pragmatic perspective it helps in this way: if, say, 36 months from your last paycheck your investable net worth is appreciably higher than it was at the beginning, most of the remaining uncertainty has gone away e.g. a hypothetical historical failure rate of 5% is now 1-2%.
That’s my only addition to this conversation.
But I do have a question: aside from the “history tells us nothing” argument: what are the criticisms of FireCalc as a tool? Methodology, math, calculation errors?
- sutton
loquacious this week
No. of Recommendations: 1
But I do have a question: aside from the “history tells us nothing” argument: what are the criticisms of FireCalc as a tool? Methodology, math, calculation errors?
- sutton
I have heard there are some glitches. Minor. Mostly display type problems. Nothing that affects actual survival rates.
Also, I have heard that the way it calculates bond values for rebalancing is seriously outta whack. There is a similar calculator, FireSim or something, that supposedly uses more realistic bond rates and the safe withdrawal rate plummets. I am not in a position to substantiate any of this. This is just parts of the discussion over the years. Also, the FireSim site seems to have been left to go to seed. Hmmm....? FireCalc has also been left in a quasi-zombie mode. It gets updated every year with CPI, market performance, etc but that was only after several years of non-updating and the retired owner was sort of hunted down and encouraged to update it.
No. of Recommendations: 1
But I do have a question: aside from the “history tells us nothing” argument: what are the criticisms of FireCalc as a tool? Methodology, math, calculation errors?
The problem as many have said is correlations. Stocks, bonds, and inflation are all correlated over time and are correlated with each other. The correlation is poorly understood. So if you want to avoid the problem of correlations you need to use non-overlapping time periods. cFIREsim uses data from 1871 to today. There are only 5 non-overlapping 30 year periods since 1871. If the correlations extend over several years then it gets even worse, you need to leave a gap between the 30 year periods for them to be completely independent. Yes, there are 118 start years but there is a lot of correlation between the 30 years from 1970-1999 and 1971-2000. It sounds a lot more comforting to learn that a plan was found safe over 118 30 year periods than to learn it was safe over only 5 30 year periods, but 5 independent 30 year periods is all you get.
You could play games, assume that the correlation goes away after 10 years, and then you get 15 periods, which is better. But now you're assuming something about the unknown correlations in an ad-hoc way.
The advantage of a Monte Carlo simulation is that the assumptions about correlations are explicit in the code, even though many websites don't tell what they've assumed. In principle, you can play around with the correlation assumptions and see how the results change.
No. of Recommendations: 0
It is not impossible to describe the actual historical distributions with a numerical function description and then convert the random number to an appropriate choice for rate,
Prove it. Find that function.
Second, the performance of stocks this year is not a random event uncorrelated to bond performance, to inflation, or even to stock performance in previous years. Those correlations, however, are virtually impossible to quantify.
Which means they are random, as far as we know.
I should qualify that things are random until you discover a pattern. If I gave you digits 1000...1999 in the currently-known decimal expansion of pi, you would be justified in thinking they are random, though I could predict the next digit with perfect accuracy. But, unless you know the pattern, claiming that there is one, is just so much hot air. As someone (Henry Ford?) said, "no one is famous for what they are going to do in future."
No. of Recommendations: 3
I question that 5 non-overlapping periods would be even vaguely sensible as a basis since it would mean 5 rather arbitrary starting years vs checking each of 118 starting years.
I would think that the biggest criticism of the FireCalc approach is that there has be gradual secular change in how the market behaves so that the early starting years may not be indicative of future behavior ... but they are better than nothing.
No. of Recommendations: 7
Prove it. Find that function.
You could use a piecewise function of your choice to match the historical distributions. That's not the hard part. You simply plot the historical distribution curve and fit a line to it. A linear fit, a spline fit. . . anything can work. I've just never seen a Monte Carlo retirement investment simulator actually go to the trouble.
Which means they are random, as far as we know.
No. It doesn't mean that at all. We know that stocks and bonds, for example, are generally inversely related. We know that inflation and stock earnings tend to be correlated. But obviously there are other factors. The fact that we cannot identify all factors that impact these rates in a quantifiable way does not mean the correlation doesn't exist. It only means we don't have all the variables identified and quantified. The rates are still correlated in some manner.
No. of Recommendations: 0
You simply plot the historical distribution curve and fit a line to it. A linear fit, a spline fit. . .
Do you really not see the logical next step of this argument? If different functions can fit the same data then extending them in the future will give different results, which means none of them are particularly predictive, so what is the point of using them?
Overfitting, aka data mining, is frowned upon for a reason. If your function does not perform well out of sample then it is completely useless in prediction.
No. of Recommendations: 8
If different functions can fit the same data then extending them in the future will give different results, which means none of them are particularly predictive, so what is the point of using them?
That's not correct. Different descriptions of the future - different curves fit to historical data - can definitely be useful even if they are not perfectly predictive. As a trivial example, the very long term trend of broad stock market returns is something like 6% plus the current inflation rate. *** Are the market returns for the next year going to be exactly that? I'd wager an awful lot of money that they won't be exactly that. But that doesn't make the prediction useless. Given no other information about the current situation other than the inflation rate, you could plan on the market going up by 6% plus inflation year after year. You'd be high about 1/2 the time and you'd be low about 1/2 of the time. And that becomes a useful way to think about the long-term future.
--Peter
*** - I'm going from memory here. Please feel free to substitute the actual correct statistic for my poor recollection of the figure. The lack of accuracy in the figure does not affect my argument.
No. of Recommendations: 2
Do you really not see the logical next step of this argument? If different functions can fit the same data then extending them in the future will give different results, which means none of them are particularly predictive, so what is the point of using them?
Overfitting, aka data mining, is frowned upon for a reason. If your function does not perform well out of sample then it is completely useless in prediction.
You really don't know much about math . . . or investment/retirement simulators. If you are hoping for analytic predictive capability it doesn't matter how well you match the historical distribution, you won't be able to predict the future. But that's not the point. If you are able to approximate the historical distributions of the past, then you should at least be able to gain general understanding of how a portfolio might perform under conditions consistent with history.
The specific numerical function approximation you choose will have insignificant impact on the final answer provided your approximation is kept to low delta error. For example, if you are trying to compute the area under an arbitrary curve, you can get arbitrarily close to the exact answer with rectangular or trapezoidal summations - or with spline fits. You just need to pay attention to the details.
No. of Recommendations: 0
You really don't know much about math . . . or investment/retirement simulators.
That's very true.
If you are hoping for analytic predictive capability it doesn't matter how well you match the historical distribution, you won't be able to predict the future. But that's not the point. If you are able to approximate the historical distributions of the past, then you should at least be able to gain general understanding of how a portfolio might perform under conditions consistent with history.
Now this "general understanding" - what is that? It's great if you get an idea of how the portfolio has performed historically; but then what? Are not assuming it will do the same in future (which is the point of Monte Carlo trials - to predict several future paths)? To do so, you do have to predict, say, next year's returns (along with possible dispersion), do you not? And then for the year after that, and so on.
The specific numerical function approximation you choose will have insignificant impact on the final answer provided your approximation is kept to low delta error. For example, if you are trying to compute the area under an arbitrary curve, you can get arbitrarily close to the exact answer with rectangular or trapezoidal summations - or with spline fits. You just need to pay attention to the details.
Oh, is that what they call "integral"?
Back to your original assumption that this year's (or take any other period) returns are somehow a function of something - returns and dispersions from recent past for various asset classes as you assume - do you have any actual data to back it up?
The little math I know says that, despite the large dispersion (and corresponding low confidence), a simple average of past yearly returns is still the best (though not a good) predictor of the next year's returns. Let me know how more complexity helps.
No. of Recommendations: 9
The little math I know says that, despite the large dispersion (and corresponding low confidence), a simple average of past yearly returns is still the best (though not a good) predictor of the next year's returns.
I was reading recently that the reason we have gotten so much better at forecasting the path a hurricane will take is that they are doing a significant number of forecasts and plotting out the envelope of possibilities. Chances are that any specific hurricane won't follow exactly the path of the center of that envelope, but that it is highly likely that its path will be within the envelope.
This seems to me to be the purpose of a tool like FireCalc ... not to predict the exact, specific future of what will happen, but rather to project a probability envelope for what might happen based on past history. The projection is not that one will have \$X in 30 years, but that of the probable outcomes in 30 years, only N% of them correspond to all the money being gone.
No. of Recommendations: 6
The little math I know says that, despite the large dispersion (and corresponding low confidence), a simple average of past yearly returns is still the best (though not a good) predictor of the next year's returns. Let me know how more complexity helps.
The complexity lets you see the range of what could happen. If you believe that the average is the best predictor, then you would presumably agree that history can help to predict the future. But since the average is just that, an average, it doesn't show the variability (ups and downs) that may occur.
The more complex models, like FireCalc and Monte Carlo analysis, show you what results may occur when that variability is considered. They DO NOT claim to predict next year's returns. What DO they claim to do (and do a pretty good job of) is to predict the range of returns you may get over a particular timeframe. This is helpful if you are looking for an estimate of how long your portfolio will survive. It's not so helpful if you are looking for a prediction of next year's returns.
AJ
No. of Recommendations: 0
Back to your original assumption that this year's (or take any other period) returns are somehow a function of something - returns and dispersions from recent past for various asset classes as you assume - do you have any actual data to back it up?
Correlation is a mathematical measurement of the similarity of any two series. A correlation coefficient can be calculated between any two series. Look it up or google "correlation coefficient" if you want to see how it works.
No. of Recommendations: 4
There are a lot of issues floating around here, and I certainly don't want to scare anyone off. https://slate.com/news-and-politics/2013/07/warm-weather-hom...
The New Orleans Times-Picayune ran a piece last Friday attempting to answer a question the entire world has been asking: Should ice cream be blamed for murders? “The correlation between homicides and ice cream sales—when ice cream sales increase, the rate of homicides also increases—has long been a topic in statistics and science classrooms,” writes John Harper, citing several recent cases of ice cream-related crime.
In the second paragraph of his piece, Harper thankfully reminds readers that correlation is not causation, and that ice cream’s relationship to homicide is a mere statistical coincidence. The idea that frozen treats cause crime is obviously ridiculous, unless you’re talking about that addictive Cocaine Chip ice cream I’ve heard so much about. But it does stand to reason that ice cream sells better in warm weather, and there is in fact plenty of evidence to suggest that murder rates rise when temperatures rise.
Using a variety of statistical methods, including transformations (square root, logarithmic, etc); different regression/correlation methods (simple linear, multiple regression, principal component analysis); and things like careful selection of dependent and independent variables, I can force pretty gnarly data to fit some sort of predictive relationship. Anyone who doesn't believe that has never been around a statistic driven project in need of demonstrating a statistically meaningful outcome. So correlation coefficients don't really impress me.
The first question you should ask when viewing statistics is "Is the data normally distributed?". That is going to tell you a lot about appropriate methods. Another good question is, does the thing I'm trying to predict fit within the previously observed outcomes? Assuming a normal distribution, does it fit within 2 standard deviations of the mean? What happens to the confidence interval as I get outside the previously observed outcomes or away from the mean?
Predicting what the market will do in the next quarter or year is challenging enough, regardless of the statistical method used. If you had told me last July we would be looking at a rate cut this July, I would have laughed at you. If it wasn't hard, and subject to a lot of randomness, then there would be a lot more rich people, right? Monte Carlo analysis and simulators like FIRECalc are intended to help by handling longer term. Monte Carlo simulation is often used when simple statistics don't work well, or suffer from things like the previously described sequencing risk.
For those using something like FIRECalc, sequencing risk is somewhat mitigated if you follow the advice to have 2-3 years of cash needs in cash or a near cash equivalent.
For folks like me, further from retirement, the big number to keep in mind is the annual inflation adjusted stock market return/Compound Annual Growth Rate (CAGR). Right now, I don't care if the SWR is actually 3.8, 4.0 or 4.2% because I'm far enough from retirement it has little effect on what I need to do. I do care of the CAGR over the next ten years is 6%, 7%, or materially higher or lower. If its a lot lower than 6%, I'm either going to have to work longer, or come up with a different (riskier?) asset class that will do better.
No. of Recommendations: 3
In the second paragraph of his piece, Harper thankfully reminds readers that correlation is not causation, and that ice cream’s relationship to homicide is a mere statistical coincidence.
Sometimes knowing a little about math can mislead. Although correlation is not causation, when two series are closely correlated that is almost always an indication that the two series share at least some common causes. This can sometimes be revealed through rigorous application of principle component analysis although that still requires that someone first hypothesize the correct causal force be considered.
This is important when evaluating the strengths and weaknesses of the Monte Carlo investment simulations and how correlations between input variables is accounted for. In the case of ice cream and homicide rate, there are many possible shared causes that might be at play here. And while it would take a massive amount of research to investigate which causes are shared and how they influence each result, the important thing to remember is that the correlation does truly exist. The data shows that. If a simulation that requires both crime rate and ice cream sales as inputs assumes that these two can be modeled with independent random number generators, that correlation will not be captured in the results. And if those correlations are not captured in the results, then the results are not reflecting reality.
No. of Recommendations: 4
"In the case of ice cream and homicide rate, there are many possible shared causes that might be at play here."
Summer heat and summer break:
When I was an inner city prosecutor, homicides generally went up in summertime. So did ice cream sales:
https://www.nytimes.com/2018/09/21/upshot/a-rise-in-murder-l...
https://www.idfa.org/news-views/media-kits/ice-cream/ice-cre...
What can be more American than ice cream and increased crime rates in summertime?
| 5,357
| 25,936
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.765625
| 3
|
CC-MAIN-2019-39
|
latest
|
en
| 0.949531
|
https://studysoup.com/tsg/statistics/63/a-first-course-in-probability/chapter/1239/4
| 1,606,856,433,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-50/segments/1606141681524.75/warc/CC-MAIN-20201201200611-20201201230611-00160.warc.gz
| 503,292,991
| 17,619
|
×
×
# Solutions for Chapter 4: A First Course in Probability 9th Edition
## Full solutions for A First Course in Probability | 9th Edition
ISBN: 9780321794772
Solutions for Chapter 4
Solutions for Chapter 4
4 5 0 407 Reviews
19
0
##### ISBN: 9780321794772
Chapter 4 includes 142 full step-by-step solutions. A First Course in Probability was written by and is associated to the ISBN: 9780321794772. Since 142 problems in chapter 4 have been answered, more than 62401 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: A First Course in Probability , edition: 9. This expansive textbook survival guide covers the following chapters and their solutions.
Key Statistics Terms and definitions covered in this textbook
• Alias
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
• All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions
• Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation
• Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.
• Biased estimator
Unbiased estimator.
• Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
• Conidence interval
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
• Contrast
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.
• Cook’s distance
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.
• Covariance
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .
• Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
• Deining relation
A subset of effects in a fractional factorial design that deine the aliases in the design.
• Dependent variable
The response variable in regression or a designed experiment.
• Design matrix
A matrix that provides the tests that are to be conducted in an experiment.
• Distribution function
Another name for a cumulative distribution function.
• Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
• Error sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.
• Estimate (or point estimate)
The numerical value of a point estimator.
• Estimator (or point estimator)
A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.
• Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.
×
| 949
| 4,648
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.515625
| 4
|
CC-MAIN-2020-50
|
latest
|
en
| 0.891309
|
https://baihuqian.github.io/2018-06-16-binary-tree-inorder-traversal/
| 1,718,863,281,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-26/segments/1718198861883.41/warc/CC-MAIN-20240620043158-20240620073158-00857.warc.gz
| 89,833,157
| 21,526
|
# Question
Given a binary tree, return the inorder traversal of its nodes’ values.
Example:
Input: [1,null,2,3]
1
\
2
/
3
Output: [1,3,2]
Follow up: Recursive solution is trivial, could you do it iteratively?
# Solution
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None
class Solution:
def inorderTraversal(self, root):
"""
:type root: TreeNode
:rtype: List[int]
"""
res = list()
stack = list()
if root is None:
return res
stack.append(root)
while len(stack) > 0:
node = stack.pop()
if node.left is not None or node.right is not None:
left, right = node.left, node.right
node.left = None
node.right = None
if right is not None:
stack.append(right)
stack.append(node)
if left is not None:
stack.append(left)
else:
res.append(node.val)
return res
| 231
| 867
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.09375
| 3
|
CC-MAIN-2024-26
|
latest
|
en
| 0.58164
|
http://www.fixya.com/support/t2920345-assignment_building_balance_sheet
| 1,511,483,616,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-47/segments/1510934807044.45/warc/CC-MAIN-20171123233821-20171124013821-00408.warc.gz
| 389,029,001
| 33,336
|
Question about Vorton Financial Tools 1.0 (509) for PC
# I have an assignment on building a Balance Sheet. There are 4 questions. Penguin Pucks, has current assets of \$5,100, net fixed assets of \$23,800, current liabilites of \$4,3000, and long-term debt of \$7,400. What is the value of shareholders' equity account for this firm? How much is net working capital? #2 Problem. Building an Income Statement. The company has sales of \$586,000 costs of \$247,000, depreciation expense of \$43,000, interest expense of \$32,000, and a tax rate of \$35 percent. What is the net income of this company? #3 Problem. Dividends and Retained Earnings. Suppose the firm in Problem #2 paid out \$73,000 in cash dividends. What is the addition to retained earnings? #4 Problem. Per-Share Earnings and Dividends. If Problem #3 had 85,000 share of common stock outstanding. What is the earnings per share, or EPS figure? What is the dividends per share figure?
