The Entropy of Recursive Markov Processes BENNY BRODDA
|
|
- Amber Hodge
- 6 years ago
- Views:
Transcription
1 Research Group for Quatitative Liguistic s KVAL PM 339 Jue Fack Stockholm 40 SWEDEN The Etropy of Recursive Markov Processes By BENNY BRODDA The work reported i this paper has bee sposored by Humaistiska forskigsr~det, Tekiska forskigsr~det ad Riksbakes Jubileumsfod, Stockholm, Swede. '.
2 THE~ENTROPY OF RECURSIVE MARKOV PROCESSES By BENNY BRODDA KVAL, Fack, Stockholm 40, Swede Summary The aim of this commuicatio is to obtai a explicit formula for calculatig the etropy of a source which behaves i accordace with the rules of a arbitrary Phrase Structure Grammar, i which relative probabilities are attached to the rules i the grammar. With this aim i mid we itroduce a alte~rative defiitio of the cocept of a PSG as a set of self-embedded (re- Cursive) Fiite State Grammars; whe the probabilities are take ito accout i such a grammar we call it a Recursive Markov Process. 1. I the first sectio we give a more detailed defiitio of what kid of Markov Processes we are goig to geeralize later o (i sec. 3), ad we also outlie the cocept of etropy i a ordiary Markov source. More details "of iformatio may be foupd~ e.g., i Khichis "Mathematical Foudatios of Iformatio Theory", N.Y. ~ 1957~ or "Iformatio Theory" by R. Ash, N. Y., A Markov Grammar tie s : is defied as a Markov Source with the followig proper- Assume that there are + 1 states, say S O, S1,..., S, i the source. S O is defied as the iitial state ad S is defied as the fial state ad the other states are called itermediate states. We shall, of course, also have a trasi- tio matrix, M = (Pij), cotaiig the, trasitio probabilities of the source. a) A trasitio from state S i to state S k is always accompaied by a produc- tio of a (o-zero) letter aik from a give fiite alphabet. Trasitio to differet states from oe give state alway s produce differet letters. b) From the" iitial state, S0~ direct or idirect trasitios should be possible to ay other state i the source. From o state is a trasitio to S O allowed. c) From ay state, direct or idirect trasitios to the fial state S should be possible. From S o trasitio is allowed to ay other state (S is a "absorbig state"). The work reported i this paper has bee sposored by Humaistiska forskigsr~det, Tekiska forskigsr~det ad Riksbakes Jubileumsfod, Stockholm, Swederi.
3 A (grammatical) sete'ce should ow be defied as the (left-to-right) cocateatio of the letters produced by the source, whe passig from the iitial state to the fial state. The legth of a setece is defied as the umber of letters i the setece. To simplify matters without droppig much of geerality we also require that d) The greatest commo divisor for all the possible legths of seteces is = l (i.e., the source becomes a aperiodic source, if it is short-circuited by idetifyig the fial ad iitial states). ~- With the properties a - d above, the source obtaied by idetifyig the fial ad iitial states is a idecomposable, ergodic Markov process (cf. Feller, "Probability Theory ad Its Applicatios", ch. 15, N. Y. s 1950). I the trasitio matrix M for a Markov grammar of our type all elemets i the first colum are zero, ad i the last row all elemets are zero except the last oe which is = 1. For a give Markov grammar we defie the ucertaity or etropy, Hi, for each state S i, i = 0, 1...,, as: Hi=~l Pij l g Pij; i= 1, Z.... j=o We also defie the etropy, H or H(M), for the grammar as = 1 (1). = x.h. 1 1 i= 0 where x = (x0, x z,..., X_l) is defied as the statioary distributio-~ the source obtaied whe S O ad S are idetified; thus x is defied as the (uique) solutio to the set of simultaeous equatios (z) xm 1 = x x0 + X l + ''" + X-1 = 1 where M 1 is formed by shiftig the last ad first colums ad the omittig the last row ad colum. The mea setece legth. ~, of the set of grammatical seteces ca ow be easily calculated as
4 (3) = 1/x 0 2. Embedded Grammars (cf. Feller, op. tit.) We ow assume that we have two Markov grammars, M ad M1, with states S O, S 1..., S, ad T o, T I,..., T m, respectively, where S O ads, T O ad T m are the correspodig iitial ad fial states. Now cosider two states S i ad S k i the grammar M; assume that the correspodig trasitio probability is = Pik" We ow trasform the grammar, M1, ito a ew oe, M], by embeddig the grammar M 2 i M 1 betwee the states S i ad Sk, a operatio which is performed by idetifyig the states T O ad T with the m states S i ad S k respectively. Or, to be more precise, assume that i the grammar M 1 the trasitios to the states Tj, j~l, has the probabilities q0j" The, i the grammar M', trasitios to a state T. from the state S. will 3 1 take place with the probability =.Pikq0 j. A retur to the state S k i the "mai" grammar from a itermediate state Tj i M 1 takes place with the probability qjm" With the coditios above fulfilled, we propose that the etropy for the. com- posed grammar be calculated accordig to the formula: (4) H(M') = H(M) + xipik " ~I " H(M ) 1 + xipik (~1-1) where H(M) is the etropy of the grammar M whe there is a ordiary co- ectio (with probability Pik) betwee the states S i ad Sk, ad where x. is 1 the iheret probability of beig i the state S. uder the same coditios. 1 ~1 is the mea setece legth of the seteces produced by the grammar M 1 aloe. (It is quite atural that this umber appears as a weight i the formula, sice if oe is producig a setece accordig to the grammar M ad arrives at the state S i ad from there "dives" ito the grammar M1, the ~1 is the expected waitig time for emergig agai i the mai grammar M.) The factor xipik may be iterpreted as the combied probability of ever arrivig at.s i ad there choosig the path over to M 1 (you may, of course, choose quite aother path from Si).
