INTRODUCTION OBSERVATIONS
|
|
- Mervyn Nash
- 5 years ago
- Views:
Transcription
1 NATURE IN SINGAPORE : Dte of Puliction: 28 Novemer 2011 Ntionl University of Singpore OBSERVATIONS OF PUPAL ECLOSION AND PHEROMONE RELEASE IN THE OLEANDER HAWKMOTH, DAPHNIS NERII (LINNAEUS, 1758) (LEPIDOPTERA: SPHINGIDAE: MACROGLOSSINAE) Tzi Ming Leong Deprtment of Biologicl Sciences, Ntionl University of Singpore 14 Science Drive 4, Singpore , Repulic of Singpore (E-mil: INTRODUCTION The cterpillrs of the olender hwkmoth, Dphnis nerii (Linneus, 1758) were previously rered to metmorphosis nd riefly descried y Leong & D Rozrio (2009) sed on encounters in Singpore. A recent rering of the sme species provided the opportunity to document the precise moment of eclosion from the pup, s well s to oserve susequent ehviour of pheromone relese y the femle hwkmoths. OBSERVATIONS On 26 Sep.2011, n ggregtion of olender hwkmoth cterpillrs (out individuls) ws encountered on n olender ush (Nerium olender, fmily Apocyncee) growing long Est Cost Terrce. The cterpillrs were mostly in their finl instr nd feeding on the leves, s well s the flowers of its hostplnt (Figs. 1, 2). When distured, the cterpillrs would disply their chrcteristic defensive posture, tucking in their heds nd exposing the prominent ocelli on the third thorcic segment (Fig. 3). Four cterpillrs were collected to e rered in cptivity. The cterpillrs demonstrted helthy ppetite for the olender leves nd y 29 Sep.2011, pre-pupl colourtion nd ehviour were noticed. By 1 Oct.2011, the cterpillrs hd lredy completed puption. Fig. 1. Finl instr cterpillr of the olender hwkmoth, Dphnis nerii, perched on its nmeske hostplnt, Nerium olender (Apocyncee) growing long Est Cost Terrce on 26 Sep Its ody length ws c. 75 mm, with til horn 4 mm long. 369
2 Leong: Pupl Eclosion nd Pheromone Relese in Dphnis nerii Fig. 2. Anterior close-up of finl instr cterpillr (s in Fig. 1) feeding on flower uds of Nerium olender. T3 Fig. 3. Typicl defensive posture of the finl instr cterpillr (ody length 80 mm). With its hed tucked ventrlly, the prominent pir of ocelli (ut only one ocellus shown here) on its third thorcic segment (T3) is clerly displyed. 370
3 NATURE IN SINGAPORE 2011 On the evening of 11 Oct.2011, the pupe displyed signs of imminent eclosion, s the pupl cuticle hd turned trnslucent nd ws delicte to the touch. At this stge, the symmetricl rrngement of its first two pirs of lims nd wings could e redily seen inside (Fig. 4). The intersegmentl memrne of its domen lso ppered slightly swollen nd distended. The first two hwkmoths emerged t c nd 2100 hours, ut the moments of eclosion were not witnessed. Close ttention ws then ptiently focused on the third hwkmoth, which eventully eclosed t precisely 2252 hours (Figs. 5, 6). The first splitting of the pupl cuticle ws preceded y noticele movements of its fore- nd midlegs. In prticulr, the midlegs pper to ply pivotl role in lifting wy the nterior thorcic shield piece. Within 10 seconds, the ody of the hwkmoth hd dvnced forwrd, with its hed entirely removed from the cephlic helmet, nd its ntenne, eyes nd prooscis were clerly visile (Fig. 5d). Twelve seconds fter the strt of eclosion, its wings hd ecome fully lierted from the pupl cse (Fig. 6). Shortly fter, the hwkmoth quickly extricted itself nd dopted n upright posture to scrmle wy in serch of the nerest possile perch (Fig. 6). In totl, the entire eclosion process ws completed in c. 18 seconds. Therefter, the hwkmoth ws provided rnch on which to extend nd stiffen its wings (Fig. 7). All four of the hwkmoths successfully eclosed eventully nd were found to e femles. Two specimens were preserved soon fter eclosion, while two others were kept live for susequent oservtion. After two dys, the hwkmoths were oserved to rch their domens while perched. Distlly, golden rown glnd ws extruded, nd upon close exmintion, slow nd delierte pulstions of the dorsl memrne could e detected (Figs. 8, 9). The rhythmic contrctions of this pheromone glnd rnged etween pulses min 1. A video clip of this process of pheromone dissemintion ws recorded nd uploded online ( The extrusion of the pheromone glnd, ccompnied y regulr pulstions occurring two dys post-eclosion my e n indiction of necessry