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# COMP MODELING & SCI CSCI 1210

UGA

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This 10 page Class Notes was uploaded by Ulises Graham Jr. on Saturday September 12, 2015. The Class Notes belongs to CSCI 1210 at University of Georgia taught by Everett in Fall. Since its upload, it has received 79 views. For similar materials see /class/202310/csci-1210-university-of-georgia in ComputerScienence at University of Georgia.

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Date Created: 09/12/15

CSCI 1210 Final Exam Vocabulary Vocabulary Ward R eferen ce Abstraction The process of selectively removing details from a real world situation to produce a manageable model Mental model Mental models are thought patterns in our minds that represent things in the real world Conceptual model Conceptual models are made up of specific defined components and rules but these rules are qualitative they can not be expressed with numbers An example ofa conceptual model is the quotNonviolent communication sm quot process model proposed by Marshall Rosenbergi In nonviolent communication we attempt to resolve a conflict situation by going through four steps Formal model Formal models are completely and carefully defined in such a way that a computer can be used to build an implementation of the model In this course we are primarily interested in formal models because they are the ones that are computable and so are used in computational science Parameter A parameter is a setting for a model one that usually does not change during one simulation but can be changed to modify the conditions of the simulation variable A variable is a quantity that changes during a simulation There are two classes of variable independent variables must be provided as inputs to the model dependent variables are related by equations or algorithms in the model to get values which depend on hence the name the other variables and their relationships Dynamic model Many models such as the STELLA epidemic model described just above have time for their independent variable Such a model is called a dynamic model The dependent variables in the epidemic model are the number of susceptible individuals and the number of infected individuals Both ofthese numbers depend on the time Deterministic model A deterministic model is one without any random components Stochastic model A stochastic model is one that contains one or more variables with a random component Usually the random component is used to model the result of a problem that is too difficult or inconvenient to solve Valid model A model that accurately represents the real world phenomena being modeled Useful model A model that does not accurately represent the real world phenomena being modeled but provides helpful insights about the real world phenomena Analytic Solution A detailed prediction ofthe result ofa model that is made by purely mathematical techniques without recourse to computer simulation Falsifiable prediction The key point about scientific hypotheses is that like the hypotheses in Clue they must make falsifiable predictions Falsifiable means that there is a possible experiment whose result might prove the hypothesis wrong A central role of scientific models is in making falsifiable predictions about the results of experiments Independent variable A variable that does not depend on the value of other variables the input to a model Dependent variable A variable that depends on the value of other variables the output from a model Occam s razor The philosophical principle quotDo not multiply entities beyond necessityquot In other words we prefer the simplest model that explains the facts we see Regression A statistical technique for creating a linear model that predicts measured data as accurately as possible Unexplained variance The difference between the predicted data values from a regression model and the measured data values Weighted Average A weighted average is a linear model in which the weights add up to 100 Index Webster s defines an index as quota number derived from a series of observations and used as an indicator or measurequot ndices protect us from data overload by collapsing many data items down to a single number Elaboration Putting more variables into a model to make it more realistic Uniform probability distribution Because the probability of each result is the same we say that this experiment is governed by the uniform probability distribution The uniform distribution is an idealized model Normal probability distribution The most frequent statistical distribution is the Normal Gaussian Distribution In a normally distributed data set the probability that data is win 1 standard deviation of the mean is 683 the probability that data is win 3 standard deviations ofthe mean is 997 so only 003 of the data is farther from the mean than 3 standard deviations Mean The mean of the curve which is the X axis value at the central point Standard deviation The standard deviation of the curve which is a statistic that measures the spread ofthe values Sampling distribution The sampling distribution will still be a normal distribution However the standard deviation of the sampling distribution will be smaller Central Limit Theorem A key result of statistics is the Central Limit Theorem which says roughly that if you take samples of some variable the average values of these samples will tend to follow the normal distribution Since scientific experiments frequently involve samples experiments tend to use the normal distribution a lot Discrete model Consisting of distinct or unconnected elements noncontinuous taking on a finite number of values not mathematically continuous Stochastic model A model that includes variables with random values is called a stochastic model Deterministic model Models without random behavior are called deterministic Continuous model A model in which the variables can take on non integer values such as 2368 is called a continuous model Cellular automaton A model run on a discrete grid of spatial cells using a discrete time chronons is called a cellular automaton Each cell in the grid is a variable site meaning that it keeps the value of a variable or set of variables Game of Life I Cambridge mathematician John Conway invented this so called quotgame in 1970 It is designed to be a very simple quotartificial lifequot example not a model of biological life but an exploration of possible self reproducing computers Despite the simple rules it shows a wide variety of interesting patterns Percolation model Percolation serves as a model itself and also as a component of other discrete models In percolation cells ofa grid are occupied or not at random When a certain percentage the percolation threshold