From chemistry-request@server.ccl.net Sun Nov 28 14:53:31 1999 Received: from nucleus.harvard.edu (nucleus.harvard.edu [140.247.90.196]) by server.ccl.net (8.8.7/8.8.7) with ESMTP id OAA26951 for ; Sun, 28 Nov 1999 14:53:31 -0500 Received: from localhost (daizadeh@localhost) by nucleus.harvard.edu (8.9.3/8.9.3) with ESMTP id NAA25947 for ; Sun, 28 Nov 1999 13:49:43 -0500 (EST) Date: Sun, 28 Nov 1999 13:49:43 -0500 (EST) From: Iraj Daizadeh To: chemistry@ccl.net Subject: Calc Binomial Dist. Function. Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Hello. The binomial prob. density function is ubiquitous in stat mech: P(x) = (N,n) * p^n * (1-p)^(N-n) The question is how does one-- practically -- compute the above formula for very large N and n. I have been playing around with the numerical recipes BICO function for N around 206 and n around 106---it returns inf or nan()--- thus P(x) is inf or nan... We understand that bico uses something akin to stirling's approx... using the relation: n! = Gamma(n+1) where Gamma is the gamma function... Is there a trick to calculation this density function...Maybe calculating first the product of the p's then dividing then multiplying by e(ln(N))... Thanks. Iraj. Iraj Daizadeh, Ph.D. Harvard University Department of Cellular and Molecular Biology The Biological Laboratories 16 Divinity Avenue Cambridge, MA 02138 Phone: (617) 495-0783 (617) 495-0560 Fax: (617) 496-4313 Email: daizadeh@nucleus.harvard.edu WebPage: http://mcb.harvard.edu/gilbert/daizadeh From chemistry-request@server.ccl.net Sun Nov 28 16:03:07 1999 Received: from mail.rwth-aachen.de (mail.RWTH-Aachen.DE [137.226.144.9]) by server.ccl.net (8.8.7/8.8.7) with ESMTP id QAA27311 for ; Sun, 28 Nov 1999 16:03:06 -0500 Received: from ac.rwth-aachen.de (zosia.dorf.RWTH-Aachen.DE) by mail.rwth-aachen.de (PMDF V5.1-12 #D3869) with ESMTP id <01JIVUXRGYS00007H6@mail.rwth-aachen.de> for CHEMISTRY@ccl.net; Sun, 28 Nov 1999 20:58:36 +0100 Date: Sun, 28 Nov 1999 21:56:46 +0100 From: Krzysztof Radacki Subject: g98 opt=(qst3, path=... question. Sender: krzys@mail.rwth-aachen.de To: CCL Message-id: <3841970E.2C1C9AB9@ac.rwth-aachen.de> Organization: RWTH Aachen MIME-version: 1.0 X-Mailer: Mozilla 4.61 [en] (X11; I; Linux 2.2.12-20 i686) Content-type: text/plain; charset=us-ascii Content-transfer-encoding: 7bit X-Accept-Language: en Hi, can somebody explain what are Initial Parameters from job with opt=(qst3, path=10). I have 11 atoms (10 +one dummy). In above mentioned table I can see 10 Rs (OK), 15 angles and 16 dihedral angels. Are these extra-angles just for information and I need to select a set defining my molecules, or there is something other wrong? regards From chemistry-request@server.ccl.net Sun Nov 28 16:14:04 1999 Received: from mtiwmhc02.worldnet.att.net (mtiwmhc02.worldnet.att.net [204.127.131.37]) by server.ccl.net (8.8.7/8.8.7) with ESMTP id QAA27380 for ; Sun, 28 Nov 1999 16:14:04 -0500 Received: from [12.77.88.179] by mtiwmhc02.worldnet.att.net (InterMail v03.02.07.07 118-134) with SMTP id <19991128200745.BYBF1865@[12.77.88.179]>; Sun, 28 Nov 1999 20:07:45 +0000 X-Sender: eaabbott@postoffice.worldnet.att.net X-Mailer: QUALCOMM Windows Eudora Pro Version 4.0 Date: Sun, 28 Nov 1999 15:06:18 -0500 To: Iraj Daizadeh From: "Elizabeth A. Abbott" Subject: Re: CCL:Calc Binomial Dist. Function. Cc: chemistry@ccl.net In-Reply-To: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Message-Id: <19991128200745.BYBF1865@[12.77.88.179]> Hi Iraj, You might want to check out _Introduction to Algorithms_ by Cormen, Leiserson, and Rivest (Chapter 6: counting and probability) and/or Knuth's _Art of Computer Programming_ Vol 2: Seminumerical Algorithms. CL&R give upper and lower bounds for (N,k). Lower bound: (n,k) = n(n-1)...(n-k+1) -------------------- k(k-1)...1 = (n/k) ( (n-1)/(k-1) ) ... ( (n-k+1)/1 ) >= (n/k) ^k Upper bound: (n,k) = n(n-1)...(n-k+1) ---------------------- k(k-1)...1 <= n^k / k! <= (en / k ) ^k since we know k! >= (k/e)^k from Stirling's apx. CL&R also give an upper bound for the binomial prob. dist. b(k;n,p) <= (np/k) ^k * (nq/(n-k) ^ (n-k) (q is just 1 -p) Sorry to switch notation from N,n to n,k on you, but I have a hard enough time getting it onto the screen without translating, too. :) Hope this is of some help. Check out Knuth. -Liz (can you tell I wandered into comp chem from cs and applied math?? :-) At 28-11-99 13:49 -0500, you wrote: > >Hello. > >The binomial prob. density function is ubiquitous in stat mech: > >P(x) = (N,n) * p^n * (1-p)^(N-n) > >The question is how does one-- practically -- compute >the above formula for very large N and n. > >I have been playing around with the numerical recipes BICO function for N >around 206 and n around 106---it returns > >inf or nan()--- thus P(x) is inf or nan... > >We understand that bico uses something akin to stirling's approx... using >the relation: n! = Gamma(n+1) where Gamma is the gamma function... > >Is there a trick to calculation this density function...Maybe calculating >first the product of the p's then dividing then multiplying by e(ln(N))... > >Thanks. Iraj. > > > >Iraj Daizadeh, Ph.D. >Harvard University >Department of Cellular and Molecular Biology >The Biological Laboratories >16 Divinity Avenue >Cambridge, MA 02138 >Phone: (617) 495-0783 > (617) 495-0560 >Fax: (617) 496-4313 >Email: daizadeh@nucleus.harvard.edu >WebPage: http://mcb.harvard.edu/gilbert/daizadeh > > > >-= This is automatically added to each message by mailing script =- >CHEMISTRY@ccl.net -- To Everybody | CHEMISTRY-REQUEST@ccl.net -- To Admins >MAILSERV@ccl.net -- HELP CHEMISTRY or HELP SEARCH >CHEMISTRY-SEARCH@ccl.net -- archive search | Gopher: gopher.ccl.net 70 >Ftp: ftp.ccl.net | WWW: http://www.ccl.net/chemistry/ | Jan: jkl@ccl.net >