A Gentle Introduction to Neural Networks (with Python)
|
|
|
- Bethanie Watson
- 5 years ago
- Views:
Transcription
1 A Gntl Introduction to Nural Ntworks (with Python) Tariq PyCon Italy April 2017
2 Background Idas DIY Handwriting Thoughts and a liv dmo!
3 Background
4 Start With Two Qustions locat popl in this photo add ths numbrs =?
5 AI is Hug!
6 Googl s and Go
7 Idas
8 Simpl Prdicting Machin
9 Simpl Prdicting Machin
10 Kilomtrs to Mils random starting paramtr try a modl - this on is linar
11 Kilomtrs to Mils not grat
12 Kilomtrs to Mils bttr
13 Kilomtrs to Mils wors!
14 Kilomtrs to Mils bst yt!
15 Ky Points xactly? Try s rk o w g in how somth w o n k. t n o D paramtrs l b ta s ju d a modl with. paramtrs th n fi r or to Us th rr a
16 Gardn Bugs
17 Classifying Bugs
18 Classifying Bugs
19 Classifying Bugs
20 Classifying Bugs
21 Ky Points ings. 1. Classifying thing th prdicting k li a d in k s is
22 Larning from Data Exampl Width Lngth Bug ladybird catrpillar
23 Larning from Data
24 Larning from Data not a good sparator
25 Larning from Data shift th lin up just abov th training data point
26 Larning from Data
27 How Do W Updat Th Paramtr? rror = targt - actual E = (A + ΔA)x - Ax ΔA = E / x
28 Hang On! Oh no! ach updat ignors prvious xampls
29 Calm Down th Larning ΔA = L (E / x) larning rat
30 Calm Down th Larning larning rat = 0.5
31 Ky Points 1. you d - nsurs o o g is g in your larn pact of im s c u d Modrating r nd your data, a ll a m o fr rn la. training data y is o n r o outlirs
32 Boolan Logic IF I hav atn my vgtabls AND I am still hungry THEN I can hav ic cram. IF it s th wknd OR I am on annual lav THEN I ll go to th park. Input A Input B AND OR
33 Boolan Logic
34 Boolan Logic
35 XOR Puzzl! Input A Input B XOR
36 XOR Solution! Us mor than on nod!
37 Ky Points gl ith just a sin w d lv o s n t b roblms ca p m o S 1. r classifir. simpl lina g togthr to in rk o w s nod multipl s u n a c u o s. 2. Y s problm th f o y n a solv m
38 Brains in Natur
39 Brains in Natur brain 0.4 grams 11,000 nurons natur s brains can at, fly, navigat, fight, communicat, play, larn.. and thy r rsilint 302 nurons 37 billion nurons (humans 20 billion)
40 Brains in Natur
41 Brains in Natur logistic function y = 1 / (1 + -x)
42 Brains in Natur
43 Artificial Nuron
44 Artificial Nural Ntwork.. finally!
45 Paus....
46 Whr Dos Th Larning Happn? link wight? sigmoid function slop?
47 Ky Points things, and d t a c ti is h do sop ct brains can l ra and imprf tu a g a N m a d 1. to ly rsilint ar incrdib omputing. c l a n io it d a lik tr signals.. un d artly inspir p s in ra b l a logic to copy bio g in ry T. 2 tworks. n l a r u n l artificia it s aramtr p l b ta s ju ad ights ar th w k in L s. 3. ing happn rn a l th whr
48 Fding Signals Forward
49 Fding Signals Forward
50 Fding Signals Forward
51 Matrix Multiplication
52 Matrix Multiplication wights incoming signals W I = X dot product
53 Ky Points tions can b la u lc a c rd a no iplication, any fdforw lt m u m h T ix tr a. 1 as m concisly d s s r p x ntwork. th p a h s t mattr wha n do matrix a c s g a u g lan. rogramming p m nd quickly o a S y tl n 2. i ic n rally ff multiplicatio
54 Ntwork Error
55 Ntwork Error
56 Intrnal Error
57 Intrnal Error
58 Matrics Again!
59 Ky Points w guid how to r o r r th br w us m m k wights. R n li. r 1 t m dl s para rfin a mo is asy - th s d o n t u tp or at th ou nd actual a d ir s 2. Th rr d twn th diffrnc b outputs. obvious. A t n is s d o n l or at intrna portion to rr o r p h in T it t li. p 3 to s pproach is a c ti is r u h hts. th link wig b rror can th g n ti a g a back prop too! 4. and ultiplication m ix tr a m as a xprssd
60 Ys, But How Do W Actually Updat Th Wights? Aaarrrggghhh!!
61 Prfct is th Enmy of Good landscap is a complicatd difficult mathmatical function.. with all kinds of lumps, bumps, kinks
62 Gradint Dscnt smallr gradint.. you r closr to th bottom tak smallr stps?
63 Ky Points of finding th y a w l a c ti c a pra t dscnt is n i d a r G 1. nctions. fu lt u c fi if d f minimum o by rshooting v o f o c n ha shallowr. avoid th c ts n a g c t u n o i Y d ra 2. g r stps if th ll a m s g in tak tion ifficult func d a is rk o tw nt f a nural n o r o rr dint dsc ra g h b y a 3. T m ights so of th link w will hlp...
