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Topic: Brownian tree

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	Contributions to Zoology
		Because a common process of character change (Brownian motion; Felsenstein, 1985) was used as the basis in all four evolutionary models, we can compare them using the concept of maximum likelihood (Edwards, 1992): the better the fit between model and data, the higher the likelihood returned.
		However, individual trees are independent and the log(likelihoods) for a given model may be summed across the full data set of twentyone trees to yield an overall measure of the goodness of fit of each model.
		Brownian motion can, however, represent change in traits under selection if the selection pressures are multifarious and constantly changing, or if lineages wander randomly from one regularlyspaced adaptive peak to another, both of which may be reasonable representations over long periods of time.
	dpc.uba.uva.nl /ctz/vol68/nr01/art01 (7031 words)

	Wikinfo \| Brownian motion
		Brownian motion is the simplest stochastic process on a continuous domain, and it is a limit of both simpler (see random walk) and more complicated stochastic processes.
		Brownian motion was discovered by the biologist Robert Brown in 1827.
		Mathematically, Brownian motion is a Wiener process in which the conditional probability distribution of the particle's position at time t+dt, given that its position at time t is p, is a Normal distribution with a mean of p+μ dt and a variance of σ
	www.wikinfo.org /wiki.php?title=Brownian_motion (648 words)

	Brownian motion - Wikipedia, the free encyclopedia
		Brownian motion is among the simplest continuous-time stochastic processes, and it is a limit of both simpler and more complicated stochastic processes (see random walk and Donsker's theorem).
		Jan Ingenhousz made some observations of the irregular motion of carbon dust on alcohol in 1785 but Brownian motion is generally regarded as having been discovered by the botanist Robert Brown in 1827.
		The first person to describe the mathematics behind Brownian motion was Thorvald N. Thiele in 1880 in a paper on the method of least squares.
	en.wikipedia.org /wiki/Brownian_motion (1386 words)

	Brownian tree (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-10-22)
		A Brownian tree, whose name is derived from Robert Brown via Brownian motion, is a form of computer art that was briefly popular in the 1990s, when home computers started to have sufficient power to simulate Brownian motion.
		Brownian trees are mathematical models of dendritic structures associated with the physical process known as diffusion-limited aggregation.
		These trees can also be grown easily in an electrodeposition cell, and are the direct result of diffusion-limited aggregation.
	www.danceage.com.cob-web.org:8888 /biography/sdmc_Brownian_tree (288 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		The meaning is represented as a vector whose every element holds two values: a maximal string whose attributes are all the same, and the attributes of that string.
		The optimizer uses a randomized algorithm to generate "parenthesizations" of the tree -- that is, an N-element meaning gets an (+ N 1)-element sequence of tags.
		Therefore, even when it finds a tree that is better than the input, this tree is only "good", not necessarily ideal.
	www.cs.brown.edu /research/plt/Notes/icfp2001-contest.txt (560 words)

	[No title]
		That the scaling limit of lattice trees should be ISE for $d>8$ was conjectured by Aldous, who has emphasized the role of ISE as a model for the random distribution of mass \cite{Aldo93}.
		ISE is super-Brownian motion (Brownian motion branching on all time scales) conditioned to have total mass 1, and is closely connected to the super-processes intensively studied in the probability literature.
		The number of such trees is given by the Catalan number $(n+1)^{-1} (^{2n}_{n})$, and hence the number of lattice embeddings is asymptotic to \eq \lbeq{emb} \frac{1}{\sqrt{\pi}} 2^{2n} (2d)^{2n-1} \frac{1}{n^{3/2}}.
	www.ma.utexas.edu /mp_arc/papers/96-444 (5147 words)

	Brownian motion biography .ms (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-10-22)
		The story goes that Brown was studying pollen particles floating in water under the microscope, and he observed minute particles within vacuoles in the pollen grains executing the jittery motion that now bears his name.
		The first to give a theory of Brownian motion was Louis Bachelier in 1900 in his PhD thesis "The theory of speculation".
		It is a mistaken belief that Albert Einstein was the first to give a mathematical theory to the Brownian motion, but considering how many people know of Bachelier, this is understandable.
	www.biography.ms.cob-web.org:8888 /Brownian_motion.html (671 words)

