text: The lease of Theme Park, Inc. Abstract: A new technique is described for electrochemical impedance spectroscopic (EIS) investigations in the plane of a polymer layer coating an electrode without crossing the interface polymer-electrolyte. If she uses the maximin criterion, how many new examiners will she decide to hire? A. The maximax criterion is much easier to do than the expected value. This mini land called "La place de Remy" is in the Walt Disney Studios park and includes a restaurant,a ride and a shop. maximin criterion: In decision theory, the pessimistic (conservative) decision making rule under conditions of uncertainty. Laplace (Bayes’) Criterion: The Laplace criterion of insufficient reason differs from the minimax regret criterion in that it involves the use of probabilities, that is, if we are uncertain as to which event will occur, we can assume (correctly or incorrectly) that all states (levels of demand) are equally likely and then assign the same probability to each of the events, i. • Laplace approximation fits the best Gaussian - Defined for both univariate and multivariate • Normalization term is useful as BIC criterion • AIC and BIC are simple but not accurate Machine Learning Srihari 25. Example 1st order sys. A decision problem, where a decision-maker is aware of various possible states of nature but has insufficient information to assign any probabilities of occurrence to them, is termed as decision-making under uncertainty. (or LaPlace) criterion, weights each state of nature equally, thus assuming that the states of nature are equally likely to occur. Inotherwords, fromthevectorﬁeldviewpoint, thetheoryofharmonicfunctions and Laplace’s equation is the same as the theory of conservative vector ﬁelds with zero divergence. b x a x 2 = b a x and c a x 2. Frequency Response Analysis & Design K. action and a particular state of nature. In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant over any plane that is perpendicular to a fixed direction in space. Oriolo) 07 Laplace transform - properties - application - response in the s-domain - transfer function - realizations - poles/zeros - poles vs eigenvalues. Kumar et al. 2-4 The Time-Integration Property 299 4. Instantly search and view photos of all homes for sale in 70068, LA now. Laplace Criterion of Rationality. Example 1: Solve using Laplace Transform Answer: First, apply the Laplace Transform Knowing that , and we get After easy algebraic manipulations we get , which implies Next, we need to use the inverse Laplace. Using the Laplace criterion, what would be the highest expected payoff? (Points : 3) $103. Given the information […]. Estimate profits under each of the two possible states of nature are as shown in the table below. A second way to study the operation of oscillators is to evaluate the characteristic equation: the roots of which are the circuit poles. must make a decision on its current capacity for next year. As described in Rue et al. For example, we might have a decision tree to help a financial institution decide whether a person should be offered a loan:. In decision theory, one of several possible prescriptions for making a decision under conditions of uncertainty; it prescribes the strategy which will Explanation of maximax criterion. Suitable cases are the Coulomb, oscillator and exponential potentials and the Yamaguchi separable non-local potential. Where do such functions and ﬁelds. The same formula is used for the NMSIMP technique, but is defined as the vertex with the lowest function value, and is defined as the vertex with the highest function value in the simplex. 1 Decision-Making Environments and Decision Criteria 19. This question, Cubic clustering criterion in R, has an answer that says to use NbClust to calculate, but that function Stack Exchange Network Stack Exchange network consists of 175 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The chance that the sample point estimate is the same. (2009), INLA can be used to estimate the posterior marginal distribution of Bayesian hierarchical models. University. Laplace's criterion can handle probability of each scenario occurrence under the supposition of insufficient data availability on the probabilities of the various outcomes; the probabilities of. Question Details. Custom formatting in Excel is extremely powerful and, well, much more useful than you might think. As the maximax choice doesn't consider risk at all it isn't usually an optimal choice. There are six locations, including:. There are many definitions of stability in the control system literature, the most common one used (for transfer functions) is the bounded-input-bounded-output stability (BIBO), which states that for a. tool is the Laplace transform. The largest payoff if you buy 20, 40, 60, and 80 bicycles are$550, 1270, 2050, and 2330 respectively. Different decision choices. We get Hence, we have. 4 Properties of Laplace Transforms 95 3. For a symmetric distribution of errors with kurtosis greater than 3, the estimates b M are more effective, i. If none of the possible consequences of decisions can be called more probable than others, i. The remainder is R( x) where x is some value dependent on x and c and includes the second- and higher-order terms of the original function. Question 1. Control Systems. In typical applications, t denotes time and ω denotes circular frequency. bg Abstract: Real decision makers partially disobey axioms of rationality and are called fuzzy. Question : ABC Inc. When the underlying probability distribution is unknown, then the. Maximax and maximin strategies Maximax. After solving the algebraic equation in frequency domain, the result then is finally transformed to time domain form to achieve the ultimate solution of the differential equation. The decision maker first calculates the average outcome for every alternative. This is used to determine if a. Laplace Transform The Laplace transform can be used to solve di erential equations. When instead the prior on ψ is elliptically Cauchy, a constant correction term must be added to the Schwarz criterion; the result then becomes a multidimensional generalization of Jeffreys's method. For these reasons alone you should take a closer look at the algorithm. If he uses the Laplace criterion, which kind of dwellings will he decide to build? single family Under the assumption of equally likely states of nature, this option's EMV is best. Come Meet Riverlands SPCA's Pets. (C) Both WAIC and WBIC are applicable even if the posterior distribution is far from any normal distribution. The Power Plot window (see Fig. A decision tree is a tree in which each branch node represents a choice between a number of alternatives, and each leaf node represents a classification or decision. The particular case of (homogeneous case) results in Laplace's equation: For example, the equation for steady, two-dimensional heat conduction is: where is a temperature that has reached steady state. In this paper the authors consider the problem of Laplace transform inversion in the case where the transform is given in a finite set of equidistant points. The Wiener criterion provides a necessary and sufficient condition on Ω to solve the Dirichlet problem of the Laplace equation (i. The Laplace criterion of insufficient reason differs from the minimax regret criterion in that it involves the use of probabilities, that is, if we are uncertain as to which event will occur, we can assume (correctly or incorrectly) that all states (levels of demand) are equally likely and then assign the same probability to each of the. This map shows the locations of air monitors in LaPlace. If he uses the Laplace criterion, which kind of dwellings will he decide to build? single family Under the assumption of equally likely states of nature, this option's EMV is best. either two or three. either medium or. if they are approximately equiprobable, then the solution can be adopted with the help of the Laplace criterion of the following form:. (or LaPlace) criterion, weights each state of nature equally, thus assuming that the states of nature are equally likely to occur. ) Creases, then it should result in a. For example, the top row represents the low demand market, which has a probability of 0. Question 2. ASSESSMENT 2: Decision-making in a business scenario Introduction Due to one American sporting apparel enterprise, which is assumed to be called the Wave Company, has entered its bottleneck of reaching the limits of growth, this report focus on that, as one CEO, how I will decide on the markets to expand to and ensure the success of this new. Be-sides being a di erent and e cient alternative to variation of parame-ters and undetermined coe cients, the Laplace method is particularly advantageous for input terms that are piecewise-de ned, periodic or im-pulsive. As you browse the options available in La Place, you will quickly discover there are 3 builders offering modular, manufactured, or mobile homes for sale in your area. , is about to expire. potential theory for the Laplace operator ∆, some properties of the Cho-quet capacity, then goes through some other characterizations of regular points and ends with the already mentioned Wiener's criterion. Binary problems, where the outcome can be either True or False are very common in data analysis, from an inference or classification point of view. When the underlying probability distribution is unknown, then the. Laplace's equation. The initial conditions for x. Unfortunately, given the diverse nature of Christianity and Judaism back then (things have not changed all that much), and the anonymity of the authors, it is impossible to determine what truly would be embarrassing or. The problem that we will solve is the calculation of voltages in a square region of spaceproblem that we will solve is the calculation of voltages in a square region of space. they have smaller variances than the estimates b from the classical LS method. Get started with Brilliant’s course library as a beginner, or dive right into the intermediate and advanced courses for professionals and lifelong learners. In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant over any plane that is perpendicular to a fixed direction in space. Perform Laplace and inverse Laplace transformation, and to use Laplace transforms to solve ordinary differential equations. Control systems, and control engineering techniques have become a pervasive part of modern technical society. Laplace's criterion can handle probability of each scenario occurrence under the supposition of insufficient data availability on the probabilities of the various outcomes; the probabilities of. Se trata de un criterio intermedio entre el criterio de Wald y el criterio maximax. " Source for meaning of Martin H. We get Hence, we have. of the system. min_criterion_value This parameter specifies the minimum value of the rules for the selected criterion. Our 1000+ Control Systems questions and answers focuses on all areas of Control Systems subject covering 100+ topics in Control Systems. Built with  All of our courses are crafted by award-winning teachers, researchers, and professionals from MIT. The Laplace criterion and the criterion of realism require more math. Regret is the difference between the payoff from the best decision and all other decision payoffs. For any position → in space and any time , the value of such a field can be written as (→,) = (→ ⋅ →,),where → is a unit-length vector, and (,) is a function that gives the field's value as from. The Maximax Criterion. John the… 3. unit step resp: resp1st. If you're behind a web filter, please make sure that the domains *. ) Solving lin. This calculator allows you to evaluate the properties of different statistical designs when planning an experiment (trial, test) utilizing a Null-Hypothesis Statistical Test to make inferences. RC Phase Shift Network. [5] Contour integration