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A quantifier shift is a logical fallacy in which the quantifiers of a statement are erroneously transposed. The change in the logical nature of the statement may not be obvious when it is stated in a natural language like English.

Definition

The fallacious deduction is that: For every A, there is a B, such that C. Therefore, there is a B, such that for every A, C.

x,yRxyyxRxy

However, an inverse switching:

yxRxyxyRxy

is logically valid.

Examples

1. Every person has a woman that is their mother. Therefore, there is a woman that is the mother of every person.

In computational number theory and computational algebra, Pollard's kangaroo algorithm (aka Pollard's lambda algorithm, see Naming below) is an algorithm for solving the discrete logarithm problem. The algorithm was introduced in 1978 by the number theorist J. M. Pollard, in the same paper [1] as his better-known rho algorithm for solving the same problem. Although Pollard described the application of his algorithm to the discrete logarithm problem in the multiplicative group of units modulo a prime p, it is in fact a generic discrete logarithm algorithm—it will work in any finite cyclic group.

The algorithm

Suppose G is a finite cyclic group of order n which is generated by the element α, and we seek to find the discrete logarithm x of the element β to the base α. In other words, we seek xZn such that αx=β. The lambda algorithm allows us to search for x in some subset {a,,b}Zn. We may search the entire range of possible logarithms by setting a=0 and b=n1, although in this case Pollard's rho algorithm is more efficient. We proceed as follows:

1. Choose a set S of integers and define a pseudorandom map f:GS.

2. Choose an integer N and compute a sequence of group elements {x0,x1,,xN} according to:

3. Compute

d=i=0N1f(xi).

Observe that:

xN=x0αd=αb+d.

4. Begin computing a second sequence of group elements {y0,y1,} according to:

and a corresponding sequence of integers {d0,d1,} according to:

dn=i=0n1f(yi).

Observe that:

yi=y0αdi=βαdi for i=0,1,,N1

5. Stop computing terms of {yi} and {di} when either of the following conditions are met:

A) yj=xN for some j. If the sequences {xi} and {yj} "collide" in this manner, then we have:
xN=yjαb+d=βαdjβ=αb+ddj(modn)xb+ddj(modn)
and so we are done.
B) di>ba+d. If this occurs, then the algorithm has failed to find x. Subsequent attempts can be made by changing the choice of S and/or f.

Complexity

Pollard gives the time complexity of the algorithm as O(ba), based on a probabilistic argument which follows from the assumption that f acts pseudorandomly. Note that when the size of the set {a, …, b} to be searched is measured in bits, as is normal in complexity theory, the set has size log(b − a), and so the algorithm's complexity is O(ba)=O(212log(ba)), which is exponential in the problem size. For this reason, Pollard's lambda algorithm is considered an exponential time algorithm. For an example of a subexponential time discrete logarithm algorithm, see the index calculus algorithm.

Naming

The algorithm is well known by two names.

The first is "Pollard's kangaroo algorithm". This name is a reference to an analogy used in the paper presenting the algorithm, where the algorithm is explained in terms of using a tame kangaroo to trap a wild kangaroo. Pollard has explained[2] that this analogy was inspired by a "fascinating" article published in the same issue of Scientific American as an exposition of the RSA public key cryptosystem. The article[3] described an experiment in which a kangaroo's "energetic cost of locomotion, measured in terms of oxygen consumption at various speeds, was determined by placing kangaroos on a treadmill".

The second is "Pollard's lambda algorithm". Much like the name of another of Pollard's discrete logarithm algorithms, Pollard's rho algorithm, this name refers to the similarity between a visualisation of the algorithm and the Greek letter lambda (λ). The shorter stroke of the letter lambda corresponds to the sequence {xi}, since it starts from the position b to the right of x. Accordingly, the longer stroke corresponds to the sequence {yi}, which "collides with" the first sequence (just like the strokes of a lambda intersect) and then follows it subsequently.

Pollard has expressed a preference for the name "kangaroo algorithm",[4] as this avoids confusion with some parallel versions of his rho algorithm, which have also been called "lambda algorithms".

See also

References

  1. J. Pollard, Monte Carlo methods for index computation mod p, Mathematics of Computation, Volume 32, 1978
  2. J. M. Pollard, Kangaroos, Monopoly and Discrete Logarithms, Journal of Cryptology, Volume 13, pp 437-447, 2000
  3. T. J. Dawson, Kangaroos, Scientific American, August 1977, pp. 78-89
  4. http://sites.google.com/site/jmptidcott2/

Template:Number-theoretic algorithmsxTemplate:In-text citations Banded Waveguides Synthesis is a physical modeling synthesis method to simulate sounds of dispersive sounding objects, or objects with strongly inharmonic resonant frequencies efficiently. It can be used to model the sound of instruments based on elastic solids such as vibraphone and marimba bars, singing bowls and bells. It can also be used for other instruments with inharmonic partials, such as membranes or plates. For example simulations of tabla drums and cymbals have been implemented using this method. Because banded waveguides retain the dynamics of the system, complex non-linear excitations can be implemented. The method was originally invented in 1999 by Georg Essl and Perry Cook to synthesize the sound of bowed vibraphone bars Template:Harv.

