SOLiD System accuracy with the Exact Call Chemistry module


 Coral Fitzgerald
 1 years ago
 Views:
Transcription
1 WHITE PPER 55 Series SOLiD System SOLiD System accuracy with the Exact all hemistry module ONTENTS Principles of Exact all hemistry Introduction Encoding of base sequences with Exact all hemistry Demonstration of increased accuracy with Exact all hemistry onclusion Bioinformatics of Exact all hemistry ppendix : Determination of base calls and quality values ppendix B: The forwardbackward algorithm 5 ppendix : Probe set design 7 Principles of Exact all hemistry Introduction The 55 Series SOLiD System is designed to provide industryleading accuracy through a unique, ligationbased sequencing methodology, Exact all hemistry (E). This distinct sequencing approach builds on SOLiD 4 System chemistry, employing sequential ligation of oligonucleotide probes labeled with one of four fluorescent dyes, whereby each probe assays multiple base positions at a time. While SOLiD 4 System chemistry interrogates every base of the DN template twice using twobase encoded probes, Exact all hemistry performs an additional inspection of the template using a new, threebase encoded probe set. This new probe set is carefully designed to complement twobase encoding and jointly form a redundant errorcorrection code. The set of all dye color measurements, each carrying information about multiple bases, is then used by a specialized decoding algorithm to establish the correct base sequence without knowledge of the reference, even in the presence of measurement errors. This strategy allows for error detection and correction, providing highly accurate results for resequencing, de novo sequencing, and rare variant detection. Encoding of base sequences with Exact all hemistry 55 Series SOLiD System Exact all hemistry is illustrated in Figure. Beads containing singlestranded copies of DN library fragments are attached to the surface of the Flowhip. These sequences are interrogated by fluorescently labeled probes that hybridize and ligate at the boundary of singlestranded and doublestranded DN. The sequencing process is organized into phases called primer rounds. Each primer round consists of hybridization of a sequencing primer with a specific offset, followed by multiple cycles of probe ligation and detection. The primer round is concluded by a reset that melts the primer and extended sequence off the template, preparing the template for the next round. SOLiD 4 System chemistry relies on performing five primer rounds using a twobase encoded probe set. In addition, E follows these five primer rounds with one additional round. This sixth round starts with the same sequencing primer as the fifth round, but uses a new, independent probe set with a specific threebase labeling. Together, the six primer rounds enable unrivaled system accuracy by forming a redundant errorcorrection code. The labeling of both probe sets, shown in Figure, is inspired by a convolutional code, a type of errorcorrection code used in digital communication systems where the encoded symbols are derived from a short subset of consecutive information symbols [. The algebraic formula used to generate them is described in ppendix.
2 Probe Set Probe Set Figure. Ligationbased sequencing with 55 Series SOLiD System Exact all hemistry.
3 Demonstration of increased accuracy with Exact all hemistry To validate this sequencing strategy, we performed SOLiD System sequencing using Exact all hemistry on templated beads containing synthetic DN templates. The color measurements were collected by the instrument and processed with the E base calling algorithms (described in detail in ppendices and B). Because the precise sequence of the DN template was known, this approach specifically allowed for direct assessment of the sequencing accuracy of Exact all hemistry, presented in Figure as a histogram of calibrated Phred scores. s the results demonstrate, Exact all hemistry determines the template sequence with extremely high accuracy, the majority of base calls achieving accuracy in excess of %. Since each base position is interrogated by multiple colors, consistent agreements between multiple color calls significantly increase the confidence in base calls. t the same time, some color errors can be corrected as a result of the singleread redundancy provided by the sixth primer round. 7 Percentage of all base calls Phred score ccuracy 9% 99% 99.9% % % % ccuracy of base calls in Phred scale 6 or above Figure. Histogram of base call accuracies expressed in calibrated Phred scale. Base calls were derived from color measurement through algorithms described in ppendices B and. onclusion Sequencing with Exact all hemistry and the 55 Series SOLiD System clearly demonstrates increased performance and accuracy, which is imperative to highthroughput detection of rare genetic variants in heterogeneous or pooled samples, as well as de novo sequencing. The multibase encoding functionality contributes to lower error rate and reduced systematic noise, resulting in unsurpassed sequencing accuracy even at low coverage. Bioinformatics of Exact all hemistry ppendix : Determination of base calls and quality values Symbol u = [u, u, u,, u K x = [x,, x,,, x,k x B = [x B,, x B,,, x B,K/5 Definition Sequence of bases in a DN fragment. Base u is the last base of the adapter ligated to the 5 end of the fragment, which is known ahead of time. Expected sequence of colors resulting from interrogating u using probe set, assuming no color errors. Expected sequence of colors resulting from interrogating u using probe set, assuming no color errors. y = [y,, y,,, y,k Noisy color measurements of x. y B = [y B,, y B,,, y B,K/5 Noisy color measurements of x B. Table. Mathematical notation for ligationbased sequencing. Symbols and corresponding definitions are indicated.