and Cauchy’s Theorem [Proofs of theorems in this section will not be examined in this course. However, note that. However, because of the x. Answer: TRUE. The Maximax criterion, or optimistic criterion is a technique used to make decisions under uncertainty. Laplace Transform The Laplace transform can be used to solve di erential equations. Keywords Laplace operator ·Delaunay triangulation ·Dirichlet energy · Simplicial surfaces ·Discrete differential geometry. Module Name Download Description Download Size; Week 1-Introduction to Signals and Systems, Signal Classification: Lecture 01: Principles of Signals and Systems- Introduction to Signals and Systems, Signal Classification – Continuous and Discrete Time Signals. We will start with finding tangent lines to polar curves. com: Burden of Dreams (The Criterion Collection): Klaus Kinski, Werner Herzog, Miguel Angel Fuentes, Father Mariano Gagnon, José Lewgoy, Evaristo Nunkuag Ikanan, Huerequeque Enrique Bohorquez, Jorge Vignati, Laplace Martins, Walter Saxer, David Pérez Espinosa, Paul Hittscher, Thomas Mauch, Elia De Rio Ene, Nelson De Rio Cenepa, Mick Jagger, Jason Robards, Carmen Correa, Les Blank. Range: real. Perform Laplace and inverse Laplace transformation, and to use Laplace transforms to solve ordinary differential equations. One of these methods is the Routh-Hurwitz criterion, which contains the necessary and sufficient conditions for the stability of the system. RC Phase Shift Network. Expected value d. Response of 1 st order system when the input is unit step - For Unit Step,. In a session I am going to present tomorrow on the beauties of my Standard Costing Variance calculation method, I am going to reveal to my delegates the following cell formatting rule: ;;; THAT is worth a fortune in…. Also called maximin. The Maximax Criterion. Suppose that {λ i} are the eigenvalues of the Laplace– Beltrami operator on an abstract Riemannian manifold Mof dimension n. The largest payoff if you buy 20, 40, 60, and 80 bicycles are $550, 1270, 2050, and 2330 respectively. The section on model selection techniques in my statistical learning glossary. A process is a spontaneous if and only if the entropy of the universe increases. It provides a formula for balancing pessimism and optimism in decision-making under uncertainty - that is, when future conditions are to some extent unknown. Oriolo) 07 Laplace transform - properties - application - response in the s-domain - transfer function - realizations - poles/zeros - poles vs eigenvalues. Typically, Chebyshev is useful when dealing with more complicated random variables, and in particular, when they are. Week 4: Introduction to stability, Routh Hurwitz stability criterion. Laplace criterion. Wald's Maximin criterion Hurwicz's criterion Maximax criterion Savage's minimax regret criterion Laplace's insufficient reason criterion. 1 Dynamical Systems For the purposes of this course, a system is an abstract object that accepts inputs and produces outputs in response. University. This selection will use the LaPlace method for the best estimate of the completion rate. We now need to discuss some calculus topics in terms of polar coordinates. This paper compares the theoretical prediction with matching. ) The payoff is the numerical value associated with an. Insufficient- Reason Criterion: Assuming equally likely probabilities for the 'occurrence of each possible state of nature. For any transformation that maps from Rn to Rn, we've done it implicitly, but it's been interesting for us to find the vectors that essentially just get scaled up by the transformations. A good elevator pitch should last no longer than a short elevator ride of 20 to 30 seconds, hence the name. S1 S2 S3 A$60 $145$120 B $75$125 $110 C$95 $85$130. Next Year's Demand Alternative Low High Expand $100$200 Subcontract $50$120 Do nothing $40$50 Using the information above, which alternative should be chosen based on the. The optional integer value specifies the number of successive iterations for which the criterion must be satisfied before the process can be terminated. Maximum Likelihood Estimator(s) I 0 b 0 same as in least squares case I 1 b 1 same as in least squares case I ˙ 2 ˙^2 = P i (Y i Y^ i)2 n I Note that ML estimator is biased as s2 is unbiased and s2 = MSE = n n 2 ^˙2. The alpha is a number between 0 and 1. Higher Order Derivatives. The four peoples work – Laplace, Wald, Hurwicz and Savage – that the Hurwicz Criterion has been based on was studied, corrected and used for over fifty years by many different people including John Milnor, G. Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and Eigen vectors. Complex exponentials. 2 Cost of Uncertainty 19. The total phase shift around a loop, as the signal proceeds from input through amplifier, feedback network back to input again, completing a loop, is precisely 0 ° or 360 °. Laplace? d. How we determine Roots and Poles of System. The essay is good, but over 15,000 words long — here's the condensed version for Bayesian newcomers like myself: Tests are not the event. Partial Fraction Expansion An important tool for inverting the z transform and converting among digital filter implementation structures is the partial fraction expansion (PFE). Stability of LTI systems - definitions - Routh stability criterion - Nonlinear systems stability (slides 1-10 and 14-15 and 41-45, slides done by Prof. The Bayesian information criterion (BIC) is a rough approximation to the marginal likelihood, based on the asymptotic behavior of the Laplace approximation as more data is observed. This leads to the system function G(s) for the system {this is the same system function used in the Nyquist criterion for stability. In a session I am going to present tomorrow on the beauties of my Standard Costing Variance calculation method, I am going to reveal to my delegates the following cell formatting rule: ;;; THAT is worth a fortune in…. Estimate profits under each of the two possible states of nature are as shown in the table below. It also determines the number of roots of a. The equally likely decision criterion finds that alternative with the highest average outcome. Entropy Criterion of Spontaneous Process. Multiply the probability of each event times the expected losses. As you see in the script, using the function "stop" I define the stopping criterion for the algebraic solver, with the help of the function "estimation", which can be defined as follows:. Answer: TRUE. Continuous cycling based PID controller tuning 9. This is a Criterion Dynamax 8" Schmidt Cassegrain Telescope made in the mid to late 70's. Stochastic modeling is a form of financial model that is used to help make investment decisions. The novel coronavirus that has infected thousands of people across the world may have mutated at least once — meaning there may be two different types of the virus causing illnesses, a new study conducted by Chinese scientists suggests. In this paper we consider the problem of Laplace transform inversion in the case where the transform is given in a set of equidistant points. I’d like to make a note of how the Bernoullis and the integer reciprocals are really two sides of the same coin and how both play a role in the Todd class criterion, and then note the relation to some important combinatorics, through a Lagrange inversion formula (LIF). Laplace transform of: Variable of function: Transform variable: Calculate: Computing Get this widget. Find the Laplace and inverse Laplace transforms of functions step-by-step. of the system. Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and Eigen vectors. John the… 3. To develop the student’s skills in applying Laplace transform to obtain transfer functions. Also, determine the best policy under uncertainty, using the Laplace rule, the Maximax rule, and the Hurwicz rule with α = 0. In this approach, the Black–Scholes equation is transformed via finite differences into a system of linear equations, where the form of the implicit operator is used to construct coarse grid projectors. Piccadilly Circus est au croisement de cinq grandes artères du West End : Piccadilly, Regent Street, Glasshouse Street, Shaftesbury Avenue et Coventry Street [1]. Throughout May, EPA celebrates 50 years of improving the nation’s air, starting with the launch of Asthma Awareness Month and Air Quality Awareness Week. Prediction of crack growth can be based on an energy balance. The L-transform F(s) is a complex function of the complex variable s = σ+iω. A criterion for the stability of periodic trajectories in a regular hexagon 57 Conclusion 77 References 79 Introduction In this article we discuss means for constructing and detecting periodic billiard trajectories in triangles, one of the main items being the study of periodic trajectories in obtuse triangles. Further information on Machine Learning can be found in the class web page lecture notes section. Laplace domain analysis (characteristic equation) b. Use our Laplace real estate filters or tour via video chat to find a home you'll love. Sales – Price Relationship Analysis. Assume that the masses involved are negligibly small and that all motions are restricted to be small; therefore, the system can be considered linear. Suppose that every time there is an opportunity for an event to happen, then it occurs with unknown probability $p$. Question : ABC Inc. 这堆先验加上 PPCA 的似然函数再跟一开始的 Bayesian model selection 搅在一起，经过合理近似（比如 Laplace 近似， 很大等等）后，最终会得到. It states that the decision maker should select the course of action whose worst (maximum) loss is better than the least (minimum) loss of all other courses of action possible in given circumstances. Feedback Control Systems (ECE 3550). Routh Stability Criterion Description: Mathematical trick to assess if a system is asymptotically stable without explicitly calculating roots Motivating Example: Design a PID controller for the following 4 8 9 6 2 1 ( ) 5 4 3 2 s s s s s G ol s Suppose some poles are unstable. What is it that we mean by literature? Popularly, and amongst the thoughtless, it is held to include everything that is printed in a book. Laplace Criterion with example [ 9:40 PM | 0 comments Advertisments Laplace use Maximum weighted average value of each decision alternative are measured and Maximum among them is selected Weighted Average = (780+900+ 1020)/3 =900. A transition can occur between the different states by an external disturbance. The Griﬃth criterion. 10 Nyquist Stability Criterion A feedback system is stable if and only if $$N=-P$$, i. Effective handling of a risk requires its assessment and its subsequent. com [email protected] Get started with Brilliant’s course library as a beginner, or dive right into the intermediate and advanced courses for professionals and lifelong learners. [Gene F Franklin; J David Powell; Abbas Emami-Naeini] -- Feedback Control of Dynamic Systems covers the material that every engineer, and most scientists and prospective managers, needs to know about feedback control-including concepts like stability,. The upper threshold RT (2) is also used to calculate SettlingMin and. Georgia Institute of Technology. That means, Nyquist plots are used to draw the complete frequency response of the open loop transfer function. The decision maker first calculates the average outcome for every alternative.   