mm-509 === Subject: Re: Correlation using FFT > To make a leaky integrator fast cross correlator, I would omit the > second coef[CapitalThorn]cient in your formula, 1-beta. > Leaving, > Sxy(i) = beta*Sxy(i-1) + X(i)*Y(i) > This makes the boundary cases nice and clean: > beta = 0 -- forget everything , use current block only > beta = 1 -- forget nothing , use entire signal If you do what you suggest you get a dc gain (ie when z=1) which is 1/(1-beta) rather than unity. Take z-transforms and the TF is (1-beta)/(1-betaz^-1) .... I see your argument - you are trying to get back to a pure integrator when beta=1 but pure integrators are not a good idea in open-loop - any slight dc-offset and off they go for a walk.Best results are obtained with beta=05 up to 0.9 (ish!). Tom === Subject: Re: Correlation using FFT >To make a leaky integrator fast cross correlator, I would omit the >second coef[CapitalThorn]cient in your formula, 1-beta. >Leaving, >Sxy(i) = beta*Sxy(i-1) + X(i)*Y(i) >This makes the boundary cases nice and clean: >beta = 0 -- forget everything , use current block only >beta = 1 -- forget nothing , use entire signal >-- Mark > If you do what you suggest you get a dc gain (ie when z=1) which is > 1/(1-beta) rather than unity. > Take z-transforms and the TF is > (1-beta)/(1-betaz^-1) .... > I see your argument - you are trying to get back to a pure integrator when > beta=1 but pure integrators are not a good idea in open-loop - any slight > dc-offset and off they go for a walk.Best results are obtained with beta=05 > up to 0.9 (ish!). > Tom I agree pure integration is a bad idea for endless input, but that was not the problem put forth. The OP didn't mention anything about an open loop. FWIW, I don't think the term unity gain is very meaningful when applied to a single buffer answer in cross-correlation. Let's hop a little further down this bunny trail ... Both systems' transfer functions contain a single pole on the real axis with magnitude beta. I suggest that the unity gain created by the (1-beta) term causes more problems than it solves. It certainly declaws the unstable pole when beta == 1 by setting the gain to zero. Unfortunately, that happens to be is the useful case of cross-correlation of two complete sequences. To have the best of both worlds, I'd split beta and 1-beta up into two gains: beta and alpha. y(i) = beta*y(i-1) + alpha*x(i) For the case when unity gain is desired, alpha = 1-beta. If integration is the goal, then alpha = beta = 1 Perhaps it comes down to personal preference. I prefer one algorithm that does two things even if it is slightly more complicated, rather than needing two algorithms. In any case, a gain is usually easy to slip in someplace computationally convenient. -- Mark === Subject: Re: Correlation using FFT >To make a leaky integrator fast cross correlator, I would omit the >second coef[CapitalThorn]cient in your formula, 1-beta. >Leaving, >Sxy(i) = beta*Sxy(i-1) + X(i)*Y(i) > >This makes the boundary cases nice and clean: >beta = 0 -- forget everything , use current block only >beta = 1 -- forget nothing , use entire signal > > >-- Mark > > If you do what you suggest you get a dc gain (ie when z=1) which is > 1/(1-beta) rather than unity. > Take z-transforms and the TF is > (1-beta)/(1-betaz^-1) .... > I see your argument - you are trying to get back to a pure integrator when > beta=1 but pure integrators are not a good idea in open-loop - any slight > dc-offset and off they go for a walk.Best results are obtained with beta=05 > up to 0.9 (ish!). > Tom > I agree pure integration is a bad idea for endless input, but that was > not the problem put forth. > The OP didn't mention anything about an open loop. > FWIW, I don't think the term unity gain is very meaningful when > applied to a single buffer answer in cross-correlation. > Let's hop a little further down this bunny trail ... > Both systems' transfer functions contain a single pole on the real axis > with magnitude beta. > I suggest that the unity gain created by the (1-beta) term causes more > problems than > it solves. It certainly declaws the unstable pole when beta == 1 by > setting the gain to zero. > Unfortunately, that happens to be is the useful case of > cross-correlation of two complete sequences. > To have the best of both worlds, I'd split beta and 1-beta up into two > gains: beta and alpha. > y(i) = beta*y(i-1) + alpha*x(i) > For the case when unity gain is desired, alpha = 1-beta. If > integration is the goal, then alpha = beta = 1 > Perhaps it comes down to personal preference. > I prefer one algorithm that does two things even if it is slightly more > complicated, rather than needing two algorithms. > In any case, a gain is usually easy to slip in someplace computationally > convenient. > -- Mark The idea comes from exponential smoothing in time-series analysis http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc431. htm If you don't put in the (1-beta) part then you get an offset ie you have to re-scale afterwards to get the right answer. You will [CapitalThorn]nd that integrators (pure) are rarely if ever used on open loop (as we have here). For example the LMS algorithm has integrators in it - as does the Kalman Filter and many such algorithms w(k+1)=w(k)+2*mu*X(k)*e(k) but it has an error term ie feedback to keep it in line!It does not matter whether integrators are analogue or digital, in open loop they are troublesome.Try putting beta=1 and see if it works.Or simpler still try integrating a pure sine-wave.Slightest dc and we are in trouble. Tom === Subject: Re: Correlation using FFT > If you don't put in the (1-beta) part then you get an offset ie you have to > re-scale afterwards to get the right > answer. On the contrary, it is impossible to get the right answer if you DO put in the 1-beta part. ... if the question being answered is the one the original poster asked: how to correlate two sequences using the fft. Or perhaps I am also guilty of assuming too much. Perhaps the OP wanted the single-valued correlation : cov(x,y) / sqrt( var(x)*var(y) ) But I don't think so. Covariance and variance operations are already linear complexity. I can't see how FFTs would make them any faster. I'm pretty sure the OP wanted cross-correlation when he asked for correlation. There is a very speci[CapitalThorn]c de[CapitalThorn]nition for cross-correlation. See http://mathworld.wolfram.com/Cross-Correlation.html or http://cnx.rice.edu/content/m10686/latest/ Notice the pure integration and in[CapitalThorn]nite bounds. The formula you posted may have uses for continuous (open loop) processing, but it is NOT cross-correlation. I can only assume the question for your right answer is how do I get a time-decaying approximation of cross-correlation. That question was never asked. You made a good suggestion that was certainly topical, considering more people read a thread than just the few persons writing it. But the OP had signals up to 45 seconds long, far from in[CapitalThorn]nite. -- Mark === Subject: Re: Correlation using FFT ... > never asked. You made a good suggestion that was certainly > topical, considering more people read a thread than just the few > persons writing it. But the OP had signals up to 45 seconds > long, far from in[CapitalThorn]nite. > -- Mark I'm one other reading the thread... maybe my contribution is far off the original goal of the OP. Just to satisfy my interest (and enhance my knowledge...), I would like to put in two more general questions: 1) given two such signals of 45 seconds, which are equal. now cut 5s from the beginning of the [CapitalThorn]rst and paste it to the end of it . then correlating this modi[CapitalThorn]ed signal with the other unmodi[CapitalThorn]ed. I reckon that the frequency content is the same except on the borders where the signal has been cut/pasted. Therefore I would expect similar FFT results and probably a high degree of correlation. My question: does correlation detect the shift of most of the signal and show good correlation? Or would the result be a low correlation because signal contents don't match at any point? 2) Given, I want to compare a signal (endless stream) with a certain pattern (short piece of signal). I expect that the signal contains pieces which are similar to the pattern, but differ either * in amplitude or * in width or * in both. Which method would be chosen to [CapitalThorn]nd the occurrences? Is cross-correlation the right approach? Or will it fail in one of the cases? Remember: it's not a current task which bothers me, it's only that I'm curious (maybe I'll need the answer soon, nevertheless ...) so it's enough to give me a direction. Bernhard === Subject: Re: Correlation using FFT > If you don't put in the (1-beta) part then you get an offset ie you have to > re-scale afterwards to get the right > answer. > On the contrary, it is impossible to get the right answer if you DO put > in the 1-beta part. > ... if the question being answered is the one the original poster asked: > how to correlate two sequences using the fft. > Or perhaps I am also guilty of assuming too much. Perhaps the OP > wanted the single-valued correlation : cov(x,y) / sqrt( var(x)*var(y) ) > But I don't think so. Covariance and variance operations are already > linear complexity. I can't see how FFTs would make them any faster. > I'm pretty sure the OP wanted cross-correlation when he asked for > correlation. > There is a very speci[CapitalThorn]c de[CapitalThorn]nition for cross-correlation. > See http://mathworld.wolfram.com/Cross-Correlation.html > or http://cnx.rice.edu/content/m10686/latest/ > Notice the pure integration and in[CapitalThorn]nite bounds. > The formula you posted may have uses for continuous (open loop) > processing, but it is NOT cross-correlation. > I can only assume the question for your right answer is how do I get > a time-decaying approximation of cross-correlation. That question was > never asked. You made a good suggestion that was certainly topical, > considering more people read a thread than just the few persons writing > it. But the OP had signals up to 45 seconds long, far from in[CapitalThorn]nite. > -- Mark It is