period for ov mturtion prior to femle receptiveness (I. J. Kitching, pers. comm., Oct.2011). The femles continued to exhiit such pheromone-relese ehviour for t lest three consecutive dys, etween c hours. They were susequently preserved s voucher specimens nd deposited t the Zoologicl Reference Collection (ZRC) of the Rffles Museum of Biodiversity Reserch (RMBR), Ntionl University of Singpore, where they re collectively ctlogued s ZRC.LEP.358 (ody lengths: mm, forewing lengths: mm). W L1 Fig. 4. Ventrl close-up of the nterior segments of the pre-eclosion pup. The pupl cuticle hs ecome trnslucent, enling cler views of the underlying wings (W) nd nterior two pirs of lims (L1, ). Photogrphed on the night of 11 Oct.2011 (2230 hours). 371
4 Leong: Pupl Eclosion nd Pheromone Relese in Dphnis nerii L3 c d Fig. 5. Pupl eclosion sequence witnessed on the night of 11 Oct.2011, t 2252 hours: c, t 4-second intervls; nd d, fter 2 seconds. nd L3 refer to the second nd third pirs of legs respectively. 372
5 NATURE IN SINGAPORE 2011 Fig. 6. Continution of pupl eclosion sequence (from Fig. 5) on 11 Oct.2011, t 2252 hours fter 6-second intervl, when the hwkmoth righted itself nd crwled wy hurriedly in serch of the nerest perch. Fig. 7. Freshly eclosed hwkmoth (s in Figs. 4 6) extending its wings:, t 2255 hours; nd, t 2300 hours. 373
6 Leong: Pupl Eclosion nd Pheromone Relese in Dphnis nerii Fig. 8. Dorsl () nd lterl () close-ups of the extruded pheromone glnd of femle hwkmoth (ZRC.LEP.358, ody length: 44 mm, forewing: 42 mm), first oserved on the morning of 14 Oct Slow nd delierte pulstions of its dorsl memrne were oserved (15 17 pulses min 1 ). 374
7 NATURE IN SINGAPORE 2011 Fig. 9. Ventrl close-up of the extruded pheromone glnd of femle hwkmoth (s in Fig. 8). ACKNOWLEDGEMENTS I m grteful to In J. Kitching (The Nturl History Museum, London) for vlule insights into the structure nd function of the pheromone glnd of the hwkmoth. The efficient review nd helpful suggestions from n enthusistic lepidopterist were much pprecited. LITERATURE CITED Leong, T. M. & V. D Rozrio, Finl instr lrve nd metmorphosis of the olender hwkmoth, Dphnis nerii (Linneus) in Singpore (Lepidopter: Sphingide: Mcroglossine). Nture in Singpore, 2:
FINAL INSTAR CATERPILLAR AND METAMORPHOSIS OF LEBEDA COGNATA GRÜNBERG, 1913 IN SINGAPORE (LEPIDOPTERA: LASIOCAMPIDAE)
NATURE IN SINGAPORE 2012 5: 129 140 Dte of Puliction: 4 My 2012 Ntionl University of Singpore FINAL INSTAR CATERPILLAR AND METAMORPHOSIS OF LEBEDA COGNATA GRÜNBERG, 1913 IN SINGAPORE (LEPIDOPTERA: LASIOCAMPIDAE)
More informationLARVA OF THE PHYTOTELM-BREEDING DAMSELFLY, PERICNEMIS STICTICA SELYS FROM FORESTS IN SINGAPORE (ODONATA: ZYGOPTERA: COENAGRIONIDAE)
NATURE IN SINGAPORE 2012 5: 103 115 Dte of Puliction: 23 Mrch 2012 Ntionl University of Singpore LARVA OF THE PHYTOTELM-BREEDING DAMSELFLY, PERICNEMIS STICTICA SELYS FROM FORESTS IN SINGAPORE (ODONATA:
More informationFINAL INSTAR CATERPILLAR AND METAMORPHOSIS OF AMBLYCHIA HYMENARIA (GUENÉE) IN SINGAPORE (LEPIDOPTERA: GEOMETRIDAE: ENNOMINAE)
NATURE IN SINGAPORE 2009 2: 267 273 Date of Publication: 24 June 2009 National University of Singapore FINAL INSTAR CATERPILLAR AND METAMORPHOSIS OF AMBLYCHIA HYMENARIA (GUENÉE) IN SINGAPORE (LEPIDOPTERA:
More informationList all of the possible rational roots of each equation. Then find all solutions (both real and imaginary) of the equation. 1.
Mth Anlysis CP WS 4.X- Section 4.-4.4 Review Complete ech question without the use of grphing clcultor.. Compre the mening of the words: roots, zeros nd fctors.. Determine whether - is root of 0. Show
More informationFINAL INSTAR CATERPILLAR AND METAMORPHOSIS OF EUMELEA LUDOVICATA GUENÉE, 1857, IN SINGAPORE (LEPIDOPTERA: GEOMETRIDAE: DESMOBATHRINAE)
NATURE IN SINGAPORE 2010 3: 21 26 Date of Publication: 25 January 2010 National University of Singapore FINAL INSTAR CATERPILLAR AND METAMORPHOSIS OF EUMELEA LUDOVICATA GUENÉE, 1857, IN SINGAPORE (LEPIDOPTERA:
More informationHomework Solution - Set 5 Due: Friday 10/03/08
CE 96 Introduction to the Theory of Computtion ll 2008 Homework olution - et 5 Due: ridy 10/0/08 1. Textook, Pge 86, Exercise 1.21. () 1 2 Add new strt stte nd finl stte. Mke originl finl stte non-finl.