In the case of the standard one-dimensional wave equation ytt=c2yxx disturbances of all frequencies travel with the same constant speed c. In dispersive media the traveling speed of disturbances depends on their frequency and we get c(ω) where ω is the frequency of the disturbance. Many physical systems are dispersive, for example the elastic beams described by the Euler-Bernoulli beam equation ytt=kyxxxx where k is a material constant.

Banded waveguides model dispersive behavior by splitting the propagation of disturbances into frequency bands. Each frequency band is modeled using a band-limited version of the standard digital waveguide method. Each frequency band is tuned to the resonant frequencies of the sounding object to be modeled to avoid any discretization error at the dominant and audible frequencies Template:Harv.

Banded waveguide synthesis is implemented in most available sound synthesis libraries and programs such as:

Sources

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We're the producer of The NORML Network, the actual host of the NORML SHOW Dwell and The NORML Stash Blog, along with NORML's Outreach Coordinator. I'm married, are living in Portland, Oregon, and I am a licensed medical marijuana caregiver in this state. I've worked days for an IT geek and night time as a professional musician. Before, I have been the host with my own political talk radio stations show on satellite radio. I am the High Times "Freedom Fighter of the Month" and I travel across the country to teach people on marijuana alter. I've dedicated my life to bringing an end to grownup marijuana prohibition and re legalizing marijuana hemp, and I'm honored for being chosen by NORML to give voice to the Marijuana Nation and speak for those who can't converse up.

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Welkos, remaining, and SappellIn 1990, just before he or she and his colleague Joel Sappell ended up about to publish a landmark collection exposing Scientology's secrets in the L . a . Times, Robert Welkos found that somebody had placed in a manila package against his home's doorstep a brochure from a mortuary, reassuring him to plan his own obituary.

He checked with the obituary home, but it said it would never solicit in that way. Then one more brochure showed up two days afterwards, left by a man spotted scurrying away by Welkos's wife.

I'd never know if the deliveries have been just a mix up or a threatening prank. Just as I have never acknowledged who made the a large number of hang up telephone calls to the home; what caused my lover's dog to go into seizures make certain that the Times published the secret teachings of Scientology; why a bogus assault complaint was submitted with the Los Angeles Police Section against Sappell by a man who is address and name proved to be phony, or why car or truck dealers we had never addressed were making inquiries within our personal credit reports.

Whenever editors ask critical questions about Scientology they are able to Nike Air Force Australia expect to endure intense individual scrutiny. Over the years, various editors have been sued, harassed, spied upon, and even been subjected to soiled tricks.

The 1990 collection by Sappell and Welkos proved to be probably the most significant journalistic projects possibly done on Scientology, and was particularly brave for the proximity from the newspaper to Scientology's Los Angeles admin headquarters.

Which makes it all the more disappointing that yesterday, the sloppiest wet kiss I've seen Scientology receive from the mainstream press in a very period of time showed up on the website of the Are generally Times, which long ago dropped the services of Welkos and Sappell.

The article has been titled "What is Scientology? A Scientologist delivers her point of view," and yes it showed up in the "Nation Now" section of the Instances website. We've asked it ourselves, knowing that readers value a primer to this kind of complex body of knowledge.

Lynch provides ask a Scientologist this question, that is, again, a good notion. We've often spoken to current church members, although usually not for your record. This is in part why Debbie Cook's infamous Fresh Year's Eve e mail was so stunning a former church New Balance Stockists London management, she insisted that she was still a member in good standing when your woman gave the world a look into the crisis that is convincing more and more longtime members to sneak away. You can send your ex questions, and she may choose to answer them. There's no indication of who she really is or where the woman lives. In extensive on the internet databases of Scientology "completions" successes classified by official church publications you cannot find any record of any Laurie Hamilton. And over recent years, Scientology experts have found that she offers extremely unusual answers for a person who claims to be a subsequent generation church member created in 1968 to parents who'd fallen in with L. Ralph Hubbard from the very beginning, the 1950 magazine of his book, Dianetics.