5
6 also say that Aik grammar/.) stads as a abbreviatio for a arbitrary setece of that We associate each grammar M! with the grammar M., j = 0, 12..., N, by 3 3 just cosiderig it as a o-recursive oe, thaf is, we cosider all the sym- bols Aik as termial symbols (eve if they are:'ot). The grammars thus ob- taied are ordiarily Markov grammars accordig to our defiitio, ad the etropies Hj = H(Mj) are easily computed accordig to formula (1), as are the statioary distributios /formula (2)/. The follwoig theorem shows how the etropies H! for the fully recursive grammars M! are coected with the J 3 umbers H.. J Theorem The etropy H! for a set of recursive Markov grammar Mj, j = 0, 1, J ca be calculated accordig to the formula..., N, (6) k j=0, 1...,N. k Here the factors Yjk are depedet oly of the probability matrix of the grammar ad the umbers ~k defied as the mea setece legth of the seteces of the grammar M~, k = 0, 1,... N, ad computable accordig to lemma below. H~ is the etropy for the grammar. The theorem above is a direct applicatio for the grammar of formula (4), sec. 2. The coefficiets Yjk i formula (6) ca, more precisely, be calculated as a sum of terms of the type xipim with the idices (i, m) are where the gram- mar M~ appears i the grammar M3~!" x i ad Pim are the compoets the sta- tioary distributio ad probability matrix for the grammar M.o, J
7 Assume ow that we have a Markov grammar of our type, but for which each trasitio will take a certai amout of time. A very atural questio is the: "What is the expected time to produce a setece i that laguage?" The aswer is i the followig lemma. Lemma Let M be a_mmarkov grammar with states Si, i= O, S are the iitial ad fial states respectively, 1...,, where S O ad Assume that each trasitio S i -. S k will take Ylk time uits. Deote the expected time for arrival at S give that the grammar is i state S i by ti, i = 0, I,...~ ~ (thus t o is the expected time for producig ase- tece). The times t I will the fulfill the followig set of simultaeously liear equatios : (7) ti = ~ Pik (tik + tk) k Formula (7) is itself a proof of the lemra. With more coveiet otatios we ca write (7) as (E - P) t = Pt where E is the uit matrix, P is the probability matrix (with P = 0) ad Pt is the vector with compoets Pi (t) =~ Pim tim' i = 0, 1...,. m The applicatio of ~he lemma for computig the umbers ~k i formula (6) is ow the followig. The trasitio times of the lemma are, of course, the expected time (or "legths" as we have called it earlier) for passig via a sub-grammar of the grammar uder cosideratio. Thus the umber tik i-~]itself the ukow etitle s ~k" 6
8 For each of the sub-grammars M~, j : 0, I,..., N, we geta set of liear J equatios of type (7) for determiig the vectors t of 1emma. The first com- poet of this vector, i.e.j the umber t O, is the equal to the expected legth, ~, of the seteces of that g~ammar. (Ufortuately, we have to compute extra the expected time for goig from ay state of the sub-gram- mars to the correspodig fial state.) The total umber of ukows ivolved whe computig the etropy of our grammar (i. e., the etropy H~) is equal to (the total umber of states i all our sub-grammars) plus (the umber of sub-grammars). This is also the umber of equatior~,_for we have + 1 e~uatios from formula (6) ad the ( + 1) sets of equatios of the type (7). We assert that all these simultaeous equatios a~e solvable, if the grammar fulfills the coditios we earlier stated for the grammar, i.e., that from 'each state i ay subgrammar exists at least oe path to the fial state of that grammar.
