To determine the thresholds for the number of hits required to assign a protein to a
|
|
|
- Ernest Goodman
- 5 years ago
- Views:
Transcription
1 SI Appendix Thresholds for the Delineation of the Gene Age Classes To determine the thresholds for the number of hits required to assign a protein to a particular age class all BLAST hits from a genome to the RefSeq database were analyzed in the following way. A distribution of the number of hits to different organisms was constructed for each category; the location of the rightmost peak of the distribution (rounded to an integer) was considered to be the effective number of genomes in a taxonomic category (e.g. see Figure A1). Fungi/ Metazoa group number of proteins number of hits Figure A1. Distribution of the number of hits from Aspfu proteins to the Fungi/Metazoa group organisms in RefSeq database. Red bar shows the effective number of genomes in the Fungi/Metazoa group (26) from the Aspfu perspective. 1
2 The threshold for the number of hits required to assign a protein to the given age class was determined as a fraction of the effective number of genomes (Table A1). Table A1. Taxonomic Class Effective No. of Genomes Threshold No. of Hits Homsa - Primates 2 1 Homsa - Mammalia 7 3 Homsa - Chordata 4 2 Homsa - Metazoa 13 6 Homsa - Fungi/Metazoa group Homsa - Eukaryota 10 5 Homsa cellular organisms Drome - Drosophila 1 1 Drome - Diptera 3 1 Drome - Insecta 3 1 Drome - Metazoa 18 9 Drome - Fungi/Metazoa group Drome - Eukaryota 10 5 Drome cellular organisms Aspfu - Aspergillus 3 1 Aspfu - Pezizomycotina 10 5 Aspfu - Ascomycota 12 6 Aspfu - Fungi 4 2 Aspfu - Fungi/Metazoa group Aspfu - Eukaryota 10 5 Aspfu cellular organisms
3 SI Text Steady-State Model of Gene Gain and Loss Consider a genome of a constant size under a steady-state process of gene acquisition and loss. Let l ( be the number of genes of the age a having the loss rate x in a genome at time t. Then l / t + l / a = xl, (1) The density function l ( should satisfy the boundary and initial conditions: l ( 0, = Cg(, (2) l( 0, = ϕ(. (3) The condition (2) means that new genes (of age zero and the loss rate x ) appear with the rate that does not depend on time, and the total number of newly acquired genes is equal to some constant C. We suppose also that the continuity condition is satisfied (see equation (7) below). Proposition. The solution of model (1)-(3) is given by the formulas and l ( = Ce ax g( at t > a tx l( ϕ ( a at t < a. Proof. The general solution of (1) is an arbitrary function of the first independent integrals of the system of ordinary differential equations dl xl = dt = da. These integrals are I1 = t a, I 2 = 2lnl + ( t + a) x. So, the general solution of equation (1) is of the form 3
4 l( x( t+ a)/ 2 F( t (4) where F ( is an arbitrary (differentiable) function. tx / 2 Then l( 0, F( = Cg(, tx / 2 and we should take F( = Ce g( at t > 0 to satisfy the boundary condition (2). ax / 2 Nex l(0, F( = ϕ( ax and we should take F( ϕ( at a > 0 to satisfy the initial condition (3). Hence, the solution of system (1)-(3) is and l( l( ( t+ a) x / 2 ( t+ a) x / 2 F( t = Ce ax g( at t > a (5) F( t tx ϕ ( a at t < a (6). To provide the continuity of the solution, we suppose that Corollaries ϕ ( 0, x ) = Cg(. (7) 1. The density l ( does not depend on t at t > a. 2. The total size of a genome at a g( L ( dx. x t > is = l dadx = C 3. The distribution of genes in a genome over loss rate g( g( f ( = l( da / L = / dx at t > a x 0 x 0 and the distribution of genes being lost at any given moment 00 0 t > a is 4
5 xf ( = g( (i.e. genes being lost have the same distribution of loss rate as genes being gained; effectively a condition of an equilibrium). 4. The distribution of genes in a genome over age p ax g( ( a) = l( dx / L g( dx / dx 0 is proportional to the Laplace transform of g(. 0 x at t > a It follows tha if the age distribution of genes in a genome p (a) is known, then we can reconstruct the distribution g ( in the gene universe, and conversely. In practice, however, the data on p(a) obtained in the present study are too crude to attempt a meaningful reconstruction of g (. Example. If g ( (the distribution of the loss rate among the genes of zero age) is a gammadistribution with the shape parameter α>1, then f ( (the distribution of the loss rate across the whole genome) is also a gamma-distribution with the shape parameter α-1 (Figure A2) and the distribution of gene ages is a Pareto distribution with a power-law tail with an exponent of α (Figure A3). Distributions of the loss rate among the genes belonging to different age classes could be quite distinct in this case (Figure A4). 5