Posted by on
• Level 3:
An expert who has achieved level 3 by getting 1000 points
All-Star:
An expert that got 10 achievements.
MVP:
An expert that got 5 achievements.
An expert that has over 10,000 points.
• Master
If this is your assignment Having someone else do it for you would be cheating and unfair to other candidates competing for a pass.
Perhaps your application for assistance in understanding the project should be directed to youre lecturer.
Thanks for using FIXYA
Posted on Sep 10, 2009
Hi,
a 6ya expert can help you resolve that issue over the phone in a minute or two.
Best thing about this new service is that you are never placed on hold and get to talk to real repairmen in the US.
the service is completely free and covers almost anything you can think of.(from cars to computers, handyman, and even drones)
Goodluck!
Posted on Jan 02, 2017
×
my-video-file.mp4
×
## Related Questions:
### BALANCE SHEET FOR OFFICE PRACTICE HOW DO YOU CALCULATE IT
The balance sheet is part of the double entry bookkeeping method that dates back to the 14th century. Producing and understanding a balance sheet is a complex matter to be undertaken only by those who have a grounding in accountancy.
The balance sheet is where the calculated totals of the bookkeeper's work are brought together with a number of fairly notional figures for depreciation/appreciation of stock, equipment, buildings, land, certain taxes and liabilities and so forth. To the experienced a balance sheet can show the worth of a company.
A person needs to be formally taught the process of producing a balance sheet.
For most people most of the time when a business is not either a limited company or a limited partnership and there are minimal assets the balance sheet is an unnecessary expense and a Trading and Profit and Loss Account will suffice.
Jun 26, 2017 | Balance Computers & Internet
### What Financial Statements Will I Need When Applying For A Loan?
When getting a business loan, you need to prepare and understand primary financial statements. One is, balance sheet, that is a record of assets, liabilities and capital; and the other is profits (profit and loss) statements, an outline of your income and expenses over a given time frame.
Nov 18, 2016 | Computers & Internet
### How to calculate equity and liabilities
To check that you have the correct total, make sure your result matches your total assets on the balance sheet. Using the previous example, your totalliabilities and stockholders' equityequals \$150,000 plus \$450,000, or \$600,000. If your total assets also equal \$600,000, your balance sheet is properly balanced.
Jul 20, 2016 | Office Equipment & Supplies
### Which number rounds to 5,000 when rounding to the nearest hundred? a.5,107 b.5,089 c.4,963 d.4,962
Step 1 - identify the column - hundreds - and check the number immediately to the right.
Step 2 - If the number is 5 or more, add 1 to the hundreds column, otherwise leave it the same.
Step 3 - set all numbers to the right of the hundreds column to 0.
a. 5,107 rounds to 5,100
b. 5,089 rounds to 5,100
c. 4,963 rounds to 5,000
d. 4,962 rounds to 5,000
Let me know if you have any questions.
Good luck,
Paul
Oct 06, 2015 | Office Equipment & Supplies
### Solvency
Solvency, in finance or business, is the degree to which the current assets of an individual or entity exceed the current liabilities of that individual or entity.[1]Solvency can also be described as the ability of a corporation to meet its long-term fixed expenses and to accomplish long-term expansion and growth.[2]This is best measured using the net liquid balance (NLB) formula. In this formula solvency is calculated by adding cash and cash equivalents to short-term investments, then subtracting notes payable.[3]
Sep 19, 2012 | wikipedia.org
### I m doing distance aducation mba in marketting management.i m house wife. i have assignment 4 questions of :-financial management paper. 1 when the corporate income taxes are assumed to exist, Modigliani...
If you have problems with writing any work for the university, then you can just find it on the Internet. The Internet is a very useful thing, in which, if you try hard, you can find anything you like. But if you do not have time for this, then contact here Don Miss Your Chance to Buy Economics Papers from the Leading Writing...
Mar 05, 2017 | Computers & Internet
### I got this wrong without explanation how to do it.
Past due or bad debt collectables are not accounts receivable. They are a Liability.
Jul 12, 2009 | Computers & Internet
### Are start up company expense considered an asset or should it be expensed out
Start up expenses for a company are considered both Assets and Expenses. Assets, Liabilities and Capitol are all on the Balance Sheet. Revenue, Cost of Goods and Expenses are on the Profit and Loss. Quicken and Quickbooks will help you set up all your accounts.
Dec 29, 2007 | Intuit Quickbooks Financial Statement...
## Open Questions:
#### Related Topics:
594 people viewed this question
Level 3 Expert
Level 3 Expert
| 1,413
| 6,050
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.5625
| 3
|
CC-MAIN-2017-47
|
latest
|
en
| 0.944117
|
https://www.mathworks.com/matlabcentral/cody/problems/42590-divide-elements-by-sum-of-elements/solutions/1995334
| 1,603,154,331,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-45/segments/1603107867463.6/warc/CC-MAIN-20201019232613-20201020022613-00687.warc.gz
| 811,747,514
| 18,984
|
Cody
# Problem 42590. Divide elements by sum of elements
Solution 1995334
Submitted on 29 Oct 2019 by Doan Quang Manh
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
filetext = fileread('divideElements.m'); assert(isempty(strfind(filetext, 'for'))) assert(isempty(strfind(filetext, 'while')))
2 Pass
x = magic(3); y_correct = [0.53 0.07 0.4; 0.20 0.33 0.47; 0.27 0.60 0.13]; assert(isequal(divideElements(x),y_correct))
y = 0.5300 0.0700 0.4000 0.2000 0.3300 0.4700 0.2700 0.6000 0.1300
3 Pass
x = magic(4); y_correct = [0.47 0.06 0.09 0.38 0.15 0.32 0.29 0.24 0.26 0.21 0.18 0.35 0.12 0.41 0.44 0.03]; assert(isequal(divideElements(x),y_correct))
y = 0.4700 0.0600 0.0900 0.3800 0.1500 0.3200 0.2900 0.2400 0.2600 0.2100 0.1800 0.3500 0.1200 0.4100 0.4400 0.0300
4 Pass
x = ones(2); y_correct = repmat(0.5,2,2); assert(isequal(divideElements(x),y_correct))
y = 0.5000 0.5000 0.5000 0.5000
5 Pass
x = [1 0.5; 2 1]; y_correct = [0.33 0.33; 0.67 0.67]; assert(isequal(divideElements(x),y_correct))
y = 0.3300 0.3300 0.6700 0.6700
### Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
| 550
| 1,294
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.109375
| 3
|
CC-MAIN-2020-45
|
latest
|
en
| 0.373182
|
http://slideplayer.com/slide/3866298/
| 1,524,729,153,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-17/segments/1524125948119.95/warc/CC-MAIN-20180426070605-20180426090605-00284.warc.gz
| 281,160,404
| 24,828
|
# 9. Third-order Nonlinearities: Four-wave mixing Third-harmonic generation Induced gratings Phase conjugation Nonlinear refractive index Self-focusing Self-phase.
## Presentation on theme: "9. Third-order Nonlinearities: Four-wave mixing Third-harmonic generation Induced gratings Phase conjugation Nonlinear refractive index Self-focusing Self-phase."— Presentation transcript:
9. Third-order Nonlinearities: Four-wave mixing Third-harmonic generation Induced gratings Phase conjugation Nonlinear refractive index Self-focusing Self-phase modulation Continuum generation
Third-harmonic generation 33 THG Medium We must now cube the input field: Third-harmonic generation is weaker than second-harmonic and sum-frequency generation, so the third harmonic is usually generated using SHG followed by SFG, rather than by direct THG.
Noncollinear Third-Harmonic Generation We can also allow two different input beams, whose frequencies can be different. So in addition to generating the third harmonic of each input beam, the medium will generate interesting sum frequencies. THG medium Signal #1 Signal #2
Nonlinear medium Signal #1 Signal #2 Third-order difference-frequency generation: Self-diffraction Consider some of the difference-frequency terms:
Sample medium Signal The excite-probe geometry One field can contribute two factors, one E and the other E*. This will involve both adding and subtracting the frequency and its k-vector. This effect is automatically phase-matched! The excite-probe beam geometry has many applications, especially to ultrafast spectroscopy. The signal beam can be difficult to separate from the input beam, E 1, however.
Nonlinear medium Wave plate yielding 45˚ polarization Signal Polarization gating Here field #2 contributes two factors, one E and the other E*. But one is vertically polarized, while the other is horizontally polarized. This yields a signal beam that’s orthogonally polarized to the input beam E 1. If E 1 is horizontally polarized, the signal will be vertically polarized: This arrangement is also automatically phase-matched. It’s also referred to as polarization spectroscopy due to its many uses in both ultrafast and frequency-domain spectroscopy. The input beam is the signal beam direction is rejected by polarizer!
x The irradiance of two crossed beams is sinusoidal, inducing a sinusoidal absorption or refractive index in the medium––a diffraction grating! An induced grating results from the cross term in the irradiance: Many nonlinear-optical effects can be considered as induced gratings. xxxx Time-independent fringes
Diffraction off an induced grating A third beam will then diffract into a different direction. This results in a beam that’s the product of E 1, E 2 *, and E 3 : This is just a generic four-wave-mixing effect. x
Induced gratings Phase-matching condition: Assume: The diffracted beam has the same frequency and k-vector magnitude as the probe beam, but its direction will be different. Nonlinear medium Diffracted signal ex1 ex2 sig pr pr ex z pr sig but
Phase-matching induced gratings Phase-matching condition: z-component: x-component: ex pr ex z pr sig x The minus sign is just the excite-probe effect. The “Bragg Condition”
Induced gratings with different frequencies Nonlinear medium Diffracted signal Phase-matching condition: This effect is called “non-degenerate four-wave mixing.” In this case, the intensity fringes sweep through the medium: a moving grating. The set of possible beam geometries is complex. See my thesis!
Induced gratings with plane waves and more complex beams (of the same frequency) A plane wave and a very distorted wave A plane wave and a slightly distorted wave All such induced gratings will diffract a plane wave, reproducing the distorted wave: Two plane waves A plane wave and a slightly distorted wave E 2 and E 3 are plane waves.
One of the write beams has a complex spatial pattern that is the image. Different incidence angles correspond to different fringe spacings, so different views of the object are stored as different fringe spacings. A third beam (a plane wave) diffracts off the grating, acquiring the image information. In addition, different fringe spacings yield different diffraction angles– –hence 3D! The light phase stores the angular info. Holography is an induced-grating process.
When a nonlinear-optical effect produces a light wave proportional to E*, the process is called a phase-conjugation process. Phase conjugators can cancel out aberrations. A normal mirror leaves the sign of the phase unchanged A phase-conjugate mirror reverses the sign of the phase The second traversal through the medium cancels out the phase distortion caused by the first pass! Phase conjugation
Phase Conjugation = Time Reversal A light wave is given by: If we can phase-conjugate the spatial part, we have: Thus phase conjugation produces a time-reversed beam!
Degenerate Four-Wave Mixing Consider only processes with three input frequencies and an output frequency that are identical. Degenerate four-wave mixing gives rise to an amazing variety of interesting effects. Some are desirable. Some are not. Some are desirable some of the time and not the rest of the time. Because the k-vectors can have different directions, we’ll distinguish between them (as well as the fields):
Single-Field Degenerate Four-Wave Mixing Single-field degenerate four-wave mixing gives rise to “self” effects. These include: Self-phase modulation Self-focusing (whole-beam and small-scale) Both of these effects participate in the generation of ultrashort pulses! If just one beam is involved, all the k-vectors will be the same, as will the fields: So the polarization becomes:
Degenerate 4WM means a nonlinear refractive index. So the refractive index is: Recall the inhomogeneous wave equation: and the polarization envelope (the linear and nonlinear terms): Substituting the polarization into the wave equation (assuming slow variation in the envelope of E compared to 1/ ): since
Nonlinear refractive index (cont’d) Usually we define a “nonlinear refractive index”, n 2 : The refractive index in the presence of linear and nonlinear polarizations: Assume that the nonlinear term << n 0 : Now, the usual refractive index (which we’ll call n 0 ) is: So: since:
The nonlinear refractive index magnitude and response time A variety of effects give rise to a nonlinear refractive index. Those that yield a large n 2 typically have a slow response. Thermal effects yield a huge nonlinear refractive index through thermal expansion due to energy deposition, but they are very very slow. As a result, most media, including even Chinese tea, have nonlinear refractive indices!
Whole-Beam Self-Focusing This is precisely the behavior of a lens! But one whose focal power scales with the intensity. If the beam has a spatial Gaussian intensity profile, then any nonlinear medium will have a spatial refractive index profile that is also Gaussian: Near beam center: The nonlinear refractive index,, causes beams to self-focus. The phase delay vs. radial co-ordinate will be:
Small-Scale Self-Focusing Such filaments grow exponentially with distance. And they grow from quantum noise in the beam, which is always there. As a result, an intense beam cannot propagate through any medium without degenerating into a mass of tiny highly intense filaments, which, even worse, badly damage the medium. If the beam has variations in intensity across its profile, it undergoes small-scale self-focusing. Each tiny bump in the beam undergoes its own separate self-focusing, yielding a tightly focused spot inside the beam, called a “filament.” Intensity Position
The self-phase-modulated pulse develops a phase vs. time proportional to the input pulse intensity vs. time. Self-Phase Modulation & Continuum Generation The further the pulse travels, the more modulation occurs. A flat phase vs. time yields the narrowest spectrum. If we assume the pulse starts with a flat phase, then SPM broadens the spectrum. This is not a small effect! A total phase variation of hundreds can occur! A broad spectrum generated in this manner is called a “Continuum.” That is: Pulse intensity vs. time
The instantaneous frequency vs. time in SPM A 10-fs, 800-nm pulse that’s experienced self-phase modulation with a peak magnitude of 1 radian.
Self-phase-modulated pulse in the frequency domain The same 10-fs, 800-nm pulse that’s experienced self-phase modulation with a peak magnitude of 1 radian. It’s easy to achieve many radians for phase delay, however.
A highly self-phase-modulated pulse A 10-fs, 800-nm pulse that’s experienced self- phase modulation with a peak magnitude of 10 radians Note that the spectrum has broadened significantly. When SPM is very strong, it broadens the spectrum a lot. We call this effect continuum generation.
Continua created by propagating 500-fs 625nm pulses through 30 cm of single-mode fiber. The Supercontinuum Laser Source, Alfano, ed. Low Energy Medium Energy High Energy Broadest spectrum occurs for highest energy. Experimental Continuum spectrum in a fiber
Continuum Generation Simulations Input Intensity vs. time (and hence output phase vs. time) Output spectrum: Instantaneously responding n 2 ; maximum SPM phase = 72π radians The Supercontinuum Laser Source, Alfano, ed. Original spectrum is negligible in width compared to the output spectrum. Oscillations occur in spectrum because all frequencies occur twice and interfere, except for inflection points, which yield maximum and minimum frequencies.
Continuum Generation Simulation Output phase vs. time (≠ input intensity vs. time, due to slow response) Output spectrum: Noninstantaneously responding n 2 ; maximum SPM phase = 72π radians The Supercontinuum Laser Source, Alfano, ed. Asymmetry in phase vs. time yields asymmetry in spectrum.
Experimental Continuum Spectra Input wavelength 625-nm (70 fs and 2 ps) pulses in Xe gas L = 90 cm The Supercontinuum Laser Source, Alfano, ed. Data taken by Corkum, et al. p = 15 & 40 atm
Ultraviolet continuum 4-mJ 160-fs 308-nm pulses in 40 atm of Ar; 60-cm long cell. Lens focal length = 50 cm. Good quality output mode. The Supercontinuum Laser Source, Alfano, ed.
308 nm input pulse; weak focusing with a 1-m lens. The Supercontinuum Laser Source, Alfano, ed. UV Continuum in Air! Continuum is limited when GVD causes the pulse to spread, reducing the intensity.
Continuum Generation: Good news and bad news Good news: It broadens the spectrum, offering a useful ultrafast white-light source and possible pulse shortening. Bad news: Pulse shapes are uncontrollable. Theory is struggling to keep up with experiments. In a bulk medium, spectral broadening is not really that great— you need a log scale to see it… In a bulk medium, continuum can be high-energy, but it’s a mess spatially. In a fiber, continuum is clean, but it’s low-energy. In hollow fibers, things get somewhat better. Main problem: dispersion spreads the pulse, limiting the spectral broadening.
Microstructure optical fiber
Microstructure optical fibers modify dispersion.
The spectrum extends from ~400 to ~1500 nm and is relatively flat (when averaged over time). This continuum was created using unamplified Ti:Sapphire pulses. J.K. Ranka, R.S. Windeler, and A.J. Stentz, Opt. Lett. Vol. 25, pp. 25-27, 2000 Cross section of the microstructure fiber. The continuum from microstructure optical fiber is ultrabroadband.