Natural language processing implementation on Romanian ChatBot
Proceedigs of the 9th WSEAS Iteratioal Coferece o SIMULATION, MODELLING AND OPTIMIZATION Natural laguage processig implemetatio o Romaia ChatBot RALF FABIAN, MARCU ALEXANDRU-NICOLAE Departmet for Iformatics
More informationE-LEARNING USABILITY: A LEARNER-ADAPTED APPROACH BASED ON THE EVALUATION OF LEANER S PREFERENCES. Valentina Terzieva, Yuri Pavlov, Rumen Andreev
Titre du documet / Documet title E-learig usability : A learer-adapted approach based o the evaluatio of leaer's prefereces Auteur(s) / Author(s) TERZIEVA Valetia ; PAVLOV Yuri (1) ; ANDREEV Rume (2) ;
More informationFuzzy Reference Gain-Scheduling Approach as Intelligent Agents: FRGS Agent
Fuzzy Referece Gai-Schedulig Approach as Itelliget Agets: FRGS Aget J. E. ARAUJO * eresto@lit.ipe.br K. H. KIENITZ # kieitz@ita.br S. A. SANDRI sadra@lac.ipe.br J. D. S. da SILVA demisio@lac.ipe.br * Itegratio
More informationarxiv: v1 [cs.dl] 22 Dec 2016
ScieceWISE: Topic Modelig over Scietific Literature Networks arxiv:1612.07636v1 [cs.dl] 22 Dec 2016 A. Magalich, V. Gemmetto, D. Garlaschelli, A. Boyarsky Uiversity of Leide, The Netherlads {magalich,
More information'Norwegian University of Science and Technology, Department of Computer and Information Science
The helpful Patiet Record System: Problem Orieted Ad Kowledge Based Elisabeth Bayega, MS' ad Samso Tu, MS2 'Norwegia Uiversity of Sciece ad Techology, Departmet of Computer ad Iformatio Sciece ad Departmet
More informationConsortium: North Carolina Community Colleges
Associatio of Research Libraries / Texas A&M Uiversity www.libqual.org Cotributors Collee Cook Texas A&M Uiversity Fred Heath Uiversity of Texas BruceThompso Texas A&M Uiversity Martha Kyrillidou Associatio
More informationCONSTITUENT VOICE TECHNICAL NOTE 1 INTRODUCING Version 1.1, September 2014
preview begis oct 2014 lauches ja 2015 INTRODUCING WWW.FEEDBACKCOMMONS.ORG A serviced cloud platform to share ad compare feedback data ad collaboratively develop feedback ad learig practice CONSTITUENT
More informationApplication for Admission
Applicatio for Admissio Admissio Office PO Box 2900 Illiois Wesleya Uiversity Bloomig, Illiois 61702-2900 Apply o-lie at: www.iwu.edu Applicatio Iformatio I am applyig: Early Actio Regular Decisio Early
More informationManagement Science Letters
Maagemet Sciece Letters 4 (24) 2 26 Cotets lists available at GrowigSciece Maagemet Sciece Letters homepage: www.growigsciece.com/msl A applicatio of data evelopmet aalysis for measurig the relative efficiecy
More informationpart2 Participatory Processes
part part2 Participatory Processes Participatory Learig Approaches Whose Learig? Participatory learig is based o the priciple of ope expressio where all sectios of the commuity ad exteral stakeholders
More informationHANDBOOK. Career Center Handbook. Tools & Tips for Career Search Success CALIFORNIA STATE UNIVERSITY, SACR AMENTO
HANDBOOK Career Ceter Hadbook CALIFORNIA STATE UNIVERSITY, SACR AMENTO Tools & Tips for Career Search Success Academic Advisig ad Career Ceter 6000 J Street Lasse Hall 1013 Sacrameto, CA 95819-6064 916-278-6231
More informationStatewide Framework Document for:
Statewide Framework Document for: 270301 Standards may be added to this document prior to submission, but may not be removed from the framework to meet state credit equivalency requirements. Performance
More informationLecture 10: Reinforcement Learning
Lecture 1: Reinforcement Learning Cognitive Systems II - Machine Learning SS 25 Part III: Learning Programs and Strategies Q Learning, Dynamic Programming Lecture 1: Reinforcement Learning p. Motivation
More informationA Minimalist Approach to Code-Switching. In the field of linguistics, the topic of bilingualism is a broad one. There are many
Schmidt 1 Eric Schmidt Prof. Suzanne Flynn Linguistic Study of Bilingualism December 13, 2013 A Minimalist Approach to Code-Switching In the field of linguistics, the topic of bilingualism is a broad one.
More informationChinese Language Parsing with Maximum-Entropy-Inspired Parser
Chinese Language Parsing with Maximum-Entropy-Inspired Parser Heng Lian Brown University Abstract The Chinese language has many special characteristics that make parsing difficult. The performance of state-of-the-art
More informationGrade 5 + DIGITAL. EL Strategies. DOK 1-4 RTI Tiers 1-3. Flexible Supplemental K-8 ELA & Math Online & Print
Standards PLUS Flexible Supplemental K-8 ELA & Math Online & Print Grade 5 SAMPLER Mathematics EL Strategies DOK 1-4 RTI Tiers 1-3 15-20 Minute Lessons Assessments Consistent with CA Testing Technology
More informationSyntax Parsing 1. Grammars and parsing 2. Top-down and bottom-up parsing 3. Chart parsers 4. Bottom-up chart parsing 5. The Earley Algorithm
Syntax Parsing 1. Grammars and parsing 2. Top-down and bottom-up parsing 3. Chart parsers 4. Bottom-up chart parsing 5. The Earley Algorithm syntax: from the Greek syntaxis, meaning setting out together
More informationSchool of Innovative Technologies and Engineering
School of Innovative Technologies and Engineering Department of Applied Mathematical Sciences Proficiency Course in MATLAB COURSE DOCUMENT VERSION 1.0 PCMv1.0 July 2012 University of Technology, Mauritius
More informationThe presence of interpretable but ungrammatical sentences corresponds to mismatches between interpretive and productive parsing.