certainly Cross Correlation. In fact the method is more general (with modi[CapitalThorn]cation) - I mentioned the Hannan-Thomson algorithm and the SCOT method for instance. In its simpler form it is just the Wiener-Kinchen theorem ie the Fourier Transform of cross-corr is power spectral density. The basic idea is found here http://www.paper.edu.cn/scholar/known/qiutianshuang/ qiutianshuang-1.pdf though it is much older. You are confusing the pure integration in smoothing the cross-periodograms with the pure integration of getting a Cross-Corr (as you point out). The method I quoted is only to smooth the cross periodogram (PSD estimate).You don't need pure integration as this happens when you do an inverse FFT ie the Wiener Kinchen theorem again. In fact you don't need to smooth the cross-periodograms at all but you would get quite a noisy estimate. Also ordinary cross-corr whether you do it in the freq domain or the ordinary method has drawbacks with certain problems - particulalry estimating time-delays (or multple time-delays) and this is why generalised cross-corr is necessary. Hope this helps you to understand. Tom === Subject: Re: hook jeeves algorithm You can [CapitalThorn]nd a discussion of the Hooke-Jeeves algorithm from Direct Optimizer Technical Reference. Direct Optimizer is a free nonlinear optimization Add-In for Microsoft Excel, and it is based on the Hooke-Jeeves algorithm. Download it from http://www.directoptimizer.com - Jorma > I'm looking for the Hook_Jeeves algorithm.Actually I've found one,but > it's not very clear.Can anyone help me in this respect? > Padideh === Subject: Re: what is the largest named number in the world??????? Graham's number is described as the largest number put to ptactical use. is 1 followed by 100 zeros - a million is 1 followed by 6 zeros. In European usage a billion used to be 1 followed by 12 zeros, and a trillion 1 followed by 18 zeros. (A milliard was 1 followed by 9 zeros). Then US usage took over - a billion being 1 followed by 9 zeros, and a trillion being 1 followed by 12 zeros. - try using Google! You will get links to other large numbers. > hi, my name is kendra, and since no one knows whatthe largest number > in the world is, i would like to know what the largest named number in > the world is!! > thanx a mill, > kendra > > A gazillion. === Subject: Re: what is the largest named number in the world??????? charset=iso-8859-1 > Graham's number is described as the largest number put to ptactical > use. > is 1 followed by 100 zeros - a million is 1 followed by 6 zeros. In > European usage a billion used to be 1 followed by 12 zeros, and a > trillion 1 followed by 18 zeros. (A milliard was 1 followed by 9 > zeros). Then US usage took over - a billion being 1 followed by 9 > zeros, and a trillion being 1 followed by 12 zeros. > - try using Google! You will get links to other large numbers. ------ I thought that these numbers were called googol and googolplex. The Google search engine (and its various relatives) have caused the the initial lower case - which means, in cricket: to dismiss (a batsman) with a googly, is also in danger of this sort of confusion these days ... John johnDOTmorrisonATtescoDOTnet -- Asking whether machines can think is like asking whether submarines can swim. - Ben Hutchings --- Outgoing mail is certi[CapitalThorn]ed Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com). === Subject: Re: what is the largest named number in the world??????? googolplex has more interesting links. My daughter (aged 7) on being told of googol and googolplex immediately followed the logic, and nows talk of googolplexplex and the like. (In speech I don't have to spell correctly!) > Graham's number is described as the largest number put to ptactical > use. > is 1 followed by 100 zeros - a million is 1 followed by 6 zeros. In > European usage a billion used to be 1 followed by 12 zeros, and a > trillion 1 followed by 18 zeros. (A milliard was 1 followed by 9 > zeros). Then US usage took over - a billion being 1 followed by 9 > zeros, and a trillion being 1 followed by 12 zeros. > - try using Google! You will get links to other large numbers. > ------ > I thought that these numbers were called googol and googolplex. > The Google search engine (and its various relatives) have caused the > the initial lower case - which means, in cricket: to dismiss (a batsman) > with a googly, is also in danger of this sort of confusion these days ... > John > johnDOTmorrisonATtescoDOTnet > -- > Asking whether machines can think is like asking whether submarines can > swim. - Ben Hutchings > --- > Outgoing mail is certi[CapitalThorn]ed Virus Free. > Checked by AVG anti-virus system (http://www.grisoft.com). === Subject: Anyone especially in this group help me/us [CapitalThorn]nd optimum lineages to beat Vegas? Hello All, My following letter to the Las Vegas Gaming Commission explains it all. All I/we need now is to [CapitalThorn]nd the optimum number of lineages. All my programming and spreadsheets carte blanche to anyone requesting it. Joel S. Mr. Peter C. Bernhard (Chairman) Mr. Dennis K. Neilander (Chairman) Mr. Arthur Marshall Mr. Bobby L. Siller Ms. Sue Wagner Mr. Scott Scherer Mr. Radha Chanderraj Mr. John T. Moran Jr. The Nevada Gaming Commission and State Gaming Control Board. 1919 East College Parkway Carson City, Nevada 89706 Gaming Commission and State Gaming Control Board: Following the bulk of this letter is a supplemental concise step by step recipe or algorithm for the end of the of the money line format of wagering as a viable wagering option for the sports book. This is not some idle boast but a statement that from overwhelming evidence derived from the specialized Excel spreadsheets I have developed. It is a very simple elegant system I formally call the Winning Percentage Underdog Martingale system or Dog Mart for short. I've already posted my Dog Mart system on the Internet to mixed reviews. I expect the company line of you/The Nevada Gaming Commission and Gaming Control Board (NGCGCB) to be one of an open invitation that Vegas is open 24 hours a day for you to ply your Dog Mart. I take the open invitation I'm assuming you'd make in the same context as the same disingenuous ones I'd assume you'd likewise make to Blackjack players that are pro[CapitalThorn]cient in counting cards. Others have made/are making similar claims before, now and will henceforth. Some dismiss my Dog Mart system (a subset of these people vehemently) out of hand, a few I know have embraced it and others are studying for themselves the viability of it. For those who expressed to me an intention to program my Dog Mart system independently will (soon) [CapitalThorn]nd they are reinventing the wheel and my spreadsheets already generate similar results in suf[CapitalThorn]cient quantity they need not a compiled version. A compiled Dog Mart program generates more data than my spreadsheets but the difference in outcome can readily be seen would be moot. I have absolutely no qualms about releasing my [CapitalThorn]ndings and relating the subtleties and intricacies of Dog Mart to you/the NGCGCB. Shortly later in this post/letter I will be making just a few formal requests from you for clari[CapitalThorn]cations of NGCGCB rulings and statutes. I include the information about my discovery and [CapitalThorn]ndings of my Dog Mart system to qualify my clari[CapitalThorn]cation queries of your of[CapitalThorn]ce not that they are not simply rhetorical questions but compelling questions that beg and deserve a formal response ... a formal response in good faith from you/the NGCGCB the text of which I look forward posting verbatim on the Internet. But [CapitalThorn]rst I've always felt if I indeed found anything substantial to beat the sports book in terms of algorithm, system or strategy. it would be inconsequential if I release and discuss it in the public domain. There is much more potential to beat the house with sports wagering versus casino games especially such as Blackjack which offer the best odds in the player's favor. The issues surrounding Blackjack are relevant to my queries with respect to sports wagering. mathematicians/statisticians such as Thorpe and Revere it has been common knowledge for several years now that by counting cards an advantage over the house can be realized with a favorable ratio of high cards to low cards in conjunction with an optimal general playing strategy. For the casino some solutions to the blackjack card counting threat were immediately apparent: add more decks, alter payouts for blackjacks and other blackjack wagering propositions, prohibit certain blackjack wagers etc. The advent of card counting at times giving the player a statistical edge over the house put casinos in somewhat of a dilemma. Blackjack (is)was certainly a popular casino game and it would be a shame to stop offering it if the card counting advantage per chance overcame all countermeasures to buffer or dissipate its effect. It turns out the problem with card counting is not so much that countermeasures to card counting aren't effective; but countermeasures to what extent? A large draw or allure of Blackjack is through a regime of optimum basic play based on extensive statistical studies and billions of simulated hands, the player can approach but never at any juncture completely overtake the hard house edge. Only through a card counting in conjunction with optimal play can the player realize an advantage over the house and then only at intermittent junctures determined primarily by the count. The countermeasures for card counters are primarily either to add extra decks and/or institute a more stringent (i.e. less) payback format. The latter, even with deceivingly small adjustments, makes Blackjack a much less attractive game that has traditionally offered close odds for the player. This can be a turn-off for many players. Currently it appears a homeostasis or balance exists where while it is still possible to beat the house at Blackjack counting cards even with multiple decks and other countermeasures, it takes the concerted, coordinated effort on the part of a specialized consortium (group) or