Motivated by the assertion that all physical systems exist in three space dimensions, and that representation in one or two space dimensions entails a large degree of approximations. d ( s) + k n ( s) = 0. As a typical reader, we have in mind a student familiar with the basic concepts of probability based on measure theory, at the level of the graduate texts of Billingsley [43] and Durrett [106], and who wants a broader perspective on the. either one or two E. The basic idea was to approximation an integral of the following form: I(t) = Z e−Nh(x)dx, (1). DC Motors) using transfer function 4. An allied problem is the study of steady-state (or dynamic) stability. Maximax, maximin and minimax regret. You choose the action that has the smallest maximum regret. Like all transforms, the Laplace transform changes one signal into another according to some fixed set of rules or equations. It contains a. They are related. Our out-patient facilities serve patients who are dependent on Heroin, OxyContin, and other Schedule II narcotics. Rv Parks in La Place on YP. The total phase shift around a loop, as the signal proceeds from input through amplifier, feedback network back to input again, completing a loop, is precisely 0 ° or 360 °. com [email protected] For any position x → {\displaystyle {\vec {x}}} in space and any time t {\displaystyle t} , the value of such a field can be written as. 2 Time-domain specifications 71 4. It states that the decision. Estimated profits (in $000s) based on next year's demand are shown in the table below. Y(s) = Laplace Transform of the unit impulse response => H(s) = Y(s)/X(s) = Y(s) Therefore: What is the transfer function of a system? Answer : It is the Laplace transform of the unit impulse response. The Ten Commandments are heuristics to help guide people through that moral maze, the ultimate simple rules. 8 Laplace Transforms Using CACSD Software 108. Laplace Transform Calculator. Laplace's equation. Risk implies a degree of uncertainty and an inability to fully control the outcomes or consequences of such an action. Also called maximin. 33 recommend M 3. In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant over any plane that is perpendicular to a fixed direction in space. 6 Laplace Transform Theorems 102 3. Join 100 million happy users! Sign Up free of charge:. The largest payoff if you buy 20, 40, 60, and 80 bicycles are$550, 1270, 2050, and 2330 respectively. The procedure to use this is to obtain the average payoff for each alternative and then choose the. Range: real; laplace_k This parameter specifies the parameter k which is used in the Laplace function calculation. These sites were selected to gauge levels of chloroprene in the outside air, using monitor siting criteria outlined in the Clean Air Act. ASSESSMENT 2: Decision-making in a business scenario Introduction Due to one American sporting apparel enterprise, which is assumed to be called the Wave Company, has entered its bottleneck of reaching the limits of growth, this report focus on that, as one CEO, how I will decide on the markets to expand to and ensure the success of this new. The equal likelihood ( or Laplace) criterion. Laplace Criterion: When investments involve uncertainty, decisions are to be based on probability of different payoff scenarios. The decision maker first calculates the average outcome for every alternative. The same formula is used for the NMSIMP technique, but is defined as the vertex with the lowest function value, and is defined as the vertex with the highest function value in the simplex. Problem 1: (Practice with Chebyshev and Cherno bounds) When using concentration bounds to analyze randomized algorithms, one often has to approach the problem in di erent ways depending on the speci c bound being used. As you browse the options available in La Place, you will quickly discover there are 3 builders offering modular, manufactured, or mobile homes for sale in your area. You can also use them to create interest in a project, idea, or product – or in yourself. A good elevator pitch should last no longer than a short elevator ride of 20 to 30 seconds, hence the name. In this paper we consider the problem of Laplace transform inversion in the case where the transform is given in a set of equidistant points. f (x , y) = - x 4 - y 4 + 4xy. Laplace criterion: • It is assumed that all states of nature will occur with equal probability •Probabilities of each state of nature is given by 1/( number of states of nature) •Steps involved: i. Making decision from payoff table by using maximax, maximin, Hurwicz, Laplace and EMV method. The larger becomes, the more the active constraints are recognized as being linearly dependent. Introduction: PID Controller Design. 10 on the Z-transform deal with the two domains separately, but often draw parallels between results in the two domains. Generalized posterior odds ratios are constructed from Laplace-type estimators which include parametric likelihood as a special case. We will start with finding tangent lines to polar curves. While LaPlace did most of his work in astronomy (one of his driving ambitions was to prove that the solar system wouldn’t fly apart), he also made fundamental discoveries in mathematics. Expected payoffs for each row. Section 3-7 : Tangents with Polar Coordinates. Hurwitz And Laplace In Business Decision Making. The relationship among the various decision variables must be directly proportional Le. In statistics, the Bayesian information criterion ( BIC) or Schwarz information criterion (also SIC, SBC, SBIC) is a criterion for model selection among a finite set of models; the model with the lowest BIC is preferred. Nyquist plots are commonly used to assess the stability of a system with feedback. if--6ne of the factor inputs (resources like material, labour, plant capacity etc. First let’s define a problem. 3) Laplace criterion: equal probabilities are assigned to the result of each strategy, from which the highest is chosen. The system given by Has a unique solution. Decision Open Not Open Drive-up window ($6,000)$20,000 Breakfast 4,000 8,000 Select the best decision, using the following decision criteria. 16, 2000: 7-9pm: Dow 641. (A) If you want to estimate the predictive loss, you had better use WAIC. Answer: TRUE. The Laplace criterion uses all the information by assigning equal probabilities to the possible pay offs for each acton and then selecting that alternative which corresponds to the maximum expected pay off. Problem 1: (Practice with Chebyshev and Cherno bounds) When using concentration bounds to analyze randomized algorithms, one often has to approach the problem in di erent ways depending on the speci c bound being used. Routh-Hurwitz criterion This is for LTI systems with a polynomial denominator (without sin, cos, exponential etc. It states that the decision. Laplace Correction for Newton's Formula. 2016-01-01. As described in Rue et al. 1 has the form of a Laplace transform, and extraction of F(T 2) via the inverse Laplace transform (ILT) is a classically ill-posed problem[2, 3]. Implicit Derivative. 4, and that there will be a high demand is 0. In the above transfer function, the power of 's' is the one in the denominator. 8)$Construct a large plant 200,000 -180,000 124,000 Construct a small plant 100,000 -20,000 76,000 Do nothing 0 0 0 Table 3. In statistics, the Bayesian information criterion (BIC) or Schwarz information criterion (also SIC, SBC, SBIC) is a criterion for model selection among a finite set of models; the model with the lowest BIC is preferred. Regret measures the difference between each action's payoff for a given state of nature and the best possible payoff for that state of nature. 15) A second table (an opportunity loss table) must be computed when applying the maximin decision. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null is one-half. com To create your new password, just click the link in the email we sent you. 7, what would be the highest. Anti-windup and bumpless transfer 10. Nyquist plots are the continuation of polar plots for finding the stability of the closed loop control systems by varying ω from −∞ to ∞. Spring 2017. Usually, to find the Laplace Transform of a function, one uses partial fraction decomposition (if needed) and then consults the table of Laplace Transforms. Introduction to Decision Analysis 19. Consider the following payoff table that represents the profits earned for each alternative (A, B, and C) under the states of nature S1, S2, and S3. , choices an individual would make, have to be encoded in a utility function, the utility function is passed through the formalism, and the output is the. The chance that the sample point estimate is the same. E E 380 | Linear Control Systems Final Exam Review Final Exam: 2:00-3:50pm, Friday, May 9, 2008, in REDC 101 Will be provided: A table of some common Laplace transform pairs as that appeared in the supplementary reading on a brief review of Laplace transform. The Savage regret criterion selects a plan which minimizes the opportunity cost of choosing a less profitable plan, viewed ex post. About Author Aamir Rana. You simply look at the best you could do under each action (the largest number in each column). Introduction to Decision Analysis 19. Prev Tutorial: Sobel Derivatives Next Tutorial: Canny Edge Detector Goal. Elle permet aux entreprises de consulter et répondre aux consultations émanant des services de l'Etat en administration centrale et en services déconcentrés, des établissements publics relevant de ceux-ci, ainsi que des chambres de commerce et d. One should spend 1 hour daily for 2-3 months to learn and assimilate Control Systems comprehensively. The section on model selection techniques in my statistical learning glossary. When the underlying probability distribution is unknown, then the. Regret measures the difference between each action’s payoff for a given state of nature and the best possible payoff for that state of nature. com To create your new password, just click the link in the email we sent you. Chapter 5-Solution Manual of Modern Control Engineering by Katsuhiko Ogata 4th edition. As a result, it is the first elementary model to use all of the available information in the payoff matrix. This would be the case with a factor (s2 + ω o 2). It states that the decision maker should select the course of action whose worst (maximum) loss is better than the least (minimum) loss of all other courses of action possible in given circumstances. ) It determines if all the roots of a polynomial lie in the open LHP (left half-plane), or equivalently, have negative real parts. Tenders Electronic Daily (TED) − the European public procurement journal. 6 Laplace Transform Theorems 102 3. How we determine Roots and Poles of System. I came across the book, ‘Computational Physics’, in the library here in the Dublin Institute of Technology in early 2012. check_circle Expert Answer. The particular case of (homogeneous case) results in Laplace's equation: For example, the equation for steady, two-dimensional heat conduction is: where is a temperature that has reached steady state. Infinite mixture models are good for constructing new distributions (such as the gamma-Poisson or the Laplace) out of more basic ones (such as binomial, normal, Poisson). , 2002 ; Venkatasubramaniam et al. The Hurwicz alpha is a criterion for decision making under complete uncertainty that represents a comprimise between the Maximin and Maximax criteria. It is the 'optimist's choice'. ) Creases, then it should result in a. The Laplace equation models the equilibrium state of a system under the supplied boundary conditions. Decision using Maximax, Maximin, Laplace and Minimax regret September 18, 2019 September 18, 2019 On-time Answers A small building contractor has recently experienced two successive years in which work opportunities exceeded the firm's capacity. We will start with finding tangent lines to polar curves. I'll tie it together further down, though. Point Estimates. The optional integer value specifies the number of successive iterations for which the criterion must be satisfied before the process can be terminated. Join 100 million happy users! Sign Up free of charge:. This leads to the system function G(s) for the system {this is the same system function used in the Nyquist criterion for stability. Keywords Laplace operator ·Delaunay triangulation ·Dirichlet energy · Simplicial surfaces ·Discrete differential geometry. 