Lecture 4: OT Syntax Sources: Kager 1999, Section 8; Legendre et al. 1998; Grimshaw 1997; Barbosa et al. 1998, Introduction; Bresnan 1998; Fanselow et al. 1999; Gibson & Broihier 1998. OT is not a theory
More informationCS 598 Natural Language Processing
CS 598 Natural Language Processing Natural language is everywhere Natural language is everywhere Natural language is everywhere Natural language is everywhere!"#$%&'&()*+,-./012 34*5665756638/9:;< =>?@ABCDEFGHIJ5KL@
More informationUniversity of Groningen. Systemen, planning, netwerken Bosman, Aart
University of Groningen Systemen, planning, netwerken Bosman, Aart IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document
More informationRemainder Rules. 3. Ask students: How many carnations can you order and what size bunches do you make to take five carnations home?
Math Concepts whole numbers multiplication division subtraction addition Materials TI-10, TI-15 Explorer recording sheets cubes, sticks, etc. pencils Overview Students will use calculators, whole-number
More informationStochastic Calculus for Finance I (46-944) Spring 2008 Syllabus
Stochastic Calculus for Finance I (46-944) Spring 2008 Syllabus Introduction. This is a first course in stochastic calculus for finance. It assumes students are familiar with the material in Introduction
More informationExemplar 6 th Grade Math Unit: Prime Factorization, Greatest Common Factor, and Least Common Multiple
Exemplar 6 th Grade Math Unit: Prime Factorization, Greatest Common Factor, and Least Common Multiple Unit Plan Components Big Goal Standards Big Ideas Unpacked Standards Scaffolded Learning Resources
More informationGCSE Mathematics B (Linear) Mark Scheme for November Component J567/04: Mathematics Paper 4 (Higher) General Certificate of Secondary Education
GCSE Mathematics B (Linear) Component J567/04: Mathematics Paper 4 (Higher) General Certificate of Secondary Education Mark Scheme for November 2014 Oxford Cambridge and RSA Examinations OCR (Oxford Cambridge
More information2014 Gold Award Winner SpecialParent
Award Wier SpecialParet Dedicated to all families of childre with special eeds 6 th Editio/Fall/Witer 2014 Desig ad Editorial Awards Competitio MISSION Our goal is to provide parets of childre with special
More informationLet s think about how to multiply and divide fractions by fractions!
Let s think about how to multiply and divide fractions by fractions! June 25, 2007 (Monday) Takehaya Attached Elementary School, Tokyo Gakugei University Grade 6, Class # 1 (21 boys, 20 girls) Instructor:
More informationInformatics 2A: Language Complexity and the. Inf2A: Chomsky Hierarchy
Informatics 2A: Language Complexity and the Chomsky Hierarchy September 28, 2010 Starter 1 Is there a finite state machine that recognises all those strings s from the alphabet {a, b} where the difference
More informationAlgebra 1 Summer Packet
Algebra 1 Summer Packet Name: Solve each problem and place the answer on the line to the left of the problem. Adding Integers A. Steps if both numbers are positive. Example: 3 + 4 Step 1: Add the two numbers.
More informationarxiv: v1 [math.at] 10 Jan 2016
THE ALGEBRAIC ATIYAH-HIRZEBRUCH SPECTRAL SEQUENCE OF REAL PROJECTIVE SPECTRA arxiv:1601.02185v1 [math.at] 10 Jan 2016 GUOZHEN WANG AND ZHOULI XU Abstract. In this note, we use Curtis s algorithm and the
More informationalso inside Continuing Education Alumni Authors College Events
SUMMER 2016 JAMESTOWN COMMUNITY COLLEGE ALUMNI MAGAZINE create a etrepreeur creatig a busiess a artist creatig beauty a citize creatig the future also iside Cotiuig Educatio Alumi Authors College Evets
More information(I couldn t find a Smartie Book) NEW Grade 5/6 Mathematics: (Number, Statistics and Probability) Title Smartie Mathematics
(I couldn t find a Smartie Book) NEW Grade 5/6 Mathematics: (Number, Statistics and Probability) Title Smartie Mathematics Lesson/ Unit Description Questions: How many Smarties are in a box? Is it the
More informationGiven a directed graph G =(N A), where N is a set of m nodes and A. destination node, implying a direction for ow to follow. Arcs have limitations
4 Interior point algorithms for network ow problems Mauricio G.C. Resende AT&T Bell Laboratories, Murray Hill, NJ 07974-2070 USA Panos M. Pardalos The University of Florida, Gainesville, FL 32611-6595
More informationTheory of Probability
Theory of Probability Class code MATH-UA 9233-001 Instructor Details Prof. David Larman Room 806,25 Gordon Street (UCL Mathematics Department). Class Details Fall 2013 Thursdays 1:30-4-30 Location to be
More informationGrade 6: Correlated to AGS Basic Math Skills
Grade 6: Correlated to AGS Basic Math Skills Grade 6: Standard 1 Number Sense Students compare and order positive and negative integers, decimals, fractions, and mixed numbers. They find multiples and