6 g( f( loss rate Figure A2. Distribution of the loss rate for the genes of zero age ( g ( ; a gammadistribution with the shape parameter α=4) and the overall distribution of the gene loss rate in the genome. p(a) age Figure A3. Distribution of the gene ages for the above model parameters. 6
7 q(x,[0-0.5]) q(x,[0.5-inf]) f( loss rate Figure A4. Distribution of the loss rate for the two age classes of genes: ages 0 to 0.5 and ages 0.5 to infinity. 7
Master Biomedizin ) UCSC & UniProt 2) Homology 3) MSA 4) Phylogeny. Pablo Mier
Master Biomedizin 2018 1) UCSC & UniProt 2) Homology 3) MSA 4) 1 12 a. All of the sequences in file1.fasta (https://cbdm.uni-mainz.de/mb18/) are homologs. How many groups of orthologs would you say there
f(s)ds, i.e. to write down the general solution in
1. First order ODEs. Simplest examples. Existence and uniqueness theorem Example 1.1. Consider the equation (1.1) x (t) = 1 This is an equation because there is an unknown: the function x(t). This is a
Elements of Bioinformatics 14F01 TP5 -Phylogenetic analysis
Elements of Bioinformatics 14F01 TP5 -Phylogenetic analysis 10 December 2012 - Corrections - Exercise 1 Non-vertebrate chordates generally possess 2 homologs, vertebrates 3 or more gene copies; a Drosophila
Laplace Transforms Chapter 3
Laplace Transforms Important analytical method for solving linear ordinary differential equations. - Application to nonlinear ODEs? Must linearize first. Laplace transforms play a key role in important
Biological Networks: Comparison, Conservation, and Evolution via Relative Description Length By: Tamir Tuller & Benny Chor
Biological Networks:,, and via Relative Description Length By: Tamir Tuller & Benny Chor Presented by: Noga Grebla Content of the presentation Presenting the goals of the research Reviewing basic terms
Bioinformatics: Network Analysis
Bioinformatics: Network Analysis Kinetics of Gene Regulation COMP 572 (BIOS 572 / BIOE 564) - Fall 2013 Luay Nakhleh, Rice University 1 The simplest model of gene expression involves only two steps: the
Connection to Laplacian in spherical coordinates (Chapter 13)
Connection to Laplacian in spherical coordinates (Chapter 13) We might often encounter the Laplace equation and spherical coordinates might be the most convenient 2 u(r, θ, φ) = 0 We already saw in Chapter
DIFFERENTIAL EQUATIONS
DIFFERENTIAL EQUATIONS Basic Terminology A differential equation is an equation that contains an unknown function together with one or more of its derivatives. 1 Examples: 1. y = 2x + cos x 2. dy dt =
PHYS 301 HOMEWORK #13-- SOLUTIONS
PHYS 31 HOMEWORK #13-- SOLUTIONS 1. The wave equation is : 2 u x = 1 2 u 2 v 2 t 2 Since we have that u = f (x - vt) and u = f (x + vt), we substitute these expressions into the wave equation.starting
Microbiome: 16S rrna Sequencing 3/30/2018
Microbiome: 16S rrna Sequencing 3/30/2018 Skills from Previous Lectures Central Dogma of Biology Lecture 3: Genetics and Genomics Lecture 4: Microarrays Lecture 12: ChIP-Seq Phylogenetics Lecture 13: Phylogenetics
Introduction to Probability and Statistics (Continued)
Introduction to Probability and Statistics (Continued) Prof. icholas Zabaras Center for Informatics and Computational Science https://cics.nd.edu/ University of otre Dame otre Dame, Indiana, USA Email:
Phylogeny 9/8/2014. Evolutionary Relationships. Data Supporting Phylogeny. Chapter 26
Phylogeny Chapter 26 Taxonomy Taxonomy: ordered division of organisms into categories based on a set of characteristics used to assess similarities and differences Carolus Linnaeus developed binomial nomenclature,
GEP Annotation Report
GEP Annotation Report Note: For each gene described in this annotation report, you should also prepare the corresponding GFF, transcript and peptide sequence files as part of your submission. Student name:
Part V. Chapter 19. Congruence of integers
Part V. Chapter 19. Congruence of integers Congruence modulo m Let m be a positive integer. Definition. Integers a and b are congruent modulo m if and only if a b is divisible by m. For example, 1. 277
1 Review of di erential calculus
Review of di erential calculus This chapter presents the main elements of di erential calculus needed in probability theory. Often, students taking a course on probability theory have problems with concepts
THEODORE VORONOV DIFFERENTIABLE MANIFOLDS. Fall Last updated: November 26, (Under construction.)