64 Climbing Down th Ntwork Error Landscap W nd to find this gradint
65 Error Gradint E = (dsird - actual)2 school lvl calculus (chain rul) de/dwij = - j. oj. (1 - oj). oi prvious nod A gntl intro to calculus
66 Updating th Wights mov wjk in th opposit dirction to th slop rmmbr that larning rat
67 DIY
68 Python Class and Functions Nural Ntwork Class Initialis Train Qury st siz, initial wights do th larning qury for answrs
69 Python has Cool Tools matrix maths numpy scipy matplotlib notbook
70 Function - Initialis # initialis th nural ntwork df init (slf, inputnods, hiddnnods, outputnods, larningrat): # st numbr of nods in ach input, hiddn, output layr slf.inods = inputnods slf.hnods = hiddnnods slf.onods = outputnods # link wight matrics, wih and who # wights insid th arrays ar w_i_j, whr link is from nod i to nod j in th nxt layr # w11 w21 # w12 w22 tc slf.wih = numpy.random.normal(0.0, pow(slf.hnods, -0.5), (slf.hnods, slf.inods)) slf.who = numpy.random.normal(0.0, pow(slf.onods, -0.5), (slf.onods, slf.hnods)) # larning rat slf.lr = larningrat # activation function is th sigmoid function slf.activation_function = lambda x: scipy.spcial.xpit(x) pass numpy.random.normal() random initial wights
71 Function - Qury combind wightd signals into hiddn layr thn sigmoid applid # qury th nural ntwork df qury(slf, inputs_list): # convrt inputs list to 2d array inputs = numpy.array(inputs_list, ndmin=2).t # calculat signals into hiddn layr hiddn_inputs = numpy.dot(slf.wih, inputs) # calculat th signals mrging from hiddn layr hiddn_outputs = slf.activation_function(hiddn_inputs) # calculat signals into final output layr final_inputs = numpy.dot(slf.who, hiddn_outputs) # calculat th signals mrging from final output layr final_outputs = slf.activation_function(final_inputs) rturn final_outputs numpy.dot() similar for output layr
72 Function - Train # train th nural ntwork df train(slf, inputs_list, targts_list): # convrt inputs list to 2d array inputs = numpy.array(inputs_list, ndmin=2).t targts = numpy.array(targts_list, ndmin=2).t sam fd forward as bfor # calculat signals into hiddn layr hiddn_inputs = numpy.dot(slf.wih, inputs) # calculat th signals mrging from hiddn layr hiddn_outputs = slf.activation_function(hiddn_inputs) # calculat signals into final output layr final_inputs = numpy.dot(slf.who, hiddn_outputs) # calculat th signals mrging from final output layr final_outputs = slf.activation_function(final_inputs) output layr rrors hiddn layr rrors # output layr rror is th (targt - actual) output_rrors = targts - final_outputs # hiddn layr rror is th output_rrors, split by wights, rcombind at hiddn nods hiddn_rrors = numpy.dot(slf.who.t, output_rrors) # updat th wights for th links btwn th hiddn and output layrs slf.who += slf.lr * numpy.dot((output_rrors * final_outputs * (1.0 - final_outputs)), numpy.transpos(hiddn_outputs)) # updat th wights for th links btwn th input and hiddn layrs slf.wih += slf.lr * numpy.dot((hiddn_rrors * hiddn_outputs * (1.0 - hiddn_outputs)), numpy.transpos(inputs)) pass updat wights
73 Handwriting
74 Handwrittn Numbrs Challng
75 MNIST Datasts MNIST datast: 60,000 training data xampls 10,000 tst data xampls
76 MNIST Datasts labl 784 pixls valus 28 by 28 pixl imag
77 Output Layr Valus
78 Exprimnts 96% is vry good! w v only usd simpl idas and cod random procsss do go wonky!
79 Mor Exprimnts 98% is amazing!
80 Thoughts
81 Pk Insid Th Mind Of a Nural Ntwork?
82 Pk Insid Th Mind Of a Nural Ntwork? this isn t don vry oftn
83 Thanks! liv dmo!
84 Finding Out Mor makyourownnuralntwork.blogspot.co.uk github.com/makyourownnuralntwork twittr.com/myonuralnt slids goo.gl/jksb62
85 Raspbrry Pi Zro It all works on a Raspbrry Pi Zro and it only costs 4 / $5!!
Calculus concepts derivatives
All rasonabl fforts hav bn mad to mak sur th nots ar accurat. Th author cannot b hld rsponsibl for any damags arising from th us of ths nots in any fashion. Calculus concpts drivativs Concpts involving
3-2-1 ANN Architecture
ARTIFICIAL NEURAL NETWORKS (ANNs) Profssor Tom Fomby Dpartmnt of Economics Soutrn Mtodist Univrsity Marc 008 Artificial Nural Ntworks (raftr ANNs) can b usd for itr prdiction or classification problms.