More informationUsing the Attribute Hierarchy Method to Make Diagnostic Inferences about Examinees Cognitive Skills in Algebra on the SAT
The Journal of Technology, Learning, and Assessment Volume 6, Number 6 February 2008 Using the Attribute Hierarchy Method to Make Diagnostic Inferences about Examinees Cognitive Skills in Algebra on the
More informationBackwards Numbers: A Study of Place Value. Catherine Perez
Backwards Numbers: A Study of Place Value Catherine Perez Introduction I was reaching for my daily math sheet that my school has elected to use and in big bold letters in a box it said: TO ADD NUMBERS
More informationOPTIMIZATINON OF TRAINING SETS FOR HEBBIAN-LEARNING- BASED CLASSIFIERS
OPTIMIZATINON OF TRAINING SETS FOR HEBBIAN-LEARNING- BASED CLASSIFIERS Václav Kocian, Eva Volná, Michal Janošek, Martin Kotyrba University of Ostrava Department of Informatics and Computers Dvořákova 7,
More informationRadius STEM Readiness TM
Curriculum Guide Radius STEM Readiness TM While today s teens are surrounded by technology, we face a stark and imminent shortage of graduates pursuing careers in Science, Technology, Engineering, and
More informationNatural Language Processing. George Konidaris
Natural Language Processing George Konidaris gdk@cs.brown.edu Fall 2017 Natural Language Processing Understanding spoken/written sentences in a natural language. Major area of research in AI. Why? Humans
More informationLanguage Independent Passage Retrieval for Question Answering
Language Independent Passage Retrieval for Question Answering José Manuel Gómez-Soriano 1, Manuel Montes-y-Gómez 2, Emilio Sanchis-Arnal 1, Luis Villaseñor-Pineda 2, Paolo Rosso 1 1 Polytechnic University
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Ch 2 Test Remediation Work Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) High temperatures in a certain
More informationProbability and Game Theory Course Syllabus
Probability and Game Theory Course Syllabus DATE ACTIVITY CONCEPT Sunday Learn names; introduction to course, introduce the Battle of the Bismarck Sea as a 2-person zero-sum game. Monday Day 1 Pre-test
More informationCal s Dinner Card Deals
Cal s Dinner Card Deals Overview: In this lesson students compare three linear functions in the context of Dinner Card Deals. Students are required to interpret a graph for each Dinner Card Deal to help
More informationGuidelines and additional provisions for the PhD Programmes at VID Specialized University
Guidelines and additional provisions for the PhD Programmes at VID Specialized University PART 1. INTRODUCTORY PROVISIONS These guidelines are additional provisions to the Regulation of 11 December 2015
More informationS T A T 251 C o u r s e S y l l a b u s I n t r o d u c t i o n t o p r o b a b i l i t y
Department of Mathematics, Statistics and Science College of Arts and Sciences Qatar University S T A T 251 C o u r s e S y l l a b u s I n t r o d u c t i o n t o p r o b a b i l i t y A m e e n A l a
More informationWorking with Rich Mathematical Tasks
Working with Rich Mathematical Tasks being good at mathematics involves many different ways of working it involves asking questions, drawing pictures and graphs, rephrasing problems, justifying methods,
More informationLearning Disability Functional Capacity Evaluation. Dear Doctor,
Dear Doctor, I have been asked to formulate a vocational opinion regarding NAME s employability in light of his/her learning disability. To assist me with this evaluation I would appreciate if you can
More informationObjective: Add decimals using place value strategies, and relate those strategies to a written method.
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 9 5 1 Lesson 9 Objective: Add decimals using place value strategies, and relate those strategies to a written method. Suggested Lesson Structure Fluency Practice
More informationPTK 90-DAY CRASH COURSE CALENDAR
PTK 90-DAY CRASH COURSE CALENDAR Dear Candidates, The Professional Teaching Knowledge (PTK) 90-Day Crash Course Calendar was originally created in our T&I Scholarship group to accelerate the completion
More informationRANKING AND UNRANKING LEFT SZILARD LANGUAGES. Erkki Mäkinen DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF TAMPERE REPORT A ER E P S I M S
N S ER E P S I M TA S UN A I S I T VER RANKING AND UNRANKING LEFT SZILARD LANGUAGES Erkki Mäkinen DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF TAMPERE REPORT A-1997-2 UNIVERSITY OF TAMPERE DEPARTMENT OF
More informationEmpiricism as Unifying Theme in the Standards for Mathematical Practice. Glenn Stevens Department of Mathematics Boston University
Empiricism as Unifying Theme in the Standards for Mathematical Practice Glenn Stevens Department of Mathematics Boston University Joint Mathematics Meetings Special Session: Creating Coherence in K-12
More informationCh VI- SENTENCE PATTERNS.