4 The 55 Series SOLiD System sequencing process can be understood as a transformation of the template base sequence u into a collection of color measurements (see Table for notation). If the colors always could be read out without errors, this conversion would be a deterministic, injective function u (x,x B ), where every possible base sequence translates to a unique color sequence. For example, a sequence u = [TTTTT (last base T of the adapter followed by 5 template bases) is expected to translate into the set of colors in Figure. In the example shown in Figure, 5 unknown template bases (excluding u ) have been converted into 8 color reads. In general, there are 4 8 (~64 billion) possible color sequences of length 8, but only 4 5 (~ billion) possible base sequences of length 5. This means that only one in every 64 possible color sequences corresponds to a base sequence. Such valid color sequences are rare and, due to the design of the probe sets, dissimilar from each other. This makes them easy to distinguish, even in the presence of some measurement noise and errors in color calls.. Primer n Primer n Primer n Primer n Primer n4 Primer n4 x, = x, = bridge probe bridge probe bridge probe bridge probe x,5 = x,4 = x, = x B, = x,7 = x,6 = x, = x,9 = x,8 = x B, = x, = x, = x,5 = x,4 = x, = x B, = Probe Set Probe Set P adapter T T T T T... u u u u u 4 u 5 u 6 u 7 u 8 u 9 u u u u u 4 u 5 B. Probe Set x = [ Base Sequence u = [ T T T T T Probe Set x B = [ Figure. Example of color encoding for base sequence u = [TTTTT. olors are arranged by () order of data acquisition; (B) base position and probe set. The optics, imaging, and image processing subsystems of the 55 Series SOLiD System produce color measurements for each DN fragment and each probe ligation cycle. Measurements for a specific bead (y and y B, see Table ) carry information about the color sequence x, x B, and indirectly about base sequence u. The unknown sequence u, hidden variables x and x B, and observed variables y and y B are linked together through a causal, statistical relation that is key to base calling (illustrated by a Bayesian network in Figure 4). u,u,u,u x, u,u,u,u 4 u,u,u 4,u 5 u,u 4,u 5,u 6 u 4,u 5,u 6,u 7 x, x, x B, x,4 x,5 The 55 Series SOLiD Sequencer performs three steps to determine individual bases and assign quality values to the calls, as illustrated in Figure 5. t the core of this process is the Bayesian inference operation that derives four conditional (posterior) probabilities, P(u i =,,,T y ), for each base position i. The general formula for such derivation is a marginalization of P(u y ) derived through the Bayes theorem from conditional probability P(y u): y, y, y, y B, Figure 4. Bayesian network linking the unknown bases and the observed color measurements. y,4 y,5
5 practical way to efficiently perform the above computation is to use dynamic programming. The 55 Series SOLiD System uses a type of dynamic programming called the forwardbackward algorithm [, which is detailed in ppendix B. The steps preceding and following the Bayesian inference are much simpler. The measurement model, evaluated before Bayesian inference, converts each color measurement y i into four individual color likelihoods P(y i x i =,,, ), which are later used within the forwardbackward algorithm to calculate P(y u). Distributions P(y i x i ) are well characterized within the 55 Series SOLiD Sequencer image processing system. Finally, the product of Bayesian inference, probabilities P(u i =,,,T y ), are converted to base calls a i through straightforward probability x x x maximization: x x x Once the base call is established, its quality value b i is directly derived from the base probability as: g gg The quality values are determined from a lookup table using the four base likelihoods as feature vectors. Measurement model Bayesian Inference Base calling olor measurements olor likelihoods Base posterior probabilities Base calls & Quality values y P(y,i x,i =,,, ) P(y B,i x B,i =,,, ) for i =,,,K for i =,,,K/5 P(u i =,,,T y ) for i =,,,K Figure 5. Base calling process performed by the 55 Series SOLiD System for Exact all hemistry. a i,b i for i =,,,K g gg ppendix B: The forwardbackward algorithm!" #$ %!" /& #$ /& %. Edge label (probe set color) x,i+ Edge label (probe set color)!" #$ %!" /& #$ /& % x B,(i+)/5 ' ' ( u i u i+ u i+ u i u i+ u i+ u i+ u i+ u i+ u i+ B. Node (base triplet) x, x, x, x B, Edge (base quadruplet) ' ' ( x,4 Node (base triplet) x,k x,k T T T T T T T T T T T T T u u u u u u u u u 4 u u 4 u 5 u 4 u 5 u 6 u K u K u K u K u K u K+ u K u K+ u K+ Figure 6. raphical representation of one base sequence u = [u,u,u,,u K as a path through a graph. () Notation for variables associated with nodes and edges. (B) Example for base sequence u = [TTTTT. The forwardbackward algorithm [ solves the Bayesian inference problem of computing all conditional probabilities P(u i =,,,T y ) of bases from measurements, which is the basis for performing base calls and calculating base quality values for each base call. The forwardbackward algorithm represents any possible sequence of bases u = [u,u,u,,u K with a path through a graph that starts with node [u,u,u and passes through nodes [u,u,u, [u,u,u 4, and so on, to node [u K,u K,u K. Figure 6B shows a path corresponding to a sequence from the example in Figure. Every edge connecting a pair of nodes [u i,u i+,u i+ and [u i+,u i+,u i+ carries information about four bases [u i,u i+,u i+,u i+, which is enough to uniquely associate it with the expected color of the probes interrogating bases [u i,u i+,u i+,u i+,u i+4 from either probe set (x,i+ ) or probe set (x B,(i+)/5 ) according to Figure. The graphical notation for values associated with nodes and edges is shown in Figure 6. The set of paths corresponding to all 4 K possible Kbase sequences can be combined into a single compact graph called a trellis (Figure 7). The trellis guarantees onetoone correspondence between any path from the left most nodes to the right most nodes and all possible base sequences, which makes it a blueprint for dynamic programming computations.