EECE 301 Signals & Systems Prof. Mark Fowler
EECE 301 Signals & Systms Prof. Mark Fowlr ot St #21 D-T Signals: Rlation btwn DFT, DTFT, & CTFT 1/16 W can us th DFT to implmnt numrical FT procssing This nabls us to numrically analyz a signal to find
Partial Derivatives: Suppose that z = f(x, y) is a function of two variables.
Chaptr Functions o Two Variabls Applid Calculus 61 Sction : Calculus o Functions o Two Variabls Now that ou hav som amiliarit with unctions o two variabls it s tim to start appling calculus to hlp us solv
Computing and Communications -- Network Coding
89 90 98 00 Computing and Communications -- Ntwork Coding Dr. Zhiyong Chn Institut of Wirlss Communications Tchnology Shanghai Jiao Tong Univrsity China Lctur 5- Nov. 05 0 Classical Information Thory Sourc
EEO 401 Digital Signal Processing Prof. Mark Fowler
EEO 401 Digital Signal Procssing Prof. Mark Fowlr Dtails of th ot St #19 Rading Assignmnt: Sct. 7.1.2, 7.1.3, & 7.2 of Proakis & Manolakis Dfinition of th So Givn signal data points x[n] for n = 0,, -1
Higher order derivatives
Robrto s Nots on Diffrntial Calculus Chaptr 4: Basic diffrntiation ruls Sction 7 Highr ordr drivativs What you nd to know alrady: Basic diffrntiation ruls. What you can larn hr: How to rpat th procss of
Unit 6: Solving Exponential Equations and More
Habrman MTH 111 Sction II: Eonntial and Logarithmic Functions Unit 6: Solving Eonntial Equations and Mor EXAMPLE: Solv th quation 10 100 for. Obtain an act solution. This quation is so asy to solv that
Learning Spherical Convolution for Fast Features from 360 Imagery
Larning Sphrical Convolution for Fast Faturs from 36 Imagry Anonymous Author(s) 3 4 5 6 7 8 9 3 4 5 6 7 8 9 3 4 5 6 7 8 9 3 3 3 33 34 35 In this fil w provid additional dtails to supplmnt th main papr
Multilayer neural networks
Topic 3 Artificial nural ntwors: Suprvisd larning Multi nural ntwors Acclratd larning in multi nural ntwors Multi nural ntwors A multi prcptron is a fdforward nural ntwor with on or mor hiddn s. Th ntwor
Section 11.6: Directional Derivatives and the Gradient Vector
Sction.6: Dirctional Drivativs and th Gradint Vctor Practic HW rom Stwart Ttbook not to hand in p. 778 # -4 p. 799 # 4-5 7 9 9 35 37 odd Th Dirctional Drivativ Rcall that a b Slop o th tangnt lin to th
Strongly Connected Components
Strongly Connctd Componnts Lt G = (V, E) b a dirctd graph Writ if thr is a path from to in G Writ if and is an quivalnc rlation: implis and implis s quivalnc classs ar calld th strongly connctd componnts
Searching Linked Lists. Perfect Skip List. Building a Skip List. Skip List Analysis (1) Assume the list is sorted, but is stored in a linked list.
3 3 4 8 6 3 3 4 8 6 3 3 4 8 6 () (d) 3 Sarching Linkd Lists Sarching Linkd Lists Sarching Linkd Lists ssum th list is sortd, but is stord in a linkd list. an w us binary sarch? omparisons? Work? What if
2008 AP Calculus BC Multiple Choice Exam
008 AP Multipl Choic Eam Nam 008 AP Calculus BC Multipl Choic Eam Sction No Calculator Activ AP Calculus 008 BC Multipl Choic. At tim t 0, a particl moving in th -plan is th acclration vctor of th particl
Mor Tutorial at www.dumblittldoctor.com Work th problms without a calculator, but us a calculator to chck rsults. And try diffrntiating your answrs in part III as a usful chck. I. Applications of Intgration
That is, we start with a general matrix: And end with a simpler matrix:
DIAGON ALIZATION OF THE STR ESS TEN SOR INTRO DUCTIO N By th us of Cauchy s thorm w ar abl to rduc th numbr of strss componnts in th strss tnsor to only nin valus. An additional simplification of th strss
Applied Statistics II - Categorical Data Analysis Data analysis using Genstat - Exercise 2 Logistic regression
Applid Statistics II - Catgorical Data Analysis Data analysis using Gnstat - Exrcis 2 Logistic rgrssion Analysis 2. Logistic rgrssion for a 2 x k tabl. Th tabl blow shows th numbr of aphids aliv and dad
SUMMER 17 EXAMINATION
(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr jct Cod: Important Instructions to aminrs: ) Th answrs should b amind by ky words and not as word-to-word as givn in th modl answr schm. ) Th modl answr
Middle East Technical University Department of Mechanical Engineering ME 413 Introduction to Finite Element Analysis
Middl East Tchnical Univrsity Dpartmnt of Mchanical Enginring ME 43 Introduction to Finit Elmnt Analysis Chaptr 3 Computr Implmntation of D FEM Ths nots ar prpard by Dr. Cünyt Srt http://www.m.mtu.du.tr/popl/cunyt