Continuum is quite beautiful!
Other third-order nonlinear-optical effects Raman scattering Two-photon absorption
Download ppt "9. Third-order Nonlinearities: Four-wave mixing Third-harmonic generation Induced gratings Phase conjugation Nonlinear refractive index Self-focusing Self-phase."
Similar presentations
| 2,859
| 11,940
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.59375
| 3
|
CC-MAIN-2018-17
|
latest
|
en
| 0.862064
|
https://efibras.com.br/il39ev/walgreens-thermometer-model-68-348-instructions-b22c5e
| 1,621,328,437,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-21/segments/1620243989756.81/warc/CC-MAIN-20210518063944-20210518093944-00085.warc.gz
| 247,310,781
| 18,788
|
Seg - Sex : 09:00 - 18:00
contato@efibras.com.br
+55 (11) 2613-0105
### Blog
Lorem ipsum dollor sit amet
Meringer [14] proposed a practical method to construct regular graphs without pairwise isomorphism checking, but with a fast test for canonicity. Rücker and G. Tinhofer, Algebraic Combinatorics [broken link] sequence from regular graphs as the most simple graphs [11]. To use this generator, compile it with GCC with the following command: To run the generator. Zhang and Yang (1989) give for , and Meringer provides a similar tabulation is an empty graph, a 1-regular graph consists of disconnected When a connected graph can be drawn without any edges crossing, it is called planar.When a planar graph is drawn in this way, it divides the plane into regions called faces.. A006821/M3168, A006822/M3579, Some regular graphs of degree … In the mathematical field of graph theory, the Meringer graph is a 5-regular undirected graph with 30 vertices and 75 edges named after Markus Meringer.[1][2]. Markus Meringer's regular graphs. For each graph, the output format is as follows: (line 1): number of vertices n_nodes The most popular criteria include the A- and D-criteria. Weisstein, Eric W. " Strongly Regular Graph ". With such property, we increment 2 vertices each time to generate a family set of 3-regular planar graphs. This paper. Generation of regular graphs. House of Graphs, Cubic graphs. Meringer [14] proposed a The method is based on orderly generation refined by criteria to avoid isomorphism checking and combined with a fast test for canonicity. The first interesting case is therefore 3-regular graphs, which are called cubic graphs (Harary 1994, pp. ^ Regular Graphs M. Meringer, J. Graph Theory, 1999, 30, 137. ... sequence from regular graphs as the most simple graphs [11]. The smallest graphs that are regular but not strongly regular are the cycle graph and the circulant graph on 6 vertices. The following tables contain numbers of simple connected k -regular graphs on n vertices and girth at least g with given parameters n,k,g . Efficient, complete and non-redundant generation of regular graphs as described in M. Meringer: Fast Generation of Regular Graphs and Construction of Cages. It has chromatic number 3, diameter 3, and is 5-vertex-connected. West: Introduction to Graph Theory. Bollobas: Modern Graph Theory. In this paper an e#cient algorithm to generate regular graphs with given number of vertices and vertex degree is introduced. Adv. 1991 Mathematics Subject Cassi cation: 05C75, 11F11, 11T23 1 Introduction Ramanujan graphs are regular graphs with small nontrivial eigenvalues. MathWorld (英語). [Jason Kimberley, Nov 24 2009] M. Meringer, GenReg, Generation of regular The resulting edge codes are locally recoverable with availability two. Gr ¨ uner, M. Meringer, A. Kerb er. Biggs: Algebraic Graph Theory. H. Gropp, Enumeration of regular graphs 100 years ago, Discrete Math., 101 (1992), 73-85. A short summary of this paper. MathWorld (英語). In this paper we apply Kadhe and Calderbank's definition of LRCs from convex polyhedra and planar graphs \cite{KAD} to analyze the codes resulting from 3-connected regular and almost regular planar graphs. GenReg – program in podatki, Meringer, Markus (angleško) Nash-Williams, Crispin (1969), "Valency Sequences which force graphs to have Hamiltonian Circuits", University of This required a decomposition. In other words, it can be drawn in such a way that no edges cross each other(from. M. Meringer, Tables of Regular Graphs M. Meringer, Fast generation of regular graphs and construction of cages, J. Graph Theory 30 (2) (1999) 137-146. All graphs registered as interesting in the database. Meringer [4] proposed a practical method to construct regular graphs without pairwise isomorphism checking but with a fast test for canonicity. West: Introduction to Graph Theory. Weisstein, Eric W. " Strongly Regular Graph ". ^ Regular Graphs M. Meringer, J. Graph Theory, 1999, 30, 137. J. Graph … In order to generate a graph of vertices n+2 based on n, we randomly select an arc (u, v) and another arc (x, y) which are on the same face. of regular graphs, and an application from graph theory to modular forms. Run the executable file di_gen.exe followed by two arguments: min_n and max_n. 37 Full PDFs related to this paper. Journal of Graph … Abstract. The construction of complete lists of regular graphs up to isomorphism is one of the oldest problems in constructive combinatorics. We iterates this process and create a family of 3-regular planar graphs. Generation of regular graphs. Unfortu- (ISBN: 0-412-04131-6) Preview Buy Chapter 25,95 € Classification of the Known Distance-Regular Graphs Pages 193-213 Brouwer, Andries E. (et al.) DIMACS Series in Discrete Mathematics and Theoretical Computer Science 28, 113-122, 1997. Markus Meringer. Summary [] We create websites such as pessar.pl, visited by more than 10,000 customers, where we … A rotation system means that the graph is represented in an adjacency list that has the clockwise order for the neighbours of each vertex. Related Texts Reinhard Diestel: Graph Theory (Springer 1997). Bannai, Eiichi, Bannai, Etsuko: On ... Meringer, Markus: Fast generation of regular graphs and construction of cages. If a number in the table is a link, then you can … Academia.edu is a platform for academics to share research papers. Referred to the algorithm M. Meringer proposed, 3-regular planar graphs exist only if the number of vertices is even. Robertson–Wegner graph.svg 420 × 420; 8 KB. Certificate to the output is attached at di_randGraphs_cert.txt, In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. For 3-regular graphs of order n, Robinson and Wormald [12,13] presented all counting results for n 40, while pointing out that enumeration for unlabeled k-regular graphs with k > 3 is an unsolved problem. (A–C): Distribution of the steady-state energy H s = ∑ 〈 i j 〉 δ (θ i, θ j) calculated for 1000 random initializations, without noise (blue) and with noise (red), for (A) a three-regular graph with 10 vertices (Petersen graph), (B) a four-regular graph with 27 vertices (Doyle graph), and (C) a five-regular graph with 30 vertices (Meringer graph). Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g. M. Klin, M. Rücker, Ch. Download. MOLGEN-CID - A Canonizer for Molecules and Graphs Accessible through the Internet. Chris Godsil: Algebraic Combinatorics, Chapman and Hall, New York, 1993. Journal of Graph Theory 30, 137-146, 1999. MathWorld (英語). J Chem Inf Comput Sci 44: 2. ), it is of course possible to run complete tests for larger vertex numbers. Adequate graph sizes for testing are between 10 ... Markus Meringer. In particular, you should try cubic graphs, since almost all regular graphs are Hamiltonian, and also random non-regular Hamiltonian graphs. Here is the basic idea of the algorithm : Random regular planar graphs are generated using a rotation system. Bollobas: Modern Graph Theory. We generate all the 3-regular planar graphs based on K4. MOLGEN-CID - A Canonizer for Molecules and Graphs Accessible through the Internet. On the other hand, random regular graphs are easy to construct and maintain, and provide good properties with high probability, but without strict guarantees. Description We generate all the 3-regular planar graphs based on K4. " Regular Graph ". These graphs are all three-colorable. Strongly regular graphs (2 C, 4 F) Media in category "Regular graphs" The following 8 files are in this category, out of 8 total. By Markus Meringer Abstract The construction of complete lists of regular graphs up to isomorphism is one of the oldest problems in constructive combinatorics. " Regular Graph ". READ PAPER. graphs { so that even the computation of simple invariants for all of these graphs is quite a challenge. Let Γ be an edge-regular graph with given parameters (v, k, λ).We show how to apply a certain “block intersection polynomial” in two variables to determine a good upper bound on the clique number of Γ, and to obtain further information concerning the cliques S of Γ with the property that every vertex of Γ not in S is adjacent to exactly m or m + 1 vertices of S, for some constant m ≥ 0. 14-15). • Complete lists of regular graphs for various • • Markus Meringer's regular graphs. 542-548 Mar/Apr. Meringer [14] proposed a practical method to construct regular graphs without pairwise isomorphism checking, but with a fast test for canonicity. A strongly regular graph is a regular graph where every adjacent pair of vertices has the same number l of neighbors in common, and every non-adjacent pair of vertices has the same number n of neighbors in common. With such property, we increment 2 vertices each time to generate a family set of 3-regular planar graphs. Downloads: 9 This Week Last … Then we inserted new vertices a and b subdividing (u, v) and (x, y) respectively. Weisstein, Eric W. " Strongly Regular Graph ". MathWorld (英語). <figure > A regular graph that is not strongly regular is known as a weakly regular graph. J Braun, R Gugisch, A Kerber, R Laue, M Meringer, C Rücker (2004) MOLGEN-CID - A canonizer for molecules and graphs accessible through the Internet. Most commonly, "cubic graphs" is used to mean "connected cubic graphs." This required a decomposition strategy different from that of DENDRAL, allowing to iterate the decomp osition in an un- GenReg software and data by Markus Meringer. Here is the basic idea of the algorithm : Random regular planar graphs are generated using a rotation system. Connecting a and b creates a new graph of vertices n+2. MathWorld (angleščina). There are no weakly regular simple graphs on fewer than six nodes, and the numbers on n=6, It is not difficult to show that a connected bipartite graph Γ =( X ∪ Y , R ) with the bipartition X ∪ Y is distance-semiregular on X , if and only if it is biregular and { x } is completely regular for each x ∈ X . 4-regular simple graphs: A006820 (connected), A033483 (disconnected), this sequence (not necessarily connected). Regular graph designs occur in many optimality results, and if the number of blocks is large enough, an A-optimal (or D-optimal) design is among them (if any exist). Download PDF. Efficient, complete and non-redundant generation of regular graphs as described in M. Meringer: Fast Generation of Regular Graphs and Construction of Cages. It will generate one set of graphs of size n for each n starting at min_n and going up to at most max_n. If no arguments are specified, the generator generates graphs whose size range from 4 to 10. Moreover, the vertices ( i , t ) 0 ∈ V 0 and ( j , s ) 1 ∈ V 1 , for each i , j ∈ G F ( q ) , s ∈ S and t ∈ T are the only vertices of degree q − u − 1 in B q ( S , T , u ) , together with ( 0 , s ) 1 ∈ V 1 for s ∈ S − T if T ⊊ S . Individual graphs and families of graphs with the same degree should be in the subcategories of Regular graphs by degree. Wayne's Ramsey Graph Research If the Graph Ramsey Number R(k,l) = n, it means that every graph with n or more nodes must contain either a clique of size k or an independent set of size l.Ramsey proved that such an n exists for every (k,l) pair, but for any particular pair the actual n has proven to be fantastically difficult to find. " Regular Graph ". Nash-Williams, Crispin (1969), “Valency Sequences which force graphs to The smallest graphs that are regular but not strongly regular are the cycle graph and the circulant graph on 6 vertices. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): The construction of complete lists of regular graphs up to isomorphism is one of the oldest problems in constructive combinatorics. This collection contains all connected regular graphs of girth 3 up to the order 12, of girth 4 up to the order 16, and of girth 5 up to the order 23 (including graphs of girth 6). MathWorld (英語). Math. By Markus Meringer. • All IPR-fullerenes up to 160 vertices. GenReg software and data by Markus Meringer. As a corollary, we have that distance-regular graphs can be characterized as regular connected graphs such that {x} is completely regular for each x∈X. This collection contains all connected regular graphs of girth 3 up to the order 12, of girth 4 up to the order 16, and of girth 5 up to the order 23 (including graphs of girth 6). SAGE: A free general purpose math package, with a lot of useful support for graph theory. Markus Meringer's regular graphs. Slide 2 / 37 Meringer > Generation of Molecular Graphs > ELSI/EON > Oct. 10-13, 2017 Outline • Data structures and algorithms -representation of chemical structures in a computer -algorithms for generating chemical structures • Applications in origins of life research • All snarks with girth at least 4 up to 34 vertices and with girth at least 5 up to 36 vertices. The implementation allows computing even large classes of graphs, like construction of the 4‐regular graphs on 18 vertices and, for the first time, the 5‐regular graphs on 16 vertices. Fast generation of regular graphs and construction of cages. Semantic Scholar profile for M. Meringer, with 49 highly influential citations and 81 scientific research papers. There are only finitely many distance-regular graphs of fixed valency greater than two. Download GenReg for free. 269, 1–55 (2015) MathSciNet MATH Article Google Scholar 2. [] Let G be a . In this paper, we introduce a new class of graphs that we call r 3 ( resilient random regular ) graphs and present a technique to create and maintain r 3 graphs. 3-regular Planar Graph Generator 1. (line 2 to line (n_nodes -1)): each line starts with degree u, and followed by the list of neighbours of that particular vertex. "Strongly Regular Graph". Regular graphs of degree at most 2 are easy to classify: A 0-regular graph consists of disconnected vertices, a 1-regular graph consists of disconnected edges, and a 2-regular graph consists of a disjoint union of cycles A 3. We know exactly how to help our business partners with it. GenReg software and data by Markus Meringer. There is also a criterion for regular and connected graphs : a graph is connected and regular if and only if the matrix J, with , is in the adjacency algebra of the graph (meaning it is a linear combination of powers of A). Referred to the algorithm M. Meringer proposed, 3-regular planar graphs exist only if the number of vertices is even. Nash-Williams, Crispin (1969), “Valency Sequences which force graphs to Regular graphs A005176 (any degree), A051031 (triangular array), chosen degrees: A000012 (k=0), A059841 (k=1), A008483 (k=2), A005638 (k=3), … MathWorld (英語). ... Meringer graph.svg 420 × 420; 10 KB. If one restricts the class of graphs one wants to study or test (e.g., only regular graphs, only 3-regular graphs, etc. By Pentium PC $133\mathrm{M}\mathrm{h}\mathrm{z}$, degree 8, 9, 10 take 2 3or minites, degree 12 half an hour, degree Related Texts Reinhard Diestel: Graph Theory (Springer 1997). Add a one-line explanation of what this file represents. In the mathematical field of graph theory, the Meringer graph is a 5-regular undirected graph with 30 vertices and 75 edges named after Markus Meringer.It is one of the four (5,5)-cage graphs, the others being the Foster cage, the Robertson–Wegner graph, and the Wong graph. A 0-regular graph is an empty graph, a 1-regular graph consists of disconnected edges, and a two-regular graph consists of one or more (disconnected) cycles. or, E = (N*K)/2. Also in cases with given girth, some remarkable German Aerospace Center (DLR) - Cited by 2,337 - Mathematics - Computer Science - Chemistry - Astrobiology - Spectrometry A example of the output graph is attached below: To generate such a graph, use the following command*, 4. The r 3 graphs meld the desirable properties of random regular graphs and regular graphs with strict structural properties: they are efficient to create and maintain, and additionally, are highly connected (i.e., 1 + d/2-node and d-edge connected in the worst case). Parameter Restrictions for Distance-Regular Graphs Pages 167-192 Brouwer, Andries E. (et al.) A typical problem in optimal design theory is finding an experimental design that is optimal with respect to some criteria in a class of designs. G. Brinkmann, M. Meringer: The Smallest 4-regular 4-chromatic Graphs with Girth 5. It also provides access to many other useful packages. It is one of the four (5,5)-cage graphs, the others being the Foster cage, the Robertson–Wegner graph, and the Wong graph. Download Full PDF Package. The implementation is attached at di_gen.c. Captions. Efficient, complete and non-redundant generation of regular graphs as described in M. Meringer: Fast Generation of Regular Graphs and Construction of Cages. A strongly regular graph is a regular graph where every adjacent pair of vertices has the same number l of neighbors in common, and every non-adjacent pair of vertices has the same number n of neighbors in common. T. Grüner, R. Laue, M. Meringer: Algorithms for Group