6 . T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T [u u u [u u u [u u u 4 [u u 4 u 5 T T T T T T T T T T T T T T T T T T T T T [u 4 u 5 u 6 T T T T T T T T T T T T T T T T T T T T T [u K u K u K T T T T T T [u K u K u K+ [u K u K+ u K+ B. T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T Figure 7. eneral structure of the trellis. [ The trellis is divided into K stages, each consisting of 56 edges connecting x two x groups x of 64 nodes. Each group of 64 nodes corresponds to all possible base triplets. t the beginning and end of each section there are 64 nodes, corresponding to all possible base triplets. Each edge corresponds to some quadruplet of bases [u i, u i+, u i+, u i+, connecting node [u i, u i+, u i+ to node [u i, u i+, u i+, u i+. [B n example subset of nodes and edges. n edge that corresponds to a quadruplet of bases [u i, u i+, u i+, u i+, has an expected color x,i+ in probe set and an expected color x B,(i+)/5 in probe set determined from Figure. Note that measurements for probe set are only available in every fifth trellis section. The algorithm determines base calls and quality values by performing the following steps: Step. For each edge in the trellis, establish edge metric γ(u i,u i+,u i+,u i+ ). Page 6, equation in Step : For each edge in the graph associated with bases u i,u i+,u i+,u i+ and colors x,i+, x B,(i+)/5, determine the edge weight: g gg Step. alculate forward node metric α(u i,u i+,u i+ ) for every node in the graph:. Initialize α(u,u,u ) to!" for nodes #$ where %!" u /& agrees #$ with /& last % base of the primer and otherwise. B. Iteratively compute all node metrics α(u i+,u i+,u i+ ) from node metrics α(u i,u i+,u i+ ) according to the formula: In the above formula, P(y,i+ x,i+ =,,, ) and P(y B,(i+)/5 x B,(i+)/5 =,,, ) are color likelihoods derived from color measurements y,i+ and y B,(i+)/5. P(u i+ ) is always assumed to be.5. Note that for any base sequence, the product of all edge weights along the corresponding path results in P(y x ) P(y B x B ) P(u) = P(y,u), is proportional to the conditional sequence probability P(u y ). The goal of the forwardbackward algorithm is the efficient marginalization of P(u y ) to obtain P(u i y ) for individual base positions. Page 7, equation in Step 5: ' ' ( Notice that summands in the above formula correspond to four edges arriving at the node [u i+,u i+,u i+ from the left.
7 Step. Each value is associated with one node in the graph. alculate backward node metric β(u i,u i+,u i+ ) for every node in Step 5. the graph: Page 7, equation alculate the in Step posterior 5: base probabilities P(u i =,,,T y ) from. Initialize β(u K,u K+,u K+ ) to for all nodes. partially marginalized probabilities from step 4. B. Iteratively compute all node metrics β(u i,u i+,u i+ ) from node metrics β(u i+,u i+,u i+ ) according to the formula: ) ) ( ) Notice that summands in the ) above formula correspond to four edges arriving at the node [u i,u i+,u i+ from the right. ( ll the steps of the decoding process have low complexity and are well suited for highperformance implementation. Step 4. alculate partially marginalized ' probabilities ) P(y,u i,u i+,u i+ ) for all base triplets as: ' ) ppendix : Probe set design + + The design of the labeling for the two probe sets is inspired by a convolutional code, a type of errorcorrecting code used in digital communication systems [. onvolutional codes have two key properties. First, they have a sliding window property, where the encoded symbols are derived from a short subset of consecutive information symbols a property that is naturally satisfied by SOLiD System chemistry. Second, convolutional codes are linear in a finite field; therefore, encoded symbols, when treated as elements from a finite field, can be computed as weighted sums of input symbols. This second property can be directly applied to probe set design. Each probe consists of five nucleotides v = [v,v,v,v 4,v 5 that specifically hybridize to complementary DN sequence, three inosines that hybridize to any sequence, and a fluorescent dye c. With four possible nucleotides (,,, and T),,4 possible probe sequences exist, each having one of four unique dyes assigned to it. Linearity of the probe set means that each of the,4 probes is assigned a dye according to the formula ) Math in finite field F(4) B + B B B) F(4) assignment to bases Template Base T Probe Base T F(4) assignment ) F(4) assignment Dyes Dye Label olor Notation F(4) assignment FM y TXR y5 c = v g + v g + v g + v 4 g 4 + v 5 g 5, where g = [g,g,g,g 4,g 5 is a vector of weights that defines the probe sets. Bases v i, dye c, and weights g i are considered to be elements of a finite (alois) field of size 4, denoted F(4) [. The correspondence between nucleotides v i, dyes c and elements of F(4) are presented in Figure 8. Figures 8B and 8 further detail the mechanics of performing multiplication and addition of elements of F(4). Probe sets presented in Figure for Exact all hemistry have been generated by formula () by assigning weights g = [,,,, to Probe Set and weights g = [,,,, to Probe Set. Figure 8. Finite field F(4). [ addition and multiplication in F(4); [B association between elements of F(4) and nucleotides; [ association between elements of F(4) and dyes. References. Lin, ostello, Error ontrol oding (nd ed.), Prentice Hall, 4, ISBN Lang, lgebra (rd ed.), Springer,, ISBN X.