syndicate to beat the casino over the long term. In a practical sense the coup cannot be accomplished by just one person. With the multiple decks and other aspects it takes more than one person to realize the odds advantage over the long term ... and it takes time. A signi[CapitalThorn]cant part of the of all the aspects comprising the balance between Blackjack player and casino I just alluded to is the casino is permitted by the NGCGCB to bar any player at their whim and caprice. Casinos proactively invite all to play without any apparent exception or condition. There is no signage stipulated by the NGCGCB requiring the casino to inform patrons of the casino's rights in this regard. Special exclusions for counters barring them from continued play have withstood multiple court challenges. In a similar sense the NGCGCB permits ambiguity to the advantage of the casino. For instance a sign can be placed over a group of slot machines stating payouts up to 99%. For many such verbiage can easily be construed that ALL the slot machines in the group pay out at 99% where really only one in the group meet the 99% criteria. Personally I've always felt the governmental regulatory agencies such as the NGCGCB had the [CapitalThorn]duciary responsibility to create a fair and level playing [CapitalThorn]eld or environment between the gambling patron and provider (i.e. the casino). Unfortunately I see I was naive. The NGCGCB is squarely in the casino's corner. ambiguous NGCGCB regulation I'll get to shortly (the crux of this letter) and one reference I've found where the Governor of Nevada OK'd a NGCGCB position to someone who currently had a [CapitalThorn]nancial interest in the slot machine industry: I currently put as much credence in the integrity and good faith intent of the NGCGCB mission statement: [E]ffective gaming regulation is required to protect Nevada's economic base and to foster a healthy business climate, one open to competition, innovation, and future growth. The Gaming Control Board and its employees will act in accordance with the highest standards of honesty, integrity, and impartiality to assure the proper performance of our business and to maintain the con[CapitalThorn]dence of the public we serve. We will seek to represent the best interests of the public and the gaming industry through a balanced and sensible approach to gaming regulation. ... as Arbeit Macht Frei (Work will set you free) on the gates of Auschwitz. effort of a Blackjack card counting syndicate to turn the tables on Las Vegas was undertaken by a group of MIT students. Their exploits how they took Vegas for three million dollars is documented in the book Bringing Down The House by Ben Mezrich. For the MIT group to realize their card counting advantage a prolonged personal presence at the Blackjack tables of all members was required. Soon it became apparent who members of the MIT consortium were and in the footsteps of many of their predecessors the members of the MIT group were banned: persona non gratis. Once the bans were put in place and disguises instituted by members of the MIT group to thwart recognition by the casinos, the members crossed the boundary from pro[CapitalThorn]table but legal bane of the casinos to pro[CapitalThorn]table and illegal bane as they became trespassers and their winnings now in this context became I'm not mistaken fraud thus stealing. With respect to Dog Mart, like Blackjack, for it to be most effective more than one Dog Mart progression (what I term a lineage) - the logical equivalent of one Blackjack player - is heavily recommended. But, unlike Blackjack Dog Mart needs no equivalent of counting cards thus a continuing personal presence in the casino (sports book). All that's required is good, consistent early money line data, mistake free processing and calculation in the Dog Mart programming and establishing as many Dog Mart lineages as possible then make wagers exactly per the system criteria. If one lineage should run into trouble, the others effectively come to it's rescue. It is the same idea with respect to the MIT Blackjack card counting consortium where success is measured in cumulative winning hands among the entire group and no one member's bad run would be devastating. Thus, I actively promote the idea and concept that a coordinated group effort can compellingly beat the Money Line. Nevada is not anymore the only destination in the world to wager sports. Regulation 22 of the of the Gaming Statutes and Regulations of the NGCGCB deals with Race Books and Sports Pools. Regulation 22 prohibits a Messenger bettor which by extension is group or syndicate wagering. 22.010 de[CapitalThorn]nes a Messenger Bettor: 8. Messenger bettor means a person who places a race book or sports pool wager for the bene[CapitalThorn]t of another for compensation. 22.060 Acceptance of wagers. 5. No book or agent or employee of a book may accept a wager from a person who the book, agent, or employee knows or reasonably should know is a messenger bettor or is placing the wager in violation of state or federal law. The repercussions for violation of 22.060.5 are pretty severe: NRS 465.101 Detention and questioning of person suspected of violating chapter; limitations on liability; posting of notice. 1. Any licensee, or his of[CapitalThorn]cers, employees or agents may question any person in his establishment suspected of violating any of the provisions of this chapter. No licensee or any of his of[CapitalThorn]cers, employees or agents is criminally or civilly liable: (a) On account of any such questioning; or (b) For reporting to the State Gaming Control Board or law enforcement authorities the person suspected of the violation. 2. Any licensee or any of his of[CapitalThorn]cers, employees or agents who has probable cause for believing that there has been a violation of this chapter in his establishment by any person may take that person into custody and detain him in the establishment in a reasonable manner and for a reasonable length of time. Such a taking into custody and detention does not render the licensee or his of[CapitalThorn]cers, employees or agents criminally or civilly liable unless it is established by clear and convincing evidence that the taking into custody and detention are unreasonable under all the circumstances. 3. No licensee or his of[CapitalThorn]cers, employees or agents are entitled to the immunity from liability provided for in subsection 2 unless there is displayed in a conspicuous place in his establishment a notice in boldface type clearly legible and in substantially this form: Any gaming licensee, or any of his of[CapitalThorn]cers, employees or agents who has probable cause for believing that any person has violated any provision of chapter 465 of NRS prohibiting cheating in gaming may detain that person in the establishment. (Added to NRS by 1971, 580; A 1973, 446; 1981, 1295; 1983, 564) In light of the severity of being on the wrong side of a Messenger Bettor accusation I would like to formally and respectfully request of the NGCGCB the following clari[CapitalThorn]cations with respect to the Messenger Bettor de[CapitalThorn]nition I contend is deceitful and ambiguous as it currently reads. My perception and/or interpretation of 22.010 is if John gives Sue $50,000 and sends her to Las Vegas and the $50,000 remains under John's name where Sue is acting as an agent for John making a wager in his behalf ... then I contend, as I'm sure you would agree, Sue falls under the de[CapitalThorn]nition of Messenger Bettor in a true sense However, if John lends Sue $50,000 in such a manner that Sue has the legal authority to spend it in any way she sees [CapitalThorn]t including but not limited to wagering ... does Sue in this context continue to fall under the de[CapitalThorn]nition of Messenger Bettor? In another variation on somewhat the same theme let's say three men, [CapitalThorn]guratively Tom, Dick and Harry go to a bank in New York and make an account that all three put in a hypothetical $50,000 where all three have equal privilege to the total $150,000. By arrangement/agreement Tom, Dick or Harry could technically walk into a bank, withdraw $150,000 and go out and spend it any way they want - whoever gets to it [CapitalThorn]rst. Let's say of the three men Harry goes to Las Vegas and wagers across several sports books $150,000. Is he considered a Messenger Bettor under 22.010? What if John and Sue are married, create a company in Arizona and pay John's brother Tom handsomely for business consulting and advice: $1,000 an hour. Tom goes to Las Vegas, does well with Dog Mart, goes back to Arizona and in a [CapitalThorn]t of brotherly love shares his winnings with John and Sue on his own volition ... Is Tom considered a Messenger Bettor under 22.010? The underlying thread between all three scenarios is the OWNERSHIP OF MONEY. I vigorously contend if a person holds clear title to funds that they may do with them as they wish FROM AN ENTIRELY LEGAL CONTEXT OR PERSPECTIVE then by de[CapitalThorn]nition they cannot be a Messenger Bettor. If not then technically a case against anybody who happens to win big at the sports book, especially against the money line, at the whim and caprice of the sports book can have their winnings withheld and be detained. I'm sure this is not the image Vegas or the NGCGCB wishes to project but this apparently is the case. Would it be possible to set up a web page forum where different scenarios could be described or detailed and you/ the NGCGCB could respond to each inquiry individually? Lastly in terms of my formal inquiries, if every such case is decided on a capricious and arbitrary individual basis, if you/the NGCGCB could succinctly list who makes these decisions I would greatly appreciate it. Respectfully, your reply to this formal request for clari[CapitalThorn]cation will demonstrate the integrity and fortitude of the NGCGCB ... your true colors so to speak. If my inquiry scenarios are answered comprehensively in plain language or ambiguous verbiage. and will look forward to your reply inquiry clari[CapitalThorn]cation correspondence in the near future. Joel