Ch VI- SENTENCE PATTERNS faizrisd@gmail.com www.pakfaizal.com It is a common fact that in the making of well-formed sentences we badly need several syntactic devices used to link together words by means
More informationExtending Place Value with Whole Numbers to 1,000,000
Grade 4 Mathematics, Quarter 1, Unit 1.1 Extending Place Value with Whole Numbers to 1,000,000 Overview Number of Instructional Days: 10 (1 day = 45 minutes) Content to Be Learned Recognize that a digit
More informationClassroom Connections Examining the Intersection of the Standards for Mathematical Content and the Standards for Mathematical Practice
Classroom Connections Examining the Intersection of the Standards for Mathematical Content and the Standards for Mathematical Practice Title: Considering Coordinate Geometry Common Core State Standards
More informationThe Evolution of Random Phenomena
The Evolution of Random Phenomena A Look at Markov Chains Glen Wang glenw@uchicago.edu Splash! Chicago: Winter Cascade 2012 Lecture 1: What is Randomness? What is randomness? Can you think of some examples
More informationAGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS
AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS 1 CALIFORNIA CONTENT STANDARDS: Chapter 1 ALGEBRA AND WHOLE NUMBERS Algebra and Functions 1.4 Students use algebraic
More informationSouth Carolina English Language Arts
South Carolina English Language Arts A S O F J U N E 2 0, 2 0 1 0, T H I S S TAT E H A D A D O P T E D T H E CO M M O N CO R E S TAT E S TA N DA R D S. DOCUMENTS REVIEWED South Carolina Academic Content
More informationPre-Algebra A. Syllabus. Course Overview. Course Goals. General Skills. Credit Value
Syllabus Pre-Algebra A Course Overview Pre-Algebra is a course designed to prepare you for future work in algebra. In Pre-Algebra, you will strengthen your knowledge of numbers as you look to transition
More informationProof Theory for Syntacticians
Department of Linguistics Ohio State University Syntax 2 (Linguistics 602.02) January 5, 2012 Logics for Linguistics Many different kinds of logic are directly applicable to formalizing theories in syntax
More informationCognitive Modeling. Tower of Hanoi: Description. Tower of Hanoi: The Task. Lecture 5: Models of Problem Solving. Frank Keller.
Cognitive Modeling Lecture 5: Models of Problem Solving Frank Keller School of Informatics University of Edinburgh keller@inf.ed.ac.uk January 22, 2008 1 2 3 4 Reading: Cooper (2002:Ch. 4). Frank Keller
More informationOn March 15, 2016, Governor Rick Snyder. Continuing Medical Education Becomes Mandatory in Michigan. in this issue... 3 Great Lakes Veterinary
michiga veteriary medical associatio i this issue... 3 Great Lakes Veteriary Coferece 4 What You Need to Kow Whe Issuig a Iterstate Certificate of Ispectio 6 Low Pathogeic Avia Iflueza H5 Virus Detectios
More informationReducing Abstraction When Learning Graph Theory
Jl. of Computers in Mathematics and Science Teaching (2005) 24(3), 255-272 Reducing Abstraction When Learning Graph Theory ORIT HAZZAN Technion-Israel Institute of Technology Israel oritha@techunix.technion.ac.il
More informationExperiments with SMS Translation and Stochastic Gradient Descent in Spanish Text Author Profiling
Experiments with SMS Translation and Stochastic Gradient Descent in Spanish Text Author Profiling Notebook for PAN at CLEF 2013 Andrés Alfonso Caurcel Díaz 1 and José María Gómez Hidalgo 2 1 Universidad
More information1.11 I Know What Do You Know?