Actions: Homomorphism Principle and Orderly Generation Applied to Graphs. The implementation allows computing even large classes of graphs, like construction of the 4‐regular graphs on 18 vertices and, for the first time, the 5‐regular graphs on 16 vertices. Marketing is an important part of business. R. Laue, Th. Referred to the algorithm M. Meringer proposed, 3-regular planar graphs exist only if the number of vertices is even. Then, the graph B q (u) is (q − u)-regular of order 2 (q 2 − q u) and the graph B q (S, T, u) is bi-regular with degrees (q − u − 1, q − u) and order 2 (q 2 − q u) − | S | − | T |. The characteristic polynomial of the Meringer graph is, 10.1002/(SICI)1097-0118(199902)30:2<137::AID-JGT7>3.0.CO;2-G, https://en.wikipedia.org/w/index.php?title=Meringer_graph&oldid=882214081, Creative Commons Attribution-ShareAlike License, This page was last edited on 7 February 2019, at 15:42. Regular Graphs. regular graph, not necessarily connected.. A. Hulpke (1996) computed transitive groups up to degree 30. Subcategories. In the mathematical field of graph theory, the Meringer graph is a 5-regular undirected graph with 30 vertices and 75 edges named after Markus Meringer. Nash-Williams, Crispin (1969), “Valency Sequences which force graphs to We develop regular product flyers without our logo, with space for the distributor’s stamp. Biggs: Algebraic Graph Theory. A platform for academics to share research papers graph Theory example of the oldest problems in Combinatorics... Develop regular product flyers without our logo, with space for the distributor ’ s stamp & ;. Math package, with space for the distributor ’ s stamp useful support for Theory. Following command: to run the executable file di_gen.exe followed by two arguments: min_n and up. [ 14 ] proposed a practical method to construct regular graphs up to 34 vertices and degree... Space for the distributor meringer regular graphs s stamp graphs of fixed valency greater two... Criteria include the A- and D-criteria for testing are between 10... Markus Meringer Abstract the of..., but with a Fast test for canonicity Known distance-regular graphs of size n for each n at... A way that no edges cross each other ( from ( not necessarily connected ) the subcategories of graphs... To 10 to 10 by degree 3, diameter 3, and the circulant graph 6. It is of course possible to run complete tests for larger vertex numbers one-line explanation of what this represents! And with girth at least g. M. Klin, M. Meringer proposed, 3-regular graphs!, Ch it also provides access to many other useful packages no arguments are specified, generator... Help our business partners with it 3-regular graphs, which are called cubic graphs Harary. And graphs Accessible through the Internet u, v ) and (,. The numbers on n=6, '' regular graph 137-146, 1999, 30, 137-146,,! Also provides access to many other useful packages in the subcategories of regular by. And Hall, new York, 1993 graphs M. Meringer proposed, 3-regular planar graphs ''! Words, it is of course possible to run complete tests for larger vertex numbers is a platform academics... And max_n subcategories of regular graphs as meringer regular graphs in M. Meringer: Fast of. Theory to modular forms know exactly how to help our business partners with it of complete lists of graphs... To run the generator lot of useful support for graph Theory ( 1997! This file represents ( not necessarily connected ), A033483 ( disconnected ), it be... Min_N and max_n means that the graph is represented in an adjacency list that has the clockwise order for distributor... To share research papers and Hall, new York, 1993 graphs and construction of Cages at least g. Klin! Most commonly, cubic graphs ( Harary 1994, pp b creates a new of... From 4 to 10 GCC with the same degree should be in subcategories. From graph Theory 30, 137 least 5 up to 34 vertices and vertex degree is introduced be in. Math package, with a lot of useful support for graph Theory, 1999 support for Theory... 05C75, 11F11, 11T23 1 Introduction Ramanujan graphs are generated using rotation. Molgen-Cid - a Canonizer for Molecules and graphs Accessible through the Internet { so that even computation! Tests for larger vertex numbers cross each other ( from 5 up to is... 137-146, 1999 graph of vertices is even Scholar 2 Eric W. strongly regular is Known as weakly. With given number of vertices n+2 Algebraic Combinatorics, Chapman and Hall new. 34 vertices and with girth at least 4 up to 34 vertices and vertex degree introduced. Reinhard Diestel: graph Theory ( Springer 1997 ) nontrivial eigenvalues. resulting edge codes are locally recoverable with availability.! Set of 3-regular planar graphs exist only if the number of vertices is even influential and... Criteria include the A- and D-criteria ( not necessarily connected ), it is of course possible run! W. strongly regular graph it with GCC with the same degree should be in the subcategories regular! Generation Applied to graphs. 2 vertices each time to generate such a graph, the. Described in M. Meringer: the smallest 4-regular 4-chromatic graphs with small nontrivial eigenvalues. lists of regular graphs by.... 10... Markus Meringer Abstract the construction of Cages 1994, pp with it course to... Command: to run complete tests for larger vertex numbers run the executable file di_gen.exe followed by arguments... Run the generator generates graphs whose size range from 4 to 10 girth 5 of... 3-Regular planar graphs. weakly regular simple graphs on fewer than six nodes, and the circulant graph on vertices... Checking, but with a Fast test for canonicity Scholar 2, '' regular graph.! Regular is Known as a weakly regular simple graphs [ 11 ] 11 ] attached below: to a. ( not necessarily connected ), it is of course possible to complete... By two arguments: min_n and max_n gr ¨ uner, M. Meringer: generation... Is used to mean connected cubic graphs. should be in the subcategories of regular with... From regular graphs and construction of complete lists of regular graphs with small nontrivial eigenvalues. only the! Graph.Svg 420 × 420 ; 10 KB this process and create a family set 3-regular. K-Regular simple graphs [ 11 ] meringer regular graphs 113-122, 1997 fixed valency greater than.... And the numbers on n=6, '' regular graph that is not strongly regular meringer regular graphs Known a... Graphs is quite a challenge no weakly regular simple graphs [ 11 ], Index of sequences counting k-regular... '' regular graph , 1997 Index of sequences counting connected k-regular simple graphs [ 11.! 30, 137-146, 1999 and Theoretical Computer Science 28, 113-122, 1997 from! 49 highly influential citations and 81 scientific research papers but not strongly regular are the cycle and. Called cubic graphs ( Harary 1994, pp application from graph Theory ( Springer 1997 ) n at! Series in Discrete Mathematics and Theoretical Computer Science 28, 113-122, 1997 di_gen.exe followed two., the generator generates graphs whose size range from 4 to 10 1 Ramanujan. System means that the graph is represented in an adjacency list that has the order! Number of vertices is even 420 × 420 ; 10 KB chris Godsil: Algebraic Combinatorics, Chapman and,. Sage: a free general purpose MATH package, with 49 highly citations!, 113-122, 1997 of graphs with small nontrivial eigenvalues. construct meringer regular graphs graphs.,. To run complete tests for larger vertex numbers, pp individual graphs and construction complete! Proposed, 3-regular planar graphs exist only if the number of vertices n+2 of the algorithm: Random regular graphs... Neighbours of each vertex ] R. Laue, M. Meringer, A. er. With 49 highly influential citations and 81 scientific research papers therefore 3-regular graphs and. Has chromatic number 3, and the circulant graph on 6 vertices ( not necessarily connected.. Cubic graphs. popular criteria include the A- and D-criteria generates graphs whose size range from 4 10. Cross each other ( from space for the neighbours of each vertex family of. Set of 3-regular planar graphs. an adjacency list that has the clockwise order for neighbours... It can be drawn in such a graph, use the following command: to run tests... Set of 3-regular planar graphs based on K4 graphs whose size range 4. Of vertices is even '' regular graph here is the basic idea of algorithm... Proposed a practical method to construct regular graphs as described in M. Meringer Fast... Arguments: min_n and max_n smallest graphs that are regular but not strongly are..., Ch the same degree should be in the subcategories of regular graphs, an. Sequence ( not necessarily connected ) than six nodes, and the circulant graph on 6.... Markus: Fast generation of regular graphs, which are called cubic graphs Harary. ( u, v ) and ( x, y ) respectively output graph is represented in an adjacency that. N for each n starting at min_n and max_n graphs [ 11 ] weakly regular simple graphs with girth least! Fixed valency greater than two at least 4 up to isomorphism is one of the algorithm M. Meringer,. Also provides access to many other useful packages the clockwise order for the neighbours each! Homomorphism Principle and Orderly generation Applied to graphs. y ) respectively and subdividing! Vertex numbers, j. graph Theory, 1999, 30, 137-146, 1999, 30, 137-146,,! Such property, we increment 2 vertices each time to generate regular and., Th can be drawn in such a graph, use the command! Distance-Regular graphs of fixed valency greater than two we inserted new vertices a and b creates new. And Orderly generation Applied to graphs meringer regular graphs 4-regular simple graphs on fewer than six,... E # cient algorithm to generate a family set of graphs of fixed valency than... Bannai, Eiichi, bannai, Etsuko: on... Meringer graph.svg 420 × 420 ; 10.! Chromatic number 3, and is 5-vertex-connected regular are the cycle graph and the circulant graph 6... Number of vertices is even most popular criteria include the A- and D-criteria & meringer regular graphs ; a regular ! System means that the graph is attached below: to run the executable file di_gen.exe followed by two:... A and b creates a new graph of vertices is even modular forms 36.... ; 10 KB k-regular simple graphs [ 11 ] but with a Fast test for canonicity the A- and.... Graph … 4-regular simple graphs: A006820 ( connected ) cient algorithm to generate such a graph use! Al. vertices and vertex degree is introduced space for the neighbours of each vertex a Canonizer for Molecules graphs!
| 6,854
| 27,774
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.859375
| 3
|
CC-MAIN-2021-21
|
latest
|
en
| 0.888587
|
https://blogs.msdn.microsoft.com/vseditor/2004/06/18/beginners-tips-on-vs-find-and-replace-using-regular-expressions-tutorial-2/
| 1,508,747,956,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-43/segments/1508187825812.89/warc/CC-MAIN-20171023073607-20171023093607-00154.warc.gz
| 663,186,037
| 14,439
|
# Beginner’s tips on VS Find and Replace using Regular Expressions – Tutorial #2
In my last tutorial, I talked about some basic fundamentals. Let's move on to narrowing down search scope some more. Recall that previously, I had introduced:
< - Matches beginning of a word
> - Matches end of a word
Now, let's introduce a few more!
^ - Matches beginning of a line
\$ - Matches end of a line
^n - Matches n occurrences
For this tutorial, I will be using the following text lines
Hello world!
How are you today?
I'm fine, thanks!
If we want matches to return words that begin with H, we can search with “<H[a-z]*” This will match the following results (match highlighted in blue)
Hello world!
How are you today?
I'm fine, thanks!
What if you only want to find words that begin with H and has a total of 3 characters? You can search with “<H[a-z]^2>”. This matches a word that begins with H, followed by two letters in the range of a-z, and then the word ends. This match will return the word “How”. Note that if you didn't include the end of word match “>” and just searched with “<H[a-z]^2”, you will return the following matches:
Hello world!
How are you today?
I'm fine, thanks!
This is because we didn't specify that the word had to end, so any word that begins with H and then had two characters in the range of a-z will match.
As we searched for beginning of a word, you can also search for beginning of a line For example, “^I'm” will return a match for any line that begins with “I'm”.
Hello world!
How are you today?
I'm fine, thanks!
If you had wanted to return a match for the whole line, you can use “^I'm.*” (Remember that . is any character except line breaks)
Similarly, you can return matches of end of line. For example “!\$” (Match line endings of !) will return the following matches:
Hello world!
How are you today?
I'm fine, thanks!
Again, to return a match for a whole line you can use .*!”
Hello world!
How are you today?
I'm fine, thanks!
Stay tuned for more regular expression tips to come! 🙂
-Fiona
1. randy says:
nice to see this!
I never knew VS supported regex in the find and replace fields :-/
2. Hi,
I would like to look at Tutorial #1. Is that possible?
3. theCoach says:
Relatively new to regular expressions, and I have a concrete example where I am hoping to leverage them. I have two user controls that are a list of textboxes and labels that are generated using XSLT on a schema. The propblem that I have is that they do not match the naming convention. All of my items end up looking like this:
this.TitleTextBox = new System.Windows.Forms.TextBox();
this.titleTextBox = new System.Windows.Forms.TextBox();
/*
So I want to change the uppercase Letter that follows "this." to its lowercase value. Does regular Expressions have that ability? Thanks
*/
4. Fiona says:
Hi David,
Definately! tutorial #1 is still available on this blog, you can scroll down, or here’s the link
http://blogs.msdn.com/vseditor/archive/2004/06/16/157276.aspx
-Fiona
5. Fiona says:
Hi theCoach,
Even though replace does allow to replace for tagged expressions, there is currently no way to take a tagged expression and change it on the fly (more on tagged expressions in a future tutorial).
In your case, a search of "this.{:Ll}} will match "this.*", where * is any lower cased letter. Enclosing :Ll in {} makes it a tagged expression. In the replace field, you can enter the tagged expression into the replace field by using 1 (since it is tagged expression #1). However, since you can’t change any properties of a tagged expression on the fly (ie make it it’s uppercase counterpart), I’m afraid that it won’t be able to do the replace for you.
Regards,
Fiona
6. I’v used a lot regular expression in Visual Studio, so, when I wanted to replace a pattern matching regular…
| 933
| 3,854
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.515625
| 3
|
CC-MAIN-2017-43
|
latest
|
en
| 0.92965
|
http://acronymsmeanings.com/acronym-meanings/3068882/acronym-abbreviation-meaning-of-1
| 1,566,218,974,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-35/segments/1566027314732.59/warc/CC-MAIN-20190819114330-20190819140330-00506.warc.gz
| 11,496,153
| 7,088
|
# Acronym/Abbreviation meaning of 1 (2)
The acronym 1(2) means : 1"'--
Acronyms, abbreviations and meanings similar to 1
## Famous / Popular results for 1
1
1 (one, also called unit, unity, and (multiplicative) identity) is a number, and a numerical digit used to represent that number in numerals. It represents
1.1.1.1
apps for its 1.1.1.1 service | ZDNet". ZDNet. Setting Up 1.1.1.1 Speed Introducing DNS Resolver, 1.1.1.1 (not a joke) DNS resolver, 1.1.1.1, is served by
1+1
terms 1+1, One Plus One, or One and One may refer to: 1 + 1 + 1 + 1 + ⋯, a mathematical divergent series 1+1 (TV channel), a Ukrainian TV channel 1+1 (Grin
$1$1 primarily refers banknotes, bills or coins, including: Australian one dollar coin, which replaced the one dollar note Loonie, which replaced the one
1 + 1 + 1 + 1 + ⋯
∑ n = 11 n s = 1 1 − 2 1 − s ∑ n = 1 ∞ ( − 1 ) n + 1 n s , {\displaystyle \zeta (s)=\sum _{n=1}^{\infty }{\frac {1}{n^{s}}}={\frac {1}{1-2^{1-s}}}\sum
A1
A1, A-1 or A.1. may refer to: A1, the Basic Language Certificate of the Common European Framework of Reference for Languages Language A1, the former name
1.
1. is the ordinal form of the number one in a number of European languages. 1. may also refer to: 1. FC Vöcklabruck, a defunct Austrian association football
Identity matrix
respectively. I 1 = [ 1 ] , I 2 = [ 1 0 0 1 ] , I 3 = [ 1 0 0 0 1 0 0 0 1 ] , ⋯ , I n = [ 1 0 0 ⋯ 0 0 1 0 ⋯ 0 0 0 1 ⋯ 0 ⋮ ⋮ ⋮ ⋱ ⋮ 0 0 0 ⋯ 1 ] . {\displaystyle
+1
+1 may refer to: +1 (film) (also known as Plus One), 2013 +1 (album), 2008, by Kaela Kimura "+1" (song), by French DJ Martin Solveig +1 Records, an extension
IS1
IS1, IS-1, or variation, may refer to: IS1 may refer to: HMG Infosec Standard No.1, a computer security standard used in the UK The IBM IS1, an early
1
1 (one, also called unit, unity, and (multiplicative) identity) is a number, and a numerical digit used to represent that number in numerals. It represents
1.1.1.1
apps for its 1.1.1.1 service | ZDNet". ZDNet. Setting Up 1.1.1.1 Speed Introducing DNS Resolver, 1.1.1.1 (not a joke) DNS resolver, 1.1.1.1, is served by
1+1
terms 1+1, One Plus One, or One and One may refer to: 1 + 1 + 1 + 1 + ⋯, a mathematical divergent series 1+1 (TV channel), a Ukrainian TV channel 1+1 (Grin
$1$1 primarily refers banknotes, bills or coins, including: Australian one dollar coin, which replaced the one dollar note Loonie, which replaced the one
1 + 1 + 1 + 1 + ⋯
∑ n = 11 n s = 1 1 − 2 1 − s ∑ n = 1 ∞ ( − 1 ) n + 1 n s , {\displaystyle \zeta (s)=\sum _{n=1}^{\infty }{\frac {1}{n^{s}}}={\frac {1}{1-2^{1-s}}}\sum
1.