Shapiro Rochester, New York (585) 473-7013 jrs_14618@yahoo.com http://home.rochester.rr.com/grassroots1 This letter is posted verbatim on the Internet Google news groups sans address Thursday 09/02/04 on: alt.gambling rec.gambling.sports and formally sent to the Nevada Gaming Commission and Gaming Control Board via U.S.P.S Certi[CapitalThorn]ed Letter Return Receipt Requested and electronically transmitted to the Nevada Gaming Commission and Control Board at the following E-Mail addresses: Executive Secretary Marilyn Epling exsec@ngc.nv.gov Following is Dog Mart succinctly explained in easy to follow steps for those at least with a passing familiarity or understanding of the mechanics of the money line versus a the more popular spread wagering format for pro and college football and basketball Also, an understanding of the mechanics or concept of a Martingale Progression; to recoup losses by continually doubling up an initial wager. Dog Mart currently is geared to beating the Money Line. Dog Mart through extensive and ongoing simulations and real data studies of several complete seasons appears to work, and work compellingly, for Major League Baseball (MLB) - the ßagship sport for Dog Mart, Professional Hockey (NHL) and pro basketball (NBA). Currently the it is unknown if the application of Dog Mart to professional (NFL) or College Football Money Lines would be viable. Dog Mart can readily be demonstrated to work better with volume (i.e. more games.) Obviously of the big four pro sports wagered in Vegas and on the Internet, football has the least number of games but has the highest volume and interest and handle in all of sports wagering Spread wagering is much more popular for basketball especially football, but while unpopular some sports books offer Money Lines for both sports. Money Lines for the NBA and NFL can be found with some searching. Whether Dog Mart can somehow be tweaked work within a spread format - the mother lode is also unknown. Dog Mart operates counter or against the grain to a more than a few handicapping conventions, logic and intuition. By all rights Dog Mart shouldn't just fail; but always fail catastrophically right out of the gate ... but simulations, studies using actual data and Dog Mart actually put into real practice has shown otherwise. Dog Mart thrives where intuitively it shouldn't! 1.) On an ongoing daily basis capture and archive the EARLY Money line (sometimes referred to as Opening Line) and game score from a consistent source - For example VegasInsider.com, Jim Feist to name a few of the more more prominent ones. The Source should be one that post an EARLY MONEY LINE and a Closing (sometimes referred to as Current) Money Line reference. The Early Money Line is what Dog Mart is tuned to. It is a standard reference. By default because it is the initial Money Line, it does not change. The Early Line or Opening line will probably, but not necessarily, be from Leroy's/American Wagering that are the source money lines and spreads for many sports books. Often Money Lines are posted only from a Favorite perspective, thus the corresponding underdog money line needs to be found or derived. There are many gambling and handicapping web pages that post Favorite and underdog Money Lines in odds archives. Many of these sites also post odds conversion charts that succinctly show the corresponding Favorite/Underdog money line values. Between the charts and numerous Favorite/Underdog listings a very accurate Underdog money line can be extrapolated in a short time. *NOTE: Only accept or tabulate underdog money lines +100 or greater. Money line Favorite/Underdog combinations can vary from sport to sport in scale and difference. 2.) On an ongoing daily basis keep track of each Underdog team's Underdog Money Line assignment and their Win/Loss performance as the season progresses at the given Money Line. underdog winning percentage (UWP) up to the current day. The UWP is simply the ratio of the number of Underdog wins at a given Underdog Money line divided by the total number of instances (losses and wins) up to the current day at the given Underdog money line. In other words in a real life example: In Mon 08/30/04 the san Francisco Giants had an Underdog money line of +145. The last previous day San Francisco (SF) had a +145 underdog was 08/26/04; a few days earlier. The Win/Loss record for SF at +145 on 08/26/04 was 2 wins and 1 loss thus it's UWP was 66.66% on 08/30/04. Every day the database is updated with the results from the previous day. This is big challenge to do manually but perhaps possible. After the database update the data is then carefully sorted by team, underdog money line, and date in some combination of descending and ascending order (user's choice) but recommended at least the dates be in ascending order. With the dates in Ascending order a chronological history of every teams WMP at various underdog money lines can more easily be used to implement Dog Mart. Example (Actual stats): +135 TWINS 03/25/04 1 0 1.0 +135 TWINS 05/14/04 2 0 1.0 +135 TWINS 06/24/04 3 0 1.0 +135 TWINS 07/28/04 4 0 1.0 3.) Usually odds archive sources post current day (i.e. today's) premium up to the minute for pay Money Lines and free non-premium or old money lines as well. The EARLY Underdog Money Line, of which Dog Mart handicapping is based falls in the latter category. In this step a comparison is made of each Underdog team's Early Money Line for the current day to it's latest UWP at that Money Line. If the Underdog team's current UWP is greater than or equal to a set UWP; usually 50%, then Underdog team takes on the status of a Quali[CapitalThorn]ed Selection. *NOTE: Usually from open to close Favorites stay Favorites and Underdogs stay Underdogs. In the relatively uncommon event (when it happens it is usually with baseball) an Underdog can ßip to Favorite and vice versa. When the Underdog becomes a Favorite it is not wagered unless iff (if and only if) the team ßips back to Underdog status again greater than or equal to a +100 Underdog. As the day progresses Money lines vacillate. The quali[CapitalThorn]ed selection Underdog team based on the Early Money Line need not stay at the original Early Line but likewise it must be +100 for it to remain a quali[CapitalThorn]ed selection. 4.) At this point the database has been updated for the current day (Step 2) and the quali[CapitalThorn]ed Underdog picks have been determined (Step 3). This counterintuitive step optimally disperses the quali[CapitalThorn]ed picks. On a piece of paper or in a spreadsheet establish X number of columns - the more the better. Each column represents a different Martingale progression; what I term a lineage. For a practical example a Dog Mart could reasonably establish 10 lineages. Thus, 10 columns on the paper or spreadsheet. For each column use a random number generator, ßip a coin or use your own random selection method so that each column has an equal chance of any of the quali[CapitalThorn]ed picks or a null/no pick to be selected. So, if there is only one quali[CapitalThorn]ed Underdog pick on a given day: say Cincinnati (CIN) each column/lineage will be populated by either CIN or a NULL/NO PICK. If the next day Seattle (SEA) and coincidentally CIN again happen to both be quali[CapitalThorn]ed Dog Mart Underdog picks then each lineage/column has a 1/3 chance of SEA, CIN or No Pick as a selection. 5.) For each column/lineage perform a Martingale progression preferably with as much a Martingale range as possible. In other words a range of $10 minimum to a sports book limit (maximum) of $5000 is preferable to a $100 limit and $1000 maximum. The $10 and $100 minimums I refer to as the Martingale base 6.) All losses start a Martingale progression. To recoup a series of straight losses the original or Martingale base wager is doubled until there is a Win or the Martingale progression goes over limit. The next wager after a Martingale progression win below limit or if the number of straight losses goes over limit the next wager always reverts to the Martingale base. If a given lineage goes over-limit, it is considered a hard loss in terms of Pro[CapitalThorn]t/Loss calculation. If the season ends in the middle of a Martingale loss streak under limit or up to the current day if the season is not complete but a study is being conducted for a given lineage then whatever losses have accumulated up to the juncture are considered hard losses as well. If you follow these six steps exactly as described you will [CapitalThorn]nd the cumulative effect of multiple lineages ALWAYS! to be pro[CapitalThorn]table. However, that said is of little consolation if all eggs are put in one lineage basket so to speak and that lineage is the one out of several that happens to go over limit. Extensive spreadsheet studies already conducted (and available per your or any reader's request) still being conducted trying to optimize Dog Mart show that for every lineage that goes over limit more than enough other pro[CapitalThorn]table successful lineages will compensate for the any given lineage that shows a loss. If one is independently wealthy and initiate, fund and support multiple lineages, the only gamble really becomes whether the sports book will allow that person to wager anymore with them or in light of Dog Mart which I've just described in detail ... if indeed the sports book would even consider continuing offering Money Lines. Currently I'm not independently wealthy to implement Dog Mart on my own. I don't like the idea of putting all my eggs into one lineage basket even if the odds indeed are in my favor. But with enough people working in concert involving discipline and trust among themselves ALL indications show pro[CapitalThorn]tability for all IS! a given. This is the crux of my formal inquiries to you. What [CapitalThorn]nancial arrangements are permissible and what aren't. I don't know the optimum number of lineages where any more really won't buy any more security or pro[CapitalThorn]tability over the long term but the number is clearly more than a couple lineages and fewer than a hundred. One doesn't need to be a mathematician