4 Vector fields Last updated: November 26, 2009. (Under construction.) 4.1 Tangent vectors as derivations After we have introduced topological notions, we can come back to analysis on manifolds. Let M
DATA ACQUISITION FROM BIO-DATABASES AND BLAST. Natapol Pornputtapong 18 January 2018
DATA ACQUISITION FROM BIO-DATABASES AND BLAST Natapol Pornputtapong 18 January 2018 DATABASE Collections of data To share multi-user interface To prevent data loss To make sure to get the right things
Appendix A. Sequences and series. A.1 Sequences. Definition A.1 A sequence is a function N R.
Appendix A Sequences and series This course has for prerequisite a course (or two) of calculus. The purpose of this appendix is to review basic definitions and facts concerning sequences and series, which
Quadratic forms. Here. Thus symmetric matrices are diagonalizable, and the diagonalization can be performed by means of an orthogonal matrix.
Quadratic forms 1. Symmetric matrices An n n matrix (a ij ) n ij=1 with entries on R is called symmetric if A T, that is, if a ij = a ji for all 1 i, j n. We denote by S n (R) the set of all n n symmetric
Exercise 5. Sequence Profiles & BLAST
Exercise 5 Sequence Profiles & BLAST 1 Substitution Matrix (BLOSUM62) Likelihood to substitute one amino acid with another Figure taken from https://en.wikipedia.org/wiki/blosum 2 Substitution Matrix (BLOSUM62)
Rapid Learning Center Chemistry :: Biology :: Physics :: Math
Rapid Learning Center Chemistry :: Biology :: Physics :: Math Rapid Learning Center Presents Teach Yourself AP Biology in 24 Hours 1/37 *AP is a registered trademark of the College Board, which does not
Continuous Random Variables and Continuous Distributions
Continuous Random Variables and Continuous Distributions Continuous Random Variables and Continuous Distributions Expectation & Variance of Continuous Random Variables ( 5.2) The Uniform Random Variable
ERRATA: Probabilistic Techniques in Analysis
ERRATA: Probabilistic Techniques in Analysis ERRATA 1 Updated April 25, 26 Page 3, line 13. A 1,..., A n are independent if P(A i1 A ij ) = P(A 1 ) P(A ij ) for every subset {i 1,..., i j } of {1,...,
Jim Lambers ENERGY 281 Spring Quarter Homework Assignment 3 Solution. 2 Ei r2 D., 4t D and the late time approximation to this solution,
Jim Lambers ENERGY 8 Spring Quarter 7-8 Homework Assignment 3 Solution Plot the exponential integral solution p D (r D,t D ) = ) ( Ei r D, 4t D and the late time approximation to this solution, p D (r
Mitochondrial Genome Annotation
Protein Genes 1,2 1 Institute of Bioinformatics University of Leipzig 2 Department of Bioinformatics Lebanese University TBI Bled 2015 Outline Introduction Mitochondrial DNA Problem Tools Training Annotation
x x 1 x 2 + x 2 1 > 0. HW5. Text defines:
Lecture 15: Last time: MVT. Special case: Rolle s Theorem (when f(a) = f(b)). Recall: Defn: Let f be defined on an interval I. f is increasing (or strictly increasing) if whenever x 1, x 2 I and x 2 >
Topology. 1 Introduction. 2 Chromosomes Topology & Counts. 3 Genome size. 4 Replichores and gene orientation. 5 Chirochores.