8 Life Technologies offers a breadth of products DN RN PROTEIN ELL ULTURE INSTRUMENTS For Research Use Only. Not intended for any animal or human therapeutic or diagnostic use. Life Technologies orporation. ll rights reserved. The trademarks mentioned herein are the property of Life Technologies orporation or their respective owners. Printed in the US. O85 Headquarters 579 Van llen Way arlsbad, 98 US Phone Toll Free in the US
Analysis of DNA methylation: bisulfite libraries and SOLiD sequencing
Analysis of DNA methylation: bisulfite libraries and SOLiD sequencing An easy view of the bisulfite approach CH3 genome TAGTACGTTGAT TAGTACGTTGAT read TAGTACGTTGAT TAGTATGTTGAT Three main problems 1.
More informationRealtime PCR: Understanding C t
APPLICATION NOTE RealTime PCR Realtime PCR: Understanding C t Realtime PCR, also called quantitative PCR or qpcr, can provide a simple and elegant method for determining the amount of a target sequence
More informationThe Basics of Graphical Models
The Basics of Graphical Models David M. Blei Columbia University October 3, 2015 Introduction These notes follow Chapter 2 of An Introduction to Probabilistic Graphical Models by Michael Jordan. Many figures
More information2.500 Threshold. 2.000 1000e  001. Threshold. Exponential phase. Cycle Number
application note RealTime PCR: Understanding C T RealTime PCR: Understanding C T 4.500 3.500 1000e + 001 4.000 3.000 1000e + 000 3.500 2.500 Threshold 3.000 2.000 1000e  001 Rn 2500 Rn 1500 Rn 2000
More informationDNA Sequencing. Ben Langmead. Department of Computer Science
DN Sequencing Ben Langmead Department of omputer Science You are free to use these slides. If you do, please sign the guestbook (www.langmeadlab.org/teachingmaterials), or email me (ben.langmead@gmail.com)
More informationCoding and decoding with convolutional codes. The Viterbi Algor
Coding and decoding with convolutional codes. The Viterbi Algorithm. 8 Block codes: main ideas Principles st point of view: infinite length block code nd point of view: convolutions Some examples Repetition
More informationSocial Media Mining. Data Mining Essentials
Introduction Data production rate has been increased dramatically (Big Data) and we are able store much more data than before E.g., purchase data, social media data, mobile phone data Businesses and customers
More informationSouth Carolina College and CareerReady (SCCCR) Algebra 1
South Carolina College and CareerReady (SCCCR) Algebra 1 South Carolina College and CareerReady Mathematical Process Standards The South Carolina College and CareerReady (SCCCR) Mathematical Process
More informationNew generation sequencing: current limits and future perspectives. Giorgio Valle CRIBI  Università di Padova
New generation sequencing: current limits and future perspectives Giorgio Valle CRIBI Università di Padova Around 2004 the Race for the 1000$ Genome started A few questions... When? How? Why? Standard
More informationGreater Nanticoke Area School District Math Standards: Grade 6
Greater Nanticoke Area School District Math Standards: Grade 6 Standard 2.1 Numbers, Number Systems and Number Relationships CS2.1.8A. Represent and use numbers in equivalent forms 43. Recognize place
More informationCORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREERREADY FOUNDATIONS IN ALGEBRA
We Can Early Learning Curriculum PreK Grades 8 12 INSIDE ALGEBRA, GRADES 8 12 CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREERREADY FOUNDATIONS IN ALGEBRA April 2016 www.voyagersopris.com Mathematical
More informationMATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab
MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab MATH 0110 is established to accommodate students desiring noncourse based remediation in developmental mathematics. This structure will
More informationAN INTRODUCTION TO ERROR CORRECTING CODES Part 1
AN INTRODUCTION TO ERROR CORRECTING CODES Part 1 Jack Keil Wolf ECE 154C Spring 2008 Noisy Communications Noise in a communications channel can cause errors in the transmission of binary digits. Transmit:
More informationMiSeq: Imaging and Base Calling
MiSeq: Imaging and Page Welcome Navigation Presenter Introduction MiSeq Sequencing Workflow Narration Welcome to MiSeq: Imaging and. This course takes 35 minutes to complete. Click Next to continue. Please
More informationIntroduction to transcriptome analysis using High Throughput Sequencing technologies (HTS)
Introduction to transcriptome analysis using High Throughput Sequencing technologies (HTS) A typical RNA Seq experiment Library construction Protocol variations Fragmentation methods RNA: nebulization,
More informationProtein Protein Interaction Networks
Functional Pattern Mining from Genome Scale Protein Protein Interaction Networks YoungRae Cho, Ph.D. Assistant Professor Department of Computer Science Baylor University it My Definition of Bioinformatics
More informationInformation Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay
Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay Lecture  17 ShannonFanoElias Coding and Introduction to Arithmetic Coding