In 2006, the researchers at Operation Clambake observed that Hamilton, for example, spoke freely about something that is assumed to get taboo among actual church associates: the condition of L. Ron Hubbard dads and moms before his death. As is possible seen in this video, 2 or 3 days after Hubbard's death in Jan, 1986, it was announced to church members at the Hollywood Palladium that will Hubbard had been as healthy as a possible ox, and had simply picked out to leave behind his body as he moved on to another planes of existence to follow further spiritual research.

Hamilton tends to make other statements about Hubbard and the foibles being less critical than Hollister Brisbane the works he put aside, and also that some of the more unusual space opera stories throughout Scientology's upper level teachings (which expense members hundreds of thousands of dollars to discover) are simply metaphors which Scientologists can opt and choose from.

Hamilton, in other words, may sound like just about no Scientologist you will encounter inside official church (in some ways, she sounds like an "independent Scientologist," who are heretics so far as David Miscavige's church is concerned). She gets long been suspected to be Womens Air Max 2012 concentrating on behalf of Scientology's Office associated with Special Affairs, which would typically vet any communication towards the public of the church's official insurance plans. Various experts have pointed out that her answers appear to be on purpose more pragmatic than the dogmatic replies church members give 1 another, and are written for a cynical public. (Mike Rinder, OSA's former management director who left in 2007, told me that he could be never heard of her. However he said he is certain that such public statements would be learned about by church officials very carefully before publication.)

Laurie Hamilton, in other words, is actually a problematic figure, especially for your journalist who wants a straight response about Scientology.

But the Times formulated problems in a couple of ways. Primary, it agreed to all of Hamilton's rules, which were extensive.

She dropped to reveal specifics about the place she lives or works for fear that some customers might hold her beliefs against her.

What follows is undoubtedly an edited transcript of an employment Fake Celine Bags interview conducted via e mail during Hamilton's request because she wished black and white clarity to the woman's answers.

This seems somewhat surprising. After 50 years associated with ex members and writers and government officials that dared to investigate or speak out there about Scientology being how was it Welkos put it? "sued, harassed, spied on, as well as subjected to dirty tricks,Inch it's Hamilton who needs security for expressing her views.

But even granting Hamilton these many power in the conversation, Lynch still could have salvaged things in the event that she'd just asked the girl (or committee, or no matter what) a few decent questions.

Just after looking at what she asked, however, I have to wonder, provide the editors down at the Periods completely forgotten Welkos and Sappell? (And i also want to stress editors. When Lynch's name is on the part, she appears to have been somewhat new to the subject of Scientology. I sent the woman an e mail asking if it was her first Scientology bit, and also if she had requested harder questions that "Hamilton" declined to answer. Still waiting for a reply.)

Here's a sample of what purchasing asked:

Does Scientology consider itself a religion?

You take issue with the depiction of Scientologists as blind readers or believers.

Do you think Scientology is actually secretive?

Hamilton is also lobbed softballs about Scientology and medicines, about what its members imagine, and about what they pay.

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jobless rate climbs to Hunting for.7 percent, highest in Thirty three years

New Jersey unemployment risen to a 33 year high of 9.7 percent in August but preliminary estimates prove that job growth continued for the second month after Seventeen months of job failures.

As the jobless rate increased from 9.3 percent, Only two,900 people found exclusive sector jobs but A couple of,100 others lost government and schools position, generating the overall jobs gain 300.

The state unemployment rate involving 9.7 percent now equals the national jobless rate.

In accordance with preliminary estimates from the Crews Department monthly survey involving employers, nonfarm wage and earnings employment in the Garden State increased to a total of three,930,500 in August.

June, New Jersey private sector employers continued to add workers for their payrolls, said Labor Commissioner David m. Socolow. is encouraging that Nj-new jersey continued to see a several month trend of private area employment stabilizing and moving in a positive direction. But the jobless rate demonstrates that there is considerably more Nike Free 5 to do to put New Jersey back to work. rate

The lack of employment rate in New Jersey leaped amazingly from 9.3 percent for you to 9.7 percent in July, matching the national figure, a state said today.

is significant since we now at the same degree as the nation, and we just shy of double number unemployment, said James Barnes, dean of the Edward J. Bloustein Institution of Planning and Open public Policy at Rutgers University. very little positive. Most of the individual factors are moving in the wrong track. state Department of Labor and Workforce Development said the full number of jobs rose by 800, though that number could be volatile. In the July review, the state said jobs rose by 5,600, nonetheless revised figures released these days indicate the state actually missing 500 jobs in that thirty days.

The private sector saw job growth of 2.9 percent rolling around in its second straight month connected with increases. Meanwhile, in the consumer sector which is about a finally of the size of the private market jobs fell by A couple of.1 percent.