to see the trend running after a multitude of studies but you do need to be a mathematician to derive the optimum number of lineages. Why Dog Mart works in a nutshell ... Losing is losing in the respect a large extended losing streak with respect to a conventional sport wagering system and something as unconventional and esoteric as Dog Mart as well can certainly result in tremendous [CapitalThorn]nancial losses. Paradoxically however, a very high winning percentage especially wins in streaks in a Dog Mart scenario pro[CapitalThorn]ts would be on the average only marginal in taking into consideration the inherent Martingale properties. In an Underdog context if a Martingale wins after several losses but below limit the payoff is not simply 1:1 but 1:Underdog odds payoff. This is a VERY important differentiation. In many traditional handicapping systems it doesn't matter what the order or dispersion of wins and losses are, what matters is there are simply more wins than losses. In Dog Mart the dispersion is really the most important aspect. In a Martingale progression after every win the wagering reverts to the base. Let's take a Martingale sequence starting at $10 loss, $20 loss, $40 loss etc. It should be readily apparent (or perhaps not) if the Win/Loss dispersion is 5 straight wins followed by 5 straight losses in a Martingale progression one will be in a serious [CapitalThorn]nancial hole. It is the worst combination. Even if the Underdog money line is +150 and $15 is realized on each of the 5 wins up front, it is all lost and more on the back 5 straight losses. In fact 5 with wins and 5 losses we can easily derive the loss (5 x $15 = $75) - $10 - $20 - $40 - $80 - $160 = -$235 An optimal con[CapitalThorn]guration or dispersion would be: W L L L L L W W W W $15 - $10 - $20 - $40 - $80 - $160 + ($320 x 1.5 = $480) + $15 + $15 + $15 = $230 If more wins are added a $230 pro[CapitalThorn]t will not be possible. This simple but graphic example that with respect to Dog Mart, dispersion is not less than but an equal partner to wins is a key underlying factor of Dog Mart success. It is the right blend/ combination of Wins/Losses AND dispersion ... and that pro[CapitalThorn]table blend almost occurs naturally. Yes, the natural distribution of just taking all Underdogs and implementing Dog Mart is almost, not quite, but almost, suf[CapitalThorn]cient to show pro[CapitalThorn]tability over the long term. This is what my spreadsheets show; spreadsheets I make available for anyone who requests them over and above a comprehensive selection of them I make available on my web page for download. Implementing a soft limit of .5 (i.e. if can be .55, .6 etc.) is analogous to a little bit of energy in the form of noise can cause an avalanche. In this case an avalanche of cumulative favorable pro[CapitalThorn]table results. === Subject: Determinant maximization with trace constraints by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i82NOLP25442; Sorry this might be a repost. I am recently working on a determinant maximization problem with trace constraint, which is: MAX det(A+FBF) with respect to F s.t. trace(FF)=C Where F is the transpose of F. Both A and B are constant diagonal matrix with positive diagonal entries. C is a constant value. Without loss of generality, we can rearrange the diagonal entries of A and B in the opposite order, e.g., A with non-decreasing diagonal entries and B with non-increasing diagonal entries. My conjecture is that under such condition, one optimal solution is the DIAGONAL matrix F with diagonal entries determined by water-[CapitalThorn]lling algorithm I am struggling for a long to prove or solve this optimization problem, but still not much progress by now. Could anyone please give me some clues or ideas of how to solve this problem? Or is there any reference helpful to me. === Subject: FE Stiffness Matrix Solution Can anyone please help me out on the problem with Finite element program I am facing with? The problem is as follows. I have all elemental stiffness matrices, connectivity table with all nodes & elements and Force vector [F]. I want to solve the structure K*X=F for X(Displacement) without writing the Global Stiffness Matrix [K] to the hard disc. This way lot of memory space can be saved. I wonder how commercial FEA software packages solve 200,000 dof structure without occupying much space on the hard disc whereas if it is to store [K] of size(200000,200000) it is a lot of space oh hard disc. I am not sure, but I guess, at the time of assembling elemental stiffness matrices only, it has to solve the respective no of equations. This way it can write only that particular solution for those equations. Then it can take the next equations to solve from If anyone can throw a light on this problem, it will be very great help for me. Any suggestion on FE coding available, any books to refer or any algorithm to assemble and solve the big structures are greately invited. Please help me out. Ravi. === Subject: Re: FE Stiffness Matrix Solution > Can anyone please help me out on the problem with Finite element > program I am facing with? > The problem is as follows. > I have all elemental stiffness matrices, connectivity table with all > nodes & elements and Force vector [F]. > I want to solve the structure K*X=F for X(Displacement) without > writing the Global Stiffness Matrix [K] to the hard disc. This way lot > of memory space can be saved. I wonder how commercial FEA software > packages solve 200,000 dof structure without occupying much space on > the hard disc whereas if it is to store [K] of size(200000,200000) it > is a lot of space oh hard disc. The matrix K will be sparse - that means that only a *very* small fraction of the entries will be nonzero. You don't need to store all the zeros. You just need to store the value *and* the position of the memory. It is then possible to solve the system K*X=F just by knowing F and the value+position of the nonzero entries in K. However writing codes to do this task well is hard - you should probably look for a library code instead of writing your own. Many books on [CapitalThorn]nite element analysis include a section on sparse linear algebra, and you really should read one. This will tell you very important properties of K for your problem that will help you choose the correct library routine - e.g: is it positive de[CapitalThorn]nite, symmetric, etc. All these properties are important. I don't know any exact book titles. You could look at the free book at: http://www-users.cs.umn.edu/~saad/books.html I like this book, however this is probably not the best beginners guide. I hope someone else can give you better precise book recommendations. So you need to [CapitalThorn]nd a sparse linear algebra library. Because this sort of problem is so very important for [CapitalThorn]nite element analysis, there are many such libraries in C and Fortran free on the web. Have a look at the guide to these libraries at: http://www.netlib.org/utk/people/JackDongarra/la-sw.html You need to look down the columns near the righthand side of the table on that page to [CapitalThorn]nd which libraries do sparse computations. So then: 0) learn some of the theory from a book, 1) choose a library and check it is suitable for your problem, then 2) read the documentation to [CapitalThorn]nd what format it uses for storing the nonzero parts of K, and then 3) get coding! Hope that helps. Andy > I am not sure, but I guess, at the time of assembling elemental > stiffness matrices only, it has to solve the respective no of > equations. This way it can write only that particular solution for > those equations. Then it can take the next equations to solve from > If anyone can throw a light on this problem, it will be very great > help for me. > Any suggestion on FE coding available, any books to refer or any > algorithm to assemble and solve the big structures are greately > invited. Please help me out. > Ravi. === Subject: Re: Freeware Eigenvector EigenValue Matrix Calculator X-RFC2646: Original You might have a look at O-Matrix http://www.omatrix.com/overview.html It includes several easy methods for eigen vectors, http://www.omatrix.com/manual/eigen.htm O-Matrix is not quite free, but fairly inexpensive and there is a trial version you can use for a month. > Does anyone know of a > Freeware Eigenvector EigenValue Matrix Calculator === Subject: Re: eigenvectors and eigenvalues code X-RFC2646: Original You might look at the netlib and lapack sources at www.netlib.org > does anybody have source code to > calculate EigenVectors and Eigenvalues for matrix 3x3,4x4,.... === Subject: solving a number pattern by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i83C4te22906; I know this may be elementary to some, but I have been given this pattern in which to state the next number and rule. I'm about to die trying to solve it. Any help would be greatly appreciated. Pattern: 0,2,24,252,3120 === Subject: Re: solving a number pattern > I know this may be elementary to some, but I have been given this > pattern in which to state the next number and rule. I'm about to die > trying to solve it. Any help would be greatly appreciated. > Pattern: 0,2,24,252,3120 First: This is not a correct newsgroup for such a question. Sci.math would have been a better choice. Second: Learn to use the On-Line Encyclopedia of Integer Sequences to answer such questions. Your sequence is given by n^n - n. See David Cantrell === Subject: Proof the irrationality of pi by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i83F3UC07880; Please I would kindly like you to proof the irrationality of pi_22/7 === Subject: Re: Proof the irrationality of pi charset=iso-8859-1 > Please I would kindly like you to proof the irrationality of pi_22/7 I can understand mentioning pi and 22/7 together, but, please: pi is irrational and 22/7 is rational. The latter is the convenient approximation to pi which a lot of learned at school. It is just that: convenient for many purposes. A (slightly) better approximation is 355/113. Again, this is rational. *Vastly* more interesting than a proof of pi's irrationality is a proof that it is transcendental ... John johnDOTmorrisonATtescoDOTnet -- Anyone who dreams of a mathematician's heaven had better reconsider, if of all its angels there be more than one mathematician. - Charles Hoy Fort, in Lo!, Chapter VIII (1931) --- Outgoing mail is certi[CapitalThorn]ed Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com). === Subject: Re: Proof the irrationality of pi > Please I would kindly like you to proof the irrationality of pi_22/7 See http://mathworld.wolfram.com/Pi.html Peter -- Peter J. Acklam - pjacklam@online.no - http://home.online.no/~pjacklam === Subject: zeros of a polynomial of third order Given the following monic polynomial: P=xi^3 - (mu+1)*(mu+2)/2*rho*xi^2 + mu*(mu+2)*rho*xi - mu*(mu+1)/2*rho=0 with mu a real number and 0 Suppose you had following assumptions (all numbers > are integers): > P = P1*P2*...