More informationAn Introduction to the Use of Bayesian Network to Analyze Gene Expression Data
n Introduction to the Use of ayesian Network to nalyze Gene Expression Data Cristina Manfredotti Dipartimento di Informatica, Sistemistica e Comunicazione (D.I.S.Co. Università degli Studi Milanoicocca
More informationIllumina Sequencing Technology
Illumina Sequencing Technology Highest data accuracy, simple workflow, and a broad range of applications. Introduction Figure 1: Illumina Flow Cell Illumina sequencing technology leverages clonal array
More informationGlencoe. correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 33, 58 84, 87 16, 49
Glencoe correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 STANDARDS 68 Number and Operations (NO) Standard I. Understand numbers, ways of representing numbers, relationships among numbers,
More informationPA Common Core Standards Standards for Mathematical Practice Grade Level Emphasis*
Habits of Mind of a Productive Thinker Make sense of problems and persevere in solving them. Attend to precision. PA Common Core Standards The Pennsylvania Common Core Standards cannot be viewed and addressed
More informationGo where the biology takes you. Genome Analyzer IIx Genome Analyzer IIe
Go where the biology takes you. Genome Analyzer IIx Genome Analyzer IIe Go where the biology takes you. To published results faster With proven scalability To the forefront of discovery To limitless applications
More informationVocabulary Cards and Word Walls Revised: June 2, 2011
Vocabulary Cards and Word Walls Revised: June 2, 2011 Important Notes for Teachers: The vocabulary cards in this file match the Common Core, the math curriculum adopted by the Utah State Board of Education,
More informationNext Generation Sequencing
Next Generation Sequencing DNA sequence represents a single format onto which a broad range of biological phenomena can be projected for highthroughput data collection Over the past three years, massively
More informationLectures 1 and 8 15. February 7, 2013. Genomics 2012: Repetitorium. Peter N Robinson. VL1: Next Generation Sequencing. VL8 9: Variant Calling
Lectures 1 and 8 15 February 7, 2013 This is a review of the material from lectures 1 and 8 14. Note that the material from lecture 15 is not relevant for the final exam. Today we will go over the material
More informationCurrent Standard: Mathematical Concepts and Applications Shape, Space, and Measurement Primary
Shape, Space, and Measurement Primary A student shall apply concepts of shape, space, and measurement to solve problems involving two and threedimensional shapes by demonstrating an understanding of:
More informationBig Ideas in Mathematics
Big Ideas in Mathematics which are important to all mathematics learning. (Adapted from the NCTM Curriculum Focal Points, 2006) The Mathematics Big Ideas are organized using the PA Mathematics Standards
More informationPrentice Hall Algebra 2 2011 Correlated to: Colorado P12 Academic Standards for High School Mathematics, Adopted 12/2009
Content Area: Mathematics Grade Level Expectations: High School Standard: Number Sense, Properties, and Operations Understand the structure and properties of our number system. At their most basic level
More informationArtificial Intelligence Mar 27, Bayesian Networks 1 P (T D)P (D) + P (T D)P ( D) =
Artificial Intelligence 15381 Mar 27, 2007 Bayesian Networks 1 Recap of last lecture Probability: precise representation of uncertainty Probability theory: optimal updating of knowledge based on new information
More informationIon Torrent Amplicon Sequencing
APPLICATION NOTE Amplicon Sequencing Ion Torrent Amplicon Sequencing Introduction The ability to sequence a genome or a portion of a genome has enabled researchers to begin to understand how the genetic
More informationDELAWARE MATHEMATICS CONTENT STANDARDS GRADES 910. PAGE(S) WHERE TAUGHT (If submission is not a book, cite appropriate location(s))
Prentice Hall University of Chicago School Mathematics Project: Advanced Algebra 2002 Delaware Mathematics Content Standards (Grades 910) STANDARD #1 Students will develop their ability to SOLVE PROBLEMS
More informationLogic, Probability and Learning
Logic, Probability and Learning Luc De Raedt luc.deraedt@cs.kuleuven.be Overview Logic Learning Probabilistic Learning Probabilistic Logic Learning Closely following : Russell and Norvig, AI: a modern
More informationFUZZY CLUSTERING ANALYSIS OF DATA MINING: APPLICATION TO AN ACCIDENT MINING SYSTEM
International Journal of Innovative Computing, Information and Control ICIC International c 0 ISSN 3448 Volume 8, Number 8, August 0 pp. 4 FUZZY CLUSTERING ANALYSIS OF DATA MINING: APPLICATION TO AN ACCIDENT
More informationA Statistical Framework for Operational Infrasound Monitoring
A Statistical Framework for Operational Infrasound Monitoring Stephen J. Arrowsmith Rod W. Whitaker LAUR 1103040 The views expressed here do not necessarily reflect the views of the United States Government,
More informationIn mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data.