of the cells is occupied a percolation will appear where the percolation is a connected set of occupied cells that splits the cell field into two parts by connecting the top and bottom In the diagram at right1 there is no percolation yet but filling in the single cell inside the circle will create a percolation Phase transition Percolation models exhibit an interesting property called phase transition The gradual addition of occupied cells eventually creates a sudden change from no percolation to having a percolation Another example of a phase transition is water freezing As the temperature of water is lowered it becomes colder and colder liquid water but is still liquid Analytic solution The ballistic model is a mathematical model With the simplest set of assumptions we can get an analytic solution one that is mathematically exact Euler s method Leonhard Euler 1707 1783 invented computational methods they were called numeric methods back then to get answers to problems that were stated mathematically but that were too difficult to solve analytically As technology has advanced we have learned to solve some of the problems that were too difficult for Euler But difficult problems continue to arise so we now have more and more difficult problems than ever before So we are very interested in methods there are many Euler s is the simplest and very useful for dealing with difficult problems Computational error Differential equation Differential equations deal with change rates of change and related rates of change we are interested in studying the changes in reality The bad news from this is that differential equations are very difficult to solve requiring considerable mathematical capability Difference equation Difference equation is an approximation and will give an approximate answer with some error always in it But introduction ofthis error is worth it to us because the difference equation can be entered directly into a computational engine Astrology Uses the relationship between visible and astronomical phenomena to apply then to events in the human world Geocentric model Earth is found at the center ofthe universe Aristotle Ptolemy Epicycles Almagest Written by Ptolemy to describe his geocentric model of the universe used widely across the ancient world as a map of the cosmos Retrograde motion Mars confused many astronomers earth s orbit is faster than other planets so we overlap the orbit of other planets and the sky appears to switch or move in a backwards direction Epicycles Explains retrograde motion Assumes that motion is circular heavens are perfect earth is center of universe Heliocentric model Proposed by Aristarchus Contradicted Aristotle theory wasn t accepted Stellar parallex Copernicus Galileo Galilei Telescope was perfected by him not created by him Discovered Jupiter s moons Johannes Kepler Orbits move in ellipses not in circles Isaac Newton Laws of motion provide the mechanism to apply Keppler s law to objects with mass and more accurately calculate orbit Law of Universal Gravitation Newton Every point pass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses Also inversely proportions to the square of the distance between them Albert Einstein Emcquot2 Einstein s cross Picture with five dots dot in center is a distant galaxy and the four dots surrounding are a galaxy even further away light from the very distant galaxy has been bent around the distant galaxy in four ways Tungska event Siberia 1908 Airburst from a meteor or comet fragment breaking up in the air before impact Very large explosion thought to be tens of meters large Chixulub event What could have wiped out the dinos 65 million years ago large crater Torino scale Probability of impact Gravity tractor Deflects asteroids from killing us Deficit When the federal government spends more than it receives in taxes for that year Deficits are financed by government debt Federal budget deficit financed by sales of treasury bonds which must be repaid to domestic or foreign leaders Balance of payments deficit financed by foreign purchase of dollars which can be exchanged for US goods and property Debt The burden of a debt depends not simply on the amount of money owed but on the amount relative to income The collective burden of our national debt depends not on the dollar amount of that debt but on the size of the debt relative to the national economy Microeconomics Studies the individual firm or family Macroeconomics Studies the entire national or world economy Ideology A set of assumptions about people and how the world works how you make decisions value judgments liberalism vs conservatism not contained only to politics Liberalism Government intervention in society is necessary and desirable excessive inequality is unjust and exploitive Conservatism Intervention in the economy should be minimal inequality is natural and necessary Spin doctoring The practice of persuading citizens to interpret the numbers in a certain way Gross Domestic Product Per capita GDP GDP Population The total amount of goods and services produced by the economy the value of all the goods and services produced in the United States Nominal GDP GDP figure that has not been adjusted for inflation Real GDP The GDP without inflation or deflation a more accurate number number of workers x productivity if gdp growth is under 3 percent it cannot outgrow unemployment Recession GDP declines for three or more consecutive three month periods Supply function When prices increase more will be supplied When prices decrease less will be supplied Demand function When prices increase less will be purchased When prices decrease more will be purchased Stable equilibrium f supply exceeds demand the price will go down the item is overstocked and will go on sale If demand exceeds supply the price will go up the item is hard to get so you must pay premium price Speculative demand Positive feedback loop is which speculative buying pushes the price even higher which provokes even more speculative buying Economic bubble Also known as speculative bubble if product purchased by speculators continues to increase in price and purchases continue and a bubble is formed the bubble crashes when it is taken back to equilibrium Greater fool theory Continual assumption that someone will buy your speculative purchase at a higher price which is foolish because you don t know when the bubble will burst Gini coefficient The Lorenz curve displays the percent of national income earned by the lowest x This number will be always less than x How much less Gini coefficient John Maynard Keynes Developed Keynesian school of thought Miltion Friedman Monetarist is supply side economics Keynesian economics Believed that recessions and depressions are caused by lack of aggregate demand how much money