...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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...spills fails to report to the housekeeping about the health hazard that can be caused by the chemical (human error). The housekeeping who is assigned to clean the spill has A maintenance supervisor calls in a temporary worker from third-party recruiting company to handle housekeeping tasks for a day. The temporary worker is assigned the task of mopping the floors. The supervisor assigns him the list of rooms to be cleaned that also includes a research laboratory, where the staff work on chemical and biological agents (situational factor). The supervisor provides required instructions and provides a PPE, which is an overalls and a pair of gloves that is to be used while cleaning the laboratory. The worker follows the instruction and cleans the laboratory but doesn’t dispose off his overalls and gloves properly instead he keeps it back in the room where housekeeping things are stored (human error). Now, anyone that is going to wear it again is at a risk of exposure to biological and chemical agents that could pose a health risks (environmental...
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...------------------------------------------------- Species in the environment, r and K selection K and r selection: * r - the intrinsic rate of increase * K - the carrying capacity for the organism in that environment * r and K selection was an early attempt to identify life-history distinctions * r-selected species do well at low population density, and are at an advantage in frequently disturbed habitats * K-selected species do well at high population density and are at an advantage in constant or predictable habitats * Heuristically very useful as it allows use to predict the types of species likely to occur under different disturbance regimes R selection: * r-selected species have a rapid rate of population increase. * This is typical of species that colonise short-lived environments or of populations that undergo large fluctuations * Eg. Weeds, aphids, bacteria K selection: * K - selected species have superior competitive ability in stable environments where rapid population growth is unimportant as the population is maintained near K Ways to categorize/class species: * By biome or community type * By life history strategy * By life reproductive strategy * By basic approach to the environment What governs the distribution of species? * Evolutionary factors populations separated on to geographically distinct regions have different evolutionary trajectories * Dispersal constraints species may not have...
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...Nature Nurture D 1 http://s2.hubimg.com/u/3627189_f520.jpg(1 August 2011) Some scientists like George Howe Colt think that people behave as they do according to genetic predisposition this is known as the nature theory of human behaviour. Other scientists believe that people think and behave in certain ways because they are taught to do so, this is known as the nurture theory of human behaviour. For Nelson Mandela in his childhood stage he was able to build a house for himself, looking after cattle, playing different types of games. This allowed him to exercise helping him physically in his childhood stage, so I think you are not born strong but you train yourself to be strong which is nurture. From the earliest moments of life, the interaction of heredity and the environment works to shape who children are and who they will become. While the genetic instructions says that a child inherits from his parents which may set out a road map for development, the environment can impact how these directions are expressed, shaped or event silenced. The complex interaction of nature and nurture does not just occur at certain moments or at certain periods of time it is persistent and lifelong. Clearly, social and emotional development can begin as early as birth, but these developments tend to be primordial and limited until the child is no longer a toddler. This is the period when children begin to develop the abilities to interact with others. These interactions can range...
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...necessarily correct. The term sex is a biological term that refers to the physical differences between males and females. If sex is the term that encompasses male or female, then what exactly is gender? Gender is a psychological term that refers to the awareness and reaction to the biological term of sex. It also is a term that can construe more than one meaning. Gender is determined by biological, psychological, and sociological factors. Gender consists of three elements: gender role, gender identity, and sexual orientation or preference (Kenyon, 1994-2006). Gender role, is defined as the outward manifestations of personality that reflect the gender identity. Basically, it occurs when someone adopts the masculine or feminine behavioral traits that are associated with each sex. Gender role is manifested within society by observable factors such as behavior and appearance (Ghosh, 2009). Gender identity refers to a person’s personal sense of whether he or she are male or female (or rarely, both or neither). Gender identity, in nearly all instances, is self-identified, as a result of a combination of inherent and extrinsic or environmental factors (Ghosh, 2009). And sexual orientation or preference is whom a person is physically and sexually attracted to. In this paper the topics of discussion will be the interaction between hormones and behaviors in addition to how these interactions affect determining gender identity. It will also explore the biological factor, and how it influences gender...