MATHEMATICS: THE LEVEL DESCRIPTIONS In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data. Attainment target
More informationTennessee Department of Education
Tennessee Department of Education Task: Pool Patio Problem Algebra I A hotel is remodeling their grounds and plans to improve the area around a 20 foot by 40 foot rectangular pool. The owner wants to use
More informationEfficient Recovery of Secrets
Efficient Recovery of Secrets Marcel Fernandez Miguel Soriano, IEEE Senior Member Department of Telematics Engineering. Universitat Politècnica de Catalunya. C/ Jordi Girona 1 i 3. Campus Nord, Mod C3,
More informationDNA Sequence Analysis
DNA Sequence Analysis Two general kinds of analysis Screen for one of a set of known sequences Determine the sequence even if it is novel Screening for a known sequence usually involves an oligonucleotide
More informationPreAlgebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems
Academic Content Standards Grade Eight Ohio PreAlgebra 2008 STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express large numbers and small
More informationFUNDAMENTALS of INFORMATION THEORY and CODING DESIGN
DISCRETE "ICS AND ITS APPLICATIONS Series Editor KENNETH H. ROSEN FUNDAMENTALS of INFORMATION THEORY and CODING DESIGN Roberto Togneri Christopher J.S. desilva CHAPMAN & HALL/CRC A CRC Press Company Boca
More informationUPDATES OF LOGIC PROGRAMS
Computing and Informatics, Vol. 20, 2001,????, V 2006Nov6 UPDATES OF LOGIC PROGRAMS Ján Šefránek Department of Applied Informatics, Faculty of Mathematics, Physics and Informatics, Comenius University,
More informationPerformance Level Descriptors Grade 6 Mathematics
Performance Level Descriptors Grade 6 Mathematics Multiplying and Dividing with Fractions 6.NS.12 Grade 6 Math : SubClaim A The student solves problems involving the Major Content for grade/course with
More informationTruSeq Custom Amplicon v1.5
Data Sheet: Targeted Resequencing TruSeq Custom Amplicon v1.5 A new and improved amplicon sequencing solution for interrogating custom regions of interest. Highlights Figure 1: TruSeq Custom Amplicon Workflow
More informationWorking with Coordinate Planes
Virtual Math Girl: Module 1 (Student) and 2 (Teacher) Working with Coordinate Planes Activities and Supplemental Materials The purpose of Virtual Math Girl Module 1 (Student) and 2 (Teacher) is to familiarize
More informationVISUAL ALGEBRA FOR COLLEGE STUDENTS. Laurie J. Burton Western Oregon University
VISUAL ALGEBRA FOR COLLEGE STUDENTS Laurie J. Burton Western Oregon University VISUAL ALGEBRA FOR COLLEGE STUDENTS TABLE OF CONTENTS Welcome and Introduction 1 Chapter 1: INTEGERS AND INTEGER OPERATIONS
More informationLecture 11: Graphical Models for Inference
Lecture 11: Graphical Models for Inference So far we have seen two graphical models that are used for inference  the Bayesian network and the Join tree. These two both represent the same joint probability
More informationT08003A. Figure 1: The Results Editor home screen.
Technical Note Dissociation Curve Analysis T08003A General Introduction to Data Analysis The aim of this Technical Note is to explain the principle of dissociation curve analysis and to guide you through
More informationMath 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.
Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used
More informationEXPONENTS. To the applicant: KEY WORDS AND CONVERTING WORDS TO EQUATIONS
To the applicant: The following information will help you review math that is included in the Paraprofessional written examination for the Conejo Valley Unified School District. The Education Code requires
More informationWhole Numbers and Integers (44 topics, no due date)
Course Name: PreAlgebra into Algebra Summer Hwk Course Code: GHMKUKPMR9 ALEKS Course: PreAlgebra Instructor: Ms. Rhame Course Dates: Begin: 05/30/2015 End: 12/31/2015 Course Content: 302 topics Whole
More informationTracking Algorithms. Lecture17: Stochastic Tracking. Joint Probability and Graphical Model. Probabilistic Tracking
Tracking Algorithms (2015S) Lecture17: Stochastic Tracking Bohyung Han CSE, POSTECH bhhan@postech.ac.kr Deterministic methods Given input video and current state, tracking result is always same. Local
More informationBlock Diagram Reduction
Appendix W Block Diagram Reduction W.3 4Mason s Rule and the SignalFlow Graph A compact alternative notation to the block diagram is given by the signal ow graph introduced Signal ow by S. J. Mason
More informationBayesian Statistics: Indian Buffet Process
Bayesian Statistics: Indian Buffet Process Ilker Yildirim Department of Brain and Cognitive Sciences University of Rochester Rochester, NY 14627 August 2012 Reference: Most of the material in this note
More informationPRACTICE BOOK COMPUTER SCIENCE TEST. Graduate Record Examinations. This practice book contains. Become familiar with. Visit GRE Online at www.gre.
This book is provided FREE with test registration by the Graduate Record Examinations Board. Graduate Record Examinations This practice book contains one actual fulllength GRE Computer Science Test testtaking
More informationPrentice Hall: Middle School Math, Course 1 2002 Correlated to: New York Mathematics Learning Standards (Intermediate)
New York Mathematics Learning Standards (Intermediate) Mathematical Reasoning Key Idea: Students use MATHEMATICAL REASONING to analyze mathematical situations, make conjectures, gather evidence, and construct
More informationLAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE
LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE MAT 119 STATISTICS AND ELEMENTARY ALGEBRA 5 Lecture Hours, 2 Lab Hours, 3 Credits Pre
More informationComplete Genomics Sequencing
TECHNOLOGY OVERVIEW Complete Genomics Sequencing Introduction With advances in nanotechnology, highthroughput instruments, and largescale computing, it has become possible to sequence a complete human
More information13.3 Inference Using Full Joint Distribution
191 The probability distribution on a single variable must sum to 1 It is also true that any joint probability distribution on any set of variables must sum to 1 Recall that any proposition a is equivalent
More informationMATHEMATICAL METHODS OF STATISTICS