10 Nyquist Stability Criterion A feedback system is stable if and only if $$N=-P$$, i. Competitor Maximum Decision Open Not Open Maximum of the row. tool is the Laplace transform. Second Derivative. Frequency Response Analysis & Design K. 2 Transfer Functions 89 3. Our next criterion is a settling time less than 3 seconds, which corresponds to a = 4. As a result, it is the first elementary model to use all of the available information in the payoff matrix. University. , 2002 ; Venkatasubramaniam et al. In this tutorial you will learn how to: Use the OpenCV function Laplacian() to implement a discrete analog of the Laplacian operator. EPA at 50: Improving the Nation’s Air. The total phase shift around a loop, as the signal proceeds from input through amplifier, feedback network back to input again, completing a loop, is precisely 0 ° or 360 °. Finite diﬀerence method Principle: derivatives in the partial diﬀerential equation are approximated by linear combinations of function values at the grid points. So the vectors that have the form-- the transformation of my vector is just equal to some scaled-up version of a vector. They are: 1) Optimistic, 2) Pessimistic, 3) Criterion of realism (Hurwicz), 4) Equally likely (Laplace) and 5) Minimax regret). Jordan Scribe: Samitha Samaranayake 1 Laplace approximation review In the previous lecture we discussed the Laplace approximation as a general way to approach marginalization problems. In a 2014 piece for the Atlantic, Noah Berlatsky went so far as to argue that Baldwin was the “greatest film critic ever” and that his 1976 book-length essay The Devil Finds Work, a “critique of the racial politics of American (and. Estimated profits (in$000s) based on next year's demand are shown in the table below. transform, Laplace transform, Z-transform. Binary problems, where the outcome can be either True or False are very common in data analysis, from an inference or classification point of view. As you see in the script, using the function "stop" I define the stopping criterion for the algebraic solver, with the help of the function "estimation", which can be defined as follows:. Lecture 02: Laplace Transform This lecture introduces the Laplace transform and its properties. Identify key characteristics of first- and second-order systems, and use block diagrams to analyze linear system performance. Laplace transform is named in honour of the great French mathematician, Pierre Simon De Laplace (1749-1827). We compare several methods of estimating Bayes factors when it is possible to simulate observations from the posterior distributions, via Markov chain Monte Carlo or other techniques. 1 Frequency-domain specifications 70 4. The “quality factor” (also known as “damping. Strictly this is only valid for steady-state signals. 15 TRANSFER FUNCTIONS & STABILITY The reader is referred to Laplace Transforms in the section MATH FACTS for preliminary material on the Laplace transform. Cauchy’s theorem and Cauchy’s integral formula. Start studying OM Chapter 5s. 3 $120$125 $145. Consider the following payoff table that represents the profits earned for each alternative (A, B, and C) under the states of nature S1, S2, and S3. Laplace Transform Calculator. Laplace's equation. Laplace Transform The Laplace transform can be used to solve di erential equations. Required arguments: X: numpy array of shape (N, K, T) containing data observations from K data sets. Using the criterion of realism and an alpha value of 0. Control systems, and control engineering techniques have become a pervasive part of modern technical society. The Maximax criterion, or optimistic criterion is a technique used to make decisions under uncertainty. (WVUE) - A drive-thru COVID-19 testing site in LaPlace opens Monday and is available to all healthcare providers and first responders. Documentation on iva_laplace(). 3 Examples of Minimax Criterion posted by John Spacey, August 22, 2017. It was based on the fact that in the edge area, the pixel intensity shows a "jump" or a high variation of intensity. either two or three. However, transient stability analysis is generally concerned with the analysis of the effects of major disturbances, such as line faults. We have a test for spam, separate from the event of actually having a spam. Using the power & sample size calculator. Criterion of Realism (Hurwicz)Criterion of Realism (Hurwicz) A weighted average compromise between opti i ti d i i titimistic and pessimistic Select a coefficient of realism α Coefficient is between 0 and 1Coefficient is between 0 and 1 A value of 1 is 100% optimistic Compute the weighted averages for each alternative. In this manuscript, we develop a multilevel framework for the pricing of a European call option based on multiresolution techniques. See reviews, photos, directions, phone numbers and more for the best Campgrounds & Recreational Vehicle Parks in La Place, LA. edu is a platform for academics to share research papers. Question 1. We will name the min-max regret criterion the criterion of min-max risk or losses caused by uncertainty of information, because this criterion guarantees that maximum of losses from the uncertainty of information is as small. Laplace Transform Calculator. As the clearing of the faulty line is delayed, A 1 increases and so does δ 1 to find A 2 = A 1 till δ 1 =δ max as shown in Fig. Electrical Engineering Section 2: Electric Circuits Network graph, KCL, KVL, Node and Mesh analysis, Transient response of dc and ac networks, Sinusoidal steady‐state analysis, Resonance, Passive filters, Ideal current and voltage sources, The. Complex exponentials. Laplace's Criterion interpreted as an ergodic growth rate under multiplicative dynamics avoids the fundamental circularity of the behavioral interpretation. G o t a d i f f e r e n t a n s w e r? C h e c k i f i t ′ s c o r r e c t. Chapter 1 Introduction 1. Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and Minima, Multiple integrals, Fourier. 2 Some Properties of the Laplace Transform 293 4. 35µm, the impact of wire resistance, capacitance and inductance (aka parasitics) becomes significant Give rise to a whole set of signal integrity issues Challenge Large run time involved (trade-off for different levels of accuracy). These are “Five Commandments” of decision-making under uncertainty. When finding the transfer function, zero initial conditions must be assumed. (A, B, C) 2. The presence of uncertainty —lack of assurance of what is to come— gives rise to risk: the possibility of incurring a significant loss. This is possible because only signals having rational Laplace transforms are considered. CRITERIO DE HURWICZ. The names of groups that serve as authors (e. In this case we are going to assume that the equation is in the form $$r = f\left( \theta \right)$$. The Bayesian information criterion (BIC) is a rough approximation to the marginal likelihood, based on the asymptotic behavior of the Laplace approximation as more data is observed. The contractor must now make a decision on capacity for next year. 10 Nyquist Stability Criterion A feedback system is stable if and only if $$N=-P$$, i. The mini-max regret criterion in managerial economics bases business decisions on the maximum regret associated with each action. Can use maximum likelihood estimate of instead of the MAP. Sales – Price Relationship Analysis. Leonid "Leo" Hurwicz (Polish pronunciation: [lɛˈɔɲit ˈxurvitʂ]; August 21, 1917 - June 24, 2008) was a Polish-American economist and mathematician, known for his work in game theory and mechanism design. Lecture notes- (QTM) Decision Theory Laplace Criterion (equally likely decision criterion) This criterion is based on, what is known as the principle of insufficient reason. University. Nyquist Path or Nyquist Contour. Consider the following payoff table that represents the profits earned for each alternative (A, B, and C) under the states of nature S1, S2, and S3. Modeling of dynamic system(4 hours) Modeling of mechanical, electrical, hydraulic and mixed-domain systems (e. mixtures of normals (often with a hierarchical model on the means and the variances);. com [email protected] Estimate profits under each of the two possible states of nature are as shown in the table below. While LaPlace did most of his work in astronomy (one of his driving ambitions was to prove that the solar system wouldn’t fly apart), he also made fundamental discoveries in mathematics. 10 on the Z-transform deal with the two domains separately, but often draw parallels between results in the two domains. Louis Malle presents his entertaining snapshot of the comings and goings on one street corner in Paris. Show Instructions In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. Criterion of Realism (Hurwicz) Decision Rule: The Criterion of Realism decision rule is an attempt to make a tradeoff between complete risk indifference (as in the Maximax rule), and total risk aversion (as in the Maximin rule). Why Use Maximax? Maximax decision making is a strategy that appeals to risk takers and business owners who like an aggressive, shoot-the-moon approach. Can someone explain to me why this property is so special and apparently makes the Laplace Transform exist? Also, my teacher says that f(t) has to be of exponential order from [0,infinity] and other sources say that it at least has to be of exponential order from [T,infinity] where T>0. Expected payoffs for each row. This is a Criterion Dynamax 8" Schmidt Cassegrain Telescope made in the mid to late 70's. A maximax strategy is a strategy in game theory where a player, facing uncertainty, makes a decision that yields the 'best of the best' outcome. INTRODUCTION TO DIGITAL FILTERS WITH AUDIO APPLICATIONS. the Laplace transform, which literally transforms the original differ-ential equation into an elementary algebraic expression. Wald’s Maximin criterion Hurwicz’s criterion Maximax criterion Savage’s minimax regret criterion Laplace’s insufficient reason criterion. As a result of the. 3$120 $125$145. Facts on Transfer Functions * Independent of input, a property of the system structure and parameters. Super Lawyers is an exclusive list of top-rated attorneys in specific practice areas who were chosen after thorough evaluation of numerous criteria. If M is isometrically immersed in Rm, then the mean curvature satisﬁes khk2 ∞ ≥ nλ k+1. This method was developed in Los Alamos during World War II by Yon Neumann and was considered classified until its brief description in Cranck and Nic'flolson (1947) and in a publication in 1950 by Charney et at. MA 225-005. • Laplace approximation fits the best Gaussian - Defined for both univariate and multivariate • Normalization term is useful as BIC criterion • AIC and BIC are simple but not accurate Machine Learning Srihari 25. To study or analyze a control system, we have to carry out the Laplace transform of the different functions (function of time). Most importantly, the optimality criterion differs from those in the now more standard subjective probability framework by not presupposing a fixed list of states of nature. The basic idea was to approximation an integral of the following form: I(t) = Z e−Nh(x)dx, (1). Regret measures the difference between each action's payoff for a given state of nature and the best possible payoff for that state of nature. Also, determine the best policy under uncertainty, using the Laplace rule, the Maximax rule, and the Hurwicz rule with α = 0. Sales – Price Relationship Analysis. The Laplace Transformation (after the French mathematician Pierre Simon Marquis de Laplace) is a method for solving differential equations, and the corresponding initial and boundary value problems. Third Derivative. ·/ and covariate u so that f. Print € Pkg of 12, gel staining trays, with lids € Prix catalogue : €267,00 Loading. Question 1. The particular case of (homogeneous case) results in Laplace's equation: For example, the equation for steady, two-dimensional heat conduction is: where is a temperature that has reached steady state. (2009), INLA can be used to estimate the posterior marginal distribution of Bayesian hierarchical models. The Laplace transformation is an important part of control system engineering. Laplace approximation The prior EBIC* Effective sample size Simulation JSM: July-August 2007 - slide #10 EBIC: a proposed solution Based on a modiﬁed Laplace approximation to m(x)for good priors: The good priors can deal with growing p The Laplace approximation retains the constant cˇ in the expansion often good even for moderate n. 2016-01-01. The equally likely decision criterion finds that alternative with the higest average outcome. To understand a Nyquist plot we first need to learn about some of the terminologies. Law Office of Robert D. Case of real roots. Closed-loop frequency response-Constant gain and phase loci, Nichol's chart and their use in stability study of systems. Using the Laplace criterion, what would be the highest expected payoff? A) \$103. One important feature of the Laplace transform is that it can transform analytic problems to algebraic. It discusses the rule or Laplace Criterion and fundaments its use to build the Lorenz Curve, LC, from datasets. transform, Laplace transform, Z-transform. 