From the NJ Unit of Labor:

Private Sector Occupation Growth Continued in August Adding 2,900 Careers; Unemployment Rate at On the lookout for.7 Percent, Continues to Match Country wide Trend

August preliminary estimations showed that private sector occupation in New Jersey continued an encouraging trend, as employers added 2,900 private field jobs. Overall, employment increased by by 800 jobs, because public sector employment refused by 2,100.

A state unemployment rate rose Zero.4 percentage point in May to 9.7 percent, reflecting the national trend. In Come july 1st, for example, the state initially reported that the economy added Several,900 jobs. On Wed, it revised the amount and said the state dropped 500 jobs.

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In the case of the standard one-dimensional wave equation ytt=c2yxx disturbances of all frequencies travel with the same constant speed c. In dispersive media the traveling speed of disturbances depends on their frequency and we get c(ω) where ω is the frequency of the disturbance. Many physical systems are dispersive, for example the elastic beams described by the Euler-Bernoulli beam equation ytt=kyxxxx where k is a material constant.

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Banded waveguide synthesis is implemented in most available sound synthesis libraries and programs such as:

Sources

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The algorithm

Suppose G is a finite cyclic group of order n which is generated by the element α, and we seek to find the discrete logarithm x of the element β to the base α. In other words, we seek xZn such that αx=β. The lambda algorithm allows us to search for x in some subset {a,,b}Zn. We may search the entire range of possible logarithms by setting a=0 and b=n1, although in this case Pollard's rho algorithm is more efficient. We proceed as follows:

1. Choose a set S of integers and define a pseudorandom map f:GS.

2. Choose an integer N and compute a sequence of group elements {x0,x1,,xN} according to:

3. Compute

d=i=0N1f(xi).

Observe that:

xN=x0αd=αb+d.

4. Begin computing a second sequence of group elements {y0,y1,} according to:

and a corresponding sequence of integers {d0,d1,} according to:

dn=i=0n1f(yi).

Observe that:

yi=y0αdi=βαdi for i=0,1,,N1

5. Stop computing terms of {yi} and {di} when either of the following conditions are met:

A) yj=xN for some j. If the sequences {xi} and {yj} "collide" in this manner, then we have:
xN=yjαb+d=βαdjβ=αb+ddj(modn)xb+ddj(modn)
and so we are done.
B) di>ba+d. If this occurs, then the algorithm has failed to find x. Subsequent attempts can be made by changing the choice of S and/or f.

Complexity

Pollard gives the time complexity of the algorithm as O(ba), based on a probabilistic argument which follows from the assumption that f acts pseudorandomly. Note that when the size of the set {a, …, b} to be searched is measured in bits, as is normal in complexity theory, the set has size log(b − a), and so the algorithm's complexity is O(ba)=O(212log(ba)), which is exponential in the problem size. For this reason, Pollard's lambda algorithm is considered an exponential time algorithm. For an example of a subexponential time discrete logarithm algorithm, see the index calculus algorithm.

Naming

The algorithm is well known by two names.

The first is "Pollard's kangaroo algorithm". This name is a reference to an analogy used in the paper presenting the algorithm, where the algorithm is explained in terms of using a tame kangaroo to trap a wild kangaroo. Pollard has explained[2] that this analogy was inspired by a "fascinating" article published in the same issue of Scientific American as an exposition of the RSA public key cryptosystem. The article[3] described an experiment in which a kangaroo's "energetic cost of locomotion, measured in terms of oxygen consumption at various speeds, was determined by placing kangaroos on a treadmill".

The second is "Pollard's lambda algorithm". Much like the name of another of Pollard's discrete logarithm algorithms, Pollard's rho algorithm, this name refers to the similarity between a visualisation of the algorithm and the Greek letter lambda (λ). The shorter stroke of the letter lambda corresponds to the sequence {xi}, since it starts from the position b to the right of x. Accordingly, the longer stroke corresponds to the sequence {yi}, which "collides with" the first sequence (just like the strokes of a lambda intersect) and then follows it subsequently.

Pollard has expressed a preference for the name "kangaroo algorithm",[4] as this avoids confusion with some parallel versions of his rho algorithm, which have also been called "lambda algorithms".

See also

References

  1. J. Pollard, Monte Carlo methods for index computation mod p, Mathematics of Computation, Volume 32, 1978
  2. J. M. Pollard, Kangaroos, Monopoly and Discrete Logarithms, Journal of Cryptology, Volume 13, pp 437-447, 2000
  3. T. J. Dawson, Kangaroos, Scientific American, August 1977, pp. 78-89
  4. http://sites.google.com/site/jmptidcott2/

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(WSMV Television set) NASHVILLE, Tenn. Portland police detained a father Monday after they uncovered pictures of his 2 year aged son packaging marijuana.