	Probability on Trees: An Introductory Climb - Peres (ResearchIndex)
		Remarkably, the same model arose independently in genetics, as a mutation model, and in mathematical physics, where it is equivalent to the Ising model on a tree.
		In Chapter 17, the Ising model on a tree is used to construct a nearest-neighbor process on Z that is "less predictable" than simple random walk.
		9 The intersection of Brownian paths as a case study of a reno..
	citeseer.ist.psu.edu /peres99probability.html (1255 words)

	IAS/Park City Mathematics Institute
		Brownian motion is the most basic stochastic process and has fundamental relations to many areas of mathematics and applications to many other fields.
		Even after over a century of mathematical study, it is at the centre of some of the most exciting developments of recent years, and some aspects of Brownian motion are not completely understood, and remain at the forefront of mathematical research today.
		Some of the topics we hope to include: higher dimensional Brownian motions, the Brownian bridge and excursion, the fundamental relation to harmonic functions and differential equations, conformal invariance of Brownian motion, the continuum random tree and its relation with branching processes, and a quick look at the Gaussian free field.
	www.admin.ias.edu /ma/current/program_undergradsummer.php (562 words)

	Stochastic topology (Tsirelson, intro)
		The leafs of the tree, (0,1,2), (0,1,0), (0,-1,0), and (0,-1,-2) are the possible sample paths (trajectories) of the process.
		Their non-discreteness prevents us from drawing "the Poisson tree" and "the Brownian tree", but still, the tree metaphor is worth noticing.
		Likewise, there are Brownian motions on a circle, on a half-line (it reflects from the endpoint), on a graph (treated here as a one-dimensional topological space, not as a discrete structure), on a plane, and many other spaces of various dimensions.
	www.math.tau.ac.il /~tsirel/st_top.html (1588 words)

	Preprints
		Generalizing results of Evans and Perkins, we represented the conditioned process both as an h-transform of the unconditioned process (that is, in terms of a martingale change of measure), and in terms of a non-homogeneous branching `backbone' throwing off unconditioned mass.
		In contrast to the higher dimensional case (where with n=1 the backbone consisted of a single path, and with n>1 of a non-homogeneous tree with n nodes), the backbone now consists of a homogeneously branching tree, possibly with infinitely many leaves.
		We write the conditioned process both as an h-transform of the unconditioned process (that is, we give it in terms of a martingale change of measure), and in terms of a non-homogeneous branching particle system with immigration of mass.
	www.math.yorku.ca /Who/Faculty/Salisbury/misc.html (824 words)

	Brownian motion (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-10-22)
		The mathematical model posits motion in which the steps are not discrete.]] The term Brownian motion (in honor of the botanist Robert Brown) refers to either The physical phenomenon that minute particles immersed in a fluid move around randomly; or The mathematical models used to describe those random movements.
		All three quoted examples of Brownian motion are cases of this: It has been argued that Lévy flights are a more accurate, if still imperfect, model of stock-market fluctuations.
		Brown, Robert, "A brief account of microscopical observations made in the months of June, July and August, 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies." Phil.
	brownian-motion.iqnaut.net.cob-web.org:8888 (841 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		Perturbation of A was either brownian or uniform.
		If it was brownian, then it started with A = 3, and was perturbed by adding a uniform random value from the range [-1, +1].
		Tree sizes are measured in the average number of nodes contained in the best of population.
	www.cs.unm.edu /~vanbelle/RA/evolvability/evolvability.html (408 words)

	Growth of the Brownian forest, Jim Pitman, Matthias Winkel
		Trees in Brownian excursions have been studied since the late 1980s.
		Forests in excursions of Brownian motion above its past minimum are a natural extension of this notion.
		Neveu, J. and Pitman, J. Renewal property of the extrema and tree property of the excursion of a one-dimensional Brownian motion.
	projecteuclid.org /Dienst/UI/1.0/Display/euclid.aop/1133965857 (488 words)