5 mGy d −1 using the Akaike Information Criterion. It is based, in part, on the likelihood function and it is closely related to the Akaike information criterion (AIC). Routh Stability Criterion Description: Mathematical trick to assess if a system is asymptotically stable without explicitly calculating roots Motivating Example: Design a PID controller for the following 4 8 9 6 2 1 ( ) 5 4 3 2 s s s s s G ol s Suppose some poles are unstable. 78 KiB, 5283 downloads) Download PDF (1. Topic: DECISION MAKING UNDER UNCERTAINTY. He is admin of official website of Govt Emerson College Multan and its social media accounts. They propose a criterion, based on cross-validation, for the optimal choice of the first data point. Louis Malle presents his entertaining snapshot of the comings and goings on one street corner in Paris. (or LaPlace) criterion, weights each state of nature equally, thus assuming that the states of nature are equally likely to occur. (2009), INLA can be used to estimate the posterior marginal distribution of Bayesian hierarchical models. Scientific Work in General. Super Lawyers is an exclusive list of top-rated attorneys in specific practice areas who were chosen after thorough evaluation of numerous criteria. In this case,. Describe the decision-making environments of certainty and uncertainty. Let X^ denote the exact mode of h , i. Laplace criterion if none of the possible consequences of decisions can be called more probable than others, i. (C) Both WAIC and WBIC are applicable even if the posterior distribution is far from any normal distribution. CRITERIO DE HURWICZ. (A, B, C) 2. Complex exponentials. 1 The Laplace Transform 86 3. determine the best policy based on the most probable future criterion. But if you have the open-loop transfer function you should find the zeros of the 1+G (s)H (s) transfer function and if they are in the left half-plane, the closed-loop system is stable. For example, we might have a decision tree to help a financial institution decide whether a person should be offered a loan:. Can someone explain to me why this property is so special and apparently makes the Laplace Transform exist? Also, my teacher says that f(t) has to be of exponential order from [0,infinity] and other sources say that it at least has to be of exponential order from [T,infinity] where T>0. Question 2. Multiply each of the terms in this row. , choices an individual would make, have to be encoded in a utility function, the utility function is passed through the formalism, and the output is the. decision making criterion 66,823 views. For a process to be Spontaneous (ΔS universe > 0 or ΔS syst + ΔS surr > 0) At equilibrium state, ΔS = 0, Limitations of ΔS criterion and need for another term We cannot find entropy change of surroundings during. Routh Stability Criterion Description: Mathematical trick to assess if a system is asymptotically stable without explicitly calculating roots Motivating Example: Design a PID controller for the following 4 8 9 6 2 1 ( ) 5 4 3 2 s s s s s G ol s Suppose some poles are unstable. Motion of rigid bodies and kinematics of mechanisms 4. Laplace transforms and dynamic response; Root locus design, examples and extensions; Bode plotting techniques and examples; Nyquist stability criterion, formation and examples; Phase and gain margins; Note on Course Availability. Step 1 The problem that John Thompson identifies is whether to expand his product line by manufacturing and marketing a new product, backyard. Partial Fraction Expansion An important tool for inverting the z transform and converting among digital filter implementation structures is the partial fraction expansion (PFE). Usually, to find the Laplace Transform of a function, one uses partial fraction decomposition (if needed) and then consults the table of Laplace Transforms. In the latter, preferences, i. more Stress Concentration Notches Holes Shoulders Square Box Beam Right Angle Beam more Column Buckling Elastic Buckling Inelastic Buckling Critical Loads Eccentric Loading Buckling Calculator more Composite Lamina Mechanics Coord. Determine the critical points and locate any relative minima, maxima and saddle points of function f defined by. Wald’s Maximin criterion Hurwicz’s criterion Maximax criterion Savage’s minimax regret criterion Laplace’s insufficient reason criterion. Perform Laplace and inverse Laplace transformation, and to use Laplace transforms to solve ordinary differential equations. In this approach, the Black–Scholes equation is transformed via finite differences into a system of linear equations, where the form of the implicit operator is used to construct coarse grid projectors. 2-1 Time Shifting 293 4. Case of real roots. The right-hand integral is A[E x(x) + x Ex/ x]. ___ Introduces some of the important uses of the basic methods that are developed -- e. Francisville, LA Raising Cane's 10k Time Trial Baton Rouge , LA. Also, determine the best policy under uncertainty, using the Laplace rule, the Maximax rule, and the Hurwicz rule with α = 0. Argument-increment Based Stability Criterion for Neutral Time Delay Systems, Proceedings of the 16th Mediterranean Conference on Control and Automation, 25-27 June 2008, Ajaccio, France, ISBN 978-1-4244-2504-4, pp. See reviews, photos, directions, phone numbers and more for the best Campgrounds & Recreational Vehicle Parks in La Place, LA. Management must decide whether to renew the lease for another 10 years or to relocate near the site of a proposed motel. 1 Introduction • A generalization of the familiar bell shaped normal density to several dimensions plays a fundamental role in multivariate analysis • While real data are never exactly multivariate normal, the normal density is often a useful approximation to the “true” population distribution. One should spend 1 hour daily for 2-3 months to learn and assimilate Control Systems comprehensively. The procedure to use this is to obtain the average payoff for each alternative and then choose the. A criterion for the stability of periodic trajectories in a regular hexagon 57 Conclusion 77 References 79 Introduction In this article we discuss means for constructing and detecting periodic billiard trajectories in triangles, one of the main items being the study of periodic trajectories in obtuse triangles. To see how it works, let’s get started with a minimal example. He is best known for his study of the solar system and orbital deviation of the planets. 27, 2000: 7-9pm: U115: Exam 3: Feb. 1 chapter questions: determining the best payoff for each alternative and choosing the alternative with the "best of the best" is the approach called, maximax, maximin, laplace, minimax regret, expected monetary value. Regret is the difference between the payoff from the best decision and all other decision payoffs. Decision analysis is a rational approach to decision making for problems where uncertainty f igures as a prominent element. Laplace Transform Calculator. La place des émotions lors du soin. Frequency Response Analysis & Design K. Answer: TRUE. Meaning: "An object that seems useless now may be just what you need at some future time, so do not discard it. In statistics, the Bayesian information criterion (BIC) or Schwarz information criterion (also SIC, SBC, SBIC) is a criterion for model selection among a finite set of models; the model with the lowest BIC is preferred. This is used to determine if a. The L-transform F(s) is a complex function of the complex variable s = σ+iω. 3 Parameterization of all stabilizing controllers 70 4. The particular case of (homogeneous case) results in Laplace's equation: For example, the equation for steady, two-dimensional heat conduction is: where is a temperature that has reached steady state. This calculator contains various models for decision-making as informed by the Decision Theory's Certainty, Uncertainty and Risk criteria. What does the performance speci cation for a rst order system tell us? How fast the system responds. As described in Rue et al. 2 The Nyquist criterion and Bode plots 63 4. An optimistic or maximax, approach to decision making under uncertainty would be choosing the best or maximum payoff for each alternative and then the. La place des émotions lors du soin. Complex exponentials. It provides a formula for balancing pessimism and optimism in decision-making under uncertainty - that is, when future conditions are to some extent unknown. David Corrigan Electronic and Electrical Engineering [email protected] Tenders Electronic Daily (TED) − the European public procurement journal. Laplace criterionの意味や使い方 ラプラス基準 - 約1153万語ある英和辞典・和英辞典。発音・イディオムも分かる英語辞書。. Nova Southeastern University. Caroline Ward (1842). Response of 1 st order system when the input is unit step - For Unit Step,. Piccadilly Circus est au croisement de cinq grandes artères du West End : Piccadilly, Regent Street, Glasshouse Street, Shaftesbury Avenue et Coventry Street [1]. In statistics, the Bayesian information criterion (BIC) or Schwarz information criterion (also SIC, SBC, SBIC) is a criterion for model selection among a finite set of models; the model with the lowest BIC is preferred. If he uses the Laplace criterion, which kind of dwellings will he decide to build? single family Under the assumption of equally likely states of nature, this option's EMV is best. The Laplace transformation is an important part of control system engineering. 3) Laplace criterion: equal probabilities are assigned to the result of each strategy, from which the highest is chosen. Why Use Maximax? Maximax decision making is a strategy that appeals to risk takers and business owners who like an aggressive, shoot-the-moon approach. Tenders Electronic Daily (TED) − the European public procurement journal. Laplace criterion is based on the principle of insufficient reason. REEF3D is free software; you can distribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. Each of the alternative de. University. As a result, the book’s emphasis is more on signal processing than discrete-time system theory, although the basic principles of the latter are adequately covered. 28) Utility theory provides a decision criterion that is superior to the EMV or EOL in that it may allow the decision maker to incorporate her own attitudes toward risk. The equal likelihood ( or Laplace) criterion. A Nyquist plot (or Nyquist Diagram) is a frequency response plot used in control engineering and signal processing. • Laplace approximation fits the best Gaussian – Defined for both univariate and multivariate • Normalization term is useful as BIC criterion • AIC and BIC are simple but not accurate Machine Learning Srihari 25. Section 3-7 : Tangents with Polar Coordinates.