Davisson Germer experiment Announcements:
Davisson Grmr xprimnt Announcmnts: Homwork st 7 is du Wdnsday. Problm solving sssions M3-5, T3-5. Th 2 nd midtrm will b April 7 in MUEN E0046 at 7:30pm. BFFs: Davisson and Grmr. Today w will go ovr th
EEO 401 Digital Signal Processing Prof. Mark Fowler
EEO 401 Digital Signal Procssing Prof. Mark Fowlr ot St #18 Introduction to DFT (via th DTFT) Rading Assignmnt: Sct. 7.1 of Proakis & Manolakis 1/24 Discrt Fourir Transform (DFT) W v sn that th DTFT is
EXST Regression Techniques Page 1
EXST704 - Rgrssion Tchniqus Pag 1 Masurmnt rrors in X W hav assumd that all variation is in Y. Masurmnt rror in this variabl will not ffct th rsults, as long as thy ar uncorrlatd and unbiasd, sinc thy
u x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula
7. Intgration by Parts Each drivativ formula givs ris to a corrsponding intgral formula, as w v sn many tims. Th drivativ product rul yilds a vry usful intgration tchniqu calld intgration by parts. Starting
Data Assimilation 1. Alan O Neill National Centre for Earth Observation UK
Data Assimilation 1 Alan O Nill National Cntr for Earth Obsrvation UK Plan Motivation & basic idas Univariat (scalar) data assimilation Multivariat (vctor) data assimilation 3d-Variational Mthod (& optimal
Lecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields
Lctur 37 (Schrödingr Equation) Physics 6-01 Spring 018 Douglas Filds Rducd Mass OK, so th Bohr modl of th atom givs nrgy lvls: E n 1 k m n 4 But, this has on problm it was dvlopd assuming th acclration
Hydrogen Atom and One Electron Ions
Hydrogn Atom and On Elctron Ions Th Schrödingr quation for this two-body problm starts out th sam as th gnral two-body Schrödingr quation. First w sparat out th motion of th cntr of mass. Th intrnal potntial
Chapter 13 GMM for Linear Factor Models in Discount Factor form. GMM on the pricing errors gives a crosssectional
Chaptr 13 GMM for Linar Factor Modls in Discount Factor form GMM on th pricing rrors givs a crosssctional rgrssion h cas of xcss rturns Hors rac sting for charactristic sting for pricd factors: lambdas
priority queue ADT heaps 1
COMP 250 Lctur 23 priority quu ADT haps 1 Nov. 1/2, 2017 1 Priority Quu Li a quu, but now w hav a mor gnral dinition o which lmnt to rmov nxt, namly th on with highst priority..g. hospital mrgncy room
Math 34A. Final Review
Math A Final Rviw 1) Us th graph of y10 to find approimat valus: a) 50 0. b) y (0.65) solution for part a) first writ an quation: 50 0. now tak th logarithm of both sids: log() log(50 0. ) pand th right
A L A BA M A L A W R E V IE W
A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N
Propositional Logic. Combinatorial Problem Solving (CPS) Albert Oliveras Enric Rodríguez-Carbonell. May 17, 2018
Propositional Logic Combinatorial Problm Solving (CPS) Albrt Olivras Enric Rodríguz-Carbonll May 17, 2018 Ovrviw of th sssion Dfinition of Propositional Logic Gnral Concpts in Logic Rduction to SAT CNFs
The Matrix Exponential
Th Matrix Exponntial (with xrciss) by Dan Klain Vrsion 28928 Corrctions and commnts ar wlcom Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix () A A k I + A + k!
Single Neuron. Hung-yi Lee
Singl Nuron Hung-yi L Singl Nuron 2 w w 2 Activation function a N w N ias Larning to say ys/no Binary Classification Larning to say ys/no Sam filtring Is an -mail sam or not? Rcommndation systms rcommnd
Middle East Technical University Department of Mechanical Engineering ME 413 Introduction to Finite Element Analysis
Middl East Tchnical Univrsity Dpartmnt of Mchanical Enginring ME Introduction to Finit Elmnt Analysis Chaptr 5 Two-Dimnsional Formulation Ths nots ar prpard by Dr. Cünyt Srt http://www.m.mtu.du.tr/popl/cunyt
MCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17)
MCB37: Physical Biology of th Cll Spring 207 Homwork 6: Ligand binding and th MWC modl of allostry (Du 3/23/7) Hrnan G. Garcia March 2, 207 Simpl rprssion In class, w drivd a mathmatical modl of how simpl
First derivative analysis
Robrto s Nots on Dirntial Calculus Chaptr 8: Graphical analysis Sction First drivativ analysis What you nd to know alrady: How to us drivativs to idntiy th critical valus o a unction and its trm points
Addition of angular momentum
Addition of angular momntum April, 0 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat th
ECE602 Exam 1 April 5, You must show ALL of your work for full credit.