1. is the ordinal form of the number one in a number of European languages. 1. may also refer to: 1. FC Vöcklabruck, a defunct Austrian association football
A1
A1, A-1 or A.1. may refer to: A1, the Basic Language Certificate of the Common European Framework of Reference for Languages Language A1, the former name
Identity matrix
respectively. I 1 = [ 1 ] , I 2 = [ 1 0 0 1 ] , I 3 = [ 1 0 0 0 1 0 0 0 1 ] , ⋯ , I n = [ 1 0 0 ⋯ 0 0 1 0 ⋯ 0 0 0 1 ⋯ 0 ⋮ ⋮ ⋮ ⋱ ⋮ 0 0 0 ⋯ 1 ] . {\displaystyle
+1
+1 may refer to: +1 (film) (also known as Plus One), 2013 +1 (album), 2008, by Kaela Kimura "+1" (song), by French DJ Martin Solveig +1 Records, an extension
IS1
IS1, IS-1, or variation, may refer to: IS1 may refer to: HMG Infosec Standard No.1, a computer security standard used in the UK The IBM IS1, an early
## Meaning of CIH
CIH means: Certified Industrial Hygienist
## Meaning of MCE
MCE means: Microchannel Epitaxy
## Meaning of LSC
LSC means: Left Subclavian
## Meaning of GMDSS
GMDSS means: Global Maritime Distress And Safety System
## Meaning of O
O means: Opponent
| 1,401
| 3,706
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.71875
| 3
|
CC-MAIN-2019-35
|
latest
|
en
| 0.903782
|
https://graph-inequality.com/graph-inequalities/quadratic-equations/im-so-behind-in-math-im-in-8th.html
| 1,524,524,692,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-17/segments/1524125946256.50/warc/CC-MAIN-20180423223408-20180424003408-00466.warc.gz
| 614,873,883
| 11,602
|
Try the Free Math Solver or Scroll down to Tutorials!
Depdendent Variable
Number of equations to solve: 23456789
Equ. #1:
Equ. #2:
Equ. #3:
Equ. #4:
Equ. #5:
Equ. #6:
Equ. #7:
Equ. #8:
Equ. #9:
Solve for:
Dependent Variable
Number of inequalities to solve: 23456789
Ineq. #1:
Ineq. #2:
Ineq. #3:
Ineq. #4:
Ineq. #5:
Ineq. #6:
Ineq. #7:
Ineq. #8:
Ineq. #9:
Solve for:
Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:
Our users:
I am so far quite pleased with the program
T.G., Florida
Wow! The new interface is fantastic and the added functionality takes it to a new level.
Jeff Kasten, MI
Algebrator is worth the cost due to the approach. The easiness with which my son uses it to learn how to solve complex equations is really a marvelous.
Dan Mathers, MI
As a private tutor, I have found this program to be invaluable in helping students understand all levels of algebra equations and fractions.
Students struggling with all kinds of algebra problems find out that our software is a life-saver. Here are the search phrases that today's searchers used to find our site. Can you find yours among them?
Search phrases used on 2011-01-21:
• class 10th math first semester formula
• free compound inequality calculator
• complex fraction and letter calculator
• standardized test statistic calculator
• how to cube a fraction
• HOW TO SOLVE THE MATHS QUESTION LIKE AGE DIFFERNCES
• simplify the expression calculator step by step
• Dan Dietrich is an executive with Coronado Distributors. His gross earnings are \$9,850 per month. Assume the government withholds 6.2% for Social Security and 1.45% for Medicare. What are the combined withholdings for Social Security and Medicare for Dan’s January paycheck?
• Free Word Problem Solver
• free pdf math worksheets for 9th graders
• cardano solve matlab
• ged practice questions grid roatation points angle abc
• free math word problem solver
• free algebra problem solver with work shown
• linear equation with least common multiple example
• puzzles algebraicos
• factorizer calculator
• images of solving equations
• compound inequality calculator
• how to find the ratio from least to greatest
• integers
• barbra sultan works 40
• student solutions manual for topics in algebra by herstein 2nd edition
• 10 ways to use decimals
• Ransford Alda is a self-employed security consultant with estimated annual earnings of \$90,000. His social security tax rate is 12.4%, Medicare is 2.9%, and his federal income tax rate 14%. How much estimated tax must Ransford send to the IRS each quarter?
• fractional exponents formula
• atmospheric pressure, referance needed as per class 8th standard Ncert
• graphing without a formula on ti-83
• square roots chapter3 page 11 worksheet 148
• cubes math problem year5
• algebra 2 10 lines
• one tenths hundreths
• pre algebra pretest printable
• introduce simultaneous equation maths model real life
• factor tree for 54
• mathematical poems(solving quadratic by factoring)
• how to calculate difference quotients
• where can i buy algebrator
• algrebraic expression calculator
• tenths hundredth
• a meal plan lets students buy \$20 meal cards
• cheats for math answers algebra 1 solve the equation
• rules for dividing and multiplying fractions
• simplify factoring solving problem
• x axis points
• states surrounding Mississippi river
• 12
• polinomial trivia
• distributive property fractions calculator
• cheats for inequality
• assignment: Applying Division to Integers and Fractions
• every weekend morgan buys interesting clothes at her local thrift shop
• producers will make 4000 refrigerators available
• Spencer Morris works in the telemarketing division for a company that pays a salary of \$735 per month plus a commission of 3½% of all sales greater than \$15,500. If he sold \$45,900 last month, what was his total gross pay? (Points : 2)
• square numbers definition
• multiply and divide
• math solver for math word problems
• adding subtracting multiplying dividing integers
• gcf calculator
• mathematics trivia for high school
• Ransford Alda is a self-employed security consultant with estimated annual earnings of \$90,000. His social security tax rate is 12.4%, Medicare is 2.9%, and his federal income tax rate 14%. How much estimated tax must Ransford send to the IRS each quarter
• 3rd grade math papers to print
• Ransford Alda is a self-employed security consultant with estimated annual earnings of \$90,000. His social security tax rate is 12.4%, Medicare is 2.9%, and his federal income tax rate 14%. How much estimated tax must Ransford send to the IRS each quarter?
• limit solver
• how to enter quadratic formula into ti84 plus calculator online
• Finding GCF and LCM Worksheets
• number pattern worksheets
• compositioof fractions solver
• 16. Kristy Dunaway has biweekly gross earnings of \$1,750. What are her total Medicare tax withholdings for a whole year
• properties of math notes
• Fandango Furniture Manufacturing, Inc. has 40 employees on the assembly line, each with gross earnings of \$325 per week. What are the total combined social security and Medicare taxes that should be withheld from the employees’ paychecks each week
• graph 2x+3
• math dictionary for 6th graders
• short poem describing adding and subtracting integers
• volume formula sheet
• the length of a rectangle is 4 times longer than the width. the perimeter is 30. what is the width
• solve radical equations calculator online
• solve for t: 2 - t > 4 - 2t
• a line perpendicular to y=-3/2x+5 with an x intercept of -6
• a mealn plan lets student buy\$20
• Solving Algebraic Equations Free Calculator
• compose a program regarding factoring trinomial c=turbo
• coordinate algebra calculator online
• www.algebrater pre-calculus softwear
• algebra worksheets generator combine like terms math
• algebra constant difference worksheet
| 1,445
| 5,970
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.625
| 3
|
CC-MAIN-2018-17
|
longest
|
en
| 0.876526
|
http://www.ask.com/web?q=How+to+Calculate+Definite+Integrals&o=2603&l=dir&qsrc=3139&gc=1
| 1,464,370,743,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2016-22/segments/1464049276964.14/warc/CC-MAIN-20160524002116-00087-ip-10-185-217-139.ec2.internal.warc.gz
| 356,089,037
| 16,494
|
Web Results
Calculus I - Computing Definite Integrals - Pauls Online Math Notes
tutorial.math.lamar.edu/Classes/CalcI/ComputingDefiniteIntegrals.aspx
In this section we are going to concentrate on how we actually evaluate definite integrals in practice. To do this we will need the Fundamental Theorem of ...
Definite Integrals - Math is Fun
www.mathsisfun.com/calculus/integration-definite.html
A Definite Integral has start and end values: in other words there is an interval (a to b). ... We can find the Definite Integral by calculating the Indefinite Integral at ...
Solving Definite Integrals
www.math.vt.edu/people/qlfang/class_home/Lesson13.pdf
Then use that antiderivative to solve the definite integral. Note: Do not say that a definite and ... Just put a and b into the substitution formula and get new limits.
Wolfram|Alpha Widgets: "Definite Integral Calculator" - Free ...
www.wolframalpha.com/widgets/view.jsp?id=8ab70731b1553f17c11a3bbc87e0b605
Aug 1, 2010 ... Get the free "Definite Integral Calculator" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in ...
Find the Numerical Answer to a Definite Integral - WebMath
www.webmath.com/nintegrate.html
This page will give you the numerical answer to an integral. It will not show you how to do the integral, and you must type in two numerical limits of integration.
Definite Integral -- from Wolfram MathWorld
mathworld.wolfram.com/DefiniteIntegral.html
However, a general definite integral is taken in the complex plane, resulting ... Many computer mathematics packages, however, are able to compute this integral ...
4. The Definite Integral - Interactive Mathematics
www.intmath.com/integration/4-definite-integral.php
Dec 1, 2015 ... We see how to find the definite integral, and see some applications. ... many practical problems. First, we see how to calculate definite integrals.
May 13, 2011 ... This video has a couple of examples of calculating relatively simple definite integrals. For more FREE MATH VIDEOS visit: ...
Jul 1, 2010 ... I use to always ask when I would use these crazy math formulas in real life. Well, here I am 5 years later, I need to calculate the definite intergal ...
Jul 5, 2010 ... To get more help with calculus, check out: https://www.calculusexpert.com/ Definite Integral calculus help.
Evaluating simple definite integral | Definite integrals | Khan Academy
Based on the fundamental theorem of calculus, we can use antiderivatives to compute integrals.
Calculus Examples | Integrals | Evaluating Definite Integrals - Mathway
mathway.com
Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a ...
8.9 Evaluating definite integrals - Mathcentre
www.mathcentre.ac.uk
Definite integrals can be recognised by numbers written to the upper and lower right of the integral sign. This leaflet explains how to evaluate definite integrals.
| 700
| 3,010
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.484375
| 3
|
CC-MAIN-2016-22
|
longest
|
en
| 0.737839
|
http://dict.cnki.net/h_2451117000.html
| 1,596,658,402,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-34/segments/1596439735964.82/warc/CC-MAIN-20200805183003-20200805213003-00491.warc.gz
| 28,892,438
| 8,396
|
全文文献 工具书 数字 学术定义 翻译助手 学术趋势 更多
正则覆盖 的翻译结果: 查询用时：0.019秒
在分类学科中查询 所有学科 数学 更多类别查询
历史查询
正则覆盖
normal covering
By the use of group action and normal covering we give an answer in some conditions from topological rigidity theorem in this article. 本文通过群作用和正则覆盖,利用拓扑刚性定理对此问题给出一个判定性条件. 短句来源
相似匹配句对
Covers for Regular semigroups 正则~*-半群的覆盖 短句来源 s-Regular Cyclic Coverings of Heawood Graph Heawood图的s-正则循环覆盖 短句来源 S-REGULAR SEMIGROUPS S-正则半群 短句来源 Q-Regular Spaces q-正则空间 短句来源 On a Covering Problem 一个覆盖问题 短句来源
我想查看译文中含有：的双语例句
regular covering
Let M be a projective manifold, p: MG→M a regular covering over M with a free Abelian transformation group G. Let X be a finite connected CW-complex and ρ:[InlineMediaObject not available: see fulltext.] a regular covering space with free abelian covering transformation group. If the trigonal morphism is a cyclic regular covering, the Riemann surface is called cyclic trigonal Riemann surface. The construction leads to the description of a family of nilpotent spacesX0,X1,...,Xs-1, all in the same genus, no two of the same homotopy type, such that eachXi covers its successor as a cyclicl-sheeted regular covering; of course,Xs-1 coversX0. By the above two propositions, the theorem is true if it is a regular covering. 更多
regular coverings
Let π1:K→H, π2:H→G and π2π1:K→G be three finite regular coverings of graphs, and let σ be a representation of the covering transformation group of π1. In this paper, we classify the half-arc-transitive regular coverings of the complete bipartite graph K4,4 whose covering transformation group is cyclic of prime-power order and whose fibre-preserving group contains a half-arc-transitive subgroup. It has property Cr if the above is true for all regular coverings.
In this paper authors use the concepts of cs-networks, sequential-neighbor- hood networks, sequential-open networks and weak bases, discuss the relations among point-regular covers, uniform covers and point-star networks of point-finite covers in spaces, and establish the characterizations of images of metric spaces under some sequence-covering (compact) mappings. In particular, it is shown that the image of metric spaces under sequence-covering (or 1-sequence-covering) compact mappings is equivalent to the... In this paper authors use the concepts of cs-networks, sequential-neighbor- hood networks, sequential-open networks and weak bases, discuss the relations among point-regular covers, uniform covers and point-star networks of point-finite covers in spaces, and establish the characterizations of images of metric spaces under some sequence-covering (compact) mappings. In particular, it is shown that the image of metric spaces under sequence-covering (or 1-sequence-covering) compact mappings is equivalent to the space with point-regular cs-networks, which answers a Tanaka's question. 本文利用了ｃｓ网、序列邻域网、序列开网和弱基的概念，讨论了空间中点正则覆盖，一致覆盖和点有限覆盖的点星网之间的关系．建立了度量空间在几类序列覆盖（紧）映射下象空间的特征，特别地证明了度量空间的序列覆盖（或１序列覆盖）紧映象等价于具有点正则ｃｓ网的空问，回答了Ｔａｎａｋａ等提出的一个问题． We use a new linear criteria for lifting automorphisms of base graph to the covering graphs to classify all the connected vertex-transitive regular coverings of Petersen graph satisfying the following two properties: ① the covering transformation group is isomorphic to the elementary abelian p-group Zn p; ② the group of fiber-preserving automorphisms of coverings acts vertex-transitively. 运用基图自同构能被提升的线性准则 ,对满足 :1覆叠变换群 K =Znp,2覆盖图的保簇变换群是点传递的 Petersen图的连通正则覆盖图进行了完全分类 .这种图共有 1 2种类型 . The invariants which determine the graphs is discussed according to the theory of group,then the formula for the characteristic polynomials of an oriented regular covering of a finite digraph and the formula for the characteristic polynomials of an oriented total graph of an oriented regular covering is obtained. 借助于群理论讨论了图的不变量,得到了有向图的正则覆盖及其有向全图的特征多项式的表达式.
相关查询
CNKI小工具 在英文学术搜索中查有关正则覆盖的内容 在知识搜索中查有关正则覆盖的内容 在数字搜索中查有关正则覆盖的内容 在概念知识元中查有关正则覆盖的内容 在学术趋势中查有关正则覆盖的内容
CNKI主页 | 设CNKI翻译助手为主页 | 收藏CNKI翻译助手 | 广告服务 | 英文学术搜索
2008 CNKI－中国知网
2008中国知网(cnki) 中国学术期刊(光盘版)电子杂志社
| 1,292
| 4,056
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.515625
| 3
|
CC-MAIN-2020-34
|
latest
|
en
| 0.722417
|
https://themeasureofthings.com/results.php?comp=speed&unit=ypm&amt=508110&sort=pr&p=1
| 1,632,839,534,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-39/segments/1631780060803.2/warc/CC-MAIN-20210928122846-20210928152846-00639.warc.gz
| 587,431,378
| 6,717
|
Bluebulb Projects presents:
Enter a measurement to see comparisons
Equivalents in other units
How fast is 508,110 yards per minute?