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## Meetup : Bristol meetup

4 15 October 2013 08:04PM

## Discussion article for the meetup : Bristol meetup

WHEN: 20 October 2013 02:00:00PM (+0100)

WHERE: Hodgkin House, 3 Meridian Place, Bristol BS8 1JG

We'll have another meetup in Bristol this upcoming Sunday, October 20, at the student house where I live. We'll officially start at 2pm to hopefully make it reasonably convenient for everyone, but at least two of us will be there from around 12, so if you want to come earlier and hang out a bit more, let me know! (benja.fallenstein@gmail.com, or PM me.)

I'll put up a LessWrong sign outside saying this, but please call me at 07463169075 or (from around 2pm on) ring the buzzer marked "Basement" when you arrive.

Also, whether or not you can attend this time, if you're interested in future meetups, please join the Google group for organizing meetup times!

## Meetup : Second Bristol meetup & mailing list for future meetups

2 06 June 2013 04:47PM

## Discussion article for the meetup : Second Bristol meetup & mailing list for future meetups

WHEN: 16 June 2013 03:00:00PM (+0100)

WHERE: Hodgkin House, 3 Meridian Place, Bristol BS8 1JG

At our lovely first meetup (four people came, if I count myself), I unfortunately forgot to take the opportunity to sort out when a good time for the next meetup would be. Sorry!

Since I'm about to be away for a while and I think others are leaving for the summer as well, I decided to just be bold once more and announce a time and hope that somebody else is free as well. But to make it easier to find good times in the future, please join the Google Group I've just created!

Last time, we ended up sitting in the cafe for hours without consuming much, so for this meetup I've booked the dining room at the student house where I live, which should be a quiet and comfortable place to talk. I'll also put up a LessWrong sign outside saying this, but please ring the buzzer marked "Basement", or you can call me at +43-660-1461996 (unfortunately I don't have a UK mobile yet, but if you ring just once, I'll come up and meet you).

Time & date is Sunday, the 16th of June, starting at 3pm. Hope that I didn't pick a terrible time and someone will be able to join me! :-)

## Meetup : First Bristol meetup

4 17 May 2013 04:52PM

## Discussion article for the meetup : First Bristol meetup

WHEN: 25 May 2013 03:00:00PM (+0100)

WHERE: Friska Queens Road (on the Clifton triangle), Bristol

Back in 2010, Bristol had 4000+ unique LW visitors, but we've never had a meetup -- let's try and see what happens! I'll be in the Friska on Queens Road (on the Clifton triangle, right next to the university campus) on Saturday the 25th at 3pm, with a LessWrong sign and a paperback of HPMOR. Anyone going to join me? :-)

## Discussion article for the meetup : First Bristol meetup

21 04 January 2013 01:57AM

In what became 5th most-read new post on LessWrong in 2012, Morendil told us about a study widely cited in its field... except that source cited, which isn't online and is really difficult to get, makes a different claim — and turns out to not even be the original research, but a PowerPoint presentation given ten years after the original study was published!

Fortunately, the original study turns out to be freely available online, for all to read; Morendil's post has a link. The post also tells us the author and the year of publication. But that's all: Morendil didn't provide a list of references; he showed how the presentation is usually cited, but didn't give a full citation for the original study.

The link is broken now. The Wayback machine doesn't have a copy. The address doesn't give hints about the study's title. I haven't been able to find anything on Google Scholar with author, year, and likely keywords.

I rest my case.

## Math appendix for: "Why you must maximize expected utility"

8 13 December 2012 01:11AM

This is a mathematical appendix to my post "Why you must maximize expected utility", giving precise statements and proofs of some results about von Neumann-Morgenstern utility theory without the Axiom of Continuity. I wish I had the time to make this post more easily readable, giving more intuition; the ideas are rather straight-forward and I hope they won't get lost in the line noise!

The work here is my own (though closely based on the standard proof of the VNM theorem), but I don't expect the results to be new.

*

I represent preference relations as total preorders $\preccurlyeq$ on a simplex $\Delta_N$; define $\prec$, $\sim$, $\succcurlyeq$ and $\succ$ in the obvious ways (e.g., $x\sim y$ iff both $x\preccurlyeq y$ and $y\preccurlyeq x$, and $x\prec y$ iff $x\preccurlyeq y$ but not $y\preccurlyeq x$). Write $e^i$ for the $i$'th unit vector in $\mathbb{R}^N$.

In the following, I will always assume that $\preccurlyeq$ satisfies the independence axiom: that is, for all $x,y,z\in\Delta_N$ and $p\in(0,1]$, we have $x\prec y$ if and only if $px + (1-p)z \prec py + (1-p)z$. Note that the analogous statement with weak preferences follows from this: $x\preccurlyeq y$ holds iff $y\not\prec x$, which by independence is equivalent to $py + (1-p)z \not\prec px + (1-p)z$, which is just $px + (1-p)z \preccurlyeq py + (1-p)z$.

Lemma 1 (more of a good thing is always better). If $x\prec y$ and $0\le p < q \le 1$, then $(1-p)x + py\prec (1-q)x + qy$.

Proof. Let $r := q-p$. Then, $(1-p)x + py = \big((1-q)x + py\big) + rx$ and $(1-q)x + qy = \big((1-q)x + py\big) + ry$. Thus, the result follows from independence applied to $x$$y$, $\textstyle\frac{1}{1-r}\big((1-q)x + py\big)$, and $r$.$\square$

Lemma 2. If $x\preccurlyeq y\preccurlyeq z$ and $x\prec z$, then there is a unique $p\in[0,1]$ such that $(1-q)x + qz \prec y$ for $q\in[0,p)$ and $y\prec (1-q)x + qz$ for $q\in(p,1]$.

Proof. Let $p$ be the supremum of all $r\in[0,1]$ such that $(1-r)x + rz\preccurlyeq y$ (note that by assumption, this condition holds for $r=0$). Suppose that $0\le q. Then there is an $r\in(q,p]$ such that $(1-r)x + rz\preccurlyeq y$. By Lemma 1, we have $(1-q)x + qz \prec (1-r)x + rz$, and the first assertion follows.

Suppose now that $p < q \le 1$. Then by definition of $p$, we do not have $(1-q)x + qz\preccurlyeq y$, which means that we have $(1-q)x + qz\succ y$, which was the second assertion.

Finally, uniqueness is obvious, because if both $p$ and $p'$ satisfied the condition, we would have $\textstyle y \prec \big(1 - \frac{p+p'}2\big)x + \frac{p+p'}2z \prec y$.$\square$

Definition 3. $x$ is much better than $y$, notation $x\succ_* y$ or $y\prec_* x$, if there are neighbourhoods $U$ of $x$ and $V$ of $y$ (in the relative topology of $\Delta_N$) such that we have $x' \succ y'$ for all $x'\in U$ and $y'\in V$. (In other words, the graph of $\succ_*$ is the interior of the graph of $\succ$.) Write $x\preccurlyeq_* y$ or $y\succcurlyeq_* x$ when $x\nsucc_* y$ ($x$ is not much better than $y$), and $x\sim_* y$ ($x$ is about as good as $y$) when both $x\preccurlyeq_* y$ and $x\succcurlyeq_* y$.