ECE62 Exam April 5, 27 Nam: Solution Scor: / This xam is closd-book. You must show ALL of your work for full crdit. Plas rad th qustions carfully. Plas chck your answrs carfully. Calculators may NOT b
Abstract Interpretation: concrete and abstract semantics
Abstract Intrprtation: concrt and abstract smantics Concrt smantics W considr a vry tiny languag that manags arithmtic oprations on intgrs valus. Th (concrt) smantics of th languags cab b dfind by th funzcion
Differentiation of Exponential Functions
Calculus Modul C Diffrntiation of Eponntial Functions Copyright This publication Th Northrn Albrta Institut of Tchnology 007. All Rights Rsrvd. LAST REVISED March, 009 Introduction to Diffrntiation of
Mathematics. Complex Number rectangular form. Quadratic equation. Quadratic equation. Complex number Functions: sinusoids. Differentiation Integration
Mathmatics Compl numbr Functions: sinusoids Sin function, cosin function Diffrntiation Intgration Quadratic quation Quadratic quations: a b c 0 Solution: b b 4ac a Eampl: 1 0 a= b=- c=1 4 1 1or 1 1 Quadratic
Basic Polyhedral theory
Basic Polyhdral thory Th st P = { A b} is calld a polyhdron. Lmma 1. Eithr th systm A = b, b 0, 0 has a solution or thr is a vctorπ such that π A 0, πb < 0 Thr cass, if solution in top row dos not ist
The pn junction: 2 Current vs Voltage (IV) characteristics
Th pn junction: Currnt vs Voltag (V) charactristics Considr a pn junction in quilibrium with no applid xtrnal voltag: o th V E F E F V p-typ Dpltion rgion n-typ Elctron movmnt across th junction: 1. n
September 23, Honors Chem Atomic structure.notebook. Atomic Structure
Atomic Structur Topics covrd Atomic structur Subatomic particls Atomic numbr Mass numbr Charg Cations Anions Isotops Avrag atomic mass Practic qustions atomic structur Sp 27 8:16 PM 1 Powr Standards/ Larning
Mathematics 1110H Calculus I: Limits, derivatives, and Integrals Trent University, Summer 2018 Solutions to the Actual Final Examination
Mathmatics H Calculus I: Limits, rivativs, an Intgrals Trnt Univrsity, Summr 8 Solutions to th Actual Final Eamination Tim-spac: 9:-: in FPHL 7. Brought to you by Stfan B lan k. Instructions: Do parts
Alpha and beta decay equation practice
Alpha and bta dcay quation practic Introduction Alpha and bta particls may b rprsntd in quations in svral diffrnt ways. Diffrnt xam boards hav thir own prfrnc. For xampl: Alpha Bta α β alpha bta Dspit
1997 AP Calculus AB: Section I, Part A
997 AP Calculus AB: Sction I, Part A 50 Minuts No Calculator Not: Unlss othrwis spcifid, th domain of a function f is assumd to b th st of all ral numbrs for which f () is a ral numbr.. (4 6 ) d= 4 6 6
SCIENCE Student Book. 3rd Grade Unit 2
SCIENCE Studnt Book 3rd Grad Unit 2 Unit 2 PLANTS SCIENCE 302 PLANTS Introduction 3 1. Plant Parts...4 Roots 6 Stms 8 Lavs 10 Food Storag Parts 11 Slf Tst 1 15 2. Plant Growth... 17 Watr and Minrals 18
6.1 Integration by Parts and Present Value. Copyright Cengage Learning. All rights reserved.
6.1 Intgration by Parts and Prsnt Valu Copyright Cngag Larning. All rights rsrvd. Warm-Up: Find f () 1. F() = ln(+1). F() = 3 3. F() =. F() = ln ( 1) 5. F() = 6. F() = - Objctivs, Day #1 Studnts will b
1 Minimum Cut Problem
CS 6 Lctur 6 Min Cut and argr s Algorithm Scribs: Png Hui How (05), Virginia Dat: May 4, 06 Minimum Cut Problm Today, w introduc th minimum cut problm. This problm has many motivations, on of which coms
1973 AP Calculus AB: Section I
97 AP Calculus AB: Sction I 9 Minuts No Calculator Not: In this amination, ln dnots th natural logarithm of (that is, logarithm to th bas ).. ( ) d= + C 6 + C + C + C + C. If f ( ) = + + + and ( ), g=
Sara Godoy del Olmo Calculation of contaminated soil volumes : Geostatistics applied to a hydrocarbons spill Lac Megantic Case
wwwnvisol-canadaca Sara Godoy dl Olmo Calculation of contaminatd soil volums : Gostatistics applid to a hydrocarbons spill Lac Mgantic Cas Gostatistics: study of a PH contamination CONTEXT OF THE STUDY
Dealing with quantitative data and problem solving life is a story problem! Attacking Quantitative Problems
Daling with quantitati data and problm soling lif is a story problm! A larg portion of scinc inols quantitati data that has both alu and units. Units can sa your butt! Nd handl on mtric prfixs Dimnsional
Pipe flow friction, small vs. big pipes
Friction actor (t/0 t o pip) Friction small vs larg pips J. Chaurtt May 016 It is an intrsting act that riction is highr in small pips than largr pips or th sam vlocity o low and th sam lngth. Friction
The Matrix Exponential
Th Matrix Exponntial (with xrciss) by D. Klain Vrsion 207.0.05 Corrctions and commnts ar wlcom. Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix A A k I + A + k!