Law enforcement said they were called of a domestic altercation between a husband and wife Throughout the investigation, officers said that they found images on Christopher Bradley's phone of his Two year old son standing at a new table and packaging bud.

I hate being in the position of getting to defend this guy. I never fond of guys who wind up in so called altercations with their wives. My partner and i not happy about cannabis consumers being irresponsible and allowing their kids access to the stash. My spouse and i disappointed every time there is a report of a cannabis consumer doing something stupid like taking pictures of their kid with pot.

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Although child abuse? I wear think so. That Celine Stockists Usa feels too severe to me. There is absolutely no report of the child remaining actually abused. The child didn Cheap New Balance 574 Australia consume any of the cannabis, which is needs to harm he could have quite possibly suffered, aside from the risk of cops bursting in with no topple warrants and automatic firearms, and even a kid eating cannabis is not going to die or undergo any lasting harm. I believe child neglect is appropriate, but if we going to charge mike geary with child abuse, in that case need to be charged as well.

We're the producer of The NORML Network, the actual host of the NORML SHOW Dwell and The NORML Stash Blog, along with NORML's Outreach Coordinator. I'm married, are living in Portland, Oregon, and I am a licensed medical marijuana caregiver in this state. I've worked days for an IT geek and night time as a professional musician. Before, I have been the host with my own political talk radio stations show on satellite radio. I am the High Times "Freedom Fighter of the Month" and I travel across the country to teach people on marijuana alter. I've dedicated my life to bringing an end to grownup marijuana prohibition and re legalizing marijuana hemp, and I'm honored for being chosen by NORML to give voice to the Marijuana Nation and speak for those who can't converse up.

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Welkos, remaining, and SappellIn 1990, just before he or she and his colleague Joel Sappell ended up about to publish a landmark collection exposing Scientology's secrets in the L . a . Times, Robert Welkos found that somebody had placed in a manila package against his home's doorstep a brochure from a mortuary, reassuring him to plan his own obituary.

He checked with the obituary home, but it said it would never solicit in that way. Then one more brochure showed up two days afterwards, left by a man spotted scurrying away by Welkos's wife.

I'd never know if the deliveries have been just a mix up or a threatening prank. Just as I have never acknowledged who made the a large number of hang up telephone calls to the home; what caused my lover's dog to go into seizures make certain that the Times published the secret teachings of Scientology; why a bogus assault complaint was submitted with the Los Angeles Police Section against Sappell by a man who is address and name proved to be phony, or why car or truck dealers we had never addressed were making inquiries within our personal credit reports.

Whenever editors ask critical questions about Scientology they are able to Nike Air Force Australia expect to endure intense individual scrutiny. Over the years, various editors have been sued, harassed, spied upon, and even been subjected to soiled tricks.

The 1990 collection by Sappell and Welkos proved to be probably the most significant journalistic projects possibly done on Scientology, and was particularly brave for the proximity from the newspaper to Scientology's Los Angeles admin headquarters.

Which makes it all the more disappointing that yesterday, the sloppiest wet kiss I've seen Scientology receive from the mainstream press in a very period of time showed up on the website of the Are generally Times, which long ago dropped the services of Welkos and Sappell.

The article has been titled "What is Scientology? A Scientologist delivers her point of view," and yes it showed up in the "Nation Now" section of the Instances website. We've asked it ourselves, knowing that readers value a primer to this kind of complex body of knowledge.

Lynch provides ask a Scientologist this question, that is, again, a good notion. We've often spoken to current church members, although usually not for your record. This is in part why Debbie Cook's infamous Fresh Year's Eve e mail was so stunning a former church New Balance Stockists London management, she insisted that she was still a member in good standing when your woman gave the world a look into the crisis that is convincing more and more longtime members to sneak away. You can send your ex questions, and she may choose to answer them. There's no indication of who she really is or where the woman lives. In extensive on the internet databases of Scientology "completions" successes classified by official church publications you cannot find any record of any Laurie Hamilton. And over recent years, Scientology experts have found that she offers extremely unusual answers for a person who claims to be a subsequent generation church member created in 1968 to parents who'd fallen in with L. Ralph Hubbard from the very beginning, the 1950 magazine of his book, Dianetics.

In 2006, the researchers at Operation Clambake observed that Hamilton, for example, spoke freely about something that is assumed to get taboo among actual church associates: the condition of L. Ron Hubbard dads and moms before his death. As is possible seen in this video, 2 or 3 days after Hubbard's death in Jan, 1986, it was announced to church members at the Hollywood Palladium that will Hubbard had been as healthy as a possible ox, and had simply picked out to leave behind his body as he moved on to another planes of existence to follow further spiritual research.