Theorem 4 (existence of a utility function). There is a $u\in\mathbb{R}^N$ such that for all $x,y\in\Delta_N$,

$\sum_i x_i\,u_i \;<\; \sum_i y_i\,u_i\;\;\iff\;\; x\prec_* y\;\;\implies\;\;x\prec y.$

Unless $x\sim y$ for all $x$ and $y$, there are $i,j\in\{1,\dotsc,N\}$ such that $u_i\neq u_j$.

Proof. Let $i$ be a worst and $j$ a best outcome, i.e. let $i,j\in\{1,\dotsc,N\}$ be such that $e^i\preccurlyeq e^k\preccurlyeq e^j$ for all $k\in\{1,\dotsc,N\}$. If $e^i\sim e^j$, then $e^i \sim e^k$ for all $k$, and by repeated applications of independence we get $x\sim e^i\sim y$ for all $x,y\in\Delta_N$, and therefore $x\sim_* y$ again for all $x,y\in\Delta_N$, and we can simply choose $u=0$.

Thus, suppose that $e^i\prec e^j$. In this case, let $u$ be such that for every $k\in\{1,\dotsc,N\}$, $u_k$ equals the unique $p$ provided by Lemma 2 applied to $e^i\preccurlyeq e^k\preccurlyeq e^j$ and $e^i\prec e^j$. Because of Lemma 1, $u_i = 0 \neq 1 = u_j$. Let $f(r) := (1-r)e^i + re^j$.

We first show that $\textstyle p := \sum_k x_k\,u_k < \sum_k y_k\,u_k =: q$ implies $x\prec y$. For every $k$, we either have $u_k < 1$, in which case by Lemma 2 we have $e^k \prec f(u_k + \epsilon_k)$ for arbitrarily small $\epsilon_k > 0$, or we have $u_k = 1$, in which case we set $\epsilon_k := 0$ and find $e^k\preccurlyeq e^j = f(u_k + \epsilon_k)$. Set $\textstyle \epsilon := \sum_k x_k\,\epsilon_k$. Now, by independence applied $N-1$ times, we have $\textstyle x = \sum_k x_k\,e^k \preccurlyeq \sum_k x_k f(u_k + \epsilon_k) = f(p+\epsilon)$; analogously, we obtain $y \succcurlyeq f(q-\delta)$ for arbitrarily small $\delta > 0$. Thus, using $p and Lemma 1, $x\preccurlyeq f(p+\epsilon)\prec f(q-\delta)\preccurlyeq y$ and therefore $x\prec y$ as claimed. Now note that if $\textstyle\sum_k x_k\,u_k < \sum_k y_k\,u_k$, then this continues to hold for $x'$ and $y'$ in a sufficiently small neighbourhood of $x$ and $y$, and therefore we have $x\prec_* y$.

Now suppose that $\textstyle \sum_k x_k\,u_k \ge \sum_k y_k\,u_k$. Since we have $u_i = 0$ and $u_j = 1$, we can find points $x'$ and $y'$ arbitrarily close to $x$ and $y$ such that the inequality becomes strict (either the left-hand side is smaller than one and we can increase it, or the right-hand side is greater than zero and we can decrease it, or else the inequality is already strict). Then, $x'\succ y'$ by the preceding paragraph. But this implies that $x\not\prec_* y$, which completes the proof.$\square$

Corollary 5. $\preccurlyeq_*$ is a preference relation (i.e., a total preorder) that satisfies independence and the von Neumann-Morgenstern continuity axiom.

Proof. It is well-known (and straightforward to check) that this follows from the assertion of the theorem.$\square$

Corollary 6. $u$ is unique up to affine transformations.

Proof. Since $u$ is a VNM utility function for $\preccurlyeq_*$, this follows from the analogous result for that case.$\square$

Corollary 7. Unless $x\sim y$ for all $x,y\in\Delta_N$, for all $r\in\mathbb{R}$ the set $\textstyle \{x\in\Delta_N : \sum_i x_i\,u_i = r\}$ has lower dimension than $\Delta_N$ (i.e., it is the intersection of $\Delta_N$ with a lower-dimensional subspace of $\mathbb{R}^N$).

Proof. First, note that the assumption implies that $N\ge 2$. Let $v\in\mathbb{R}^N$ be given by $v_i = 1$, $\forall i$, and note that $\Delta_N$ is the intersection of the hyperplane $A := \{x\in\mathbb{R}^N : x\cdot v = 1\}$ with the closed positive orthant $\mathbb{R}^N_+$. By the theorem, $u$ is not parallel to $v$, so the hyperplane $B_r := \{x\in\mathbb{R}^N : x\cdot u = r\}$ is not parallel to $A$. It follows that $A\cap B_r$ has dimension $N-2$, and therefore $\textstyle\{x\in\Delta_N : \sum_i x_i\,u_i = r\} \;=\; A\cap B_r\cap\mathbb{R}^N_+$ can have at most this dimension. (It can have smaller dimension or be the empty set if $A\cap B_r$ only touches or lies entirely outside the positive orthant.)$\square$

## Why you must maximize expected utility

18 13 December 2012 01:11AM

This post explains von Neumann-Morgenstern (VNM) axioms for decision theory, and what follows from them: that if you have a consistent direction in which you are trying to steer the future, you must be an expected utility maximizer. I'm writing this post in preparation for a sequence on updateless anthropics, but I'm hoping that it will also be independently useful.

The theorems of decision theory say that if you follow certain axioms, then your behavior is described by a utility function. (If you don't know what that means, I'll explain below.) So you should have a utility function! Except, why should you want to follow these axioms in the first place?

A couple of years ago, Eliezer explained how violating one of them can turn you into a money pump — how, at time 11:59, you will want to pay a penny to get option B instead of option A, and then at 12:01, you will want to pay a penny to switch back. Either that, or the game will have ended and the option won't have made a difference.

When I read that post, I was suitably impressed, but not completely convinced: I would certainly not want to behave one way if behaving differently always gave better results. But couldn't you avoid the problem by violating the axiom only in situations where it doesn't give anyone an opportunity to money-pump you? I'm not saying that would be elegant, but is there a reason it would be irrational?

It took me a while, but I have since come around to the view that you really must have a utility function, and really must behave in a way that maximizes the expectation of this function, on pain of stupidity (or at least that there are strong arguments in this direction). But I don't know any source that comes close to explaining the reason, the way I see it; hence, this post.

I'll use the von Neumann-Morgenstern axioms, which assume probability theory as a foundation (unlike the Savage axioms, which actually imply that anyone following them has not only a utility function but also a probability distribution). I will assume that you already accept Bayesianism.

*

Epistemic rationality is about figuring out what's true; instrumental rationality is about steering the future where you want it to go. The way I see it, the axioms of decision theory tell you how to have a consistent direction in which you are trying to steer the future. If my choice at 12:01 depends on whether at 11:59 I had a chance to decide differently, then perhaps I won't ever be money-pumped; but if I want to save as many human lives as possible, and I must decide between different plans that have different probabilities of saving different numbers of people, then it starts to at least seem doubtful that which plan is better at 12:01 could genuinely depend on my opportunity to choose at 11:59.

So how do we formalize the notion of a coherent direction in which you can steer the future?

## Pascal's Mugging for bounded utility functions

8 06 December 2012 10:28PM

This is Pascal's Mugging: Someone comes to you and says, "Give me five dollars, and I'll use my powers from outside the matrix to grant you 4^^^^4 years of fun." And they're lying, of course, but under a Solomonoff prior, the probability that they're not, though surely very small, isn't going to be less than one in 3^^^3; and so if you shut up and multiply, it's clear that the expected utility of paying up outweighs the expected utility of anything sensible you might be doing with those five dollars, and therefore—

Well, fortunately, if you're afraid that your utility-maximizing AI will end up paying all its money to the first clever mugger to come along and ask: never to worry! It will do so only if it can't think of anything better to do with five dollars, after all. So to avoid being mugged, all it has to do is to think of a harebrained scheme for spending \$5 that has more than a one-in-4^^^4 chance of providing 5^^^^5 years of fun. Problem solved.

If, however, you would like to be there be a chance greater than one-in-hell that your AI ends up doing something actually useful, you'll need to do something else. And the simplest answer is to adopt a bounded utility function: any positive singularity gives at least 50 utils, a billion years gives 80 utils, a googol years gives 99 utils, a googolplex years gives 99.9 utils, and 4^^^^4 years of fun give 100 utils (minus epsilon).

This will, indeed, solve the problem. Probability of getting mugged: used to be one (minus epsilon, of course); has now been brought down to zero. That's right: zero.

(Plus epsilon.)

But let's suppose that the impossible happens, and the universe turns out to be able to support TREE(100) years of fun, and we've already lived out 4^^^^4 of them, and the AI has long since folded up operations and faded out of existence because humanity has become sufficiently sane that we no longer need it—

And lo, someone comes to you and says, "Alas, you're not really experiencing 4^^^^4 years of fun here; you're really a mere billion-year-old living in a very convincing simulation. Give me five dollars, and I'll use my powers from outside the matrix to extend your lifespan to a googol years."

And they're lying, of course — but it has been a long time indeed since you last faced a choice that could make a difference of nineteen whole utils...

*

If you truly have a bounded utility function, you must agree that in this situation, paying up is exactly what you'd want to do. Even though it means that you will not experience 4^^^^4 years of fun, even conditional on the universe being capable of supporting TREE(100) of them.