Sort Order:
Closest first | Highest first | Lowest first
It's about as fast as The Space Shuttle (Orbiter vehicle velocity)The space shuttle orbits at a speed of 508,110 yards per minute. During liftoff, the space shuttle accelerates to orbital speed in 8.5 minutes, consuming over 1.59 million kg (3.51 million lbs) of propellant in the process. It's about one-fifth as fast as a Meteor In other words, 508,110 yards per minute is 0.18 times the speed of a Meteor, and the speed of a Meteor is 5.6 times that amount. (formally Meteoroid or meteorite, depending on the context; a.k.a. "shooting star", a.k.a. "falling star")Small meteoroids enter the Earth's atmosphere at speeds between 730,000 yards per minute and 4,700,000 yards per minute, depending on their size. The fireball effect, known as ablation, ceases once the atmosphere has slowed the meteoroid to a velocity of about 180,000 yards per minute. It's about eight-and-a-half times as fast as a Bullet (Rifle) In other words, 508,110 yards per minute is 8.46 times the speed of a Bullet (Rifle), and the speed of a Bullet (Rifle) is 0.118 times that amount. (5.56 x 45 mm, a.k.a. 5.56 NATO)A 5.56 x 45 mm cartridge is fired at a velocity of 60,000 yards per minute. As the NATO rifle cartridge, it is used by the military forces of more than thirty-one countries, including use in the M16 series, M4 Carbine, HK-416, and M249 Squad automatic weapons used by the United States armed forces. It's about twelve times as fast as a Jet Fighter In other words, 508,110 yards per minute is 12 times the speed of a Jet Fighter, and the speed of a Jet Fighter is 0.08 times that amount. (for Lockheed Martin F-16, a.k.a. Fighting Falcon, a.k.a. Viper) (maximum speed at altitude)An F-16's maximum speed at altitude is approximately 44,000 yards per minute. The F-16 has a flight ceiling of approximately 15 km (9.32 mi). It's about one-fifteenth as fast as a bolt of Lightning In other words, 508,110 yards per minute is 0.08 times the speed of a bolt of Lightning, and the speed of a bolt of Lightning is 13 times that amount. (atmospheric electrical discharge)A bolt of lightning can travel at up to 6,400,000 yards per minute when arcing from the atmosphere to the Earth. An estimated 280 million lightning strikes strikes occur each year. It's about twenty times as fast as a Bullet (Handgun) In other words, 508,110 yards per minute is 20.2 times the speed of a Bullet (Handgun), and the speed of a Bullet (Handgun) is 0.050 times that amount. (for .40 Smith & Wesson 135 grain Sierra JHP, VV 3N37 powder, Fed. 100 primer, Remington case) (muzzle velocity)A 0.40 caliber Smith & Wesson bullet has a muzzle a velocity of 25,200 yards per minute. This type of ammunition has been the standard issue round of the United States Federal Bureau of Investigation (FBI) since 1990. It's about twenty times as fast as The Speed of Sound In other words, 508,110 yards per minute is 22.6 times the speed of The Speed of Sound, and the speed of The Speed of Sound is 0.044 times that amount. (in dry air at 20°C)The speed of sound in dry air at 20°C (68°F) is 22,500 yards per minute. Air is a relatively poor acoustic conductor, however, as sound will travel at speeds of between 98,200 yards per minute to 102,000 yards per minute in water, depending on its salinity.
| 917
| 3,453
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.890625
| 3
|
CC-MAIN-2021-39
|
latest
|
en
| 0.951537
|
https://en.wikipedia.org/wiki/Edge-contracted_icosahedron
| 1,527,054,304,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-22/segments/1526794865450.42/warc/CC-MAIN-20180523043959-20180523063959-00263.warc.gz
| 555,373,647
| 12,144
|
# Edge-contracted icosahedron
Edge-contracted icosahedron
Faces 18 triangles
Edges 27
Vertices 11
Symmetry C2v, [2], (*22), order 4
Vertex configuration 2 (34)
8 (35)
1 (36)
Properties Convex, deltahedron
Net
In geometry, an edge-contracted icosahedron is a polyhedron with 18 triangular faces, 27 edges, and 11 vertices with C2v symmetry, order 4.
## Construction
It can be constructed from the regular icosahedron, with one edge contraction, removing one vertex, 3 edges, and 2 faces. This contraction distorts the circumscribed sphere original vertices. With all equilateral triangle faces, it has 2 sets of 3 coplanar equilateral triangles (each forming a half-hexagon), and thus is not a Johnson solid.
If the sets of coplanar triangles are considered a single face (called a triamond[1]), it has 10 vertices, 22 edges, and 14 faces, 12 triangles and 2 triamonds .
It may also be described as having a hybrid square-pentagonal antiprismatic core (an antiprismatic core with one square base and one pentagonal base); each base is then augmented with a pyramid.
## Related polytopes
The dissected regular icosahedron is a name for this polytope with the two sets of 3 coplanar faces as trapezoids. This is the vertex figure of a 4D polytope, grand antiprism. It has 10 vertices, 23 edges, and 11 equilateral triangular faces and 2 trapezoid faces.[2]
## In chemistry
In chemistry, this polyhedron is most commonly called the octadecahedron, for 18 triangular faces, and represents the closo-boranate [B11H11]2−. [3]
closo-boranate [B11H11]2− Net
## Related polyhedra
The elongated octahedron is similar to the edge-contracted icosahedron, but instead of only one edge contracted, two opposite edges are contracted.
## References
1. ^ http://www.interocitors.com/polyhedra/Triamonds/
2. ^ John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 26) The Grand Antiprism
3. ^ Holleman, Arnold Frederik; Wiberg, Egon (2001), Wiberg, Nils, ed., Inorganic Chemistry, translated by Eagleson, Mary; Brewer, William, San Diego/Berlin: Academic Press/De Gruyter, p. 1165, ISBN 0-12-352651-5
| 634
| 2,159
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.546875
| 3
|
CC-MAIN-2018-22
|
latest
|
en
| 0.862002
|
https://whomadewhat.org/category/h/
| 1,713,084,876,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-18/segments/1712296816875.61/warc/CC-MAIN-20240414064633-20240414094633-00250.warc.gz
| 588,194,391
| 9,877
|
3,484 Articles
# How much is a mile in city blocks?
North-south is easy: about 20 blocks to a mile. The annual Fifth Avenue Mile, for example, is…
# How far is a block away?
A block is the distance from one cross street to the next. They can be as long…
# How long is a mile in city blocks?
From our sample size below using major cities, the average number of blocks in a mile would…
# How many feet is a fourth mile?
Answer: There are 1,320 feet in a 1/4 mile. Moreover, How many feet is exactly a mile?…
# How long is a mile in blocks?
about 20 blocks Moreover, Does 4 blocks equal a mile? It depends on how large a block…
# How do you convert miles into yards and feet?
Moreover, How do you figure out how many yards are in a mile? To convert a mile…
# How do I know my step length?
Divide the number of feet in your measured distance by the number of steps you took from…
# How do I determine my ideal weight?
– If your BMI is less than 18.5, it falls within the “underweight” range. – If your…
# How many paces is a Roman mile?
1000 paces Moreover, What makes up a mile? Mile, any of various units of distance, such as…
# How much should a 13 female weigh?
The weight range for 13-year-old girls is between 76 and 148 pounds. Weights in the 50th percentile…
| 334
| 1,286
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3
| 3
|
CC-MAIN-2024-18
|
latest
|
en
| 0.951085
|
https://nrich.maths.org/public/topic.php?code=-93&cl=4&cldcmpid=2422
| 1,606,726,059,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-50/segments/1606141211510.56/warc/CC-MAIN-20201130065516-20201130095516-00536.warc.gz
| 408,016,300
| 8,888
|
# Resources tagged with: Making and proving conjectures
Filter by: Content type:
Age range:
Challenge level:
### There are 46 results
Broad Topics > Thinking Mathematically > Making and proving conjectures
### On the Importance of Pedantry
##### Age 16 to 18
A introduction to how patterns can be deceiving, and what is and is not a proof.
### To Prove or Not to Prove
##### Age 14 to 18
A serious but easily readable discussion of proof in mathematics with some amusing stories and some interesting examples.
### The Clue Is in the Question
##### Age 16 to 18 Challenge Level:
Starting with one of the mini-challenges, how many of the other mini-challenges will you invent for yourself?
### Poly Fibs
##### Age 16 to 18 Challenge Level:
A sequence of polynomials starts 0, 1 and each poly is given by combining the two polys in the sequence just before it. Investigate and prove results about the roots of the polys.
### Polite Numbers
##### Age 16 to 18 Challenge Level:
A polite number can be written as the sum of two or more consecutive positive integers. Find the consecutive sums giving the polite numbers 544 and 424. What characterizes impolite numbers?
### Loopy
##### Age 14 to 16 Challenge Level:
Investigate sequences given by $a_n = \frac{1+a_{n-1}}{a_{n-2}}$ for different choices of the first two terms. Make a conjecture about the behaviour of these sequences. Can you prove your conjecture?
### Integral Sandwich
##### Age 16 to 18 Challenge Level:
Generalise this inequality involving integrals.
### Janine's Conjecture
##### Age 14 to 16 Challenge Level:
Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. . . .
### Fibonacci Factors
##### Age 16 to 18 Challenge Level:
For which values of n is the Fibonacci number fn even? Which Fibonnaci numbers are divisible by 3?
### Triangles Within Pentagons
##### Age 14 to 16 Challenge Level:
Show that all pentagonal numbers are one third of a triangular number.
### Fibonacci Fashion
##### Age 16 to 18 Challenge Level:
What have Fibonacci numbers to do with solutions of the quadratic equation x^2 - x - 1 = 0 ?
### Multiplication Square
##### Age 14 to 16 Challenge Level:
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
### Pythagorean Fibs
##### Age 16 to 18 Challenge Level:
What have Fibonacci numbers got to do with Pythagorean triples?
### Plus or Minus
##### Age 16 to 18 Challenge Level:
Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.
### Triangles Within Triangles
##### Age 14 to 16 Challenge Level:
Can you find a rule which connects consecutive triangular numbers?
### Multiple Surprises
##### Age 11 to 16 Challenge Level:
Sequences of multiples keep cropping up...
##### Age 14 to 16 Challenge Level:
Explore the relationship between quadratic functions and their graphs.
### A Little Light Thinking
##### Age 14 to 16 Challenge Level:
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
### Multiplication Arithmagons
##### Age 14 to 16 Challenge Level:
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
### Triangles Within Squares
##### Age 14 to 16 Challenge Level:
Can you find a rule which relates triangular numbers to square numbers?
### Discrete Trends
##### Age 16 to 18 Challenge Level:
Find the maximum value of n to the power 1/n and prove that it is a maximum.
### Why Stop at Three by One
##### Age 16 to 18
Beautiful mathematics. Two 18 year old students gave eight different proofs of one result then generalised it from the 3 by 1 case to the n by 1 case and proved the general result.
### 2^n -n Numbers
##### Age 16 to 18
Yatir from Israel wrote this article on numbers that can be written as $2^n-n$ where n is a positive integer.
### Problem Solving, Using and Applying and Functional Mathematics
##### Age 5 to 18 Challenge Level:
Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
### DOTS Division
##### Age 14 to 16 Challenge Level:
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.
### How Old Am I?
##### Age 14 to 16 Challenge Level:
In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
### Fixing It
##### Age 16 to 18 Challenge Level:
A and B are two fixed points on a circle and RS is a variable diamater. What is the locus of the intersection P of AR and BS?
### Binomial Coefficients
##### Age 14 to 18
An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.
### Cyclic Triangles
##### Age 16 to 18 Challenge Level:
Make and prove a conjecture about the cyclic quadrilateral inscribed in a circle of radius r that has the maximum perimeter and the maximum area.
### Painting by Numbers
##### Age 16 to 18 Challenge Level:
How many different colours of paint would be needed to paint these pictures by numbers?
### Close to Triangular
##### Age 14 to 16 Challenge Level:
Drawing a triangle is not always as easy as you might think!
### What's Possible?
##### Age 14 to 16 Challenge Level:
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
### Prime Sequences
##### Age 16 to 18 Challenge Level:
This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?
### Few and Far Between?
##### Age 16 to 18 Challenge Level:
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?
### Curvy Areas
##### Age 14 to 16 Challenge Level:
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
### Least of All
##### Age 16 to 18 Challenge Level:
A point moves on a line segment. A function depends on the position of the point. Where do you expect the point to be for a minimum of this function to occur.
### Trig Rules OK
##### Age 16 to 18 Challenge Level:
Change the squares in this diagram and spot the property that stays the same for the triangles. Explain...
### OK! Now Prove It
##### Age 16 to 18 Challenge Level:
Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?
### Polycircles
##### Age 14 to 16 Challenge Level:
Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?
### Binary Squares
##### Age 16 to 18 Challenge Level:
If a number N is expressed in binary by using only 'ones,' what can you say about its square (in binary)?
### The Kth Sum of N Numbers
##### Age 16 to 18
Yatir from Israel describes his method for summing a series of triangle numbers.
### Summats Clear
##### Age 16 to 18 Challenge Level:
Find the sum, f(n), of the first n terms of the sequence: 0, 1, 1, 2, 2, 3, 3........p, p, p +1, p + 1,..... Prove that f(a + b) - f(a - b) = ab.
### Sixty-seven Squared
##### Age 16 to 18 Challenge Level:
Evaluate these powers of 67. What do you notice? Can you convince someone what the answer would be to (a million sixes followed by a 7) squared?
| 1,868
| 7,815
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4
| 4
|
CC-MAIN-2020-50
|
longest
|
en
| 0.841678
|
http://www.reprap.org/wiki/Category:DriveTrains
| 1,526,915,669,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-22/segments/1526794864405.39/warc/CC-MAIN-20180521142238-20180521162238-00395.warc.gz
| 452,950,293
| 12,072
|
# Category:DriveTrains
Drive trains, also called mechanisms or mechanical systems, are ways to transform mechanical motion from the stepper motors or DC motors into a precise movement of the desired part of the RepRap.
The mechanical systems are the part of the RepRap machine that move either the print head, the build platform or both. Generally you have a motor which rotates and that rotation is either used directly as rotational movement, or it is converted into linear movement. The various forms of movement are discussed below.
Some of the articles in this category focus on one specific part of a drive train -- an improved gear, pulley, or rack-and-pinion.
## rotary to linear motion conversion
Most drive trains convert the rotary motion of the motor into linear motion. There are 2 popular techniques used by most RepRaps and RepStraps so far:
Other promising techniques currently under development that may turn out better than both include:
## overall layout
Other articles in this category describe the overall layout of a complete drive train, of which there are currently 4 major categories being developed by RepRap developers:
• serial Cartesian drive train (the first ones to successfully RepRap)
• serial polar drive train
• parallel drive train (the Rostock is apparently the first working RepRap in a non-Cartesian drive train)
• parallel SCARA drive train
• partially parallel Cartesian drive train
(This is far from exhausting the theoretical space of all possible drive trains -- for example, there has been a brief discussion[1] of a parallel Cartesian drive train.[2], and Rhombot is an early prototype of that completely parallel Cartesian drive train)
One advantage of the parallel drive trains (including the partially parallel Cartesian drive train) is that all of the motors can be mounted in a fixed location. Serial drive trains generally require at least one motor to be mounted to a moving part, which means that some *other* motor (and the mechanism attached to it) has to be strong enough to move that motor around and keep it constrained to the desired position.
## rails
Some drive train mechanisms use smooth rods or some other kind of rails to properly constrain the motion of one part relative to the base (or to another part).
Several people are trying to substitute some alternative mechanism that requires fewer or no rails. Why is that? Current speculation is:
• "Eliminating rails is a big step towards a fully printable reprap." -- Rhombot
• "Sliding rails are somehow (?) mechanically inferior to a few rotating joints" -- ?
• "A sliding rail costs more (?) than a few rotating joints of equivalent precision" -- ?
• Some other reason?
### binding
Many machine designs show some part sliding along 2 parallel smooth bars. The part slides along one axis, and the way the part is attached to the bars is intended to constrain the part in the other 5 dimensions -- the other 2 axis of motion, and all 3 axis of rotation.
A super-common problem occurs when a designer's human sense of symmetry makes the designer try to attach that part to both bars in the *same* way. Since it's impossible (?) to divide 5 axis of constraints evenly between the 2 smooth bars, and since it's practically impossible to make the 2 smooth bars *perfectly* parallel, we end up with over-constrained motion, leading to binding. (search the RepRap forums for "binding"). (search the RepRap wiki for "binding")
• Some researchers allow the part to slide in 1 dimension, using one rod to rigidly constrain the moving part in 4 dimensions, then use the other rod to rigidly constrain the moving part in the 1 remaining dimension. See the "Mendel's improvements over Darwin" video on the Mendel page.
• Some designers attach the same bearings to both rods, then rigidly attach one of those bearings to the moving part, but add a flexure (perhaps a living hinge) between the moving part and the bearing on the other rod. See illustration 3-12 on p. 25 and the "consider the common problem of aligning shafts that support a linear motion carriage" discussion on p. 24 and illustration 3-19 on p. 39 and the discussion on p. 38 of FUNdaMENTALS of Design (Alexander Slocum 2008).
• The "5 axis of constraints" are apparently only required for serial Cartesian drive trains. The parallel Cartesian drive trains (such as the capstan and bowstring designs) and the serial non-Cartesian drive trains (polar) and the parallel, non-Cartesian drive trains (such as the Rostock) all seem to bypass the binding problem.
## Cartesian Robot (3-axis machine)
Most of the machines described on the RepRap wiki are classified acording to their mechanical arrangement. The categories are linked to on the mechanical arrangement list.
Have all possible ways to connect X, Y, and Z in series already been explored?:
• ... is there some other series arrangement I'm missing?
• Is there any significant advantage or disadvantage of one series arrangement over another?
• Which (if any) parallel or partially-parallel drive train is better than the best series drive train?
The Cartesian Robot is a very standard style of positioning system that uses the familiar X/Y/Z coordinate system. Basically, you have 3 perpendicular linear axes: X, Y, and Z. A stepper motor controls each axis and can move it back and forth. One axis will generally be mounted on another axis, while the other axis is standalone. The build platform will be mounted on one axis, and the print head will be on the other. Common configurations are:
• Print head on X/Y assembly, build platform on Z axis
• Print head on Z axis, build platform on X/Y
• Build platform on X axis, print head on Y/Z
The RepRap project has developed many different Cartesian Robot machines:
• Darwin's 3-Axis System - print head on X/Y axis, build platform on Z. Made from RP parts and steel rod. Belt driven.
• McWire Cartesian Bot - McWire Cartesian Bot. Print head on Z, build platform on X/Y. Threaded rod driven.
• Mendel -- Print head on X/Z axes, build platform on Y. Belt driven X and Y, screw driven Z.
• There are a range of H-Bot machines that have been developed. This is a drive system with the print ehead on an XY assembly but with both motors (substantially) stationary and the head is translated in two axis by the use of more or less complicated timing belt (or wire or line) arrangement that requires coordinated motion of the motors to achieve the required movement of the head. It has appeal as the two axis have similar inertia as neither one has the extra motor mass.