50 SECONDARY MATH 1 // MODULE 1 1.11 I Know What Do You Know? A Practice Understanding Task CC BY Jim Larrison https://flic.kr/p/9mp2c9 In each of the problems below I share some of the information that
More informationGCSE. Mathematics A. Mark Scheme for January General Certificate of Secondary Education Unit A503/01: Mathematics C (Foundation Tier)
GCSE Mathematics A General Certificate of Secondary Education Unit A503/0: Mathematics C (Foundation Tier) Mark Scheme for January 203 Oxford Cambridge and RSA Examinations OCR (Oxford Cambridge and RSA)
More informationMath 96: Intermediate Algebra in Context
: Intermediate Algebra in Context Syllabus Spring Quarter 2016 Daily, 9:20 10:30am Instructor: Lauri Lindberg Office Hours@ tutoring: Tutoring Center (CAS-504) 8 9am & 1 2pm daily STEM (Math) Center (RAI-338)
More informationVISION, MISSION, VALUES, AND GOALS
6 VISION, MISSION, VALUES, AND GOALS 2010-2015 VISION STATEMENT Ohloe College will be kow throughout Califoria for our iclusiveess, iovatio, ad superior rates of studet success. MISSION STATEMENT The Missio
More informationChapter 4 - Fractions
. Fractions Chapter - Fractions 0 Michelle Manes, University of Hawaii Department of Mathematics These materials are intended for use with the University of Hawaii Department of Mathematics Math course
More informationCreating a Test in Eduphoria! Aware
in Eduphoria! Aware Login to Eduphoria using CHROME!!! 1. LCS Intranet > Portals > Eduphoria From home: LakeCounty.SchoolObjects.com 2. Login with your full email address. First time login password default
More informationPM tutor. Estimate Activity Durations Part 2. Presented by Dipo Tepede, PMP, SSBB, MBA. Empowering Excellence. Powered by POeT Solvers Limited
PM tutor Empowering Excellence Estimate Activity Durations Part 2 Presented by Dipo Tepede, PMP, SSBB, MBA This presentation is copyright 2009 by POeT Solvers Limited. All rights reserved. This presentation
More informationCo-op Placement Packet
Co-op Placement Packet Career Services, 900 Asp Ave, Suite 323, OMU, Norman, OK, 73019 Phone: (405) 325-1974 Fax: (405) 325-3402 www.hiresooner.com ENROLLING IN THE CO-OP COURSE HOW 1. Obtain permission
More informationLEXICAL COHESION ANALYSIS OF THE ARTICLE WHAT IS A GOOD RESEARCH PROJECT? BY BRIAN PALTRIDGE A JOURNAL ARTICLE
LEXICAL COHESION ANALYSIS OF THE ARTICLE WHAT IS A GOOD RESEARCH PROJECT? BY BRIAN PALTRIDGE A JOURNAL ARTICLE Submitted in partial fulfillment of the requirements for the degree of Sarjana Sastra (S.S.)
More informationProbabilistic Latent Semantic Analysis
Probabilistic Latent Semantic Analysis Thomas Hofmann Presentation by Ioannis Pavlopoulos & Andreas Damianou for the course of Data Mining & Exploration 1 Outline Latent Semantic Analysis o Need o Overview
More informationSOUTHERN MAINE COMMUNITY COLLEGE South Portland, Maine 04106
SOUTHERN MAINE COMMUNITY COLLEGE South Portland, Maine 04106 Title: Precalculus Catalog Number: MATH 190 Credit Hours: 3 Total Contact Hours: 45 Instructor: Gwendolyn Blake Email: gblake@smccme.edu Website:
More informationSummer Assignment AP Literature and Composition Mrs. Schwartz
2015-2016 Summer Assignment AP Literature and Composition Mrs. Schwartz Contact Information: Email: meschwar@vbschools.com or bschwar12@gmail.com Edmodo Group Code: 534ta8 OVERVIEW This summer, you will
More informationLecture 1: Machine Learning Basics
1/69 Lecture 1: Machine Learning Basics Ali Harakeh University of Waterloo WAVE Lab ali.harakeh@uwaterloo.ca May 1, 2017 2/69 Overview 1 Learning Algorithms 2 Capacity, Overfitting, and Underfitting 3
More informationInstructor: Matthew Wickes Kilgore Office: ES 310
MATH 1314 College Algebra Syllabus Instructor: Matthew Wickes Kilgore Office: ES 310 Longview Office: LN 205C Email: mwickes@kilgore.edu Phone: 903 988-7455 Prerequistes: Placement test score on TSI or
More informationArtificial Neural Networks written examination
1 (8) Institutionen för informationsteknologi Olle Gällmo Universitetsadjunkt Adress: Lägerhyddsvägen 2 Box 337 751 05 Uppsala Artificial Neural Networks written examination Monday, May 15, 2006 9 00-14
More informationBIOL Nutrition and Diet Therapy Blinn College-Bryan Campus Course Syllabus Spring 2011
BIOL 1322 - Nutrition and Diet Therapy Blinn College-Bryan Campus Course Syllabus Spring 2011 A3 1. COURSE TITLE, NUMBER, AND SECTION BIOL 1322-A3: M 5:40 p.m.-8:20 p.m. 2. INSTRUCTOR INFORMATION INSTRUCTOR:
More informationINSTRUCTOR'S GUIDE PRONUNCIATION - Levels 1 & REVIEW LESSON I
PRONUNCIATION - Levels 1 & 2 - - REVIEW LESSON I SOUNDS TO BE REVIEWED: b & v d g j l t m & n r Note: These sounds are the hardest for students to pronounce correctly. It is important that they learn proper
More informationTransfer Learning Action Models by Measuring the Similarity of Different Domains
Transfer Learning Action Models by Measuring the Similarity of Different Domains Hankui Zhuo 1, Qiang Yang 2, and Lei Li 1 1 Software Research Institute, Sun Yat-sen University, Guangzhou, China. zhuohank@gmail.com,lnslilei@mail.sysu.edu.cn
More informationDERMATOLOGY. Sponsored by the NYU Post-Graduate Medical School. 129 Years of Continuing Medical Education
Advaces i DERMATOLOGY THURSDAY - FRIDAY JUNE 7-8, 2012 New York, NY Sposored by the NYU Post-Graduate Medical School 129 Years of Cotiuig Medical Educatio THE RONALD O. PERELMAN DEPARTMENT OF DERMATOLOGY
More informationOn the Formation of Phoneme Categories in DNN Acoustic Models
On the Formation of Phoneme Categories in DNN Acoustic Models Tasha Nagamine Department of Electrical Engineering, Columbia University T. Nagamine Motivation Large performance gap between humans and state-
More informationSyntactic systematicity in sentence processing with a recurrent self-organizing network
Syntactic systematicity in sentence processing with a recurrent self-organizing network Igor Farkaš,1 Department of Applied Informatics, Comenius University Mlynská dolina, 842 48 Bratislava, Slovak Republic
More informationGraduate Program in Education
SPECIAL EDUCATION THESIS/PROJECT AND SEMINAR (EDME 531-01) SPRING / 2015 Professor: Janet DeRosa, D.Ed. Course Dates: January 11 to May 9, 2015 Phone: 717-258-5389 (home) Office hours: Tuesday evenings
More informationFocus of the Unit: Much of this unit focuses on extending previous skills of multiplication and division to multi-digit whole numbers.