Topology 1 Introduction 2 3 Genome size 4 Replichores and gene orientation 5 Chirochores 6 G+C content 7 Codon usage 27 marc.bailly-bechet@univ-lyon1.fr The big picture Eukaryota Bacteria Many linear chromosomes
PH.D. PRELIMINARY EXAMINATION MATHEMATICS
UNIVERSITY OF CALIFORNIA, BERKELEY Dept. of Civil and Environmental Engineering FALL SEMESTER 2014 Structural Engineering, Mechanics and Materials NAME PH.D. PRELIMINARY EXAMINATION MATHEMATICS Problem
MEM 255 Introduction to Control Systems: Modeling & analyzing systems
MEM 55 Introduction to Control Systems: Modeling & analyzing systems Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University Outline The Pendulum Micro-machined capacitive accelerometer
ON THE DIFFERENCE BETWEEN THE CONCEPTS "COMPOUND" AND "COMPOSED" POISSON PROCESSES. CARL PHILIPSON Stockholm, Sweden
ON THE DIFFERENCE BETWEEN THE CONCEPTS "COMPOUND" AND "COMPOSED" POISSON PROCESSES CARL PHILIPSON Stockholm, Sweden In the discussion in the ASTIN Colloquium 1962, which followed my lecture on the numerical
Linear maps. Matthew Macauley. Department of Mathematical Sciences Clemson University Math 8530, Spring 2017
Linear maps Matthew Macauley Department of Mathematical Sciences Clemson University http://www.math.clemson.edu/~macaule/ Math 8530, Spring 2017 M. Macauley (Clemson) Linear maps Math 8530, Spring 2017
Regular finite Markov chains with interval probabilities
5th International Symposium on Imprecise Probability: Theories and Applications, Prague, Czech Republic, 2007 Regular finite Markov chains with interval probabilities Damjan Škulj Faculty of Social Sciences
Comparing downside risk measures for heavy tailed distributions
Comparing downside risk measures for heavy tailed distributions Jon Danielsson Bjorn N. Jorgensen Mandira Sarma Casper G. de Vries March 6, 2005 Abstract In this paper we study some prominent downside
Laplace Transforms. Chapter 3. Pierre Simon Laplace Born: 23 March 1749 in Beaumont-en-Auge, Normandy, France Died: 5 March 1827 in Paris, France
Pierre Simon Laplace Born: 23 March 1749 in Beaumont-en-Auge, Normandy, France Died: 5 March 1827 in Paris, France Laplace Transforms Dr. M. A. A. Shoukat Choudhury 1 Laplace Transforms Important analytical
Math 416 Lecture 3. The average or mean or expected value of x 1, x 2, x 3,..., x n is
Math 416 Lecture 3 Expected values The average or mean or expected value of x 1, x 2, x 3,..., x n is x 1 x 2... x n n x 1 1 n x 2 1 n... x n 1 n 1 n x i p x i where p x i 1 n is the probability of x i
FINAL EXAM SOLUTIONS, MATH 123
FINAL EXAM SOLUTIONS, MATH 23. Find the eigenvalues of the matrix ( 9 4 3 ) So λ = or 6. = λ 9 4 3 λ = ( λ)( 3 λ) + 36 = λ 2 7λ + 6 = (λ 6)(λ ) 2. Compute the matrix inverse: ( ) 3 3 = 3 4 ( 4/3 ) 3. Let
Definition 5.1. A vector field v on a manifold M is map M T M such that for all x M, v(x) T x M.
5 Vector fields Last updated: March 12, 2012. 5.1 Definition and general properties We first need to define what a vector field is. Definition 5.1. A vector field v on a manifold M is map M T M such that
PROBABILITY DISTRIBUTION
PROBABILITY DISTRIBUTION DEFINITION: If S is a sample space with a probability measure and x is a real valued function defined over the elements of S, then x is called a random variable. Types of Random
JUST THE MATHS UNIT NUMBER ORDINARY DIFFERENTIAL EQUATIONS 1 (First order equations (A)) A.J.Hobson
JUST THE MATHS UNIT NUMBER 5. ORDINARY DIFFERENTIAL EQUATIONS (First order equations (A)) by A.J.Hobson 5.. Introduction and definitions 5..2 Exact equations 5..3 The method of separation of the variables
Direct Proof and Proof by Contrapositive
Dr. Nahid Sultana October 14, 2012 Consider an implication: p q. Then p q p q T T T T F F F T T F F T Consider an implication: p q. Then p q p q T T T T F F F T T F F T Consider x D, p(x) q(x). It can
Gillespie s Algorithm and its Approximations. Des Higham Department of Mathematics and Statistics University of Strathclyde
Gillespie s Algorithm and its Approximations Des Higham Department of Mathematics and Statistics University of Strathclyde djh@maths.strath.ac.uk The Three Lectures 1 Gillespie s algorithm and its relation
MAS 6217 (Fall 2017) Number Theory and Cryptography (Yiu) Class Notes, August 24.