Solution of Assignment #2
olution of Assignmnt #2 Instructor: Alirza imchi Qustion #: For simplicity, assum that th distribution function of T is continuous. Th distribution function of R is: F R ( r = P( R r = P( log ( T r = P(log
UNTYPED LAMBDA CALCULUS (II)
1 UNTYPED LAMBDA CALCULUS (II) RECALL: CALL-BY-VALUE O.S. Basic rul Sarch ruls: (\x.) v [v/x] 1 1 1 1 v v CALL-BY-VALUE EVALUATION EXAMPLE (\x. x x) (\y. y) x x [\y. y / x] = (\y. y) (\y. y) y [\y. y /
Calculus II (MAC )
Calculus II (MAC232-2) Tst 2 (25/6/25) Nam (PRINT): Plas show your work. An answr with no work rcivs no crdit. You may us th back of a pag if you nd mor spac for a problm. You may not us any calculators.
The van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012
Th van dr Waals intraction D. E. Sopr 2 Univrsity of Orgon 20 pril 202 Th van dr Waals intraction is discussd in Chaptr 5 of J. J. Sakurai, Modrn Quantum Mchanics. Hr I tak a look at it in a littl mor
u r du = ur+1 r + 1 du = ln u + C u sin u du = cos u + C cos u du = sin u + C sec u tan u du = sec u + C e u du = e u + C
Tchniqus of Intgration c Donald Kridr and Dwight Lahr In this sction w ar going to introduc th first approachs to valuating an indfinit intgral whos intgrand dos not hav an immdiat antidrivativ. W bgin
22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches.
Subjct Chmistry Papr No and Titl Modul No and Titl Modul Tag 8/ Physical Spctroscopy / Brakdown of th Born-Oppnhimr approximation. Slction ruls for rotational-vibrational transitions. P, R branchs. CHE_P8_M
Differential Equations
Prfac Hr ar m onlin nots for m diffrntial quations cours that I tach hr at Lamar Univrsit. Dspit th fact that ths ar m class nots, th should b accssibl to anon wanting to larn how to solv diffrntial quations
Gradebook & Midterm & Office Hours
Your commnts So what do w do whn on of th r's is 0 in th quation GmM(1/r-1/r)? Do w nd to driv all of ths potntial nrgy formulas? I don't undrstand springs This was th first lctur I actually larnd somthing
Quasi-Classical States of the Simple Harmonic Oscillator
Quasi-Classical Stats of th Simpl Harmonic Oscillator (Draft Vrsion) Introduction: Why Look for Eignstats of th Annihilation Oprator? Excpt for th ground stat, th corrspondnc btwn th quantum nrgy ignstats
1 Isoparametric Concept
UNIVERSITY OF CALIFORNIA BERKELEY Dpartmnt of Civil Enginring Spring 06 Structural Enginring, Mchanics and Matrials Profssor: S. Govindj Nots on D isoparamtric lmnts Isoparamtric Concpt Th isoparamtric
Math 120 Answers for Homework 14
Math 0 Answrs for Homwork. Substitutions u = du = d d = du a d = du = du = u du = u + C = u = arctany du = +y dy dy = + y du b arctany arctany dy = + y du = + y + y arctany du = u du = u + C = arctan y
3 2x. 3x 2. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Math B Intgration Rviw (Solutions) Do ths intgrals. Solutions ar postd at th wbsit blow. If you hav troubl with thm, sk hlp immdiatly! () 8 d () 5 d () d () sin d (5) d (6) cos d (7) d www.clas.ucsb.du/staff/vinc
Summer Reading Activities!
HOOT FLUSH SCAT CHOMP From Bstslling Author Summr Rading Activitis! Flush Word Find Can you find all 14 words in th puzzl blow? S W I M E N J L P H S P A R R D A Z A G A Z E I B H O T L V S C N U D H I
orbiting electron turns out to be wrong even though it Unfortunately, the classical visualization of the
Lctur 22-1 Byond Bohr Modl Unfortunatly, th classical visualization of th orbiting lctron turns out to b wrong vn though it still givs us a simpl way to think of th atom. Quantum Mchanics is ndd to truly
u 3 = u 3 (x 1, x 2, x 3 )
Lctur 23: Curvilinar Coordinats (RHB 8.0 It is oftn convnint to work with variabls othr than th Cartsian coordinats x i ( = x, y, z. For xampl in Lctur 5 w mt sphrical polar and cylindrical polar coordinats.
(1) Then we could wave our hands over this and it would become:
MAT* K285 Spring 28 Anthony Bnoit 4/17/28 Wk 12: Laplac Tranform Rading: Kohlr & Johnon, Chaptr 5 to p. 35 HW: 5.1: 3, 7, 1*, 19 5.2: 1, 5*, 13*, 19, 45* 5.3: 1, 11*, 19 * Pla writ-up th problm natly and
Higher-Order Discrete Calculus Methods
Highr-Ordr Discrt Calculus Mthods J. Blair Prot V. Subramanian Ralistic Practical, Cost-ctiv, Physically Accurat Paralll, Moving Msh, Complx Gomtry, Slid 1 Contxt Discrt Calculus Mthods Finit Dirnc Mimtic
a g f 8 e 11 Also: Minimum degree, maximum degree, vertex of degree d 1 adjacent to vertex of degree d 2,...