More informationp-adic Egyptian Fractions
p-adic Egyptin Frctions Contents 1 Introduction 1 2 Trditionl Egyptin Frctions nd Greedy Algorithm 2 3 Set-up 3 4 p-greedy Algorithm 5 5 p-egyptin Trditionl 10 6 Conclusion 1 Introduction An Egyptin frction
More informationHamiltonian Cycle in Complete Multipartite Graphs
Annls of Pure nd Applied Mthemtics Vol 13, No 2, 2017, 223-228 ISSN: 2279-087X (P), 2279-0888(online) Pulished on 18 April 2017 wwwreserchmthsciorg DOI: http://dxdoiorg/1022457/pmv13n28 Annls of Hmiltonin
More informationLinear Systems with Constant Coefficients
Liner Systems with Constnt Coefficients 4-3-05 Here is system of n differentil equtions in n unknowns: x x + + n x n, x x + + n x n, x n n x + + nn x n This is constnt coefficient liner homogeneous system
More informationDesigning finite automata II
Designing finite utomt II Prolem: Design DFA A such tht L(A) consists of ll strings of nd which re of length 3n, for n = 0, 1, 2, (1) Determine wht to rememer out the input string Assign stte to ech of
More informationLecture 09: Myhill-Nerode Theorem
CS 373: Theory of Computtion Mdhusudn Prthsrthy Lecture 09: Myhill-Nerode Theorem 16 Ferury 2010 In this lecture, we will see tht every lnguge hs unique miniml DFA We will see this fct from two perspectives
More information1 Nondeterministic Finite Automata
1 Nondeterministic Finite Automt Suppose in life, whenever you hd choice, you could try oth possiilities nd live your life. At the end, you would go ck nd choose the one tht worked out the est. Then you
More informationLecture 3: Equivalence Relations
Mthcmp Crsh Course Instructor: Pdric Brtlett Lecture 3: Equivlence Reltions Week 1 Mthcmp 2014 In our lst three tlks of this clss, we shift the focus of our tlks from proof techniques to proof concepts
More informationLecture 08: Feb. 08, 2019
4CS4-6:Theory of Computtion(Closure on Reg. Lngs., regex to NDFA, DFA to regex) Prof. K.R. Chowdhry Lecture 08: Fe. 08, 2019 : Professor of CS Disclimer: These notes hve not een sujected to the usul scrutiny
More informationCSCI 340: Computational Models. Transition Graphs. Department of Computer Science
CSCI 340: Computtionl Models Trnsition Grphs Chpter 6 Deprtment of Computer Science Relxing Restrints on Inputs We cn uild n FA tht ccepts only the word! 5 sttes ecuse n FA cn only process one letter t
More information10. AREAS BETWEEN CURVES
. AREAS BETWEEN CURVES.. Ares etween curves So res ove the x-xis re positive nd res elow re negtive, right? Wrong! We lied! Well, when you first lern out integrtion it s convenient fiction tht s true in
More informationINTRODUCTION OBSERVATIONS
NATURE IN SINGAPORE 2011 4: 251 258 Date of Publication: 9 September 2011 National University of Singapore THE BROWN FORM FINAL INSTAR CATERPILLAR OF THE HAWKMOTH, ACHERONTIA LACHESIS (FABRICIUS, 1798)
More informationName Ima Sample ASU ID
Nme Im Smple ASU ID 2468024680 CSE 355 Test 1, Fll 2016 30 Septemer 2016, 8:35-9:25.m., LSA 191 Regrding of Midterms If you elieve tht your grde hs not een dded up correctly, return the entire pper to
More informationCS 311 Homework 3 due 16:30, Thursday, 14 th October 2010
CS 311 Homework 3 due 16:30, Thursdy, 14 th Octoer 2010 Homework must e sumitted on pper, in clss. Question 1. [15 pts.; 5 pts. ech] Drw stte digrms for NFAs recognizing the following lnguges:. L = {w
More informationCS 330 Formal Methods and Models
CS 330 Forml Methods nd Models Dn Richrds, George Mson University, Spring 2017 Quiz Solutions Quiz 1, Propositionl Logic Dte: Ferury 2 1. Prove ((( p q) q) p) is tutology () (3pts) y truth tle. p q p q
More informationFINAL INSTAR CATERPILLARS AND METAMORPHOSIS OF ACHERONTIA LACHESIS (FABRICIUS, 1798) IN SINGAPORE (LEPIDOPTERA: SPHINGIDAE: SPHINGINAE: ACHERONTIINI)
NATURE IN SINGAPORE 2011 4: 101 114 Date of Publication: 25 May 2011 National University of Singapore FINAL INSTAR CATERPILLARS AND METAMORPHOSIS OF ACHERONTIA LACHESIS (FABRICIUS, 1798) IN SINGAPORE (LEPIDOPTERA:
More informationFINAL INSTAR CATERPILLAR AND METAMORPHOSIS OF CALLITEARA HORSFIELDII (SAUNDERS) IN SINGAPORE (LEPIDOPTERA: LYMANTRIIDAE: ORGYIINI)
NATURE IN SINGAPORE 2009 2: 443 447 Date of Publication: 3 December 2009 National University of Singapore FINAL INSTAR CATERPILLAR AND METAMORPHOSIS OF CALLITEARA HORSFIELDII (SAUNDERS) IN SINGAPORE (LEPIDOPTERA:
More informationCS 330 Formal Methods and Models Dana Richards, George Mason University, Spring 2016 Quiz Solutions