MAS 6217 (Fall 2017) Number Theory and Cryptography (Yiu) Class Notes, August 24. Linear Diophantine equations Theorem 1. Let a, b, c be integers, a and b nonzero, and d := gcd(a, b). Consider the linear
Classification and Viruses Practice Test
Classification and Viruses Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Biologists use a classification system to group organisms in part
MATH 117 LECTURE NOTES
MATH 117 LECTURE NOTES XIN ZHOU Abstract. This is the set of lecture notes for Math 117 during Fall quarter of 2017 at UC Santa Barbara. The lectures follow closely the textbook [1]. Contents 1. The set
Phylogeny and the Tree of Life
Chapter 26 Phylogeny and the Tree of Life PowerPoint Lecture Presentations for Biology Eighth Edition Neil Campbell and Jane Reece Lectures by Chris Romero, updated by Erin Barley with contributions from
Chapter 5. Proteomics and the analysis of protein sequence Ⅱ
Proteomics Chapter 5. Proteomics and the analysis of protein sequence Ⅱ 1 Pairwise similarity searching (1) Figure 5.5: manual alignment One of the amino acids in the top sequence has no equivalent and
Lecture 5: Moment generating functions
Lecture 5: Moment generating functions Definition 2.3.6. The moment generating function (mgf) of a random variable X is { x e tx f M X (t) = E(e tx X (x) if X has a pmf ) = etx f X (x)dx if X has a pdf
ELEG 833. Nonlinear Signal Processing
Nonlinear Signal Processing ELEG 833 Gonzalo R. Arce Department of Electrical and Computer Engineering University of Delaware arce@ee.udel.edu February 15, 25 2 NON-GAUSSIAN MODELS 2 Non-Gaussian Models
Math 3013 Problem Set 4
(e) W = {x, 3x, 4x 3, 5x 4 x i R} in R 4 Math 33 Problem Set 4 Problems from.6 (pgs. 99- of text):,3,5,7,9,,7,9,,35,37,38. (Problems,3,4,7,9 in text). Determine whether the indicated subset is a subspace
ENGI 4430 PDEs - d Alembert Solutions Page 11.01
ENGI 4430 PDEs - d Alembert Solutions Page 11.01 11. Partial Differential Equations Partial differential equations (PDEs) are equations involving functions of more than one variable and their partial derivatives
15B. Isometries and Functionals 1
5B. Isometries and Functionals Isometries If the important functions between vector spaces V and W are those that preserve linearity (i.e., linear transformations), then the important functions between
E[X n ]= dn dt n M X(t). ). What is the mgf? Solution. Found this the other day in the Kernel matching exercise: 1 M X (t) =
![E[X n ]= dn dt n M X(t). ). What is the mgf? Solution. Found this the other day in the Kernel matching exercise: 1 M X (t) =](/thumbs/94/121808901.jpg "E[X n ]= dn dt n M X(t). ). What is the mgf? Solution. Found this the other day in the Kernel matching exercise: 1 M X (t) =")
Chapter 7 Generating functions Definition 7.. Let X be a random variable. The moment generating function is given by M X (t) =E[e tx ], provided that the expectation exists for t in some neighborhood of
Chemical Kinetics I: The Dry Lab. Up until this point in our study of physical chemistry we have been interested in
Chemical Kinetics I: The Dry Lab Up until this point in our study of physical chemistry we have been interested in equilibrium properties; now we will begin to investigate non-equilibrium properties and
Annotation of Drosophila grimashawi Contig12
Annotation of Drosophila grimashawi Contig12 Marshall Strother April 27, 2009 Contents 1 Overview 3 2 Genes 3 2.1 Genscan Feature 12.4............................................. 3 2.1.1 Genome Browser:
16. Working with the Langevin and Fokker-Planck equations
16. Working with the Langevin and Fokker-Planck equations In the preceding Lecture, we have shown that given a Langevin equation (LE), it is possible to write down an equivalent Fokker-Planck equation
A Note on Tail Behaviour of Distributions. the max domain of attraction of the Frechét / Weibull law under power normalization
ProbStat Forum, Volume 03, January 2010, Pages 01-10 ISSN 0974-3235 A Note on Tail Behaviour of Distributions in the Max Domain of Attraction of the Frechét/ Weibull Law under Power Normalization S.Ravi
Unit Two: Biodiversity. Chapter 4