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...Job evaluation is defined as a systematic process of determining the relative worth of jobs in relation to other job in order to establish which jobs should be paid more than others within an organization (Snell & Bohlander, 2010). The goal of job evaluation is to achieve internal equity during the salary system formation. In other word, job evaluation means the process of objectively determining the relative worth of jobs within an organization. It involves a systematic study and analysis of job duties and requirements. The evaluation is based on a number of compensable factors. Job evaluation can measure the value of all jobs within an organization and produces a rank order ranging from entry level positions to the most senior positions within an organization. It provides a framework to administer pay. The purpose of job evaluation is to helps established internal equity between various jobs in which wage paid is equal to the value of the job. When establishing the worth of a position, issues of internal equity are considered. Internal equity is defined as fairness in the relationship of a job’s salary range when compared with the salary ranges of similar jobs within the organization. The salary range for a job is considered internally equitable if the salary is commensurate with responsibility level of the position. It is important that a job evaluation is felt to be fair by everyone in the organisation. Effective communication, ongoing consultation and transparency are...
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...Data Classification Standard is a guideline of how a business or organization should handle as well as secure their different array of data. With this particular report it will describe the “Internal Use Only” data of an Investment firm. Internal use only should tell you that this is information that is seen by employees of a company and no one else. There are 3 domains that could be under this umbrella of internal use only these would be the User Domain, Workstation Domain and the LAN domain. First we have the User Domain which defines the employees that will access the company’s information systems. This particular domain is the weakest link in the domain infrastructure due the users on this system that don’t think about the vulnerabilities and threats which include lack of user awareness, apathy towards policies, policy violations, downloads of personal or files that could malicious. Each of these risks is presented on an everyday basis that could compromise a company’s internal data. Secondly, you have the workstation domain, which is the domain where most of the users connect to the organizations infrastructure. This domain should require very tight security as well as access rights. Meaning, each user on the domain should only have the right to access what they need to be able to do their job productively and no more. This will have an impact in lowering the chance of breach in security. Some threats with this domain include; Unauthorized access to workstations...
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...Biology essay – Relationships and interactions There are many different types of relationships and interactions between organisms. Every organism is in some way connected or associated with another. Some organisms need to depend on other organisms to survive which shows how important some of these relationships or interactions can be in biology. Interaction is a vital part of how many organisms develop over time. Predation is a main example of a relationship between organisms. Predation involves predators and prey, such as a fox catching and eating a rabbit. There are two other forms of predation called, parasitism and grazing. Parasitism is where the host organism is exploited and used for benefit by the other organism called a parasite. An example of parasitism is fleas which live on the skin of other animals and feed on their blood which helps the flea but only weakens the animal. Grazing is where the predator eats the prey but does not kill it, for example a cow eating grass. Predators play an important role in an ecosystem for if they did not exist then a single species could become dominant over others. Grazing is important as it helps to keep grassland from growing out of control. If predation in a certain ecosystem were to be effected then it would change the balance of the whole ecosystem. For example if wolves were removed from a forest ecosystem then there would be much more rabbits and deer around. This huge population of rabbits and deer would significantly decrease...
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...EBOLA VIRUS DISEASE AND NATIONAL SECURITY IN NIGERIA: AN APPRAISAL INTRODUCTION 1. Governments worldwide desire an epidemic free and healthy nation. The outbreak of the highly contagious Ebola Virus Disease (EVD) with fatality rate of up to 90 per cent could become an epidemic if not contained. It is a serious concern to governments since it threatens the health and Well-being of the Citizens (WC) and invariably the National Security (NS) of countries. 2. In the United States of America (USA), the infection of 2 missionaries with EVD while working in Liberia, prompted President Obama to stress that EVD is a threat to the NS of USA. The current EVD outbreak in West Africa has reached an epidemic level and has spread across Liberia, Sierra Leone and Guinea. By 25 Oct 14, World Health Organization (WHO) reported 10,141 cases. The fatalities have negative effect on human resource and businesses, restrict movement and cause general panic thereby affecting the NS of these countries. 3. In Nigeria, there were confirmed cases of EVD in Lagos and Rivers States. The Federal Government of Nigeria’s (FGN) efforts at isolating, treating and monitoring EVD cases led to its containment and thereby made WHO to declare Nigeria EVD free on 20 Oct 14. Despite these efforts, EVD could re-occur as seen in other countries and could threaten NS of Nigeria. The purpose of this paper therefore is to discuss EVD as it affects NS in Nigeria. The paper will cover conceptual...
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