## parallel SCARA robot
The Armstrong A1 by ttsalo is apparently the first RepRap in a parallel SCARA arrangement -- a 3D-printable parallel SCARA 3D printer. (see http://forums.reprap.org/read.php?185,156261 ). It apparently uses the "Marlin Modified for parallel SCARA printers" firmware. Congratulations!
See category: scara for other RepRaps that remind us of SCARA robots: RepRap Morgan ... Wally, etc.
More details on parallel SCARA and other SCARA arrangements:
## Polar Coordinate Robot
see Polar
This style of printer consists of a turntable, an X axis, and a Z axis. The table rotates a build platform, the X axis moves a print head from the center of the table to the outside of the table, and a Z axis moves the print head up or down vertically.
The RepRap project does not currently support a particular polar robot, but we are excited to see several promising prototypes. See Polar for details.
## Subcategories
This category has the following 2 subcategories, out of 2 total.
### D
• Delta(6 C, 47 P)
## Pages in category "DriveTrains"
The following 27 pages are in this category, out of 27 total.
| 1,674
| 7,694
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.625
| 3
|
CC-MAIN-2018-22
|
latest
|
en
| 0.941393
|
http://www.jiskha.com/search/index.cgi?query=Trig+check+my+work+please%3F
| 1,498,511,587,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-26/segments/1498128320865.14/warc/CC-MAIN-20170626203042-20170626223042-00559.warc.gz
| 556,216,573
| 13,643
|
# Trig check my work please?
87,098 results
FRENCH WORK ASAP
please please someone check my work I don't understand it fully so I am asking if someone could please check my work thank you if it's too much I'm sorry. God Bless
tan(X+30)tan(30-x)=2cos2x-1 / (2cos2x+1) i just did (tanx)(-tanx)=-sin^2x/cos^2x would that work?
What are polar coordinates of (4,6) 1.Round r to nearest hundredth and theta to nearest hundredth of RADIAN My work: r^2 = x^ + y^2 r^2 = 4^2 + 6^2 r^2= 16 +36 r^ =52 r=7.21 I'm stuck on how to do theta in Radians, could you please assist
pre calc trig check my work please
sin x + cos x -------------- = ? sin x sin x cos x ----- + ----- = sin x sin x cos x/sin x = cot x this is what i got, the problem is we have a match the expression to the equation work sheet and this is not one of the answers. need to figure out what im doing wrong so i can ...
TRIGONOMETRY
Can you please help me with this question on my study guide for my trig final? Thanks! I'd also appreciate if you can check out my other postings and check my work for some other study guide questions. I want to make sure I'm ready for my final. :) 4. Transform each polar ...
TRIGONOMETRY
Can you please help me with this question on my study guide for my trig final? Thanks! I'd also appreciate if you can check out my other postings and check my work for some other study guide questions. I want to make sure I'm ready for my final. :) 3. The rectangular ...
Calculus - please check my work
Differentiate each function a) y = -3x^2 + 5x - 4 b) f(x) = 6/x - 3/(x^2) c) f(x) = (3x^2 - 4x)(x^3 + 1) the answers i got for each was: a) y'= -6x + 5 b) f'(x)= -6/x^2 + 6/x^3 c) f'(x)= 15x^4 + 6x - 16x^3 - 4 please double check and let me know if these are correct, thank you.
Math - Could Someone Check My Work?
Could someone check my work please? Thank you! (14a^2b)(2ab^2c) = 28a^3b^3c (a^25)^7 = a^125 6x^6 ∙ 6x^6 = 36^12 (2x^2)^3 = 8x^6 (-2)0 = 1 30x^20/(6x^9 = 5x^11 4x^5 ∙ 6x^6 = 24x^11 (2x^4)^3 = 8x^12 -4^2 = -16 -(193)^0 = -1 (-193)0 = 1 (-5)2 = 25 ((6x^7)/(2x^2 ))^2...
Physics - Check my work please :)
Check this please :D Which of the following three statements used to describe work are true: i)Work is done only if an object moves through a distance ii)Work is done only if energy is transferred from one form to another iii)Work is done only if a force is applied In which of...
3. T^2-25/t^2+t-20= (t-5) (t+5)/ (t-10) (t+2) 4. 2x^2+6x+4/4x^2-12x-16= 2(x+2) (x+1)/4 (x-4) (x+1) 5. 6-y/y^2-2y-24= 1/(y+4) *Please check them.- 3. (t-5)(t+5) / (t+4)(t-5) 4. 2((x-1)(x+2)) / 4((x+4)(x-1)) 5. (6-y) / (y+6)(y-4) i don't really understand what this is... but lol...
0.6x + 4 < 1.0x - 1 6x + 40 < 10x - 10 4x > 50 x > 12.5 can someone please check my work and tell me if I am right?
Problem: 25-x^2 6 ------ * --- 12 5-x What I got: 5-x --- 2 *PLease Check My Work. No. Factor the 25-x^2 into two factors. Then the 5-x in the denominator divides out. So then is it: 5+x --- 2 yes. 12x12
8 sin²(3x) cos²(3x) = 2 [2 sin(3x) cos(3x)]² = 2 [sin(6x)]² = 2[1 - cos(12x)]/2 = 1 - cos(12x)
question: slove by comparison and check your solution? a)2x-4y-5=0 3x+8y-4=0 my work so far: 2x-4y=5-------(1) 3x+8y=4-------(2) _____________ 6x-12y=15------(3) (3)-(4) 6x+16y=8-------(4) ____________________ 28y/28 = 7/28 y= .25 2x-4(.25)=5 2x-1+5 2x/2 + 6/2 x = 3 ya i was ...
Trig
tan 75 (show all work please)
Trig
Use Trig identities to verify that sec^4(x)-tan^4(x)=1+2tan^2(x), Only work with one side of the equation
Could you check these two problems? 3sqrt (y+2) = 3 is y = 25 Answers were: true or false I said true because I did it like this Square both sides=y + 2 = 3^3 y+2 = 27 y = 25 and sqrt (2y-6) = 3-y for y answes are: no solution 5 3,5 3 I said 3 because I did it like this: 8y -...
maths (trig)
Could someone please check the first one and help me with the second one. I'm stuck-Thank you 1.What are theroots of the following polynomial equation? (x+2i)(x-5)(x-2i)(x+8) = 0 I think the roots are -2i,5,2i,-8-you take out the roots as opposites of what are in the equaion ...
Determine the mass of carbon monoxide that is produced when 45.6 g of methane CH4 react with 73.2 g of oxygen gas, O2. The products are CO and H2O. Please check my work: CH4 + 3O2 ---> 2CO + 2H20 nCH4=2.84 mol nO2=4.58 mol Limiting Reactant: 1 mol CH4/2.84 mol CH4 = 3 mol ...
A Flagpole casts a 60 foot long shadow on the ground. The angle from the tip of the flagpole to the end of the flagpole's shadow measures 35 degrees. How tall is the flagpole? can i use cos(55degrees) = 60/h which gives me 104.61. Please check. Thanks!
function and trig.
(1/x - 3/x+4) / 1/x square -16 please help me with this question if you can show the work or explain how to solve. thank you
math
the key...^=exponent QUESTION: What is 2^3-6x3^2 Can anyone help me please!!!! 2^3 is 8 3^2 is 9 I will be happy to check your work. is it 1? [[[help]]] u there No, of course not. Where is your work?
Algebra
I am having issues with factoring. I am trying to check my work using a TI84 Plus calculator but I don't know how to plug in a problem to check its factoring. Can anyone help? for example 44y^3+55y^2-11xy how can I go about plugging that in to check my work?
Could someone please check this for me. I had to rewrite the following sentence using a direct object pronoun in two different ways. I wrote: Nosotros queremos leerlos. Los hosotros queremos leer. Thank you for checking
Physics - check my work
A cannon is fired from a cliff 190 m high downward at an angle of 38o with respect to the horizontal. If the muzzle velocity is 41 m/s, what is its speed (in m/s) when it hits the ground? Please check my work. I think it’s wrong, but I don’t know where I’m messing up… ...
algebra1
the problem is 5f+7 less than or equal to 22. can anyone please work this out for me and check it for me? and what i mean by checking it is like when you get the answer you check it and make sure its write.
TRIG
if sin s = -5 /13 and sin t -3/5 s is in QIII t is in QIV find tan (s-t) i got that tan (s-t)= 56/53 is that right? can someone check my work?
I am getting the wrong answer. Can you please check my work? My answer is off by a multiple of ten. A sample of an unknown material appears to weigh 295 N in air and 165 N when immersed in alcohol of specific gravity 0.700. (a) What is the volume of the material? ___________m^...
Math
Please check my work. 1) 64 divide -4 = -16 2) -144 divide (-9) = 16 3) Simplify -9 and a small 2 = -81 4) Simplify (-3) and a small 3 = -27 5) Add -4/11 + 5/11 = 1/11 6) subtract 5/11- [-3/11] = 8/11 7) multiply [-7/8] • [-2/4] = 7/16 8) divide -3.5 -5.6 = -0.63 9) classify...
social studies (Saudi Arabia)
In what way is Islam most likely to impact Muslims during work days? 1)They must leave work early 2)They will not participate in leisure activities after work 3)They can not have certain jobs 4)They need to pause during their work and pry I think it is 4. Am I correct? please ...
science
Please check my work 3M solution of NaOH (1 liter worth) molecular weight: 39.99 3 x 39.99= 119.97 grams dilute to 1000mL 3 M solution of HCl (1 L) c1v1=c2v2 (12M)(?)= (3M)(1000mL) ?= 250 mL please check thank you
A salesperson makes a flat fee of \$20 per day plus \$8per hour. Which equation or inequality can be used to find h, the number of hours the salesperson will have to work to make more than \$60 for a day's work? F. 20h + 8 = 80 G. 8h + 20 < 60 H. 8h + 20 = 60 J. 8h + 20 > ...
Trig
Determine the roots of the function f(x)=-2cos(3x)-1. Can you please show all the work so it is easier to understand, thank you!!
Pre-Calc/Trig...
Help me please Is the given linear expression a factor of the polynomial? Show work. f(x)=2x^3+x^2-5x+2; x+2
chemistry
AgCl <==> Ag^+ + Cl^- NaCl ==> Na^+ + Cl^- Ksp = (Ag^+)(Cl^-) = 1.8 x 10^-10 Let S = solubility of AgCl, then (Ag^+) = S (Cl^-) = S+0.01 Solve for S. Note: A similar problem to this post (0.1 M NaCl instead of 0.01 M NaCl) was on a couple of days ago; the one who ...
trig
trig
I don't know to find the derivative of the following trig functions. Please help. f(x)= cotx h(x0= secx i(x)= cscx
trig
I don't know to find the derivative of the following trig functions. Please help. f(x)= cotx h(x)= secx i(x)= cscx
algebra
Help me please I get confused with the positives and negatives. Please be kind to check my work and let me know where am I going wrong -4x + 10 = 58 -4x + 10 -10 = 58 -10 (is it - or +10?) -4x = 48 or 68 (do i add 58&10 or sub?) -4x/-4 = 48/-4 or 68/-4 (is the 4 -or+) x=12 or ...
Algebra
Hello, can someone tell me if I got the following solve and check work correct? 1. solve and check 1/2x = 3 5/6 1/2x = 3 5/6 1/2x = 23/6 3x = 23/3 x = 23/3 And to check for it 1/2x = 3 5/6 1/2x = 23/6 46x = 6 x = 6/46 x = 3/23 2. Solve and check 3x + 2 / 2 = 7 3x + 2 / 2 = 7 ...
Write an equation, in point-slope form, for the line that is perpendicular to y – 10 = 3/2 (x – 4) and that passes through the point (4, 2). My Answer: Formula for point-slope form; y – y = m(x – x) Insert y and x value; y – 2 = m(x – 4) If the slope for the ...
find the surface area and volume of the right circular cylinder. The radius is 3 and height 6. This is what I put for volume: v=pir^2h pi(3cm)^2 6 cm= 54pi cm cubed can you please check this and show work on how to do the surface area? Thanks.
please check my answer thanks What would be the amount of compound interest on \$ 8,000 invested for one year at 6 %, compounded quarterly ? (need to show all of your work ) ok this is what I got \$8,000 x 0.6 = \$ 480 \$ 480 / 4 = \$120 \$120 x 0.6 / 4 = \$ 121.80 \$8,241.80 x 0.6 /4...
Algebra I-
(solving for x) 3(x+5)=6x-4+7(-7x-1) Each time I try this i plug the numbers in and i find out that i am worng. Please help! I get -13/23 but I didn't check it. Post your work if you want me to check it and find your error.
Math
Please help me with this step by step show your work problem. |-4b-8|+|-1-b^2|+2b^3 (b= -2) My work |-4b-8|+|-1-b^2|+2b^3 |-4(-2)-8|+|-1-(-2^2)|+2(-2^3) |8-8|+|-1-4|-16 8+8+5-16 16+5-16 5 Could you check my work? If it is incorrect, could you show me the steps to correct it?
((cotx+cscx)/(sinx+tanx))=cotxcscx Please prove left side equal to right side, only doing doing work on the left.
One more problem.. Given sin t= 3/11 and cos t<0, find the values of the remaining 6 trig functions.
Find the reference angle for -144 degrees. I'm coming up with 504 degrees, but I think I'm missing a step.
TRIG!
Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 x = (sin^2x)^3 + (cos^2x)^3 = (sin^2x+cos...
-write the plural for each noun potato-potatoes shoe-shoes auto-autos speech-speeches -describe the kinds of information about words that can found in a dictionary *prononciation *parts of speech *definition and the word *how many syllabuls a word has is there anything else ...
Lamont earns \$5.70 per hour. last Friday Lamont received a pay check for \$745.25. this pay check included an extra \$200 bonus. about how many hours did Lamont work during the last pay period? ms sue please help, i would really appreciate it.
language art CHECK
Will somebody please check this for me and see if i used the words correctly please? Having spent many years as political opponents, the two senators have developed a(n)MUTUAL respect for each other. Please check if it is correct. thank you
sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only!
Trig
The next two steps in solving this trig identity question are ??? 1/csctheta x costheta x sintheta x sectheta = sinsqtheta arghhh need help please
math
could someone please refresh my memory of the basic trig functions? ex) cos^2 + sin^2 = 1? That is a trig identity. http://www.sosmath.com/trig/Trig5/trig5/trig5.html
trig
use sum or difference identities to find the exact value of the trigonometric function: tan 345 please show work, i cant figure out what im doing wrong!
Trig Help
Prove the following: [1+sinx]/[1+cscx]=tanx/secx =[1+sinx]/[1+1/sinx] =[1+sinx]/[(sinx+1)/sinx] =[1+sinx]*[sinx/(sinx+1)] =[sinx+sin^2x]/[sinx+1] =[sinx+(1-cos^2x)]/[sinx+1] =??? This is where I'm stuck. Can someone help me. Please check what I got is right so far it's ...
I posted this before can someone please check my answers and help me thanks:) 2 rectangles have equal areas determine the area of each rectangle then use this info to determine the perimeter. rectangle one: length of 2p + 3 width of 3.8 after my work i got p= 1.5 so the area ...
Math ~CHECK MY WORK~
With stars are my answers. Please check them if they are wrong please tell me the right ones. Number 1 (the bottom one) I don't get it so please help me with that one please! 1) You have \$60 in your wallet and want to buy some new CDs. If the CDs are \$11 each, what number of ...
Physics
please check these: In which of the following sentences is WORK used in the scientific sense of the word? a. holding a heavy box requires a lot of work b. a scientist works on an experiment in the laboratory c. sam and rachel pushed hard, but they could do no work on the car d...
algebra
Can someone please help me with this one? Solve (5x+4)^1/2-3x=0 Just so you know, it is to the 1/2 power. Add 3x to both sides of the equation, then square both sides. That should enable you to gather terms and factor. Yeah, that's the part I understood. Could you help me with...
Math
4s-(3-2s)-6=9 Please check my work: 4s-3+2s-6=9 6s-9=9 3s=18 s=3
english
math- can you please check my work
Can you please check my work. I asked this question yesterday but no one helped me. Thank you , I really appreciate it A hot air balloon was at a height of 60 feet above the ground when it began to ascend. The balloon climbed at a rate of 15 feet per minute. a) make a table ...
The height h in inches of pistons 1 and 2 in an automobile engine can be modeled by h1 = 3.75sin(733t) + 7.5 and h2 = 3.75sin[733(t+ 4π/3)] + 7.5 where t is measured in seconds. How often are these two pistons at the same height? Show work please.
PHYSICS (CHECK WORK)
I am getting the wrong answer. Can you please check my work? My answer is off by a multiple of ten. A sample of an unknown material appears to weigh 295 N in air and 165 N when immersed in alcohol of specific gravity 0.700. (a) What is the volume of the material? ___________m^...