*PN > P,X1,...,XN given positive integers > how could one determine Pi factors so that all quotients > Pi/Xi are (almost) equal? (geometrically, how could one > analyze a given number P into a product of N factors that > are proportional to the dimensions of an N-dimensional space?) > Any insight that could lead to the de[CapitalThorn]nition of an algorithm > (probably iterative, if not recursive) would be appreciated. Divide both sides of P = P1*P2*...*PN by X1*X2*...*XN: P P1*P2*...*PN ------------ = ------------- X1*X2*...*XN X1*X2*...*XN Since Pi/Xi are (almost) equal we can write P Pi ------------ ~= ( -- ) ^ N X1*X2*...*XN Xi Solving for Pi gives P Pi ~= Xi * ( ------------ ) ^ 1/N X1*X2*...*XN === Subject: Re: optimization problem > Divide both sides of P = P1*P2*...*PN by X1*X2*...*XN: > P P1*P2*...*PN > ------------ = ------------- > X1*X2*...*XN X1*X2*...*XN > Since Pi/Xi are (almost) equal we can write > P Pi > ------------ ~= ( -- ) ^ N > X1*X2*...*XN Xi > Solving for Pi gives > P > Pi ~= Xi * ( ------------ ) ^ 1/N > X1*X2*...*XN hoped for! === Subject: Solving N-Way ANCOVA with QR decomposition Solving N-Way ANCOVA with QR decomposition I am trying to run an N-way ANCOVA (Analysis of Covariance = N-way ANOVA + one covariate) in Matlab by taking advantage of Matlab function Ôanovan'. I do realize that there is a one-way ANCOVA function Ôaoctool' in Matlab, but unfortunately there is no such a thing for N-way ANCOVA, and the situation for the N-way seems to be slightly different due to the complication of higher number of factors. My understanding is that in Ôanovan', all the factors are coded with dummy variables taking values based on their levels. In the end we have a general linear model y = X*b + e where y is the observation nx1 vector, X is the design matrix of nxm, b mx1 regression coef[CapitalThorn]cient vector, and e random error nx1 vector. This leads us to solve normal equation for least squares estimation X'Xb = X'y Due to the coding with dummy variables, design matrix X is rank de[CapitalThorn]cit as rank(X)Does anyone here know about the Meschach math library? (Pros cons etc) ? === Subject: Re: Meschach math library > I used it. It seems to work as advertized. It takes some time to [CapitalThorn]gure out > the matrix format. >Does anyone here know about the Meschach math library? (Pros cons etc) ? Yes, it's a decent C linalg library. I believe it comes along with a con[CapitalThorn]gure script (for compiling on various machines). I and colleagues use it in some of our internal software. I haven't had personal contact with it for quite some time, so I don't know if it's being maintained. If you need Win32 #ifdefs and the like, holler back. === Subject: Proxscal in SPSS 12.0 I used the evaluation version of SPSS 12.0 to run some MDS analysis (using the Proxscal method). Now, after the evaluation version expired, I bought the license for SPSS 12.0. After I installed it and tried to use it, it does not give me the option for Proxscal. All it does it to give me two options (i.e., ALSCAL; and Reliability Analysis) when I click on Analyze, then, Scale. It gave me three options in the evaluation version. What is the problem here? Does Proxscal come with a separete module and I have to purchase it separately? Ô`'`'`'`[CapitalO Tilde]`'`'`'`'`[ CapitalOTilde]`'`'`'`[CapitalOT ilde]'`'`'`'`[Ca pitalOTilde]`'`'`'`[CapitalOTil de]`'`'`'`'`[Cap italOTilde]`'`'`'` '`'`'`'`[Capita lOTilde]`'` sci.psychology.research is a moderated newsgroup. here bimonthly or the charter on the web at http://psychcentral.com/spr/ Submissions are acknowledged automatically. === Subject: Applied Continuous Markov Random Fields? In [CapitalThorn]ltering applications (continuous and continuous-discrete [CapitalThorn]ltering), it is common to model the process dynamics using linear stochastic differential equations such as dx(t)/dt = F(t) x(t) + L(t) w(t) (1a) or in more rigorous terms dx(t) = F(t) x(t) dt + L(t) dB(t) (1b) where x(t) in R^n is the state and w(t) = dB(t)/dt is a white noise process with spectral density Q(t). In practical point of view a very useful result is that the solution x(t) is a Gaussian process with mean m(t) and covariance P(t) which are given by differential equations dm/dt = F(t) m (2) dP/dt = F(t) P + P F^T(t) + L(t) Q(t) L^T(t) (3) Markov random [CapitalThorn]elds, at least in discrete case, can be considered as [CapitalThorn]ltering problems with multidimensional time coordinates (e.g., the spatial coordinates). In discrete case the spatial dependencies can be eliminated by using pseudo-measurements, but how about the continuous time coordinate case? - What are the Markov random [CapitalThorn]eld counterparts of the equations (1a) and (1b)? Some kind of stochastic partial differential equations? - Is it possible to derive some kind of partial differential equations for mean and covariance of the [CapitalThorn]eld, similarly as equations (2) and (3) in [CapitalThorn]ltering applications? - Is it possible to generalize the Kalman-Bucy [CapitalThorn]lter and smoother to estimation of MRF's? I have seen probability theoretical constructions of Markov random [CapitalThorn]elds with continuous time coordinates, but I'm still looking for be very useful. -- - Simo === Subject: Chemistry's relations with Math and Physics In case a woman farts on the a cake, what do you expect to happen next - will it light her farts or blow the candles with her warm wet putrid-smelling loud fart? Steve The Combined Gas Law Volume and Moles (Avogadro's Law) Partial Pressures Combined Gas Law P1V1 = P2V2 T1 T2 Molar Volume At STP 16.0 g CH4 1 mole 1 mole 1mole (STP) (STP) (STP) V = 22.4 L V = 22.4 L V = 22.4 L So if she farts 16 grams of methane gas, it contains a mole, which is 6.03X10^23 (603 and 23 zeros), which are equivalent to [CapitalThorn]lling a 22.4 liter of volume. Now, that ammount of gas is more than able to burn a cake off its candles, or put them out. The question at stake is, which one is gonna happen - a repetition of a fart-burning humoristic play that's bound to turn the entire cake into a [CapitalThorn]reball, or simply putting out the ßame by anal means instead of orally? === Subject: Re: C Code for Solving Cubic Equation by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i84L7fv23651; Can u please help me solve this equation: 2x^3-4x^2+4x-5 === Subject: Re: C Code for Solving Cubic Equation > Can u please help me solve this equation: 2x^3-4x^2+4x-5 x= 1.691413979781736791928865605753225218385767646924689709712476 53660042218 82598621061910196993833760041854439412283188699569453978764996 7776724327739 72524333785009651494666379039862278853347609945672447512653685 1976675056601 24505261926285723849836543307694536772110226059573976178029251 8037276835830 82139471019738503895039891671793503133851060952260083254158942 7521219622098 75291561630750689133002461941632530983319793017899175015921110 2265685891922 57558165393284205545535122780489033575042733863589662737877357 5740116734312 21780626370010418532906409247941913471219368101415049001739234 8828222544014 874450757915458335646 error abs 5.01565e-617 If you want some perl code, e-mail me. -- http://www.telecable.es/personales/gamo/ GED/GB d+ s+:+ a C++ U+++ P+++ L++ E---- W++ N++ o K+ w O+ M- V PS++ PE++ Y PGP+ t 5-- X+ R-- tv-- b++ DI++ D+ G- e+++ h+ r-- z perl -e Ôprint 111_111_111**2,n;' === Subject: Re: C Code for Solving Cubic Equation > Can u please help me solve this equation: 2x^3-4x^2+4x-5 > x= 1.691413979781736791928865605753225218385767646924689709712476 53660042218 > 82598621061910196993833760041854439412283188699569453978764996 7776724327739 > 72524333785009651494666379039862278853347609945672447512653685 1976675056601 > 24505261926285723849836543307694536772110226059573976178029251 8037276835830 > 82139471019738503895039891671793503133851060952260083254158942 7521219622098 > 75291561630750689133002461941632530983319793017899175015921110 2265685891922 > 57558165393284205545535122780489033575042733863589662737877357 5740116734312 > 21780626370010418532906409247941913471219368101415049001739234 8828222544014 > 874450757915458335646 > error abs 5.01565e-617 That last digit should be a 3, not a 6. :-) Peter -- Peter J. Acklam - pjacklam@online.no - http://home.online.no/~pjacklam === Subject: Re: C Code for Solving Cubic Equation ... > 874450757915458335646 > error abs 5.01565e-617 > That last digit should be a 3, not a 6. :-) > Peter The precision was set on bits (2048), thus the last digits are sometimes wrong. But I could increase the precision! How many bits do you want? ;-) > -- > Peter J. Acklam - pjacklam@online.no - http://home.online.no/~pjacklam -- http://www.telecable.es/personales/gamo/ GED/GB d+ s+:+ a C++ U+++ P+++ L++ E---- W++ N++ o K+ w O+ M- V PS++ PE++ Y PGP+ t 5-- X+ R-- tv-- b++ DI++ D+ G- e+++ h+ r-- z perl -e Ôprint 111_111_111**2,n;' === Subject: Re: C Code for Solving Cubic Equation > ... > 874450757915458335646 > error abs 5.01565e-617 > That last digit should be a 3, not a 6. :-) > The precision was set on bits (2048), thus the last digits are > sometimes wrong. But I could increase the precision! How many > bits do you want? ;-) Nah, I can compute it by myself... :-) #!