Warmup: Lt b 2 c 3 d 1 12 6 4 5 10 9 7 a 8 11 (i) Vriy tat G is connctd by ivin an xampl o a walk rom vrtx a to ac o t vrtics b. (ii) Wat is t sortst pat rom a to c? to? (iii) Wat is t lonst pat rom a
Solution: APPM 1360 Final (150 pts) Spring (60 pts total) The following parts are not related, justify your answers:
APPM 6 Final 5 pts) Spring 4. 6 pts total) Th following parts ar not rlatd, justify your answrs: a) Considr th curv rprsntd by th paramtric quations, t and y t + for t. i) 6 pts) Writ down th corrsponding
A. Limits and Horizontal Asymptotes ( ) f x f x. f x. x "±# ( ).
A. Limits and Horizontal Asymptots What you ar finding: You can b askd to find lim x "a H.A.) problm is asking you find lim x "# and lim x "$#. or lim x "±#. Typically, a horizontal asymptot algbraically,
Davisson Germer experiment
Announcmnts: Davisson Grmr xprimnt Homwork st 5 is today. Homwork st 6 will b postd latr today. Mad a good guss about th Nobl Priz for 2013 Clinton Davisson and Lstr Grmr. Davisson won Nobl Priz in 1937.
Multiple Short Term Infusion Homework # 5 PHA 5127
Multipl Short rm Infusion Homwork # 5 PHA 527 A rug is aministr as a short trm infusion. h avrag pharmacokintic paramtrs for this rug ar: k 0.40 hr - V 28 L his rug follows a on-compartmnt boy mol. A 300
Slide 1. Slide 2. Slide 3 DIGITAL SIGNAL PROCESSING CLASSIFICATION OF SIGNALS
Slid DIGITAL SIGAL PROCESSIG UIT I DISCRETE TIME SIGALS AD SYSTEM Slid Rviw of discrt-tim signals & systms Signal:- A signal is dfind as any physical quantity that varis with tim, spac or any othr indpndnt
ECE 407 Computer Aided Design for Electronic Systems. Instructor: Maria K. Michael. Overview. CAD tools for multi-level logic synthesis:
407 Computr Aidd Dsign for Elctronic Systms Multi-lvl Logic Synthsis Instructor: Maria K. Michal 1 Ovrviw Major Synthsis Phass Logic Synthsis: 2-lvl Multi-lvl FSM CAD tools for multi-lvl logic synthsis:
COMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas (Monday, April 04, 2005, 8:35 AM) PART I: CHAPTER TWO COMB MATH.
C:\Dallas\0_Courss\03A_OpSci_67\0 Cgh_Book\0_athmaticalPrliminaris\0_0 Combath.doc of 8 COPUTER GENERATED HOLOGRAS Optical Scincs 67 W.J. Dallas (onday, April 04, 005, 8:35 A) PART I: CHAPTER TWO COB ATH
ph People Grade Level: basic Duration: minutes Setting: classroom or field site
ph Popl Adaptd from: Whr Ar th Frogs? in Projct WET: Curriculum & Activity Guid. Bozman: Th Watrcours and th Council for Environmntal Education, 1995. ph Grad Lvl: basic Duration: 10 15 minuts Stting:
Molecular Orbitals in Inorganic Chemistry
Outlin olcular Orbitals in Inorganic Chmistry Dr. P. Hunt p.hunt@imprial.ac.uk Rm 167 (Chmistry) http://www.ch.ic.ac.uk/hunt/ octahdral complxs forming th O diagram for Oh colour, slction ruls Δoct, spctrochmical
Junction Tree Algorithm 1. David Barber
Juntion Tr Algorithm 1 David Barbr Univrsity Collg London 1 Ths slids aompany th book Baysian Rasoning and Mahin Larning. Th book and dmos an b downloadd from www.s.ul.a.uk/staff/d.barbr/brml. Fdbak and
Roadmap. XML Indexing. DataGuide example. DataGuides. Strong DataGuides. Multiple DataGuides for same data. CPS Topics in Database Systems
Roadmap XML Indxing CPS 296.1 Topics in Databas Systms Indx fabric Coopr t al. A Fast Indx for Smistructurd Data. VLDB, 2001 DataGuid Goldman and Widom. DataGuids: Enabling Qury Formulation and Optimization
LR(0) Analysis. LR(0) Analysis
LR() Analysis LR() Conlicts: Introuction Whn constructing th LR() analysis tal scri in th prvious stps, it has not n possil to gt a trministic analysr, caus thr ar svral possil actions in th sam cll. I
Sec 2.3 Modeling with First Order Equations
Sc.3 Modling with First Ordr Equations Mathmatical modls charactriz physical systms, oftn using diffrntial quations. Modl Construction: Translating physical situation into mathmatical trms. Clarly stat
Answer Homework 5 PHA5127 Fall 1999 Jeff Stark
Answr omwork 5 PA527 Fall 999 Jff Stark A patint is bing tratd with Drug X in a clinical stting. Upon admiion, an IV bolus dos of 000mg was givn which yildd an initial concntration of 5.56 µg/ml. A fw
FEM FOR HEAT TRANSFER PROBLEMS دانشگاه صنعتي اصفهان- دانشكده مكانيك
FEM FOR HE RNSFER PROBLEMS 1 Fild problms Gnral orm o systm quations o D linar stady stat ild problms: For 1D problms: D D g Q y y (Hlmholtz quation) d D g Q d Fild problms Hat transr in D in h h ( D D
ECE 2210 / 00 Phasor Examples
EE 0 / 00 Phasor Exampls. Add th sinusoidal voltags v ( t ) 4.5. cos( t 30. and v ( t ) 3.. cos( t 5. v ( t) using phasor notation, draw a phasor diagram of th thr phasors, thn convrt back to tim domain
Where k is either given or determined from the data and c is an arbitrary constant.