CS 330 Forml Methods nd Models Dn Richrds, George Mson University, Spring 2016 Quiz Solutions Quiz 1, Propositionl Logic Dte: Ferury 9 1. (4pts) ((p q) (q r)) (p r), prove tutology using truth tles. p
More information1 From NFA to regular expression
Note 1: How to convert DFA/NFA to regulr expression Version: 1.0 S/EE 374, Fll 2017 Septemer 11, 2017 In this note, we show tht ny DFA cn e converted into regulr expression. Our construction would work
More informationAssignment 1 Automata, Languages, and Computability. 1 Finite State Automata and Regular Languages
Deprtment of Computer Science, Austrlin Ntionl University COMP2600 Forml Methods for Softwre Engineering Semester 2, 206 Assignment Automt, Lnguges, nd Computility Smple Solutions Finite Stte Automt nd
More informationState space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies
Stte spce systems nlysis (continued) Stbility A. Definitions A system is sid to be Asymptoticlly Stble (AS) when it stisfies ut () = 0, t > 0 lim xt () 0. t A system is AS if nd only if the impulse response
More informationFirst Midterm Examination
24-25 Fll Semester First Midterm Exmintion ) Give the stte digrm of DFA tht recognizes the lnguge A over lphet Σ = {, } where A = {w w contins or } 2) The following DFA recognizes the lnguge B over lphet
More informationCompiler Design. Fall Lexical Analysis. Sample Exercises and Solutions. Prof. Pedro C. Diniz
University of Southern Cliforni Computer Science Deprtment Compiler Design Fll Lexicl Anlysis Smple Exercises nd Solutions Prof. Pedro C. Diniz USC / Informtion Sciences Institute 4676 Admirlty Wy, Suite
More informationANALYSIS OF THE DESTRUCTION OF THE OLD BRIDGE ACCORDING TO ACCESSIBLE VIDEO TAPES Muhmed Sućesk, PhD. C. E. Sloodn Jnković, PhD. M. E. prof. retired Aco Šiknić, PhD. M. E. ZAGREB, JANUARY 2006 1. GEOGRAPHICAL
More informationFINAL INSTAR CATERPILLARS AND METAMORPHOSIS OF SPILARCTIA HYPOGOPA (HAMPSON, 1907) IN SINGAPORE (LEPIDOPTERA: EREBIDAE: ARCTIINAE)
NATURE IN SINGAPORE 2010 3: 187 193 Date of Publication: 31 August 2010 National University of Singapore FINAL INSTAR CATERPILLARS AND METAMORPHOSIS OF SPILARCTIA HYPOGOPA (HAMPSON, 1907) IN SINGAPORE
More information3 x x x 1 3 x a a a 2 7 a Ba 1 NOW TRY EXERCISES 89 AND a 2/ Evaluate each expression.
SECTION. Eponents nd Rdicls 7 B 7 7 7 7 7 7 7 NOW TRY EXERCISES 89 AND 9 7. EXERCISES CONCEPTS. () Using eponentil nottion, we cn write the product s. In the epression 3 4,the numer 3 is clled the, nd
More informationFarey Fractions. Rickard Fernström. U.U.D.M. Project Report 2017:24. Department of Mathematics Uppsala University
U.U.D.M. Project Report 07:4 Frey Frctions Rickrd Fernström Exmensrete i mtemtik, 5 hp Hledre: Andres Strömergsson Exmintor: Jörgen Östensson Juni 07 Deprtment of Mthemtics Uppsl University Frey Frctions
More informationI1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3
2 The Prllel Circuit Electric Circuits: Figure 2- elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is
More informationSection - 2 MORE PROPERTIES
LOCUS Section - MORE PROPERTES n section -, we delt with some sic properties tht definite integrls stisf. This section continues with the development of some more properties tht re not so trivil, nd, when
More informationSection 6: Area, Volume, and Average Value
Chpter The Integrl Applied Clculus Section 6: Are, Volume, nd Averge Vlue Are We hve lredy used integrls to find the re etween the grph of function nd the horizontl xis. Integrls cn lso e used to find
More information14 Science Drive 4, Singapore , Republic of Singapore 2 Central Nature Reserve, National Parks Board
NATURE IN SINGAPORE 2011 4: 203 211 Date of Publication: 8 July 2011 National University of Singapore RECORDS OF THE BLACK AND GOLDEN CICADA, HUECHYS FUSCA DISTANT, 1892 IN SINGAPORE, WITH NATURAL HISTORY
More informationFormal Languages and Automata
Moile Computing nd Softwre Engineering p. 1/5 Forml Lnguges nd Automt Chpter 2 Finite Automt Chun-Ming Liu cmliu@csie.ntut.edu.tw Deprtment of Computer Science nd Informtion Engineering Ntionl Tipei University
More information80 CHAPTER 2. DFA S, NFA S, REGULAR LANGUAGES. 2.6 Finite State Automata With Output: Transducers
80 CHAPTER 2. DFA S, NFA S, REGULAR LANGUAGES 2.6 Finite Stte Automt With Output: Trnsducers So fr, we hve only considered utomt tht recognize lnguges, i.e., utomt tht do not produce ny output on ny input
More information7.2 The Definite Integral