Hamilton tends to make other statements about Hubbard and the foibles being less critical than Hollister Brisbane the works he put aside, and also that some of the more unusual space opera stories throughout Scientology's upper level teachings (which expense members hundreds of thousands of dollars to discover) are simply metaphors which Scientologists can opt and choose from.

Hamilton, in other words, may sound like just about no Scientologist you will encounter inside official church (in some ways, she sounds like an "independent Scientologist," who are heretics so far as David Miscavige's church is concerned). She gets long been suspected to be Womens Air Max 2012 concentrating on behalf of Scientology's Office associated with Special Affairs, which would typically vet any communication towards the public of the church's official insurance plans. Various experts have pointed out that her answers appear to be on purpose more pragmatic than the dogmatic replies church members give 1 another, and are written for a cynical public. (Mike Rinder, OSA's former management director who left in 2007, told me that he could be never heard of her. However he said he is certain that such public statements would be learned about by church officials very carefully before publication.)

Laurie Hamilton, in other words, is actually a problematic figure, especially for your journalist who wants a straight response about Scientology.

But the Times formulated problems in a couple of ways. Primary, it agreed to all of Hamilton's rules, which were extensive.

She dropped to reveal specifics about the place she lives or works for fear that some customers might hold her beliefs against her.

What follows is undoubtedly an edited transcript of an employment Fake Celine Bags interview conducted via e mail during Hamilton's request because she wished black and white clarity to the woman's answers.

This seems somewhat surprising. After 50 years associated with ex members and writers and government officials that dared to investigate or speak out there about Scientology being how was it Welkos put it? "sued, harassed, spied on, as well as subjected to dirty tricks,Inch it's Hamilton who needs security for expressing her views.

But even granting Hamilton these many power in the conversation, Lynch still could have salvaged things in the event that she'd just asked the girl (or committee, or no matter what) a few decent questions.

Just after looking at what she asked, however, I have to wonder, provide the editors down at the Periods completely forgotten Welkos and Sappell? (And i also want to stress editors. When Lynch's name is on the part, she appears to have been somewhat new to the subject of Scientology. I sent the woman an e mail asking if it was her first Scientology bit, and also if she had requested harder questions that "Hamilton" declined to answer. Still waiting for a reply.)

Here's a sample of what purchasing asked:

Does Scientology consider itself a religion?

You take issue with the depiction of Scientologists as blind readers or believers.

Do you think Scientology is actually secretive?

Hamilton is also lobbed softballs about Scientology and medicines, about what its members imagine, and about what they pay.

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jobless rate climbs to Hunting for.7 percent, highest in Thirty three years

New Jersey unemployment risen to a 33 year high of 9.7 percent in August but preliminary estimates prove that job growth continued for the second month after Seventeen months of job failures.

As the jobless rate increased from 9.3 percent, Only two,900 people found exclusive sector jobs but A couple of,100 others lost government and schools position, generating the overall jobs gain 300.

The state unemployment rate involving 9.7 percent now equals the national jobless rate.

In accordance with preliminary estimates from the Crews Department monthly survey involving employers, nonfarm wage and earnings employment in the Garden State increased to a total of three,930,500 in August.

June, New Jersey private sector employers continued to add workers for their payrolls, said Labor Commissioner David m. Socolow. is encouraging that Nj-new jersey continued to see a several month trend of private area employment stabilizing and moving in a positive direction. But the jobless rate demonstrates that there is considerably more Nike Free 5 to do to put New Jersey back to work. rate

The lack of employment rate in New Jersey leaped amazingly from 9.3 percent for you to 9.7 percent in July, matching the national figure, a state said today.

is significant since we now at the same degree as the nation, and we just shy of double number unemployment, said James Barnes, dean of the Edward J. Bloustein Institution of Planning and Open public Policy at Rutgers University. very little positive. Most of the individual factors are moving in the wrong track. state Department of Labor and Workforce Development said the full number of jobs rose by 800, though that number could be volatile. In the July review, the state said jobs rose by 5,600, nonetheless revised figures released these days indicate the state actually missing 500 jobs in that thirty days.

The private sector saw job growth of 2.9 percent rolling around in its second straight month connected with increases. Meanwhile, in the consumer sector which is about a finally of the size of the private market jobs fell by A couple of.1 percent.

From the NJ Unit of Labor:

Private Sector Occupation Growth Continued in August Adding 2,900 Careers; Unemployment Rate at On the lookout for.7 Percent, Continues to Match Country wide Trend

August preliminary estimations showed that private sector occupation in New Jersey continued an encouraging trend, as employers added 2,900 private field jobs. Overall, employment increased by by 800 jobs, because public sector employment refused by 2,100.