people want to spend believes during recession government should create additional aggregate demand through government spending Supply side economics Idea that the government can stimulate supply directly by giving tax breaks and incentives to typically upper income individuals who have the money to invest Franklin Roosevelt Elected during great depression pioneer in implementing Keynesian economics Ronald Reagan Moved country away from Keynesian and towards supply side economics Productivity Output by worker value of goods and services that can be produced by a single worker Labor force participation rate number ofjobsworking age population Quantitative easing Banks stimulating the economy Stock A reservoir of some kind of stuff that changes over time Flow Arrows oftransition Connector The red lines Infection Invasion by a pathogen to cause disease Onset Transition from incubating to infected stage Recovery Transition from ill to immune transition from susceptible to incubating Herd immunity population starts to decline and the disease dies out and epidemic never takes place IPAT formula I environmental impact P population A affluence T technology Technology must go down because ofthe amount of pollution per dollar Ecological footprint Total land area that would be needed to support city country or other population unit T factor in IPAT Technology must go down in order to reduce pollution because of the amount of pollution per dollar Paul Ehrlich Economist Julian Simon made a bet ecologist Paul Ehrlich that prices of nonrenewable sources would fall Erlich lost and had to pay Simon 1000 He also offer to bet Simon on each ofthe 15 ecological indicators are getting worse Thought of the IPAT formula Parson Malthus Exponential Growth Model Norman Borlaug father of green evolution won nobel prize in 1970 attained the highest wheat yield in history short stalks that didn t allow them to fall over stopped the food crisis he said that if the world population continues to increase at this rate we will destroy our species under attack from environmental and social critics his agricultural techniques were not the problem but the population growth that required them nightmare people would starve because we wouldn t have enough food but avoided this because the growth rate was not exponential and declined Cornucopians Continued progress of material items can be continued by advances in technology enough matter and energy on earth to provide for peek of population Julian Simon Hubbert Peak The oil rate follows a bell shaped curve Scenario run ofa model with certain parameters Demographic transition describes a specific pattern of changes in birth and death rates as civilization becomes more affluent death and birth rates become low and gives to a steady sustainable population four stages 1 High birth rate and high but fluctuating death rate 2 Declining death rates and continuing high birth rates 3 Declining birth and death rates 4 Low death rates and low but fluctuating birth rates Demographic momentum Human population notes and lecture Ozone Clorofluorocarbon Used as refrigerants Albedo Is the fraction of solar energy shorterwave radiation reflected from the Earth back into space It is a measure ofthe reflectivity ofthe earth s surface ce esp w snow on top of it has a high albedo most sunlight hitting the surface bounces back towards space Greenhouse gas Any of several gases present in the Earth s atmosphere including water vapor carbon dioxide and CFCs that contribute to the greenhouse effect Infrared light Radiation with a longer wavelength than visible light which is blocked by the Earth s atmosphere Also called longwave radiation Svente Arrhenius was the first scientist to investigate the possible effect of C02 in warming the atmosphere in 1896 His primitive calculations yielded predictions of global warming that are surprisingly similar to today s sophisticated computer models Roger Revelle the oceanographer Roger Revelle discovered that the fate of carbon in the ocean was far more complex As a by product ofthis research Revelle realized that COZdissolving in the surface layer ofthe ocean would also stay in the upper layer This meant that the surface layer would soon become saturated with C02 and no more could be absorbed into the ocean until the slow process of ocean mixing took effect Revelle reasoned that if the C02 could not dissolve in the oceans then it would build up in the atmosphere resulting in global warming At this point these predictions were purely speculative no one had yet attempted to measure the change in atmospheric C02 content from year to year Keeling curve Measurements of atmospheric C02 concentration made by Charles Keeling and his associates starting in 1957 and continuing Energy balance model The simplest possible model of global temperature considers the Earth as a featureless spherical blob that is heated by the rays of the sun Some ofthe incoming solar energy is reflected back out into space General Circulation model Intergovernmental Panel on Climate Change the Intergovernmental Panel on Climate Change Anthropogenic Global Warming Global warming caused by humans Climate sensitivity measure of how responsive the temperature of the climate system is to a change in the radiative forcing It is usually expressed as the temperature change associated with a doubling ofthe concentration of carbon dioxide in Earth s atmosphere quotStarley s Grand Challenge Existing climate models that assumed C02 levels were the cause of climate change models used were human emissions which give off C02 quotStarley s Smoking Gunquot James Lovelock British scientist who invented the electron capture detector Using a telescope he observed the atmospheres of earth venus and marshe found that venus and mars are in chemical equilibrium but earth is far from it Gaia hypothesis Gaia a collection of negative feedback loops which stabilize the earths physical environment to be favorable for life problem unconscious cooperation could not have evolved lovelock responded with daisyworld a computer simulation that showed organisms can unconsciously cooperate to regulate temp when world is cold black gets bigger and vice versa influential equilibrium and optimizing Forcing An input into a dynamic system from outside the system Anthropogenic carbon is a forcing for the natural carbon cycle quotHockey Stick curve The quothockey stick chart is considered to be a quotsmoking gun ie a piece of evidence so strong that it cannot be refuted The recent spike in global temperatures has no precedent in the last 1000 years The models predict this spike on the basis of anthropogenic global warming but no plausible explanation in terms of purely natural forces can explain it

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