MATHEMATICAL METHODS OF STATISTICS By HARALD CRAMER TROFESSOK IN THE UNIVERSITY OF STOCKHOLM Princeton PRINCETON UNIVERSITY PRESS 1946 TABLE OF CONTENTS. First Part. MATHEMATICAL INTRODUCTION. CHAPTERS
More informationMATCH Commun. Math. Comput. Chem. 61 (2009) 781788
MATCH Communications in Mathematical and in Computer Chemistry MATCH Commun. Math. Comput. Chem. 61 (2009) 781788 ISSN 03406253 Three distances for rapid similarity analysis of DNA sequences Wei Chen,
More informationBayesian networks  Timeseries models  Apache Spark & Scala
Bayesian networks  Timeseries models  Apache Spark & Scala Dr John Sandiford, CTO Bayes Server Data Science London Meetup  November 2014 1 Contents Introduction Bayesian networks Latent variables Anomaly
More informationIllinois State Standards Alignments Grades Three through Eleven
Illinois State Standards Alignments Grades Three through Eleven Trademark of Renaissance Learning, Inc., and its subsidiaries, registered, common law, or pending registration in the United States and other
More informationBookTOC.txt. 1. Functions, Graphs, and Models. Algebra Toolbox. Sets. The Real Numbers. Inequalities and Intervals on the Real Number Line
College Algebra in Context with Applications for the Managerial, Life, and Social Sciences, 3rd Edition Ronald J. Harshbarger, University of South Carolina  Beaufort Lisa S. Yocco, Georgia Southern University
More informationHidden Markov Models
8.47 Introduction to omputational Molecular Biology Lecture 7: November 4, 2004 Scribe: HanPang hiu Lecturer: Ross Lippert Editor: Russ ox Hidden Markov Models The G island phenomenon The nucleotide frequencies
More information096 Professional Readiness Examination (Mathematics)
096 Professional Readiness Examination (Mathematics) Effective after October 1, 2013 MISGFLD096M02 TABLE OF CONTENTS PART 1: General Information About the MTTC Program and Test Preparation OVERVIEW
More informationKnowing and Using Number Facts
Knowing and Using Number Facts Use knowledge of place value and Use knowledge of place value and addition and subtraction of twodigit multiplication facts to 10 10 to numbers to derive sums and derive
More informationPrentice Hall Mathematics: Course 1 2008 Correlated to: Arizona Academic Standards for Mathematics (Grades 6)
PO 1. Express fractions as ratios, comparing two whole numbers (e.g., ¾ is equivalent to 3:4 and 3 to 4). Strand 1: Number Sense and Operations Every student should understand and use all concepts and
More informationStatistics Graduate Courses
Statistics Graduate Courses STAT 7002Topics in StatisticsBiological/Physical/Mathematics (cr.arr.).organized study of selected topics. Subjects and earnable credit may vary from semester to semester.
More informationFinal Project Report
CPSC545 by Introduction to Data Mining Prof. Martin Schultz & Prof. Mark Gerstein Student Name: Yu Kor Hugo Lam Student ID : 904907866 Due Date : May 7, 2007 Introduction Final Project Report Pseudogenes
More informationImage Segmentation Preview Segmentation subdivides an image to regions or objects Two basic properties of intensity values Discontinuity Edge detection Similarity Thresholding Region growing/splitting/merging
More informationMath Review. for the Quantitative Reasoning Measure of the GRE revised General Test
Math Review for the Quantitative Reasoning Measure of the GRE revised General Test www.ets.org Overview This Math Review will familiarize you with the mathematical skills and concepts that are important
More informationparent ROADMAP MATHEMATICS SUPPORTING YOUR CHILD IN HIGH SCHOOL
parent ROADMAP MATHEMATICS SUPPORTING YOUR CHILD IN HIGH SCHOOL HS America s schools are working to provide higher quality instruction than ever before. The way we taught students in the past simply does
More informationOverview. Essential Questions. Precalculus, Quarter 4, Unit 4.5 Build Arithmetic and Geometric Sequences and Series
Sequences and Series Overview Number of instruction days: 4 6 (1 day = 53 minutes) Content to Be Learned Write arithmetic and geometric sequences both recursively and with an explicit formula, use them
More informationA Correlation of Pearson Texas Geometry Digital, 2015
A Correlation of Pearson Texas Geometry Digital, 2015 To the Texas Essential Knowledge and Skills (TEKS) for Geometry, High School, and the Texas English Language Proficiency Standards (ELPS) Correlations
More informationX On record with the USOE.
Textbook Alignment to the Utah Core Algebra 2 Name of Company and Individual Conducting Alignment: Chris McHugh, McHugh Inc. A Credential Sheet has been completed on the above company/evaluator and is
More informationprinceton univ. F 13 cos 521: Advanced Algorithm Design Lecture 6: Provable Approximation via Linear Programming Lecturer: Sanjeev Arora
princeton univ. F 13 cos 521: Advanced Algorithm Design Lecture 6: Provable Approximation via Linear Programming Lecturer: Sanjeev Arora Scribe: One of the running themes in this course is the notion of
More informationNEW MEXICO Grade 6 MATHEMATICS STANDARDS
PROCESS STANDARDS To help New Mexico students achieve the Content Standards enumerated below, teachers are encouraged to base instruction on the following Process Standards: Problem Solving Build new mathematical
More informationMaximum Weight Basis Decoding of Convolutional Codes
Maximum Weight Basis Decoding of Convolutional Codes Suman Das, Elza Erkip, Joseph R Cavallaro and Behnaam Aazhang Abstract In this paper we describe a new suboptimal decoding technique for linear codes
More informationLogistic Regression. Jia Li. Department of Statistics The Pennsylvania State University. Logistic Regression
Logistic Regression Department of Statistics The Pennsylvania State University Email: jiali@stat.psu.edu Logistic Regression Preserve linear classification boundaries. By the Bayes rule: Ĝ(x) = arg max
More informationRUTHERFORD HIGH SCHOOL Rutherford, New Jersey COURSE OUTLINE STATISTICS AND PROBABILITY
RUTHERFORD HIGH SCHOOL Rutherford, New Jersey COURSE OUTLINE STATISTICS AND PROBABILITY I. INTRODUCTION According to the Common Core Standards (2010), Decisions or predictions are often based on data numbers
More informationHow is genome sequencing done?