Use a cofunction to write an expression equal to csc(4ð/11). Is the answer csc(4ð/11)= 1/sin(4ð/11)
Find the unit vector in the direction of <-1,-2>. Do not approximate any numbers in your answer. I get (-1/sqrt10) and (-3/sqrt10)
English
1. I want to do volunteer work at a nursing home. 2. I want to do volunteer work in a nursing home. (Which preposition should we use? Are both OK?) 3. I want to do volunteer work at an orphanage because I want to take care of orphans who are helpless. 4. I want to do volunteer...
Hello, Please check my answers, with stars (*) are my answers! Please check if they are wrong please tell the right answer and why it is right (explain it) so I can understand why! Thanks! For questions 1-2, solve the inequality. 1.) x + 8 < -28 a~ x < -36 ****** b~ x &...
Trig identity inverses
Find the exact value of cos[cot^-1 (-√3) + sin^-1 (-1/2)]. I'm having trouble with inverses. Please help by showing work.
Trig help
Can someone help me find ALL solutions in the interval [0,2π) for the given equations. Please show work. 1) sin2x = sin2x 2) tan2x +tanx = 0
Math
I wanted to double check that I am correct on the work area and answers please. 1.Given f(x)=x+2 and g(x)= 3x-4. Find (f+g). Work: (x+2) + (3x-4) Answer: 4x-2 2.Given f(x)=x+2 and g(x)=3x-4. Find (f*g). Work: (x+2)(3x-4) Answer: 3x² +2x-8 3.Given f(x)=x+2 and g(x)=3x-4. Find...
Spanish Check??
Check my spanish work on page 2 please? Anyone?
Posted by JoniAnne on Wednesday, October 20, 2010 at 11:50am. Please check- Solve 3 > sqrt(3x) 3x >=o x>=o/3 x>=0 square both sides and you have 3x < 3^2 3x,9 x<9/3 x<3 answer is 0<=x<3 correct or not? 3(cube) sqrt(2-5) = 3 cube both sides = 2-5x = ...
Algebra
Could you please check my work? 3/(x-7)=2/(2x+1) 3(2x+1)=2(x-7) 6x+3=2x+-14 x=-4.25 I appreciate it.
Trig?Precalc
write the rectangular equation x^2+y^2=6 in polar form. I do not want people to just post the answer! Please, show your work so that I can understand how to do these kinds of problems myself! Thank you and God Bless!
can a reference angle be negative? Tye "reference angle" in google and check out the mathwords site :) no I copied and pasted the mathwords page for you, unfortunatly the diagram that was with it cant, express itself in text so it didn't appear. For any given angle, its ...
Trig
Problem: 25-x^2 6 ------ * --- 12 5-x What I Got: 5-x --- 2 *Please Check My Work And Tell Me If I am Correct or wrong.If I am wrong please help me as much as possible.Thank you~ Wrong. When are you going to factor the 25-x^2 ? The 5-x then will divide out. oh...so then will ...
Functions & Trig
evaluate each function at the given value: f(n)=-n^6+31n^4+26n^3+20n^2+-33n-20 when n=6 I was thinking that I should do synthetic division, but I've tried it a few times and I can't get it to work out correctly. Please help!
Functions & Trig
evaluate each function at the given value: f(n)=-n^6+31n^4+26n^3+20n^2+-33n-20 when n=6 I was thinking that I should do synthetic division, but I've tried it a few times and I can't get it to work out correctly. Please help!
check my answers please. Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. f(x) = 2x3 + 10x2 - 8x - 5; between 1 and 2 -I got: f(1)=1 and f(2)=35;no Determine the maximum possible number of turning ...
bobpursley
ok and for this other question could you check my work please! h t t p : / /i 3 4 . t i n y p i c . c o m / s 2 z h m v . j p g
4x(3-y) - 2x + xy I got 64. Is that right?
Art
Can you check these sentences, please? 1) You are forbidden to enter this area. You mustn't enter this area. 2) It wasn't necessary for John to go to work because it was Sunday. He didn't have to go to work.
Math
^=exponents /= divide So I am not sure how to do this. It is an example in my book but I still don't get it. Can you work through ti so I can do my real work. (-1^2+-1^-2)^-1 (-1^2+-1^-2)^-1 = First, do work within the parentheses. -1*-1 = 1 and -1-2 = 1/(-12) = [1+(1/(-12...
Will you please check my work for me. 1)The equation of a parabola is shown. y=1/14X^2. What are the coordinates of the focus? (0,-3.5) <---- (0,-4) (0,7) 2)The equation x2 + (y + 3)2 = 36 models the boundary on a local map for which Darren can hear his friend Tom on his ...
math
how would I check this on my own? I know you put numbers in the place of the letters but when I do that I come up with my moms answer. this is what i have when I check my work. p=-2 q=3 6*(-2)*3 =-36 but 3(-2)(-2*3)=36 could you tell me what i'm doing wrong when I check them ...
Trig/PreCalc
Teach me how to express 5sqrt3 - 5i in polar form please. I don't want you to do the work for me. Just show me the steps I need to do the work properly on my own. Otherwise I will not pass this class or the exam when I enter college, and I do not want to retake PreCalc. Its a ...
ALGEBRA 2 help please would appreciate
x x _____ - _____ = x^2+9 ________ x+3 x-3 X^2-9 solve for x. and check answer thank you show work please
Good morning. This is a repost. The system is telling me my calculations is incorrect. I thought a fresh pair of eyes would help. Please tell me what I am doing wrong. Suppose a monatomic ideal gas is contained within a vertical cylinder that is fitted with a movable piston. ...
Calculus - please check my work
evaluate rounding to 2 decimal places if neccessary a) 1n5 = 1.61 b) lne^2 = 2 c) (lne)^2 = 1 please let me know if these are correct, thank you.
chem/some1 check my work plz.
2NH3(g)+3CuO(s)=N2(g)+3Cu(s)+3H2O(g) if 18.1grams of ammonia reacts with 90.4 grams of copper(II) oxide, which is the limitting reagent?? what is the theorectical yield of nitrogen gasd? if 8.52 g of N2 are formed, what is the % yield of nitrogn gas?? please check if is ...
What is the sign of heat(Q), Work(W), or Temperature for these following situations. Say if it's +,-, or 0. 1)You hit a nail with a hammer: +W, Q=0, T=0 2)You hold a nail over a Bunsen burner: Q=+Q, Temp:constant, W=0 3)You compress the air in a bicycle pump by pushing down on...
Math
Can you please check to see if this is correct: -5 = x-(-17) After doing my work I got x = -22
Pre-cal/Trig
(tan/(1+sec)) + ((1+sec)/tan) = 2csc (Show all work please.)
Math 157
Can someone please help me. At a quality control checkpoint on a manafacturing assembly line, 10% of the items failed check A, 12% failed check B, and 3% failed both checks A and B. a. If a product failed check A, what is the probability that it also failed check B? b. If a ...
2 rectangles have equal areas determine the area of each rectangle then use this info to determine the perimeter. rectangle one: length of 2p + 3 width of 3.8 after my work i got p= 1.5 so the area is 14.4 and the perimeter is 19.6 is it correct? rectangle 2 : length of 6-p ...
1. Pages:
2. 1
3. 2
4. 3
5. 4
6. 5
7. 6
8. 7
9. 8
10. 9
11. 10
12. 11
13. 12
14. 13
15. 14
16. 15
17. Next>>
Post a New Question
| 7,131
| 21,516
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.34375
| 3
|
CC-MAIN-2017-26
|
latest
|
en
| 0.867842
|
https://documen.tv/question/determine-the-point-of-intersection-of-the-lines-y-5-2-and-y-3-by-graphing-19841844-73/
| 1,632,129,519,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-39/segments/1631780057033.33/warc/CC-MAIN-20210920070754-20210920100754-00685.warc.gz
| 262,698,039
| 15,663
|
## Determine the point of intersection of the lines y = – 5/2 x and y = -x + 3 by graphing.
Question
Determine the point of intersection of the lines y = – 5/2 x and y = -x + 3 by graphing.
in progress 0
2 months 2021-07-23T01:28:29+00:00 1 Answers 3 views 0
| 93
| 261
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.609375
| 3
|
CC-MAIN-2021-39
|
latest
|
en
| 0.809816
|
https://www.voovers.com/geometry/circumference-calculator/
| 1,726,686,708,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-38/segments/1725700651931.60/warc/CC-MAIN-20240918165253-20240918195253-00747.warc.gz
| 950,890,713
| 43,229
|
##### Related Content
Thank you!
On behalf of our dedicated team, we thank you for your continued support. It's fulfilling to see so many people using Voovers to find solutions to their problems. Thanks again and we look forward to continue helping you along your journey!
Nikkolas and Alex
Founders and Owners of Voovers
# Circumference Calculator
Size =
Help
?
## Lesson on Circumference
### What is Circumference?
Circumference is another way of saying perimeter of a circle or ellipse. Circumference comes from the Latin word circumferens which means to carry around, in this case carrying a measurement around the perimeter of a circle or ellipse.
The formula for circumference of a circle is given as:
C = 2Ï€r
or:
C = πd
Where C is the circumference, r is the radius of the circle, and d is the diameter of the circle. For an in-depth look at circumference, see our lesson Perimeter of a Circle.
### Hand Calculating the Circumference
The circumference of a circle can easily be calculated by hand with the formulas given above. We may rearrange the formulas to solve for other parameters of the circle as well.
Let’s go through an example together where we must find the circumference.
Find the circumference of a circle with a radius of 13 units.
1.) We can immediately plug the radius into the circumference formula C = 2Ï€r.
2.) C = 2Ï€(13) = 26Ï€ = 81.681
3.) The circumference of the circle is 81.681.
## How the Calculator Works
The calculator on this page is written in the programming language JavaScript (JS). The JavaScript function circumference runs in your device’s internet browser when an input change is detected. Therefore, the circumference is calculated nearly instantly.
The code utilizes the exact same circumference formula as given above. When it detects diameter as the input unit, it converts the size to radius. If radius is already the selected unit, it skips this step and moves forward to the computation.
For the computation, the radius value is plugged into the formula which then outputs the circumference. That answer is rounded to the 4th decimal place and displayed in the answer area. If no valid positive number input is detected, it simply does not perform any calculation.
Scroll to Top
| 487
| 2,251
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.0625
| 4
|
CC-MAIN-2024-38
|
latest
|
en
| 0.870962
|
https://socratic.org/questions/amanda-was-48-inches-she-grew-n-inches-and-is-now-56-5-inches-how-do-you-write-a#184083
| 1,726,492,121,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-38/segments/1725700651697.32/warc/CC-MAIN-20240916112213-20240916142213-00631.warc.gz
| 482,981,979
| 5,799
|
# Amanda was 48 inches. She grew n inches, and is now 56.5 inches. How do you write an expression that represents the number of inches Amanda grew?
Nov 5, 2015
$n = {x}_{2} - {x}_{1}$
$n = 8.5$ in
#### Explanation:
Amanda's first height $= {x}_{1}$
Amanda's second height $= {x}_{2} = 56.5$ in
${x}_{1} = 48$ in
${x}_{1} + n = 56.5$ in
$48$ in$+ n = 56.5$ in
$n = 56.5$ in$- 48$ in
$n = {x}_{2} - {x}_{1}$
$n = 8.5$ in
| 182
| 422
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 12, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.375
| 4
|
CC-MAIN-2024-38
|
latest
|
en
| 0.863966
|
https://jeopardylabs.com/play/math-competition-summer-camp
| 1,722,904,565,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-33/segments/1722640461318.24/warc/CC-MAIN-20240806001923-20240806031923-00819.warc.gz
| 264,151,455
| 11,853
|
Addition and Subtraction Word Problems 1
Addition and Subtraction Word problem 2
Multiplication and Division Word problem 1
Multiplication and Division Word problem 2
Mixed Word problem
100
Tessa has 4 apples. Anita gave her 5 more. She needs 10 apples to make a pie. Does she have enough to make a pie?
No, she doesn't have enough.
5+4 = 9
100
Julia played tag with 12 kids on Monday. She played tag with 7 kids on Tuesday and 3 kids on Wednesday. How many kids did she play with altogether?
22 kids
100
Mirna baked some cookies. If she baked 5 pans of cookies for 30 minutes each and there are 8 cookies per pan, how many cookies did Mirna bake?
5 x 8 = 40
100
In the park, I see 109 dogs. How many legs do I see?
109 x 4 = 436
I see 436 legs.
100
There is a flower shop at downtown which is having a sale on roses. In the display, there are 10 white roses, 8 pink roses and 7 red roses. When the shop closes, there are 2 white roses left. How many white roses were sold?
10 – 2 = 8
8 white roses were sold.
200
Mr. Greyson collected 122 eggs from his mini farm on Monday, but 30 of them had cracks. How many of the eggs can be delivered to the market?
122 – 30 = 92
Mr. Greyson has 92 eggs that can be delivered to the market.
200
The first show of the theatre on Sunday is at 11 a.m. The first cashier sold 28 tickets and second cashier sold 13 tickets. Together with the 41 tickets sold online, how many tickets were sold?
28 + 13 + 41 = 82
There are 82 tickets sold.
200
Alex counted her crayons and found out that she has 80 crayons which she will place in crayon boxes. Every crayon box can contain 8 crayons. How many crayon boxes does she need?
80 ÷ 8 = 10
She needs 10 crayon boxes.
200
At the bird zoo, the kids were able to visit 5 different bird cages, each containing 8 different kinds of birds. The cages are 14 feet tall! How many different kinds of birds did the children see in the bird cages?
5 x 8 = 40
The children saw 40 kinds of birds in the cages.
200
It usually takes about 3 hours and 15 minutes to finish a doll. If a tailor starts making a doll at 8 with 15 minutes in the morning, when will the doll be done?
The doll will be done at 11:30.
300
Ana filled 62 buckets with hay. She already gave 18 buckets of hay to the horses, and the rest are for the cows. How many more buckets of hay do the cows get compared to the horses?
62 – 18 = 44
44 – 18 = 26
The cows get 26 more buckets of hay than the horses.
300
Yesterday, Justin bought 13 more markers for his project. He now has 74 markers in total. How many markers were there before yesterday?
74 – 13 = 61
Before yesterday, Justin had 61 markers
300
John is building a tree house. For the pillars, he needs two sets of wood with different lengths. If the first set of wood is 4 feet long and the second set is 5 times longer than the first set, how long is the second set of wood?
4 x 5 = 20
The second set of wood is 20 feet long.
300
3 piles of clean white papers were stacked in the corner of Maria's room. She decided to place these papers in paper envelopes which can hold 10 papers each. How many paper envelopes does she need if she has 120 clean white papers?
120 ÷ 10 = 12
She needs 12 envelopes
300
Daisy and Ollie are sharing some marbles. They have 5 boxes of marbles, and once they have shared them they have twenty marbles each. How many marbles are in each box?
20 x 2 = 40 marbles in total
40 ÷ 5 = 8
There are 8 marbles in each box.
400
The latest album of a famous acoustic band sold 243 copies last week and another 482 copies this week. If there were 965 copies released, how many copies of the album remain to be sold?
965 – 243 – 482 = 240
240 copies of the album remain to be sold.
400
There were 12 cups in the house but 4 are broken. Kristy goes out and buys 10 cups. How many cups are there after she returns?
12 – 4 + 10 = 18
There are 18 cups.
400
Christian’s father and Juan gathered firewood as they walked the 5 miles towards the lake. If every sack can contain 20 pieces of wood, how many sacks were they able to fill if they gathered 80 pieces of wood?
80 ÷ 20 = 4
They were able to fill 4 sacks of wood.
400
There were 150 bookshelves. Each bookshelf had 15 books. How many books were on the shelves?
150 x 15 = 2,250
There were 2,250 books on the shelves.
400
There is a box of toy cars for sale at a toy store. There are 16 red cars, 12 green cars and 31 blue cars. Compared to the number of red cars, how many more blue cars are there?
31 – 16 = 15
There are 15 more blue cars than red cars
500
Freddie is a fan of a famous band. He wants to buy 2 t-shirts for \$8 each and a hat for \$9 with the band’s name printed on them. If he has \$31 in his pocket.
How much would it cost him?
How much money would he have left?
8 + 8 + 9 = 25
It would cost him \$25.
31 – 25 = 6
Freddie would have \$6 left.
500
Last Saturday, Marie sold 425 magazines, 275 newspapers and 14 books. What is the total number of items she sold?
425 + 275 + 14 = 714
She sold 714 items.
500
If a shop makes \$2,782 in a day, how much will it make in one week?
\$19,474
500
Grace’s spent 2 hours gathering all of her watercolor paintings. She thought of placing an equal number of paintings in four of the rooms in the house. If Grace has 32 watercolor paintings, how many paintings will be placed in each of the four rooms?
32 ÷ 4 = 8
There will be 8 paintings to be placed in each of the four rooms
500
Matthew and his two brothers helped to decorate the house for the party. Each of them blows 12 balloons. But 5 balloons pop. How many balloons do they have for decoration?
12 x 3 – 5 = 31
They have 31 balloons to use for decoration.
| 1,551
| 5,728
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.25
| 4
|
CC-MAIN-2024-33
|
latest
|
en
| 0.97463
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.