Approximate Time Frame: 3-4 weeks Connections to Previous Learning: In fourth grade, students fluently multiply (4-digit by 1-digit, 2-digit by 2-digit) and divide (4-digit by 1-digit) using strategies
More informationBooks Effective Literacy Y5-8 Learning Through Talk Y4-8 Switch onto Spelling Spelling Under Scrutiny
By the End of Year 8 All Essential words lists 1-7 290 words Commonly Misspelt Words-55 working out more complex, irregular, and/or ambiguous words by using strategies such as inferring the unknown from
More informationIntroduction to Simulation
Introduction to Simulation Spring 2010 Dr. Louis Luangkesorn University of Pittsburgh January 19, 2010 Dr. Louis Luangkesorn ( University of Pittsburgh ) Introduction to Simulation January 19, 2010 1 /
More informationENGBG1 ENGBL1 Campus Linguistics. Meeting 2. Chapter 7 (Morphology) and chapter 9 (Syntax) Pia Sundqvist
Meeting 2 Chapter 7 (Morphology) and chapter 9 (Syntax) Today s agenda Repetition of meeting 1 Mini-lecture on morphology Seminar on chapter 7, worksheet Mini-lecture on syntax Seminar on chapter 9, worksheet
More informationELPAC. Practice Test. Kindergarten. English Language Proficiency Assessments for California
ELPAC English Language Proficiency Assessments for California Practice Test Kindergarten Copyright 2017 by the California Department of Education (CDE). All rights reserved. Copying and distributing these
More informationGraduation Initiative 2025 Goals San Jose State
Graduation Initiative 2025 Goals San Jose State Metric 2025 Goal Most Recent Rate Freshman 6-Year Graduation 71% 57% Freshman 4-Year Graduation 35% 10% Transfer 2-Year Graduation 36% 24% Transfer 4-Year
More informationMathematics. Mathematics
Mathematics Program Description Successful completion of this major will assure competence in mathematics through differential and integral calculus, providing an adequate background for employment in
More informationSmiley Face Feedback Form
Smiley Face Free PDF ebook Download: Smiley Face Download or Read Online ebook smiley face feedback form in PDF Format From The Best User Guide Database Monitoring the young persons and carers feedback
More informationWeek 4: Action Planning and Personal Growth
Week 4: Action Planning and Personal Growth Overview So far in the Comprehensive Needs Assessment of your selected campus, you have analyzed demographic and student learning data through the AYP report,
More informationSSIS SEL Edition Overview Fall 2017
Image by Photographer s Name (Credit in black type) or Image by Photographer s Name (Credit in white type) Use of the new SSIS-SEL Edition for Screening, Assessing, Intervention Planning, and Progress
More information6 Financial Aid Information
6 This chapter includes information regarding the Financial Aid area of the CA program, including: Accessing Student-Athlete Information regarding the Financial Aid screen (e.g., adding financial aid information,
More informationCriterion Met? Primary Supporting Y N Reading Street Comprehensive. Publisher Citations
Program 2: / Arts English Development Basic Program, K-8 Grade Level(s): K 3 SECTIO 1: PROGRAM DESCRIPTIO All instructional material submissions must meet the requirements of this program description section,
More informationIntroduction to Causal Inference. Problem Set 1. Required Problems
Introduction to Causal Inference Problem Set 1 Professor: Teppei Yamamoto Due Friday, July 15 (at beginning of class) Only the required problems are due on the above date. The optional problems will not
More informationEEAS 101 BASIC WIRING AND CIRCUIT DESIGN. Electrical Principles and Practices Text 3 nd Edition, Glen Mazur & Peter Zurlis
EEAS 101 REQUIRED MATERIALS: TEXTBOOK: WORKBOOK: Electrical Principles and Practices Text 3 nd Edition, Glen Mazur & Peter Zurlis Electrical Principles and Practices Workbook 3 nd Edition, Glen Mazur &
More information