How is genome sequencing done? Using 454 Sequencing on the Genome Sequencer FLX System, DNA from a genome is converted into sequence data through four primary steps: Step One DNA sample preparation; Step
More informationIntroduction to nextgeneration sequencing data
Introduction to nextgeneration sequencing data David Simpson Centre for Experimental Medicine Queens University Belfast http://www.qub.ac.uk/researchcentres/cem/ Outline History of DNA sequencing NGS
More informationClovis Community College Core Competencies Assessment 2014 2015 Area II: Mathematics Algebra
Core Assessment 2014 2015 Area II: Mathematics Algebra Class: Math 110 College Algebra Faculty: Erin Akhtar (Learning Outcomes Being Measured) 1. Students will construct and analyze graphs and/or data
More informationAlgorithm & Flowchart & Pseudo code. Staff Incharge: S.Sasirekha
Algorithm & Flowchart & Pseudo code Staff Incharge: S.Sasirekha Computer Programming and Languages Computers work on a set of instructions called computer program, which clearly specify the ways to carry
More informationWhy? A central concept in Computer Science. Algorithms are ubiquitous.
Analysis of Algorithms: A Brief Introduction Why? A central concept in Computer Science. Algorithms are ubiquitous. Using the Internet (sending email, transferring files, use of search engines, online
More information2DI36 Statistics. 2DI36 Part II (Chapter 7 of MR)
2DI36 Statistics 2DI36 Part II (Chapter 7 of MR) What Have we Done so Far? Last time we introduced the concept of a dataset and seen how we can represent it in various ways But, how did this dataset came
More informationCS 188: Artificial Intelligence. Probability recap
CS 188: Artificial Intelligence Bayes Nets Representation and Independence Pieter Abbeel UC Berkeley Many slides over this course adapted from Dan Klein, Stuart Russell, Andrew Moore Conditional probability
More informationAnalysis of Bayesian Dynamic Linear Models
Analysis of Bayesian Dynamic Linear Models Emily M. Casleton December 17, 2010 1 Introduction The main purpose of this project is to explore the Bayesian analysis of Dynamic Linear Models (DLMs). The main
More informationMicrosoft Mathematics for Educators:
Microsoft Mathematics for Educators: Familiarize yourself with the interface When you first open Microsoft Mathematics, you ll see the following elements displayed: 1. The Calculator Pad which includes
More informationCOGNITIVE TUTOR ALGEBRA
COGNITIVE TUTOR ALGEBRA Numbers and Operations Standard: Understands and applies concepts of numbers and operations Power 1: Understands numbers, ways of representing numbers, relationships among numbers,
More informationTechnical Note. Roche Applied Science. No. LC 19/2004. Color Compensation
Roche Applied Science Technical Note No. LC 19/2004 Purpose of this Note Color The LightCycler System is able to simultaneously detect and analyze more than one color in each capillary. Due to overlap
More informationA Little Set Theory (Never Hurt Anybody)
A Little Set Theory (Never Hurt Anybody) Matthew Saltzman Department of Mathematical Sciences Clemson University Draft: August 21, 2013 1 Introduction The fundamental ideas of set theory and the algebra
More informationResearch on the UHF RFID Channel Coding Technology based on Simulink
Vol. 6, No. 7, 015 Research on the UHF RFID Channel Coding Technology based on Simulink Changzhi Wang Shanghai 0160, China Zhicai Shi* Shanghai 0160, China Dai Jian Shanghai 0160, China Li Meng Shanghai
More informationPowerTeaching i3: Algebra I Mathematics
PowerTeaching i3: Algebra I Mathematics Alignment to the Common Core State Standards for Mathematics Standards for Mathematical Practice and Standards for Mathematical Content for Algebra I Key Ideas and
More informationAlgebra 1 2008. Academic Content Standards Grade Eight and Grade Nine Ohio. Grade Eight. Number, Number Sense and Operations Standard
Academic Content Standards Grade Eight and Grade Nine Ohio Algebra 1 2008 Grade Eight STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express
More informationNetwork (Tree) Topology Inference Based on Prüfer Sequence
Network (Tree) Topology Inference Based on Prüfer Sequence C. Vanniarajan and Kamala Krithivasan Department of Computer Science and Engineering Indian Institute of Technology Madras Chennai 600036 vanniarajanc@hcl.in,
More informationCrosswalk Directions:
Crosswalk Directions: UMS Standards for College Readiness to 2007 MLR 1. Use a (yes), an (no), or a (partially) to indicate the extent to which the standard, performance indicator, or descriptor of the
More informationModelbased Synthesis. Tony O Hagan
Modelbased Synthesis Tony O Hagan Stochastic models Synthesising evidence through a statistical model 2 Evidence Synthesis (Session 3), Helsinki, 28/10/11 Graphical modelling The kinds of models that
More informationOPRE 6201 : 2. Simplex Method
OPRE 6201 : 2. Simplex Method 1 The Graphical Method: An Example Consider the following linear program: Max 4x 1 +3x 2 Subject to: 2x 1 +3x 2 6 (1) 3x 1 +2x 2 3 (2) 2x 2 5 (3) 2x 1 +x 2 4 (4) x 1, x 2
More informationPennsylvania System of School Assessment
Pennsylvania System of School Assessment The Assessment Anchors, as defined by the Eligible Content, are organized into cohesive blueprints, each structured with a common labeling system that can be read
More information