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In computational number theory and computational algebra, Pollard's kangaroo algorithm (aka Pollard's lambda algorithm, see Naming below) is an algorithm for solving the discrete logarithm problem. The algorithm was introduced in 1978 by the number theorist J. M. Pollard, in the same paper [1] as his better-known rho algorithm for solving the same problem. Although Pollard described the application of his algorithm to the discrete logarithm problem in the multiplicative group of units modulo a prime p, it is in fact a generic discrete logarithm algorithm—it will work in any finite cyclic group.

The algorithm

Suppose G is a finite cyclic group of order n which is generated by the element α, and we seek to find the discrete logarithm x of the element β to the base α. In other words, we seek xZn such that αx=β. The lambda algorithm allows us to search for x in some subset {a,,b}Zn. We may search the entire range of possible logarithms by setting a=0 and b=n1, although in this case Pollard's rho algorithm is more efficient. We proceed as follows:

1. Choose a set S of integers and define a pseudorandom map f:GS.

2. Choose an integer N and compute a sequence of group elements {x0,x1,,xN} according to:

3. Compute

d=i=0N1f(xi).

Observe that:

xN=x0αd=αb+d.

4. Begin computing a second sequence of group elements {y0,y1,} according to:

and a corresponding sequence of integers {d0,d1,} according to:

dn=i=0n1f(yi).

Observe that:

yi=y0αdi=βαdi for i=0,1,,N1

5. Stop computing terms of {yi} and {di} when either of the following conditions are met:

A) yj=xN for some j. If the sequences {xi} and {yj} "collide" in this manner, then we have:
xN=yjαb+d=βαdjβ=αb+ddj(modn)xb+ddj(modn)
and so we are done.
B) di>ba+d. If this occurs, then the algorithm has failed to find x. Subsequent attempts can be made by changing the choice of S and/or f.

Complexity

Pollard gives the time complexity of the algorithm as O(ba), based on a probabilistic argument which follows from the assumption that f acts pseudorandomly. Note that when the size of the set {a, …, b} to be searched is measured in bits, as is normal in complexity theory, the set has size log(b − a), and so the algorithm's complexity is O(ba)=O(212log(ba)), which is exponential in the problem size. For this reason, Pollard's lambda algorithm is considered an exponential time algorithm. For an example of a subexponential time discrete logarithm algorithm, see the index calculus algorithm.

Naming

The algorithm is well known by two names.

The first is "Pollard's kangaroo algorithm". This name is a reference to an analogy used in the paper presenting the algorithm, where the algorithm is explained in terms of using a tame kangaroo to trap a wild kangaroo. Pollard has explained[2] that this analogy was inspired by a "fascinating" article published in the same issue of Scientific American as an exposition of the RSA public key cryptosystem. The article[3] described an experiment in which a kangaroo's "energetic cost of locomotion, measured in terms of oxygen consumption at various speeds, was determined by placing kangaroos on a treadmill".

The second is "Pollard's lambda algorithm". Much like the name of another of Pollard's discrete logarithm algorithms, Pollard's rho algorithm, this name refers to the similarity between a visualisation of the algorithm and the Greek letter lambda (λ). The shorter stroke of the letter lambda corresponds to the sequence {xi}, since it starts from the position b to the right of x. Accordingly, the longer stroke corresponds to the sequence {yi}, which "collides with" the first sequence (just like the strokes of a lambda intersect) and then follows it subsequently.

Pollard has expressed a preference for the name "kangaroo algorithm",[4] as this avoids confusion with some parallel versions of his rho algorithm, which have also been called "lambda algorithms".

See also

References

  1. J. Pollard, Monte Carlo methods for index computation mod p, Mathematics of Computation, Volume 32, 1978
  2. J. M. Pollard, Kangaroos, Monopoly and Discrete Logarithms, Journal of Cryptology, Volume 13, pp 437-447, 2000
  3. T. J. Dawson, Kangaroos, Scientific American, August 1977, pp. 78-89
  4. http://sites.google.com/site/jmptidcott2/

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Sources

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In the case of the standard one-dimensional wave equation ytt=c2yxx disturbances of all frequencies travel with the same constant speed c. In dispersive media the traveling speed of disturbances depends on their frequency and we get c(ω) where ω is the frequency of the disturbance. Many physical systems are dispersive, for example the elastic beams described by the Euler-Bernoulli beam equation ytt=kyxxxx where k is a material constant.

Banded waveguides model dispersive behavior by splitting the propagation of disturbances into frequency bands. Each frequency band is modeled using a band-limited version of the standard digital waveguide method. Each frequency band is tuned to the resonant frequencies of the sounding object to be modeled to avoid any discretization error at the dominant and audible frequencies Template:Harv.