Exponntial growth and dcay applications W wish to solv an quation that has a drivativ. dy ky k > dx This quation says that th rat of chang of th function is proportional to th function. Th solution is
CS 6353 Compiler Construction, Homework #1. 1. Write regular expressions for the following informally described languages:
CS 6353 Compilr Construction, Homwork #1 1. Writ rgular xprssions for th following informally dscribd languags: a. All strings of 0 s and 1 s with th substring 01*1. Answr: (0 1)*01*1(0 1)* b. All strings
Problem Set 6 Solutions
6.04/18.06J Mathmatics for Computr Scinc March 15, 005 Srini Dvadas and Eric Lhman Problm St 6 Solutions Du: Monday, March 8 at 9 PM in Room 3-044 Problm 1. Sammy th Shark is a financial srvic providr
[ ] 1+ lim G( s) 1+ s + s G s s G s Kacc SYSTEM PERFORMANCE. Since. Lecture 10: Steady-state Errors. Steady-state Errors. Then
![[ ] 1+ lim G( s) 1+ s + s G s s G s Kacc SYSTEM PERFORMANCE. Since. Lecture 10: Steady-state Errors. Steady-state Errors. Then](/thumbs/79/79716622.jpg "[ ] 1+ lim G( s) 1+ s + s G s s G s Kacc SYSTEM PERFORMANCE. Since. Lecture 10: Steady-state Errors. Steady-state Errors. Then")
SYSTEM PERFORMANCE Lctur 0: Stady-tat Error Stady-tat Error Lctur 0: Stady-tat Error Dr.alyana Vluvolu Stady-tat rror can b found by applying th final valu thorm and i givn by lim ( t) lim E ( ) t 0 providd
3 Noisy Channel model
3 Noisy Channl modl W obsrv a distortd mssag R (forign string f). W hav a modl on how th mssag is distortd (translation modl t(f )) and also a modl on which original mssags ar probabl (languag modl p()).
perm4 A cnt 0 for for if A i 1 A i cnt cnt 1 cnt i j. j k. k l. i k. j l. i l
h 4D, 4th Rank, Antisytric nsor and th 4D Equivalnt to th Cross Product or Mor Fun with nsors!!! Richard R Shiffan Digital Graphics Assoc 8 Dunkirk Av LA, Ca 95 rrs@isidu his docunt dscribs th four dinsional
What are those βs anyway? Understanding Design Matrix & Odds ratios
Ral paramtr stimat WILD 750 - Wildlif Population Analysis of 6 What ar thos βs anyway? Undrsting Dsign Matrix & Odds ratios Rfrncs Hosmr D.W.. Lmshow. 000. Applid logistic rgrssion. John Wily & ons Inc.
Fourier Transforms and the Wave Equation. Key Mathematics: More Fourier transform theory, especially as applied to solving the wave equation.
Lur 7 Fourir Transforms and th Wav Euation Ovrviw and Motivation: W first discuss a fw faturs of th Fourir transform (FT), and thn w solv th initial-valu problm for th wav uation using th Fourir transform
Search sequence databases 3 10/25/2016
Sarch squnc databass 3 10/25/2016 Etrm valu distribution Ø Suppos X is a random variabl with probability dnsity function p(, w sampl a larg numbr S of indpndnt valus of X from this distribution for an
First order differential equation Linear equation; Method of integrating factors
First orr iffrntial quation Linar quation; Mtho of intgrating factors Exampl 1: Rwrit th lft han si as th rivativ of th prouct of y an som function by prouct rul irctly. Solving th first orr iffrntial
Kernels. ffl A kernel K is a function of two objects, for example, two sentence/tree pairs (x1; y1) and (x2; y2)
Krnls krnl K is a function of two ojcts, for xampl, two sntnc/tr pairs (x1; y1) an (x2; y2) K((x1; y1); (x2; y2)) Intuition: K((x1; y1); (x2; y2)) is a masur of th similarity (x1; y1) twn (x2; y2) an ormally: