...Stage II Maths Studies | Directed Investigation - CODES | | | | Suppose all letters are given a number from 1 to 26. E.g. a=1, b=2, c=3 etc then “put out the cat” becomes 16 21 20 15 21 20 20 8 5 3 1 20. If we use the following randomly chosen matrix A= 1483852321 ------------------------------------------------- as a multiplier for each of these then ‘put’ = B = 16 21 20 becomes 452 273 110 1. Verify this and ascertain the code for “out”, “the”, and “cat”. How can this message be coded by one matrix calculation? PUT = 16 21 20 x 1483852321 = 16 x 14+21 x 8+20 x 316 x 8+21 x 5+20 x 2(16 x 3+21 x 2+20 x 1) = 224+168+60 128+105+40 (48+42+20) ------------------------------------------------- = 452 273 110 OUT = 15 21 20 x 1483852321 = 15 x 14+21 x 8+20 x 315 x 8+21 x 5+20 x 2(15 x 3+21 x 2+20 x 1) = 210+168+60 120+105+40 (45+42+20) ------------------------------------------------- = 438 265 107 THE = 20 8 5 x 1483852321 = 20 x 14+8 x 8+5 x 320 x 8+8 x 5+5 x 2(20x 3+8 x 2+5 x 1) = 280+64+15 160+40+10 (60+16+5) ------------------------------------------------- = 359 210 81 CAT = 3 1 20 x 1483852321 = 3 x 14+1 x 8+20 x 33 x 8+1 x 5+20 x 2(3x 3+1 x 2+20 x 1) = 42+8+60 24+5+40 (9+2+20) = 110 69 31 This message can be coded by one matrix calculation by putting it vertically in a 3 x 4 matrix and then multiplying it by the randomly chosen matrix like so: C A T T H E O U ...
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...Environmental scan What is it? The environmental scan provides a systematic overview of the external factors that are important to the organisation (or sector) and indicates whether the organisation can influence them or not. In general the factors are classified in factors influencing the demand/need for services (and products), the supply of inputs to the project/organisation concerned, the competition and collaboration and general policy factors. The factors are also classified with respect to the positive (+) or negative (-) influence on the organisation and whether or not the factor can be influenced or just be appreciated (known and understood). What can you do with it? Making an environmental scan results in identifying the impact of relevant factors in the environment of an organisation or sector. Whereas people often complain as powerless victims about negative factors in their environment, the environmental scan helps you to take action or adapt yourself to your environment. Scanning promotes an active response to positive (opportunities) and compliant factors, and leads to insights how to live with the ‘hard facts’. While the scan is a simple tool, it nevertheless helps to get a comprehensive view of the chief factors, helping to go beyond reacting to scattered observations. Basic (sub-) questions • Which (negative) factors are most opportune to try to influence? • Which factors are most crucial to adapt your behaviour to? • What are opportunities...
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...2.9 Cholesky Decomposition 89 compared to N 2 for Levinson’s method. These methods are too complicated to include here. Papers by Bunch [6] and de Hoog [7] will give entry to the literature. CITED REFERENCES AND FURTHER READING: Golub, G.H., and Van Loan, C.F. 1989, Matrix Computations, 2nd ed. (Baltimore: Johns Hopkins University Press), Chapter 5 [also treats some other special forms]. Forsythe, G.E., and Moler, C.B. 1967, Computer Solution of Linear Algebraic Systems (Englewood Cliffs, NJ: Prentice-Hall), §19. [1] Westlake, J.R. 1968, A Handbook of Numerical Matrix Inversion and Solution of Linear Equations (New York: Wiley). [2] von Mises, R. 1964, Mathematical Theory of Probability and Statistics (New York: Academic Press), pp. 394ff. [3] Levinson, N., Appendix B of N. Wiener, 1949, Extrapolation, Interpolation and Smoothing of Stationary Time Series (New York: Wiley). [4] Robinson, E.A., and Treitel, S. 1980, Geophysical Signal Analysis (Englewood Cliffs, NJ: PrenticeHall), pp. 163ff. [5] Bunch, J.R. 1985, SIAM Journal on Scientific and Statistical Computing, vol. 6, pp. 349–364. [6] de Hoog, F. 1987, Linear Algebra and Its Applications, vol. 88/89, pp. 123–138. [7] Sample page from NUMERICAL RECIPES IN FORTRAN 77: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43064-X) Copyright (C) 1986-1992 by Cambridge University Press. Programs Copyright (C) 1986-1992 by Numerical Recipes Software. Permission is granted for internet users to make one paper copy for their own personal...
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...Department of Mathematical Sciences MATH103 Introduction to Linear Algebra Lecturer: Prof. Victor Goryunov Office: Room 519, Mathematical Sciences Building; email: goryunov@liv.ac.uk Lectures: Monday 1pm and 2pm in Lecture Theatre B, Central Teaching Hub (no. 221 on the Campus Map), Tuesday 13.00 in Lecture Theatre (room 101), Electrical Engineering Building (no. 235 on the map). Attendance at lectures is compulsory. (See the Student Charter.) Make sure you scan your card. Tutorials: Normally on Tuesday afternoon. The tutorials will be in groups of about 20. They form an integral part of the course and attendance is compulsory. They start in Week 1. Set work Work will be set by the lecturer weekly on Monday at the 2pm lecture. It will be already available on VITAL from the previous Friday. The set work consist of two very similar parts: • set C – for solving and detailed discussion at the coming Tuesday tutorial, and • set H – written solutions to which you should hand to your MATH103 tutor by 4 pm next Thursday. All the problems are to be studied before the Tuesday tutorial. Your submitted solutions are marked by your tutor and handed back the following Tuesday; the lecturer’s solutions are available online the same day. Web publications All module materials will be available on VITAL as soon as they are needed in the class. Hard copies of some houndouts will also be distributed, but only once. Closer to the end of the semester, past papers will be put on VITAL. Class Tests There...
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...Computer Project: QR Method for Calculating Eigenvalues Name _____________________________ Purpose: To see how eigenvalues can be calculated by iterative methods that employ QR factorization, and get some understanding of why such methods work. This type of algorithm is used in all professional software for general eigenvalue calculations today, such as MATLAB's eig function. Prerequisite: Sections 5.2 and 6.4 MATLAB functions used: qr, *, eye, :, tic, toc , for, eig qreigdat, qrbasic, qrshift and randint from Lay's Toolbox Part I. Background. It is not easy to calculate eigenvalues for most matrices. Characteristic polynomials are difficult to compute. Even if you know the characteristic polynomial, algorithms such as Newton's method for finding zeros cannot be depended upon to produce all the zeros with reasonable speed and accuracy. Fortunately, numerical analysts have found an entirely different way to calculate eigenvalues of a matrix A, using the fact that any matrix similar to A has the same eigenvalues. The idea is to create a sequence of matrices similar to A which converges to an upper triangular matrix; if this can be done then the diagonal entries of the limit matrix are the eigenvalues of A. The remarkable discoveries are that the method can be done with great accuracy, and it will converge for almost all matrices. In practice the limit matrix is just block upper triangular, not truly triangular (because only real arithmetic is done), but it is still easy to...
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...Matrix Calculations Using Calculators The calculators most commonly used by Foundation Studies students at UTAR are Casio fx-350MS, fx-570MS, and fx-570ES. Casio fx-350MS has no matrix function and cannot be used to perform matrix calculation. Both Casio fx-570MS and Casio fx-570ES have matrix mode. Casio fx-570ES can display fully a 3×3 matrix with all its 9 elements visible. Casio fx-570MS has only a 2-line display and can only show matrix elements one at a time. Hence the operations for matrix computation are different for these two series of calculators. The general procedures in matrix calculations are as follows: (1) Enter Matrix mode of the calculators. (2) Assign a variable to store the matrix. There are 3 variables available: MatA, MatB, and MatC. (3) Select the dimension or order (1×1 to 3×3) of the matrix. (4) Input the elements of the matrix; the data will be automatically saved in the matrix variable assigned. (5) Exit the matrix input or edit mode by pressing the coloured AC key. (6) Press SHIFT MATRIX or SHIFT MAT (Matrix function is at numeric key 4) to recall the stored matrix and perform matrix calculations as needed. (a) Casio fx-570ES (a) Entering a matrix. 1. 2. 3. 4. Press the MODE key. Select 6:Matrix mode. A display Matrix? will be shown to let us select one of the 3 possible matrix variables allowable. Let us choose 1:MatA by pressing 1. The next display permits us to select the order (m×n) of the matrix MatA. Let us choose 1: 3×3 by pressing 1. An...
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...Assignment 1 Yang Liu May 5, 2015 Assignment 1, Part 1 (1) Table 0.1: Estimate a logit using solver Product of probability Log likelihood Intercept Eduation coefficient Age coefficient 2.06641E-11 -24.60262143 -11.15550863 0.531907452 0.113507304 (2) M EE d = M E Ag e = βE d e X β (1 + e X β )2 β Ag e e X β (1 + e X β )2 = 1 N βE d (i ) e X βi Σ N 1 (1 + e X βi )2 = 1 N β Ag e(i ) e X βi Σ N 1 (1 + e X βi )2 1 Result: Table 0.2: Add caption Marginal Edu effect Marginal age effect 0.085732302 0.018294992 (3) Table 0.3: linear probability model Coefficients t Stat -1.541134276 0.097414096 0.020646694 Intercept EDUC AGE Std. Err. 0.429125046 0.025225082 0.005153578 -3.591340779 3.861794961 4.00628341 (4) H = −Σi p i (1 − p i )x i x i = X ΩX The diagonal of matrix Ω equal to p i (1 − p i ) The Hessian matrix 8.058949138 105.838015 300.4357025 H = 105.838015 1434.435526 3840.728111 300.4357025 3840.728111 12190.99391 (0.1) The variance-covariance matrix equals to the inverse of Hessian matrix Table 0.4: variance-covariance matrix Constant Constant Edu Age Edu Age 10.2699517 -0.511915922 -0.091816163 -0.511915922 0.029972725 0.003172894 -0.09182 0.003173 0.001345 2 (5) According to Student’s t distribution, under 49 freedom degree, the probabilities that these coefficients are 0s are less than 0.005. We can say these...
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...supporting evidence, the different ‘proximate’ and ‘fundamental’ determinants of poverty The World Bank states: “Poverty is hunger. Poverty is lack of shelter. Poverty is being ill and not being able to see a doctor. Poverty is not having the ability to go to school and not being able to read. Poverty is being in unemployment. Poverty is losing a child to illness brought about by unclean water. Poverty is powerlessness, lack of representation and freedom.” (World Bank, as cited in Lang 2007, p.31). More than three billion people live on less than $2.50 a day which is approximately half the world’s population. In 2005, the developing world had about 72 million children of primary school age not enrolled in school; of this 72 million, 57 percent of them were girls. Each year, 2.2 million children die because they lack immunisation (Globalissues.org, 2013). This essay will discuss the fundamental determinants of poverty with the two main contenders being geography and institution. It would also discuss the proximate determinants of poverty in Kenya. What causes poverty is an important question when trying to explain poverty, but it is not one which can easily be answered. These causes can be grouped into ‘proximate’, ‘intermediate’ and ‘fundamental’ causes of poverty. The proximate cause is the ‘nearest cause’ in the chain of causation, ABCDE. The fundamental cause is what sets the chain of causation in motion. The fundamental cause of E is A, and B, C and D are intermediate causes...
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...July 26, 2014 Epidemiology on Mononucleosis Mononucleosis is a viral disease caused by the Epstein-Barr virus (EBV), that affects people between the ages of ten and thirty-five, but anyone at any age can contract the disease. This disease is found mainly in adolescents. It is also known as “the kissing disease”, and it is indistinguishable from other members of the herpes virus group (123helpme, 2014). The most frequent mode of transmission is intimate salivary contact. It can also be transmitted from shared drinking and eating utensils, toothbrushes, etc. Mono is not likely to spread by sneezing or from hard surface contact. It is also known as Glandular Fever, because it affects the lymph nodes in the neck, arm pits and groin. It may last anywhere from one to eight weeks, and some people suffer from mononucleosis for months at a time. It is all dependent of one’s immune system. Recuperation is a slow process, which can demand twice as much sleep and resting periods. This disease can drain strength and energy and as well muscle loss. Balance is also affected. Usually exposure to this virus happens at late adolescence for half the population. The peak incidence for girls is 14-16 and boys 16-18. After initial contact with the virus, there is an incubation period of 4-6 weeks and then the symptoms start appearing. Symptoms include fever, sore throat and lymph adenopathy. Fevers may reach as high as 102 degrees Fahrenheit and may remain high for 3-4 weeks. Other symptoms...
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...Paragraph 1: Introduction (100 words) It is important to look at how and why researchers may link medical information with other non-medical information, for example, where people live, their income and their education. An understanding of how these factors affect an individual’s health can help us to look beyond the healthcare system for ways to improve the health of New Zealanders. These factors are called the social determinants of health. This essay will take a closer look at some of these social determinants and how they can influence people’s health and well-being. It will also discuss research articles that provide examples of influences of social determinants of health relating to adults. Paragraph 2: SDH approach. Your discussion...
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...Was fundamental analysis redundant in the period during the Global Financial Crisis (GFC)? 3/21/2014 ABC Was fundamental analysis redundant in the period during the Global Financial Crisis (GFC)? Fundamental analysis is the process of evaluating the value of any security and certificate by analyzing the real time factors, which are based on qualitative and quantitative factors. Economic and the social factors also effect while you are finding out the intrinsic value of any security or asset. Fundamental analysis when made for evaluating the value of security all the factors that can affect the security considered like macroeconomic factors, microeconomic factors and the company based factors. Not only have the external factors about the internal factors also affected the value of any asset (Bedford, 2008). You need to consider in fundamental analysis: * Market analysis * Company analysis * Industry analysis For an investor the fundamental analysis is very important to invest in any asset or security. The investor when found the intrinsic value of security with its current value than this make easy for them to invest or not. Global financial crises are the period, which is experienced by the society, and the marketers, a situation of great difficulty in the world where nothing is stable in any state of the world. The economic situation in the global crises become worst and the purchase power of the customer reduces, and this is a difficult time for the...
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...Technical analysis involves identifying crowd behavior in order to join the crowd and take advantage of its momentum and direction. This is called the bandwagon effect. Here’s how a bandwagon works: A fresh piece of news comes out, a majority of traders interpret it as favorable to a security, and buying overwhelms selling so that the price rises. You profit by going with the flow. Then when everyone is jumping off the bandwagon, you jump, too. As market participants get excited about a security, they become increasingly bullish and either buy for the first time or add to positions, a phase namedenamed accumulation. When traders become disillusioned about the prospect of their security price rising, they sell, in a phase named distribution. To buy 100 shares of a stock is to enter a position. To buy another 100 shares for a total of 200 is toadd to your position. If you have 500 shares and sell half, you would be reducing your position. To sell all the shares you own is to square your position. When you’re square (also called flat), you have no position in the security. All your money is in cash. You’re neutral. After traders have been accumulating the security on rising prices, eventually the price goes too far.Too far is a relative term and can be defined in any number of equally valid ways, but basically it means any price extreme that’s wildly abnormal, statistically speaking. When a price has reached or surpassed a normal limit, it’s at an extreme....
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...3/14/2014 1 RELATIVE VALUATION Introduction 2 The majority of equity research reports are based on multiples Most analysts use relative valuation because it is safer It is a short term strategy Forward multiples are better then historical ones because the price is related to expected cash flow Relative valuations usually means that you need to: 1. 2. 3. Come up with comparable companies Standardize by dividing by something common to all stocks Compare based on certain rules of thumbs related to each ratio that are commonly used in decision making 1 3/14/2014 The four Stages in Relative Valuation 3 1. 2. 3. 4. Multiples are easy to use and easy to misuse. There are four basic steps to using multiples wisely and for detecting misuse in the hands of others Define the multiple 1. Look at how it is computed (Consistency of numerator and denominator): Example P/E vs. P/EBITDA 2. Sometimes, the multiples with the same names can be computed differently(uniformity of definition) Describe the multiple : Look at the cross sectional distribution of the to know what is median multiple Analyze the multiple: embedded in each multiple there are key DCF factors that are driving the multiple (i.e. DCF assumptions that you are trying to run from) Conclude: Only after I follow the first three steps, I can reach a conclusion. P/E ratio - Define 4 Consistent , how much price you are willing...
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...Shiller mean by Behavioral Finance? Behavioral Finance is the collaboration between finance and other social sciences. This field of research is focused on determining the precise degree to which various market forces—including rational analysis of company-specific and macroeconomic fundamentals; human and social psychology; and cultural trends—influence investors’ expectations and determine their level of confidence or fear. Behaviorists believe that at times, the real determinants of stock market movements are the forces of human and cultural psychology, oranimal spirits (a term coined by economist John Maynar 2. How does Behavioral Finance contrast with Efficient Market Theory? Behavioral finance takes issue with two crucial implications of the EMH: (1) that the majority of investors make rational decisions based on available information; and (2) that the market price is always right. Behaviorists believe that numerous factors—irrational as well as rational—drive investor behavior. In sharp contrast to efficient markets theorists, behaviorists believe that investors frequently make irrational decisions and that the market price is not always a fair estimate of the underlying fundamental value. Still, many proponents of behavioral finance agree with at least one implication of the efficient market theory—that it’s not possible to reliably earn abnormal returns. 3. What prediction does Efficient Market Theory make about stock prices? Samuelson and Fama state that...
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...Chapter 7: Prospective Analysis: Valuation Theory and Concepts Copyright (c) 2008 Thomson South-Western, a part of the Thomson Corporation. Thomson, the Star logo, and South-Western are trademarks used herein under license. Chapter 7: Prospective Analysis: Valuation Theory and Concepts Palepu & Healy Key Concepts in Chapter 7 • Forecasts (Ch. 6) are converted into estimates of value. • Discounted future dividends, cash flows, and abnormal earnings may be used to estimate value. • Price-based multiples may also be used as value estimates. • No method by itself dominates any of the others. Copyright (c) 2008 Thomson South-Western, a part of the Thomson Corporation. Thomson, the Star logo, and South-Western are trademarks used herein under license. Chapter 7: Prospective Analysis: Valuation Theory and Concepts Palepu & Healy Discounted Dividends Valuation • The present value of future cash flows to shareholders is the basis of the discounted dividends method. • This method is the basis for most theoretical approaches to stock valuation, including the other methods discussed in this chapter. Where re is the cost of equity capital Copyright (c) 2008 Thomson South-Western, a part of the Thomson Corporation. Thomson, the Star logo, and South-Western are trademarks used herein under license. Chapter 7: Prospective Analysis: Valuation Theory and Concepts Palepu & Healy Discounted Abnormal Earnings • Abnormal earnings are...
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