Banded waveguide synthesis is implemented in most available sound synthesis libraries and programs such as:

Sources

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Template:Sound synthesis typesyIn computational number theory and computational algebra, Pollard's kangaroo algorithm (aka Pollard's lambda algorithm, see Naming below) is an algorithm for solving the discrete logarithm problem. The algorithm was introduced in 1978 by the number theorist J. M. Pollard, in the same paper [1] as his better-known rho algorithm for solving the same problem. Although Pollard described the application of his algorithm to the discrete logarithm problem in the multiplicative group of units modulo a prime p, it is in fact a generic discrete logarithm algorithm—it will work in any finite cyclic group.

The algorithm

Suppose G is a finite cyclic group of order n which is generated by the element α, and we seek to find the discrete logarithm x of the element β to the base α. In other words, we seek xZn such that αx=β. The lambda algorithm allows us to search for x in some subset {a,,b}Zn. We may search the entire range of possible logarithms by setting a=0 and b=n1, although in this case Pollard's rho algorithm is more efficient. We proceed as follows:

1. Choose a set S of integers and define a pseudorandom map f:GS.

2. Choose an integer N and compute a sequence of group elements {x0,x1,,xN} according to:

3. Compute

d=i=0N1f(xi).

Observe that:

xN=x0αd=αb+d.

4. Begin computing a second sequence of group elements {y0,y1,} according to:

and a corresponding sequence of integers {d0,d1,} according to:

dn=i=0n1f(yi).

Observe that:

yi=y0αdi=βαdi for i=0,1,,N1

5. Stop computing terms of {yi} and {di} when either of the following conditions are met:

A) yj=xN for some j. If the sequences {xi} and {yj} "collide" in this manner, then we have:
xN=yjαb+d=βαdjβ=αb+ddj(modn)xb+ddj(modn)
and so we are done.
B) di>ba+d. If this occurs, then the algorithm has failed to find x. Subsequent attempts can be made by changing the choice of S and/or f.

Complexity

Pollard gives the time complexity of the algorithm as O(ba), based on a probabilistic argument which follows from the assumption that f acts pseudorandomly. Note that when the size of the set {a, …, b} to be searched is measured in bits, as is normal in complexity theory, the set has size log(b − a), and so the algorithm's complexity is O(ba)=O(212log(ba)), which is exponential in the problem size. For this reason, Pollard's lambda algorithm is considered an exponential time algorithm. For an example of a subexponential time discrete logarithm algorithm, see the index calculus algorithm.

Naming

The algorithm is well known by two names.

The first is "Pollard's kangaroo algorithm". This name is a reference to an analogy used in the paper presenting the algorithm, where the algorithm is explained in terms of using a tame kangaroo to trap a wild kangaroo. Pollard has explained[2] that this analogy was inspired by a "fascinating" article published in the same issue of Scientific American as an exposition of the RSA public key cryptosystem. The article[3] described an experiment in which a kangaroo's "energetic cost of locomotion, measured in terms of oxygen consumption at various speeds, was determined by placing kangaroos on a treadmill".

The second is "Pollard's lambda algorithm". Much like the name of another of Pollard's discrete logarithm algorithms, Pollard's rho algorithm, this name refers to the similarity between a visualisation of the algorithm and the Greek letter lambda (λ). The shorter stroke of the letter lambda corresponds to the sequence {xi}, since it starts from the position b to the right of x. Accordingly, the longer stroke corresponds to the sequence {yi}, which "collides with" the first sequence (just like the strokes of a lambda intersect) and then follows it subsequently.

Pollard has expressed a preference for the name "kangaroo algorithm",[4] as this avoids confusion with some parallel versions of his rho algorithm, which have also been called "lambda algorithms".

See also

References

  1. J. Pollard, Monte Carlo methods for index computation mod p, Mathematics of Computation, Volume 32, 1978
  2. J. M. Pollard, Kangaroos, Monopoly and Discrete Logarithms, Journal of Cryptology, Volume 13, pp 437-447, 2000
  3. T. J. Dawson, Kangaroos, Scientific American, August 1977, pp. 78-89
  4. http://sites.google.com/site/jmptidcott2/

Template:Number-theoretic algorithmsx Bxy

It is fallacious to conclude that there is some particular concept to which everyone subscribes.

It is valid to conclude that each person believes a given concept. But it is entirely possible that each person believes in a unique concept.

References

  • Robert Audi (General Editor), The Cambridge Dictionary of Philosophy (Second Edition), 1999, pp. 272-3.
  • A. R. Lacey, Dictionary of Philosophy (Third Revised Edition) (Barnes & Noble, 1996).
  • Introduction to Logic, Harry J. Gensler, p. 220
  • Antony G. Flew, Dictionary of Philosophy: Revised Second Edition
  • Harry J. Gensler, Historical Dictionary of Logic

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