	CONTML - Gene Frequencies
		The topology of the tree is given by an unrooted tree diagram.
		The tree does not necessarily have all tips contemporary, and the log likelihood may be either positive or negative (this simply corresponds to whether the density function does or does not exceed 1) and a negative log likelihood does not indicate any error.
		The description of the tree includes approximate standard errors on the lengths of segments of the tree.
	www.dbbm.fiocruz.br /molbiol/contml.html (1334 words)

	Favorite points, cover times and fractals (Site not responding. Last check: 2007-10-22)
		A common theme is the tree like correlation structure of excursion counts around different centers, which makes a multi-scale refinement of the second moment method effective.
		Brownian motion to planar SRW via KMT construction (Section 5.1).
		Peres An invitation to sample path of Brownian motion (which deals with fractal geometry of simpler random sets related to the sample path of the Brownian motion).
	www-stat.stanford.edu /~amir/math-232/plan.html (390 words)

	Statistical Framework for Phylogenomic Analysis of Gene Family Expression Profiles -- Gu 167 (1): 531 -- Genetics
		Schematic of a gene family tree, where y is the expression level at node A, the common ancestor of genes i and j.
		The phylogenetic tree of the GlnS gene family, inferred from the multialignment of amino acid sequences including eukaryotes and prokaryotes.
		For the three-gene tree (Fig 1B), it is given by
	www.genetics.org /cgi/content/full/167/1/531 (3779 words)

	Random trees and applications, Jean-François Le Gall
		In the continuous setting, we use the formalism of real trees, which yields an elegant formulation of the convergence of rescaled discrete trees towards continuous objects.
		We explain the coding of real trees by functions, which is a continuous version of the well-known coding of discrete trees by Dyck paths.
		The last section is an introduction to the theory of the Brownian snake, which combines the genealogical structure of random real trees with independent spatial motions.
	projecteuclid.org /Dienst/UI/1.0/Display/euclid.ps/1132583290 (207 words)

	Call Options on Dividend-Paying Stocks (Site not responding. Last check: 2007-10-22)
		This is the case in the top tree, where the American option is worth $7.04, and the European option is worth $7.00.
		In the second tree (where the American call is worth $6.99, and the European call is worth $6.95), we assume that the stock price ex-dividend follows geometric Brownian motion.
		In this tree, as in the previous one, the European option value is obtained by not allowing early exercise and discounting the (risk-neutral) probability-weighted option values at expiration.
	finance.eller.arizona.edu /lam/wkend/q06.html (352 words)

	Brownian motion (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-10-22)
		An example of 1000 steps of Brownian motion in two dimensions.
		The origin of the motion is at [0,0] and the x and y components of each step are independently and normally distributed with a variance of 2 and a mean of zero.
		It is a mistaken belief that Albert Einstein was the first to give a mathematical theory to the Brownian motion, but considering how few people know of Bachelier, this is understandable.
	brownian-motion.kiwiki.homeip.net.cob-web.org:8888 (866 words)

	CiteULike: ansobol's brownian-motion (Site not responding. Last check: 2007-10-22)
		Relativistic Brownian motion: From a microscopic binary collision model to the Langevin equation
		Brownian motion, random walks on trees, and harmonic measure on polynomial Julia sets
		Brownian motion and diffusion: from stochastic processes to chaos and beyond
	www.citeulike.org /user/ansobol/tag/brownian-motion (535 words)

	"Davar Khoshnevisan's Publications" (Site not responding. Last check: 2007-10-22)
		Sectorial Local Non-Determinism and the Geometry of the Brownian Sheet (with Dongsheng Wu and Yimin Xiao).
		An Extreme-Value Analysis of the LIL for Brownian Motion (with David A. Levin and Zhan Shi) Electr.
		Boundary crossings and the distribution function of the maximum of Brownian sheet (w/ E. Csáki and Z. Shi), Stoch.
	www.math.utah.edu:8080 /~davar/publications.html (784 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		This is the (very) preliminary results of running evolvability experiments using various amounts of Brownian noise.
		In terms of tree sizes, we see code bloat in all Brownian cases, but not in the Uniform case.
		About the only thing we can say so far for Brownian is that the results are less noisy.
	www.cs.unm.edu /~vanbelle/RA/evoUvsB/evoUvsB.html (247 words)

	contml
		If the U (User Tree) option is used and more than one tree is supplied, the program also performs a statistical test of each of these trees against the one with highest likelihood.
		If there are two user trees, the test done is one which is due to Kishino and Hasegawa (1989), a version of a test originally introduced by Templeton (1983).
		They pointed out that a correction for the number of trees was necessary, and they introduced a resampling method to make this correction.
	evolution.genetics.washington.edu /phylip/doc/contml.html (1714 words)

	Cover Time and Favourite Points for Planar Random Walks
		The proofs for the upper bounds rely on the second moment method, the approximation of random walks by Brownian motions, and an underlying tree structure for the occupation of small disks by a Brownian motion.
		We shall in a first time sketch a proof of this conjecture and apply then the KMT approximation theorem of the Brownian motion by the standard random walk.
		Note that the Brownian motion between two successful points x and y before reaching the boundary may again be modelized by a tree structure, and that the same technique as for trees works once more (with many technical issues).
	pauillac.inria.fr /algo/seminars/sem00-01/dembo2.html (1418 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		Brownian path, independent of the order of the method or the !
		Brownian tree stuff integer :: nsteps, nsteps_last = -1, nsteps_most = - 1, treedepth !!!
		Calculate depth of Brownian tree (treedepth = 0 means just base layer) treedepth = int(log(real(nsteps, kind=wp)) / log(2.0_wp) + 0.5_wp) if (2**treedepth.ne.
	george.ph.utexas.edu /~dsteck/code/sderk90.2.0.2/sderk90.f90 (5846 words)

	Homepage Dr. Peter Mörters (Site not responding. Last check: 2007-10-22)
		This includes stochastic analysis, large deviation theory, Hausdorff dimension, Brownian motion and its intersection properties, super-Brownian motion and other spatial branching processes, stochastic process with interactions, stochastic processes in random media and applications of probability in analysis and outside mathematics.
		On the multifractal spectrum for branching measure on a Galton-Watson tree
		Multifractal analysis of branching measure on a Galton-Watson tree with Narn-Rueih Shieh.
	people.bath.ac.uk /maspm (707 words)

	CONTML - Gene Frequencies and Continuous Characters Maximum Likelihood method
		It is based on the model of Edwards and Cavalli-Sforza (1964; Cavalli-Sforza and Edwards, 1967).
		This enables us to use the Brownian motion model on the resulting coordinates, in an approximation equivalent to using Cavalli-Sforza and Edwards's (1967) chord measure of genetic distance and taking that to give distance between particles undergoing pure Brownian motion.
		Then the pairwise statistical test of Templeton (1983) as modified for likelihoods by Kishino and Hasegawa (1989) is carried out.
	cmgm.stanford.edu /phylip/contml.html (1316 words)

	Evolution of the bacterial flagellum
		However, published attempts to explain flagellar origins suffer from vagueness and are inconsistent with recent discoveries and the constraints imposed by Brownian motion. A new model is proposed based on two major arguments.
		While “Evolution in (Brownian) Space” was admittedly a first attempt, and I was a dedicated enthusiast rather than a professional, I think the model has stood up rather well over the last two and a half years.
		Rizzotti (2000) and others (e.g., Koch, 2003) have suggested that the last common ancestor of bacteria was gram positive. However, the very general consideration that most of the bacterial phyla are gram negative, including the many different taxa that come out as basal on different analyses, weighs against this hypothesis.
	www.talkdesign.org /faqs/flagellum.html (8497 words)

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