7.2 The Definite Integrl the definite integrl In the previous section, it ws found tht if function f is continuous nd nonnegtive, then the re under the grph of f on [, b] is given by F (b) F (), where
More informationIntermediate Math Circles Wednesday, November 14, 2018 Finite Automata II. Nickolas Rollick a b b. a b 4
Intermedite Mth Circles Wednesdy, Novemer 14, 2018 Finite Automt II Nickols Rollick nrollick@uwterloo.c Regulr Lnguges Lst time, we were introduced to the ide of DFA (deterministic finite utomton), one
More informationLab 11 Approximate Integration
Nme Student ID # Instructor L Period Dte Due L 11 Approximte Integrtion Ojectives 1. To ecome fmilir with the right endpoint rule, the trpezoidl rule, nd Simpson's rule. 2. To compre nd contrst the properties
More information4.1. Probability Density Functions
STT 1 4.1-4. 4.1. Proility Density Functions Ojectives. Continuous rndom vrile - vers - discrete rndom vrile. Proility density function. Uniform distriution nd its properties. Expected vlue nd vrince of
More informationFirst Midterm Examination
Çnky University Deprtment of Computer Engineering 203-204 Fll Semester First Midterm Exmintion ) Design DFA for ll strings over the lphet Σ = {,, c} in which there is no, no nd no cc. 2) Wht lnguge does
More informationCS 310 (sec 20) - Winter Final Exam (solutions) SOLUTIONS
CS 310 (sec 20) - Winter 2003 - Finl Exm (solutions) SOLUTIONS 1. (Logic) Use truth tles to prove the following logicl equivlences: () p q (p p) (q q) () p q (p q) (p q) () p q p q p p q q (q q) (p p)
More information4 VECTORS. 4.0 Introduction. Objectives. Activity 1
4 VECTRS Chpter 4 Vectors jectives fter studying this chpter you should understnd the difference etween vectors nd sclrs; e le to find the mgnitude nd direction of vector; e le to dd vectors, nd multiply
More informationHeavy tail and stable distributions
Hevy til nd stle distriutions J.K. Misiewicz Deprtment of Mthemtics nd Informtion Science Technicl University of Wrsw X or its distriution hs hevy til if E(X ) =. X or its distriution hs hevy til of order
More informationDomino Recognizability of Triangular Picture Languages
Interntionl Journl of Computer Applictions (0975 8887) Volume 57 No.5 Novemer 0 Domino Recognizility of ringulr icture Lnguges V. Devi Rjselvi Reserch Scholr Sthym University Chenni 600 9. Klyni Hed of
More informationMinimal DFA. minimal DFA for L starting from any other
Miniml DFA Among the mny DFAs ccepting the sme regulr lnguge L, there is exctly one (up to renming of sttes) which hs the smllest possile numer of sttes. Moreover, it is possile to otin tht miniml DFA
More information, if x 1 and f(x) = x, if x 0.
Indin Institute of Informtion Technology Design nd Mnufcturing, Kncheepurm Chenni 600 7, Indi An Autonomous Institute under MHRD, Govt of Indi An Institute of Ntionl Importnce wwwiiitdmcin COM05T Discrete
More informationConvert the NFA into DFA
Convert the NF into F For ech NF we cn find F ccepting the sme lnguge. The numer of sttes of the F could e exponentil in the numer of sttes of the NF, ut in prctice this worst cse occurs rrely. lgorithm:
More informationTriangles The following examples explore aspects of triangles:
Tringles The following exmples explore spects of tringles: xmple 1: ltitude of right ngled tringle + xmple : tringle ltitude of the symmetricl ltitude of n isosceles x x - 4 +x xmple 3: ltitude of the
More informationCentrum voor Wiskunde en Informatica REPORTRAPPORT. Supervisory control for nondeterministic systems
Centrum voor Wiskunde en Informtic REPORTRAPPORT Supervisory control for nondeterministic systems A. Overkmp Deprtment of Opertions Reserch, Sttistics, nd System Theory BS-R9411 1994 Supervisory Control
More informationTorsion in Groups of Integral Triangles
Advnces in Pure Mthemtics, 01,, 116-10 http://dxdoiorg/1046/pm011015 Pulished Online Jnury 01 (http://wwwscirporg/journl/pm) Torsion in Groups of Integrl Tringles Will Murry Deprtment of Mthemtics nd Sttistics,
More information12.1 Nondeterminism Nondeterministic Finite Automata. a a b ε. CS125 Lecture 12 Fall 2014
CS125 Lecture 12 Fll 2014 12.1 Nondeterminism The ide of nondeterministic computtions is to llow our lgorithms to mke guesses, nd only require tht they ccept when the guesses re correct. For exmple, simple
More information5. (±±) Λ = fw j w is string of even lengthg [ 00 = f11,00g 7. (11 [ 00)± Λ = fw j w egins with either 11 or 00g 8. (0 [ ffl)1 Λ = 01 Λ [ 1 Λ 9.
Regulr Expressions, Pumping Lemm, Right Liner Grmmrs Ling 106 Mrch 25, 2002 1 Regulr Expressions A regulr expression descries or genertes lnguge: it is kind of shorthnd for listing the memers of lnguge.
More informationQuadratic Forms. Quadratic Forms
Qudrtic Forms Recll the Simon & Blume excerpt from n erlier lecture which sid tht the min tsk of clculus is to pproximte nonliner functions with liner functions. It s ctully more ccurte to sy tht we pproximte
More informationAlg 3 Ch 7.2, 8 1. C 2) If A = 30, and C = 45, a = 1 find b and c A
lg 3 h 7.2, 8 1 7.2 Right Tringle Trig ) Use of clcultor sin 10 = sin x =.4741 c ) rete right tringles π 1) If = nd = 25, find 6 c 2) If = 30, nd = 45, = 1 find nd c 3) If in right, with right ngle t,
More informationCSE396 Prelim I Answer Key Spring 2017
Nme nd St.ID#: CSE96 Prelim I Answer Key Spring 2017 (1) (24 pts.) Define A to e the lnguge of strings x {, } such tht x either egins with or ends with, ut not oth. Design DFA M such tht L(M) = A. A node-rc
More informationRiemann is the Mann! (But Lebesgue may besgue to differ.)
Riemnn is the Mnn! (But Lebesgue my besgue to differ.) Leo Livshits My 2, 2008 1 For finite intervls in R We hve seen in clss tht every continuous function f : [, b] R hs the property tht for every ɛ >
More informationɛ-closure, Kleene s Theorem,
DEGefW5wiGH2XgYMEzUKjEmtCDUsRQ4d 1 A nice pper relevnt to this course is titled The Glory of the Pst 2 NICTA Resercher, Adjunct t the Austrlin Ntionl University nd Griffith University ɛ-closure, Kleene
More informationCS103B Handout 18 Winter 2007 February 28, 2007 Finite Automata
CS103B ndout 18 Winter 2007 Ferury 28, 2007 Finite Automt Initil text y Mggie Johnson. Introduction Severl childrens gmes fit the following description: Pieces re set up on plying ord; dice re thrown or
More informationCMPSCI 250: Introduction to Computation. Lecture #31: What DFA s Can and Can t Do David Mix Barrington 9 April 2014
CMPSCI 250: Introduction to Computtion Lecture #31: Wht DFA s Cn nd Cn t Do Dvid Mix Brrington 9 April 2014 Wht DFA s Cn nd Cn t Do Deterministic Finite Automt Forml Definition of DFA s Exmples of DFA
More informationGolden Section Search Method - Theory
Numericl Methods Golden Section Serch Method - Theory http://nm.mthforcollege.com For more detils on this topic Go to http://nm.mthforcollege.com Click on Keyword Click on Golden Section Serch Method You
More information3 Regular expressions
3 Regulr expressions Given n lphet Σ lnguge is set of words L Σ. So fr we were le to descrie lnguges either y using set theory (i.e. enumertion or comprehension) or y n utomton. In this section we shll
More informationParse trees, ambiguity, and Chomsky normal form
Prse trees, miguity, nd Chomsky norml form In this lecture we will discuss few importnt notions connected with contextfree grmmrs, including prse trees, miguity, nd specil form for context-free grmmrs
More informationFinite Automata-cont d
Automt Theory nd Forml Lnguges Professor Leslie Lnder Lecture # 6 Finite Automt-cont d The Pumping Lemm WEB SITE: http://ingwe.inghmton.edu/ ~lnder/cs573.html Septemer 18, 2000 Exmple 1 Consider L = {ww
More informationRiemann Sums and Riemann Integrals
Riemnn Sums nd Riemnn Integrls Jmes K. Peterson Deprtment of Biologicl Sciences nd Deprtment of Mthemticl Sciences Clemson University August 26, 2013 Outline 1 Riemnn Sums 2 Riemnn Integrls 3 Properties
More informationFormal languages, automata, and theory of computation
Mälrdlen University TEN1 DVA337 2015 School of Innovtion, Design nd Engineering Forml lnguges, utomt, nd theory of computtion Thursdy, Novemer 5, 14:10-18:30 Techer: Dniel Hedin, phone 021-107052 The exm
More informationCoalgebra, Lecture 15: Equations for Deterministic Automata
Colger, Lecture 15: Equtions for Deterministic Automt Julin Slmnc (nd Jurrin Rot) Decemer 19, 2016 In this lecture, we will study the concept of equtions for deterministic utomt. The notes re self contined
More informationDiscrete Mathematics and Probability Theory Spring 2013 Anant Sahai Lecture 17
EECS 70 Discrete Mthemtics nd Proility Theory Spring 2013 Annt Shi Lecture 17 I.I.D. Rndom Vriles Estimting the is of coin Question: We wnt to estimte the proportion p of Democrts in the US popultion,
More informationLINEAR ALGEBRA APPLIED
5.5 Applictions of Inner Product Spces 5.5 Applictions of Inner Product Spces 7 Find the cross product of two vectors in R. Find the liner or qudrtic lest squres pproimtion of function. Find the nth-order
More informationRiemann Sums and Riemann Integrals
Riemnn Sums nd Riemnn Integrls Jmes K. Peterson Deprtment of Biologicl Sciences nd Deprtment of Mthemticl Sciences Clemson University August 26, 203 Outline Riemnn Sums Riemnn Integrls Properties Abstrct
More informationThe larval development from prezoea to megalopa and juvenile stages of Allopetrolisthes punctatus (Guérin, 1835) (Decapoda, Anomura, Porcellanidae)
Lt. Am. J. Aqut. Res., 46(4): 820-824, 2018 DOI: 10.3856/vol46-issue4-fulltext-19 Lrvl development of Allopetrolisthes puncttus 820 1 Short Communiction The lrvl development from prezoe to meglop nd juvenile
More informationTremor-rich shallow dyke formation followed by silent magma flow at Bárðarbunga in Iceland
In the formt provided y the uthors nd unedited. SUPPLEMENTARY INFORMATION DOI: 1.138/NGEO9 Tremor-rich shllow dyke formtion followed y silent mgm flow t Bárðrung in Icelnd 1,, 1, 3 1, 1 1, NATURE GEOSCIENCE
More informationThe Modified Heinz s Inequality
Journl of Applied Mthemtics nd Physics, 03,, 65-70 Pulished Online Novemer 03 (http://wwwscirporg/journl/jmp) http://dxdoiorg/0436/jmp03500 The Modified Heinz s Inequlity Tkshi Yoshino Mthemticl Institute,
More informationArrow s Impossibility Theorem
Rep Voting Prdoxes Properties Arrow s Theorem Arrow s Impossiility Theorem Leture 12 Arrow s Impossiility Theorem Leture 12, Slide 1 Rep Voting Prdoxes Properties Arrow s Theorem Leture Overview 1 Rep
More informationCSCI 340: Computational Models. Kleene s Theorem. Department of Computer Science
CSCI 340: Computtionl Models Kleene s Theorem Chpter 7 Deprtment of Computer Science Unifiction In 1954, Kleene presented (nd proved) theorem which (in our version) sttes tht if lnguge cn e defined y ny
More informationThe Shortest Confidence Interval for the Mean of a Normal Distribution
Interntionl Journl of Sttistics nd Proility; Vol. 7, No. 2; Mrch 208 ISSN 927-7032 E-ISSN 927-7040 Pulished y Cndin Center of Science nd Eduction The Shortest Confidence Intervl for the Men of Norml Distriution
More informationResistive Network Analysis
C H A P T E R 3 Resistive Network Anlysis his chpter will illustrte the fundmentl techniques for the nlysis of resistive circuits. The methods introduced re sed on the circuit lws presented in Chpter 2:
More information7.1 Integral as Net Change and 7.2 Areas in the Plane Calculus
7.1 Integrl s Net Chnge nd 7. Ares in the Plne Clculus 7.1 INTEGRAL AS NET CHANGE Notecrds from 7.1: Displcement vs Totl Distnce, Integrl s Net Chnge We hve lredy seen how the position of n oject cn e
More informationClassification: Rules. Prof. Pier Luca Lanzi Laurea in Ingegneria Informatica Politecnico di Milano Polo regionale di Como
Metodologie per Sistemi Intelligenti Clssifiction: Prof. Pier Luc Lnzi Lure in Ingegneri Informtic Politecnico di Milno Polo regionle di Como Rules Lecture outline Why rules? Wht re clssifiction rules?
More informationState Minimization for DFAs
Stte Minimiztion for DFAs Red K & S 2.7 Do Homework 10. Consider: Stte Minimiztion 4 5 Is this miniml mchine? Step (1): Get rid of unrechle sttes. Stte Minimiztion 6, Stte is unrechle. Step (2): Get rid
More informationMTH 505: Number Theory Spring 2017
MTH 505: Numer Theory Spring 207 Homework 2 Drew Armstrong The Froenius Coin Prolem. Consider the eqution x ` y c where,, c, x, y re nturl numers. We cn think of $ nd $ s two denomintions of coins nd $c
More informationLAMEPS Limited area ensemble forecasting in Norway, using targeted EPS
Limited re ensemle forecsting in Norwy, using trgeted Mrit H. Jensen, Inger-Lise Frogner* nd Ole Vignes, Norwegin Meteorologicl Institute, (*held the presenttion) At the Norwegin Meteorologicl Institute
More informationTalen en Automaten Test 1, Mon 7 th Dec, h45 17h30
Tlen en Automten Test 1, Mon 7 th Dec, 2015 15h45 17h30 This test consists of four exercises over 5 pges. Explin your pproch, nd write your nswer to ech exercise on seprte pge. You cn score mximum of 100
More informationArrow s Impossibility Theorem
Rep Fun Gme Properties Arrow s Theorem Arrow s Impossiility Theorem Leture 12 Arrow s Impossiility Theorem Leture 12, Slide 1 Rep Fun Gme Properties Arrow s Theorem Leture Overview 1 Rep 2 Fun Gme 3 Properties
More informationDiscrete Mathematics and Probability Theory Summer 2014 James Cook Note 17
CS 70 Discrete Mthemtics nd Proility Theory Summer 2014 Jmes Cook Note 17 I.I.D. Rndom Vriles Estimting the is of coin Question: We wnt to estimte the proportion p of Democrts in the US popultion, y tking
More informationContinuous Random Variables Class 5, Jeremy Orloff and Jonathan Bloom
Lerning Gols Continuous Rndom Vriles Clss 5, 8.05 Jeremy Orloff nd Jonthn Bloom. Know the definition of continuous rndom vrile. 2. Know the definition of the proility density function (pdf) nd cumultive
More informationON ALTERNATING POWER SUMS OF ARITHMETIC PROGRESSIONS
ON ALTERNATING POWER SUMS OF ARITHMETIC PROGRESSIONS A. BAZSÓ Astrct. Depending on the prity of the positive integer n the lternting power sum T k n = k + k + + k...+ 1 n 1 n 1 + k. cn e extended to polynomil
More informationTutorial Automata and formal Languages
Tutoril Automt nd forml Lnguges Notes for to the tutoril in the summer term 2017 Sestin Küpper, Christine Mik 8. August 2017 1 Introduction: Nottions nd sic Definitions At the eginning of the tutoril we
More information(e) if x = y + z and a divides any two of the integers x, y, or z, then a divides the remaining integer
Divisibility In this note we introduce the notion of divisibility for two integers nd b then we discuss the division lgorithm. First we give forml definition nd note some properties of the division opertion.
More information12 TRANSFORMING BIVARIATE DENSITY FUNCTIONS
1 TRANSFORMING BIVARIATE DENSITY FUNCTIONS Hving seen how to trnsform the probbility density functions ssocited with single rndom vrible, the next logicl step is to see how to trnsform bivrite probbility
More informationProblem Set 9. Figure 1: Diagram. This picture is a rough sketch of the 4 parabolas that give us the area that we need to find. The equations are:
(x + y ) = y + (x + y ) = x + Problem Set 9 Discussion: Nov., Nov. 8, Nov. (on probbility nd binomil coefficients) The nme fter the problem is the designted writer of the solution of tht problem. (No one
More information1B40 Practical Skills
B40 Prcticl Skills Comining uncertinties from severl quntities error propgtion We usully encounter situtions where the result of n experiment is given in terms of two (or more) quntities. We then need
More informationCS415 Compilers. Lexical Analysis and. These slides are based on slides copyrighted by Keith Cooper, Ken Kennedy & Linda Torczon at Rice University
CS415 Compilers Lexicl Anlysis nd These slides re sed on slides copyrighted y Keith Cooper, Ken Kennedy & Lind Torczon t Rice University First Progrmming Project Instruction Scheduling Project hs een posted
More information4.6 Numerical Integration
.6 Numericl Integrtion 5.6 Numericl Integrtion Approimte definite integrl using the Trpezoidl Rule. Approimte definite integrl using Simpson s Rule. Anlze the pproimte errors in the Trpezoidl Rule nd Simpson
More informationDFA minimisation using the Myhill-Nerode theorem
DFA minimistion using the Myhill-Nerode theorem Johnn Högerg Lrs Lrsson Astrct The Myhill-Nerode theorem is n importnt chrcteristion of regulr lnguges, nd it lso hs mny prcticl implictions. In this chpter,
More informationChapter 9 Definite Integrals
Chpter 9 Definite Integrls In the previous chpter we found how to tke n ntiderivtive nd investigted the indefinite integrl. In this chpter the connection etween ntiderivtives nd definite integrls is estlished
More informationg i fφdx dx = x i i=1 is a Hilbert space. We shall, henceforth, abuse notation and write g i f(x) = f
1. Appliction of functionl nlysis to PEs 1.1. Introduction. In this section we give little introduction to prtil differentil equtions. In prticulr we consider the problem u(x) = f(x) x, u(x) = x (1) where
More informationModel Reduction of Finite State Machines by Contraction
Model Reduction of Finite Stte Mchines y Contrction Alessndro Giu Dip. di Ingegneri Elettric ed Elettronic, Università di Cgliri, Pizz d Armi, 09123 Cgliri, Itly Phone: +39-070-675-5892 Fx: +39-070-675-5900
More information