Unit Two: Biodiversity Chapter 4 A. Classifying Living Things (Ch.4 - page 100) Scientific knowledge is constantly evolving ( changing ): new evidence is discovered laws and theories are tested and possibly
ELEMENTS OF PROBABILITY THEORY
ELEMENTS OF PROBABILITY THEORY Elements of Probability Theory A collection of subsets of a set Ω is called a σ algebra if it contains Ω and is closed under the operations of taking complements and countable
MATH 251 Final Examination August 14, 2015 FORM A. Name: Student Number: Section:
MATH 251 Final Examination August 14, 2015 FORM A Name: Student Number: Section: This exam has 11 questions for a total of 150 points. Show all your work! In order to obtain full credit for partial credit
Sobolev spaces. May 18
Sobolev spaces May 18 2015 1 Weak derivatives The purpose of these notes is to give a very basic introduction to Sobolev spaces. More extensive treatments can e.g. be found in the classical references
Formulas for probability theory and linear models SF2941
Formulas for probability theory and linear models SF2941 These pages + Appendix 2 of Gut) are permitted as assistance at the exam. 11 maj 2008 Selected formulae of probability Bivariate probability Transforms
STAT 430/510 Probability Lecture 16, 17: Compute by Conditioning
STAT 430/510 Probability Lecture 16, 17: Compute by Conditioning Pengyuan (Penelope) Wang Lecture 16-17 June 21, 2011 Computing Probability by Conditioning A is an arbitrary event If Y is a discrete random
A field F is a set of numbers that includes the two numbers 0 and 1 and satisfies the properties:
Byte multiplication 1 Field arithmetic A field F is a set of numbers that includes the two numbers 0 and 1 and satisfies the properties: F is an abelian group under addition, meaning - F is closed under
GENE ONTOLOGY (GO) Wilver Martínez Martínez Giovanny Silva Rincón
GENE ONTOLOGY (GO) Wilver Martínez Martínez Giovanny Silva Rincón What is GO? The Gene Ontology (GO) project is a collaborative effort to address the need for consistent descriptions of gene products in
Calculus for the Life Sciences II Assignment 6 solutions. f(x, y) = 3π 3 cos 2x + 2 sin 3y
Calculus for the Life Sciences II Assignment 6 solutions Find the tangent plane to the graph of the function at the point (0, π f(x, y = 3π 3 cos 2x + 2 sin 3y Solution: The tangent plane of f at a point
Discontinuous Distributions in Mechanics of Materials
Discontinuous Distributions in Mechanics of Materials J.E. Akin, Rice University 1. Introduction The study of the mechanics of materials continues to change slowly. The student needs to learn about software
Chapter 2 Vector-matrix Differential Equation and Numerical Inversion of Laplace Transform
Chapter 2 Vector-matrix Differential Equation and Numerical Inversion of Laplace Transform 2.1 Vector-matrix Differential Equation A differential equation and a set of differential (simultaneous linear
THE ROYAL STATISTICAL SOCIETY GRADUATE DIPLOMA
THE ROYAL STATISTICAL SOCIETY 4 EXAINATIONS SOLUTIONS GRADUATE DIPLOA PAPER I STATISTICAL THEORY & ETHODS The Societ provides these solutions to assist candidates preparing for the examinations in future
On perturbations in the leading coefficient matrix of time-varying index-1 DAEs
On perturbations in the leading coefficient matrix of time-varying index-1 DAEs Institute of Mathematics, Ilmenau University of Technology Darmstadt, March 27, 2012 Institute of Mathematics, Ilmenau University
Summary of time independent electrodynamics
hapter 10 Summary of time independent electrodynamics 10.1 Electrostatics Physical law oulomb s law charges as origin of electric field Superposition principle ector of the electric field E(x) in vacuum
CH. 18 Classification
CH. 18 Classification Name:_ 1. Biologists use a classification system to group organisms in part because organisms a. are going extinct. b. are very numerous and diverse. c. are too much alike. d. share
1/30. Rigid Body Rotations. Dave Frank
. 1/3 Rigid Body Rotations Dave Frank A Point Particle and Fundamental Quantities z 2/3 m v ω r y x Angular Velocity v = dr dt = ω r Kinetic Energy K = 1 2 mv2 Momentum p = mv Rigid Bodies We treat a rigid