/bin/sh cat < Can u please help me solve this equation: 2x^3-4x^2+4x-5 > x= 1.691413979781736791928865605753225218385767646924689709712476 53660042218 > 82598621061910196993833760041854439412283188699569453978764996 7776724327739 > 72524333785009651494666379039862278853347609945672447512653685 1976675056601 > 24505261926285723849836543307694536772110226059573976178029251 8037276835830 > 82139471019738503895039891671793503133851060952260083254158942 7521219622098 > 75291561630750689133002461941632530983319793017899175015921110 2265685891922 > 57558165393284205545535122780489033575042733863589662737877357 5740116734312 > 21780626370010418532906409247941913471219368101415049001739234 8828222544014 > 874450757915458335646 > error abs 5.01565e-617 > If you want some perl code, e-mail me. The program to do that is: #include #include int main(void) { int n: double results[3]; cubic(2.0,-4.0,4.0,-5.0,&n,results); for (int i=0; i Can u please help me solve this equation: 2x^3-4x^2+4x-5 -0.6635739 === Subject: Re: C Code for Solving Cubic Equation by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i85Ltj014043; > Can u please help me solve this equation: 2x^3-4x^2+4x-5 >-0.6635739 Yes, I realize that people who just post a polynomial (which isn't even an equation) and insist that you give them the answer don't deserve much consideration but he did say please and giving a wrong answer like that is just cruel! (Oh, wait, did you mistake this for + 5 instead of -5?) What I did, assuming you meant 2x^3- 4x^2+ 4x- 5= 0, was use my handy-dandy TI83 calculator to graph the function and then zoom in on the x-intercept: x= 1.6911543 approximately is the only real root. You could also use Newton's method. If f(x) is a differentiable function with derivative f'(x), then the recursion x_(n+1)= x_n- f(x_n)/f'(x_n) will, if it converges, converge to a root. Whether it converges, and, if so, to which root depends upon the choice of x_0. Here, f(x)= 2x^3- 4x^2+ 4x- 5 and f'(x)= 6x^2- 8x+ 4 so x_n+1= xn- (2x_n^3- 4x_n^2+ 4x_n- 5)/(6x_n^2- 8x_n+ 4). If we take x_0= 0 as an easy starting value, f(0)= -5 and f'(1)= 4 so x_1= 0-(-5)/(4)= 1.25. f(1.25)= -2.34375 and f'(1.25)= 3.375 so x_2= 1.25-(-2.34375)/(3.375)= 1.944444. f(1.94444)= 2.35768 and f'(1.944444)= 11.12963 so x_3= 1.944444- (2.35768)/(11.12963)= 1.732606. That will converge fairly quickly to 1.69... Newton's method works quickly but if you are not familiar with calculus (and derivatives) you might be more comfortable with a very simple method: f(0)= -5 and f(2)= 3 so there must be a place where f(x)= 0 between 0 and 2. Where between? Why not try half way between: x= 1. f(1)=-3 so there must be a solution between 1 and 2. Again, try halfway between: 1.5. f(1.5)= -1.25. Since that is negative, there must be a solution between 1.5 and 2. (1.5+ 2)/2= 1.75 and f(1.75)= .46875. Since that is positive, there must be a solution between 1.5 and 1.75. Continue in that way until you have enough accuracy. === Subject: Re: C Code for Solving Cubic Equation >Can u please help me solve this equation: 2x^3-4x^2+4x-5 >-0.6635739 > Yes, I realize that people who just post a polynomial (which isn't > even an equation) and insist that you give them the answer don't > deserve much consideration but he did say please and giving a wrong > answer like that is just cruel! > (Oh, wait, did you mistake this for + 5 instead of -5?) Yes I did. I acknowledged my mistake a few minutes later in another thread but it was too late. I typed 5 instead of -5. I hope you will forgive me such a mistake. === Subject: Re: C Code for Solving Cubic Equation > Can u please help me solve this equation: 2x^3-4x^2+4x-5 > -0.6635739 Set x = -0.6635739 into 2x^3-4x^2+4x-5 and you get -10. Peter -- Peter J. Acklam - pjacklam@online.no - http://home.online.no/~pjacklam === Subject: How to approximate the number of zeros of an analytic function in a domain? by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i84L7fd23683; Hi there, When working with complex analytic functions, you can get the number of zeros by the Argument Principle. But in practiacl uses, you can only approximate the integral f'/f. My question is, are there any other Ôalgorithms' to approximate the number of zeros of an analytic function in a given domain? I've seen a reference to one different way of working out the variation of the argument of the function on the boundery of the domain, but I didn't really understand it. So if you know this method, please do share. Dror Speiser === Subject: Math equation with function ln by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i850PcF06809; Could someone please tell me how to tackle the following equation: -4.54=-2.23+2.48ln(3.45/2.21X) I attempted taking the ln of 2.48, then distributing the number to the numbers in the parenthesis, but the answer was incorrect. The correct Stephanie Cruz === Subject: Re: Math equation with function ln X-RFC2646: Original > Could someone please tell me how to tackle the following equation: > -4.54=-2.23+2.48ln(3.45/2.21X) -2.31=2.48 ln(3.45/2.21X) -0.93145=ln(3.45/2.21X) exp(-0.93145)=3.45/2.21X 0.39398=3.45/2.21X 0.39398=1.56109X 0.25237=x But the answer is 3.96244 if you meant (which I think you did) 3.45/(2.21X) in the origin problem (the convention rule of operations interprets the X in 3.45/2.21X as being multiplied by 3.45/2.21 so you need put the parenthesis). > I attempted taking the ln of 2.48, then distributing the number to the > numbers in the parenthesis, I have no idea what that means but it is probably something mathematically wrong.0 In no way in solving the problem would you want to take the ln of 2.48. > The correct > answer is 4.13, and I keep getting a smaller number. Not for the problem you gave--maybe someone badly approximated e in doing the exp. === Subject: Re: Math equation with function ln >Could someone please tell me how to tackle the following equation: > -4.54=-2.23+2.48ln(3.45/2.21X) >I attempted taking the ln of 2.48, then distributing the number to the >numbers in the parenthesis, but the answer was incorrect. The correct Rearrange your equation so that it has form W = ln(U) then you get exp(W) = U easy to solve from that point. >Stephanie Cruz -- David B. Chorlian Neurodynamics Lab SUNY/HSCB chorlian@cns.hscbklyn.edu davidc@panix.com === Subject: Gamma Function boundary=----=_NextPart_000_0059_01C492A5.981CCD20 ------------------------------------------------------------- -------- charset=utf-8 In order to test a (precise and very fast) library of transcendental functions, together with a graphical interface for real-time analysis, selected functions are being made available to the public for evaluation and critique. Currently you may enjoy the marvels of the: Gamma Function - (x) The computer program runs in MS DOS or Windows (with standard con[CapitalThorn]gurations) on standard x86 machines with an FPU and SVGA. Detailed speci[CapitalThorn]cations and GUI description are available at: www.iging.com/Transcendental. Your constructive feedback is very much appreciated. Dan Baruth x86igingcom === Subject: Re: Gamma Function > In order to test a (precise and very fast) > library of transcendental functions, together > with a graphical interface for real-time > analysis, selected functions are being made > available to the public for evaluation and > critique. Currently you may enjoy the marvels > of the: > Gamma Function - ?(x) > The computer program runs in MS DOS or Windows > (with standard con[CapitalThorn]gurations) on standard x86 > machines with an FPU and SVGA. Detailed > speci[CapitalThorn]cations and GUI description are available > at: www.iging.com/Transcendental. > Your constructive feedback is very much > appreciated. > Dan Baruth > x86igingcom How precise and how fast? Maybe you should provide code suitable for benchmarking. -- There are two things you must never attempt to prove: the unprovable -- and the obvious. -- Democracy: The triumph of popularity over principle. -- http://www.crbond.com === Subject: Re: Gamma Function charset=iso-8859-1 : : > In order to test a (precise and very fast) : > library of transcendental functions, together : > with a graphical interface for real-time : > analysis, selected functions are being made : > available to the public for evaluation and : > critique. Currently you may enjoy the marvels : > of the: : > Gamma Function - ?(x) : > The computer program runs in MS DOS or Windows : > (with standard con[CapitalThorn]gurations) on standard x86 : > machines with an FPU and SVGA. Detailed : > speci[CapitalThorn]cations and GUI description are available : > at: www.iging.com/Transcendental. : > Your constructive feedback is very much : > appreciated. : > Dan Baruth : > x86igingcom : How precise and how fast? Maybe you should provide code : suitable for benchmarking. Both depend on the particular argument of the function. For the Gamma function the orders of magnitude are: 17 decimal digits and 5E-7 seconds, respectively. For applications of a function (library) or the graphical analysis program, please contact me by e-mail. D. Baruth x86igingcom === Subject: Re: Gamma Function charset=iso-8859-1 : Both depend on the particular argument of the function. For the : Gamma function the orders of magnitude are: 17 decimal digits : and 5E-7 seconds, respectively. Dan === Subject: Derivatives of matrix problem Hi Anyone who know derivatives of (xx')/(x'x) with respect to x, where x is a column vector and symbol Ô denote transpose. Linke === Subject: New mathematics/physical sciences positions at http://jobs.phds.org New job listings at http://jobs.phds.org - Jobs for PhDs List your job at no cost! http://jobs.phds.org/jobs/post * Assistant, Associate or Full Professor-Genomic Biology: University at Buffalo-Dept of Biological Sciences, Buffalo, NY. The Department of Biological Sciences ( http://www.biology.buffalo.edu ) at the University at Buffalo , the largest and most comprehensive campus in the SUNY system is seeking outstanding applicants for a tenured or tenure-track... === Subject: [CapitalThorn]nding complex eigenvalues X-RFC2646: Original I know that the QR algorithm is used to [CapitalThorn]nd real eigenvalues of a matrix, but what about complex ones? how are they typically found