1. The population of a bacteria culture increases at the rate of 3 times the square root of the present population.
1. The population of a bacteria culture increases at the rate of 3 times the square root of the present population. A. Model the population P = P(t) of the bacteria population with a differential equation.
THE INVERSE FUNCTION THEOREM
THE INVERSE FUNCTION THEOREM W. PATRICK HOOPER The implicit function theorem is the following result: Theorem 1. Let f be a C 1 function from a neighborhood of a point a R n into R n. Suppose A = Df(a)
General Least Squares Fitting
Appendix B General Least Squares Fitting B.1 Introduction Previously you have done curve fitting in two dimensions. Now you will learn how to extend that to multiple dimensions. B.1.1 Linearizable Non-linear
7.4* General logarithmic and exponential functions
7.4* General logarithmic and exponential functions Mark Woodard Furman U Fall 2010 Mark Woodard (Furman U) 7.4* General logarithmic and exponential functions Fall 2010 1 / 9 Outline 1 General exponential
Shape of the return probability density function and extreme value statistics
Shape of the return probability density function and extreme value statistics 13/09/03 Int. Workshop on Risk and Regulation, Budapest Overview I aim to elucidate a relation between one field of research
Two viewpoints on measure valued processes
Two viewpoints on measure valued processes Olivier Hénard Université Paris-Est, Cermics Contents 1 The classical framework : from no particle to one particle 2 The lookdown framework : many particles.
DIFFERENTIAL EQUATIONS
DIFFERENTIAL EQUATIONS 1. Basic Terminology A differential equation is an equation that contains an unknown function together with one or more of its derivatives. 1 Examples: 1. y = 2x + cos x 2. dy dt
MATH 307: Problem Set #3 Solutions
: Problem Set #3 Solutions Due on: May 3, 2015 Problem 1 Autonomous Equations Recall that an equilibrium solution of an autonomous equation is called stable if solutions lying on both sides of it tend
Exercises with solutions (Set D)
Exercises with solutions Set D. A fair die is rolled at the same time as a fair coin is tossed. Let A be the number on the upper surface of the die and let B describe the outcome of the coin toss, where
The Dirichlet s P rinciple. In this lecture we discuss an alternative formulation of the Dirichlet problem for the Laplace equation:
Oct. 1 The Dirichlet s P rinciple In this lecture we discuss an alternative formulation of the Dirichlet problem for the Laplace equation: 1. Dirichlet s Principle. u = in, u = g on. ( 1 ) If we multiply
A Marshall-Olkin Gamma Distribution and Process
CHAPTER 3 A Marshall-Olkin Gamma Distribution and Process 3.1 Introduction Gamma distribution is a widely used distribution in many fields such as lifetime data analysis, reliability, hydrology, medicine,
Stability of Stochastic Differential Equations
Lyapunov stability theory for ODEs s Stability of Stochastic Differential Equations Part 1: Introduction Department of Mathematics and Statistics University of Strathclyde Glasgow, G1 1XH December 2010
MTHSC 3190 Section 2.9 Sets a first look
MTHSC 3190 Section 2.9 Sets a first look Definition A set is a repetition free unordered collection of objects called elements. Definition A set is a repetition free unordered collection of objects called
Solutions to Laplace s Equations- II
Solutions to Laplace s Equations- II Lecture 15: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay Laplace s Equation in Spherical Coordinates : In spherical coordinates
BLAST: Target frequencies and information content Dannie Durand
Computational Genomics and Molecular Biology, Fall 2016 1 BLAST: Target frequencies and information content Dannie Durand BLAST has two components: a fast heuristic for searching for similar sequences
Supplementary materials Quantitative assessment of ribosome drop-off in E. coli
Supplementary materials Quantitative assessment of ribosome drop-off in E. coli Celine Sin, Davide Chiarugi, Angelo Valleriani 1 Downstream Analysis Supplementary Figure 1: Illustration of the core steps
MCE693/793: Analysis and Control of Nonlinear Systems
MCE693/793: Analysis and Control of Nonlinear Systems Introduction to Nonlinear Controllability and Observability Hanz Richter Mechanical Engineering Department Cleveland State University Definition of
ESL Chap3. Some extensions of lasso
ESL Chap3 Some extensions of lasso 1 Outline Consistency of lasso for model selection Adaptive lasso Elastic net Group lasso 2 Consistency of lasso for model selection A number of authors have studied
STATICS. FE Review. Statics, Fourteenth Edition R.C. Hibbeler. Copyright 2016 by Pearson Education, Inc. All rights reserved.