numerically? === Subject: 2 triginometric equations with 2 unknowns (angles) For spatial management, I need to [CapitalThorn]gure out how to simplify (solve) a system of 2 triginometric equations with 2 unknowns: A cos(a) - B cos(b) = C1 (1) A sin(a) - B sin(b) = C2 (2) A, B, C1, C2 are constants, the only unknowns are the angles (a) and (b). A simple system of 2 equations with 2 unknowns, but the problem gains complexity when trasforming one of the sines to a cosine (or vise versa), where you end up with a messy quadratic equation to the 4th power: cos(a) = sqrt( 1 - sin(a)*sin(a) ) Is there a way to simplify equations (1) and (2), trying to solve (a) and (b)? === Subject: Re: 2 triginometric equations with 2 unknowns (angles) > For spatial management, I need to [CapitalThorn]gure out how to simplify (solve) a > system of 2 triginometric equations with 2 unknowns: > A cos(a) - B cos(b) = C1 (1) > A sin(a) - B sin(b) = C2 (2) > A, B, C1, C2 are constants, the only unknowns are the angles (a) and > (b). A simple system of 2 equations with 2 unknowns, but the problem > gains complexity when trasforming one of the sines to a cosine (or > vise versa), where you end up with a messy quadratic equation to the > 4th power: > cos(a) = sqrt( 1 - sin(a)*sin(a) ) > Is there a way to simplify equations (1) and (2), trying to solve (a) > and (b)? you have the intersection of two circes, 1) centered at 0 with radus A and a second centered at (C1,C2) and radius B,. There are either zero or two solutions. let (x,y) be a point on both circles x^2 + y^2 = A^2 (eq A) (x-C1)^2 + (y-C2)^2 = B^2 (eq B) expamding eq A - eq B yields a linear equation between x and y. {x^2 -(x-C1)^2 }+ {y^2 - (y-C2)^2 }- = A^2 -B^2 (2x-C1)*C!2 + (2y-C2)*C2 = A^2 - B^2 solving ths for x in terms of y gives x = D1 + D2 y (eq C) substituting eq C into eq A gives a quaratic for y. now two points or none are found if the quadradic has no real roots. (x1,y1),(x2,y2) These points substituted in the eqs below gives a,b via atan2(). x = A cos(a) = C1 + B cos(b) y = A sin(a) = C2 B sin(b) a = atan2(y,x), b = atan2(y-C2.x-C1) === Subject: Re: 2 triginometric equations with 2 unknowns (angles) >For spatial management, I need to [CapitalThorn]gure out how to simplify (solve) a >system of 2 triginometric equations with 2 unknowns: > A cos(a) - B cos(b) = C1 (1) > A sin(a) - B sin(b) = C2 (2) >A, B, C1, C2 are constants, the only unknowns are the angles (a) and >(b). A simple system of 2 equations with 2 unknowns, but the problem >gains complexity when trasforming one of the sines to a cosine (or >vise versa), where you end up with a messy quadratic equation to the >4th power: >cos(a) = sqrt( 1 - sin(a)*sin(a) ) >Is there a way to simplify equations (1) and (2), trying to solve (a) >and (b)? Eliminating a gives (B*cos(b) + C1)^2 + (B*sin(b) + C2)^2 = A^2 which should have a familiar solution. -- During a wedding ceremony, members of the audience cried. Scientists examined the tears. They determined the liquid was eye dew. pmontgom@cwi.nl Microsoft Research and CWI Home: Bellevue, WA === Subject: Re: 2 triginometric equations with 2 unknowns (angles) (dealing with powers of 4), but then realised that A and B were linked (long story), so the hole equation boils down to: cos (f-a) = C/k Now I've resolved my trilateration equations... === Subject: Re: Accuracy of solvers of nolinear equations by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i86CrvD21905; possibility to increase the accuracy of function fsolve. Because if there isn't I would rather use Mathematica's FindRoot which is by default a factor ten more accurate. zabig === Subject: Re: Links to Chi Square C/C++ routines by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i86CrtQ21772; please send me about the complete reference of c++ routines === Subject: Re: Sharp EL-5103 calculator Manual by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i86Crtv21819; I have the english section of the manual. If you are interested let me know. I loved the calculator and was looking for replacement. Mine was stolen last year. It was 25 years old! Raj >Will pay more than the original retail price for >a Sharp EL-5103 calculator in good working condition. >The manual for the calculator is desirable but not necessary. >Will consider buying any other small, _programmable_, >leatherette-covered Sharp calculator model. >Not interested in the EL-506 or other non-programmable models, >or in the larger models that use the BASIC language (I have those). >-- >John Chandler >jpc@a.cs.okstate.edu === Subject: Req: Help with a math problem Can anyone help solve any one of these problems? What is the sum of a 4 digit number divided by a 3 digit number, and the remainder is 60. What is the sum of a 5 digit number divided by a 3 digit number, and the remainder is 24. What is the sum of a 6 digit number divided by a 3 digit number, and the remainder is 30. I hope the questions/syntax is correct. slim === Subject: Re: Req: Help with a math problem > Can anyone help solve any one of these problems? > What is the sum of a 4 digit number divided by a 3 digit number, and > the remainder is 60. > What is the sum of a 5 digit number divided by a 3 digit number, and > the remainder is 24. > What is the sum of a 6 digit number divided by a 3 digit number, and > the remainder is 30. > I hope the questions/syntax is correct. > slim Sum(Sum(i,where i>=1000 and i<=9999 and rem(i,j)=60),j=100..999)=112943025 Sum(Sum(i,where i>=10000 and i<=99999 and rem(i,j)=24),j=100..999)=11416577217 Sum(Sum(i,where i>=100000 and i<=999999 and rem(i,j)=30),j=100..999)=1141956296677 === Subject: Re: Req: Help with a math problem >Message-id: > Can anyone help solve any one of these problems? >What is the sum of a 4 digit number divided by a 3 digit number, and >the remainder is 60. The answer is zero ( or rather, undeterminable ). If all you do is divide one number by another.... no summing has occured. Dan :-) >What is the sum of a 5 digit number divided by a 3 digit number, and >the remainder is 24. >What is the sum of a 6 digit number divided by a 3 digit number, and >the remainder is 30. >I hope the questions/syntax is correct. >slim === Subject: Re: Req: Help with a math problem > Can anyone help solve any one of these problems? > What is the sum of a 4 digit number divided by a 3 digit number, and > the remainder is 60. > What is the sum of a 5 digit number divided by a 3 digit number, and > the remainder is 24. > What is the sum of a 6 digit number divided by a 3 digit number, and > the remainder is 30. > I hope the questions/syntax is correct. > slim do your own homework === Subject: Re: Req: Help with a math problem : :> Can anyone help solve any one of these problems? :> :< :> :> slim : :do your own homework Hmm Not quite. I didn't feel like i had to explain why i needed the info, but since you're interested/trolling/whatever. I have a friend who has a son (7th grade, btw) that needed help, so my friend (who doesn't use a computer too tuff much less frequent ngs) asked me for help so that he could help his kid. Not that it's anybody's problem but theirs, but he needed help, and since he's a close friend, i would do almost anything (within reason ) to help him/them. I wish it was my homework for 7th grade. I'm 49 now, but i recall having a great time in school back then, although i skipped far too many math classes : slim === Subject: Re: C Code for Solving Cubic Equation > Can u please help me solve this equation: 2x^3-4x^2+4x-5 These are the solutions from a program written in PL/I:- The coef[CapitalThorn]cients are: A= 2.00000000000000000E+0000; B=-4.00000000000000000E+0000; C= 4.00000000000000000E+0000; D=-5.00000000000000000E+0000; The roots are: X1= 1.69141397978173139E+0000 X2= 1.54293010109134306E-0001+1.20592160038153532E+0000I; X3= 1.54293010109134306E-0001-1.20592160038153532E+0000I; The latter two roots are complex: real part followed by imaginary part. === Subject: Tangent to a surface If a curve(c) is de[CapitalThorn]ned by interpolating between two vectors (a,b) for n E r+ 0<=n<=1, for example using this formula: c = a * n^2 + b * (1-n)^2 And a surface(s) is interpolated between two curves (c1,c2) for m E r+ 0<=m<=1, for example using this formula: s = c1 * m^2 + c2 * (1-n)^2 The formulas needn't take this form but have a similar input/output, now the question: If a line starts at vector (v), what is the relationship of n to m for which a tangent from s(n,m) passes through v? === Subject: Exact Rational Interpolation by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i86NGA008005; Can you suggest me an effective rational interpolation algorithm. The algorithm must interpolate rational function R(x)=P(x)/Q(x) (where dgP(x)=m and dgQ(x)=n, m and n are known [CapitalThorn]xed numbers) through m+n+2 points (x_i, r_i). Also, approximative algorithms (such as Pade approximation) are not solving the problem. Marko Petkovic === Subject: Re: How to calculate the correct penis length of a man? by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i86NGCG08106; > If you only know his height and the diameter of his arse? > How can I calculate the penis length from this data? >The angle of the dangle is proportional to the tilt of the kilt. what? could you explain that so that one you dropped out of high school could understand? === Subject: Re: How to calculate the correct penis length of a man? > If you only know his height and the diameter of his arse? > > How can I calculate the penis length from this data? >The angle of the dangle is proportional to the tilt of the kilt. > what? could you explain that so that one you dropped out of high > school could understand? If you really need explanation, then it's high time to enroll at the nearest abbey where they'll undoubtedly supply you with all necessary accruements for a live unlived. Good luck, Gerry T. === Subject: Re: Meschach math library by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i86NGAR08013; I tried to compile Meschach using Visual Studio.Net 2k3 but i didn't succeed :(, so i used Linux comiler. Now i hope that i'll be able to compile C code under Windows using your compiler.