STATICS FE Review 1. Resultants of force systems VECTOR OPERATIONS (Section 2.2) Scalar Multiplication and Division VECTOR ADDITION USING EITHER THE PARALLELOGRAM LAW OR TRIANGLE Parallelogram Law: Triangle
Math 110 (S & E) Textbook: Calculus Early Transcendentals by James Stewart, 7 th Edition
Math 110 (S & E) Textbook: Calculus Early Transcendentals by James Stewart, 7 th Edition 1 Appendix A : Numbers, Inequalities, and Absolute Values Sets A set is a collection of objects with an important
arxiv:cond-mat/ v2 [cond-mat.stat-mech] 23 Feb 1998
![arxiv:cond-mat/ v2 [cond-mat.stat-mech] 23 Feb 1998](/thumbs/78/77115469.jpg "arxiv:cond-mat/ v2 [cond-mat.stat-mech] 23 Feb 1998")
Multiplicative processes and power laws arxiv:cond-mat/978231v2 [cond-mat.stat-mech] 23 Feb 1998 Didier Sornette 1,2 1 Laboratoire de Physique de la Matière Condensée, CNRS UMR6632 Université des Sciences,
LECTURE 16 GAUSS QUADRATURE In general for Newton-Cotes (equispaced interpolation points/ data points/ integration points/ nodes).
CE 025 - Lecture 6 LECTURE 6 GAUSS QUADRATURE In general for ewton-cotes (equispaced interpolation points/ data points/ integration points/ nodes). x E x S fx dx hw' o f o + w' f + + w' f + E 84 f 0 f
Unravelling the biochemical reaction kinetics from time-series data
Unravelling the biochemical reaction kinetics from time-series data Santiago Schnell Indiana University School of Informatics and Biocomplexity Institute Email: schnell@indiana.edu WWW: http://www.informatics.indiana.edu/schnell
Continuous Random Variables
1 / 24 Continuous Random Variables Saravanan Vijayakumaran sarva@ee.iitb.ac.in Department of Electrical Engineering Indian Institute of Technology Bombay February 27, 2013 2 / 24 Continuous Random Variables
Announcements: 1. Labs meet this week 2. Lab manuals have been ordered 3. Some slides from each lecture will be on the web 4. Study questions will be
Announcements: 1. Labs meet this week 2. Lab manuals have been ordered 3. Some slides from each lecture will be on the web 4. Study questions will be posted after each lecture Prokaryotes Eukaryotes Protozoa
DIFFERENTIAL EQUATIONS
DIFFERENTIAL EQUATIONS 1. Basic Terminology A differential equation is an equation that contains an unknown function together with one or more of its derivatives. 1 Examples: 1. y = 2x + cos x 2. dy dt
ENGI 9420 Lecture Notes 8 - PDEs Page 8.01
ENGI 940 Lecture Notes 8 - PDEs Page 8.01 8. Partial Differential Equations Partial differential equations (PDEs) are equations involving functions of more than one variable and their partial derivatives
The goal of this chapter is to study linear systems of ordinary differential equations: dt,..., dx ) T
1 1 Linear Systems The goal of this chapter is to study linear systems of ordinary differential equations: ẋ = Ax, x(0) = x 0, (1) where x R n, A is an n n matrix and ẋ = dx ( dt = dx1 dt,..., dx ) T n.