[ETA: To clarify, by "4^^^^4", I really mean any number so large that your utility function assigns (100 - epsilon) utils to it. It's possible to have a utility function where this is only true for infinite numbers which are so incredibly infinite that, given a particular formal language, their definition is so long and complicated that no mere human-sized mind could comprehend it. See this comment thread for discussion of bounded utility functions that assign significant weight to very large lifetimes.]

## A model of UDT with a concrete prior over logical statements

39 28 August 2012 09:45PM

I've been having difficulties with constructing a toy scenario for AI self-modification more interesting than Quirrell's game, because you really want to do expected utility maximization of some sort, but currently our best-specified decision theories search through the theorems of one particular proof system and "break down and cry" if they can't find one that tells them what their utility will be if they choose a particular option. This is fine if the problems are simple enough that we always find the theorems we need, but the AI rewrite problem is precisely about skirting that edge. It seems natural to want to choose some probability distribution over the possibilities that you can't rule out, and then do expected utility maximization (because if you don't maximize EU over some prior, it seems likely that someone could Dutch-book you); indeed, Wei Dai's original UDT has a "mathematical intuition module" black box which this would be an implementation of. But how do you assign probabilities to logical statements? What consistency conditions do you ask for? What are the "impossible possible worlds" that make up your probability space?

Recently, Wei Dai suggested that logical uncertainty might help avoid the Löbian problems with AI self-modification, and although I'm sceptical about this idea, the discussion pushed me into trying to confront the logical uncertainty problem head-on; then, reading Haim Gaifman's paper "Reasoning with limited resources and assigning probabilities to logical statements" (which Luke linked from So you want to save the world) made something click. I want to present a simple suggestion for a concrete definition of "impossible possible world", for a prior over them, and for an UDT algorithm based on that. I'm not sure whether the concrete prior is useful—the main point in giving it is to have a concrete example we can try to prove things about—but the definition of logical possible worlds looks like a promising theoretical tool to me.

## How to cheat Löb's Theorem: my second try

14 22 August 2012 06:21PM

In his open problems talk, Eliezer explains how Löb's theorem prevents you from having a consistent proof system P with an axiom schema that anything P proves is actually true, and asks how we can then "build an AI that could completely rewrite itself, without decreasing the amount of trust it had in math every time it executed that self-rewrite" (18:46).

Recently, I posted about an attempt to apply a general trick for avoiding diagonalization problems to a minimal toy version of this problem. Since then, Wei Dai has posted an interesting quining approach to the same toy problem, and Giles had a promising idea for doing something similar in a different way and will hopefully do a write-up filling in the details. Unfortunately my own "proof" turned out to be broken.

I think I've fixed the problem and made the proof more comprehensible and intuitive in the process. (To avoid confusion, note that what I'm proving is slightly different from, though related to, what I did in the previous post.) However, getting the details right seems to be far from trivial, so I would very much appreciate if people checked my new argument, and told me that it looks okay / where it goes wrong / where they get lost. Thanks in advance!

I'll be more explicit about quoting/unquoting than before, which means I'll need to introduce some notation. However, to sustain you through the schlep of preliminaries, I thought I'd start with an informal summary.

## An angle of attack on Open Problem #1

28 18 August 2012 12:08PM

There is a problem with the proof here and I have to think about whether I can fix it. Thanks to I have posted a new and hopefully correct proof attempt. Thanks again to vi21maobk9vp!

In his talk on open problems in Friendly AI, Eliezer's first question is how, given Löb's theorem, an AI can replace itself with a better expected utility maximizer that believes in as much mathematics as the original AI. I know exactly one trick for that sort of problem, so I decided to try that on a toy variant. To my surprise, it more or less just worked. Therefore:

Professor Quirrell proposes a game. You start with a score of one. Professor Quirrell moves first, by choosing a computer program and showing you its source code. You then have three options: Take your winnings; double down; or self-destruct.

If you take your winnings, the game ends, and your score is converted to Quirrell points.

If you self-destruct, the game ends, your score is lost, you'll be sent to bed without dinner, you'll lose 150 House points, Rita Skeeter will write a feature alleging that you're a Death Eater, and Professor Quirrell will publicly critique your performance. You are advised not to pick this option.

If you double down, your score doubles, and you advance to the next round. Professor Quirrell again moves first by choosing a computer program. Then, it's your turn—except that this time, you don't get to choose your move yourself: instead, it'll be chosen by Professor Quirrell's program from the previous round.

Professor Quirrell will endeavor to present an educational sequence of programs.

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# Question on what is being repeated in this repeated measures ANOVA

I am replicating a two-way repeated measures ANOVA in a journal for practice. There are:

• One dependent variable density (I chose one from multiple dv presented in journal)
• Fixed factor of drought (wet/dry year) Years
• Fixed factor of grazing (no/light/moderate intensity) Land_use

The data is collected from 10 plots for each grazing treatment for three months in each of the two years (wet/dry). The paper considered monthly observations as replications (thus 30 replicates per treatment), and integrated month as random factor.

Question: Is this a repeated measure because the drought factor was examined in the same plots (experience wet (2012) and then dry (2013))? Or is it because the dependent variable was measured in the same plot for three months (Jul-Sep for each grazing&drought pair)?

I don't think the latter is correct since month is considered as replications. But I saw from many websites that in repeated measures we compare more than two timepoints or conditions, whereas I only have two drought conditions.

Could someone clarify please? I am struggling ...

The repeated-measures tag description is your friend here:


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# Mean values theorem and countable sets

The mean values theorem says that there exists a $c∈(u,v)$ such that $$f(v)-f(u)=f′(c)(v-u)$$ My question is: Assume that $u$ is a root of $f$, hence we obtain $$f(v)=f′(c)(v-u)$$ Assume that $f$ is a non-zero analytic function in the whole real line. My interest is about the real $c∈(u,v)$. I believe that the set of those $c$ is countable, otherwise we conclud that $f′(c)$ is constant (in an open set containing $c$) since $v$ is a constant and hence $f$ is identically zero. Also, I think that the set of those $c$ is finite in number or as equivalent classes (for analytic functions) but I am not able to prove that.

I can define the equivalence relation $ℜ$ by $$cℜd⇔f^{(1)}(c)=((1-t)/(1-u)).f^{(1)}(d)$$

where $u∈ℝ$ such that $g(u)=0$, $c∈(u,v)$ and $t∈ℝ$ such that $g(t)=0$, $d∈(t,v)$

• Check $f = \operatorname{id}$. – Lord_Farin Apr 26 '13 at 9:47

Zeroes of a non zero analytic function are isolated, and because $\mathbb{R}$ is separable, a discrete set is at most countable.
Therefore, if $\{c \in (u,v) \mid f(v)=f'(c)(v-u) \}$ is uncountable, $f'$ is identically equal to $f(v)/(v-u)$. In particular, $f$ is linear.
• @ Seirios: How can prove that the set of those $c$ is finite in number or as equivalent classes. – Germany Apr 26 '13 at 10:02
• @ Seirios: This is the question: Define that equivalence relation. I guess that its expression is related to this equation $f(v)=f(u)+f′(c)(v-u)$. – Germany Apr 26 '13 at 11:04
• Without additional conditions, you can define $x \mathcal{R} y$ for all $x,y$; then there is only one equivalent class. – Seirios Apr 26 '13 at 11:07
• @ Seirios: The relation can be defined by: $c∼d$⇔ $g′(c)=(((v-t)/(v-u)))g′(d)$ where $c∈(u,v)$ and $d∈(t,v)$ – Germany Apr 26 '13 at 11:09


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## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson

# Chapter 4 - Polynomials - 4.2 Negative Exponents and Scientific Notations - 4.2 Exercise Set: 125

#### Answer

$(-17)^{-8}$ is positive because when the negative exponent rule is applied, the denominator's power is even (which is $8$). Any non-zero real number raised to an even power is positive. Refer to the step-by-step part below for a detailed explanation.

#### Work Step by Step

RECALL: For any nonzero real number $a$, $a^m$ is positive when $m$ is an even integer. The reason for this is that an even power $m$ means there are $\frac{m}{2}$ pairs of identical factors. Since the product of two numbers with the same sign is positive, then having $\frac{m}{2}$ pairs of identical factors means that the product will surely be positive. Note that $a^{-m} = \dfrac{1}{a^m}, m \ne 0$. Applying this to $(-17)^{-8}$ gives $\dfrac{1}{(-17)^8}$. Since the denominator involves an even power of $-17$, then the denominator is positive. Thus, the quotient will also be positive as the quotient of two positive numbers is positive.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


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# Limit of f along an indicated curve?

1. Sep 28, 2011

### SithsNGiggles

I have a problem here with a the syntax of a question.

1. The problem statement, all variables and given/known data

"Compute the limit of f as (x,y) approaches (0,0) along the indicated curves.

f(x,y) = (x2 - y2)/(x2 + y2)

2. Relevant equations

a) y = x
b) y = x/2
c) y = x2
d) y = 2x

3. The attempt at a solution

I haven't quite started, I've spent most of my time trying to figure out what the conditions under the question meant and how they would change the process of finding the limit.

If it means anything, I'm expected to use the sequence definition of limits (which I'm capable of doing, I just don't know how to begin).

2. Sep 28, 2011

### dynamicsolo

The idea with specifying functions y = g(x) as approach paths to the origin is that you can substitute for y in f(x,y) to reduce the problem to finding a limit of a function of just one variable...

3. Sep 28, 2011

### SithsNGiggles

So I replace y with the corresponding relation in a-d, right? I'm doing this, so I that I now have f(xn,yn) = (xn2 - (xn2)2)/(xn2 + (xn2)2).
(for part c)

Since I now get 0/0, what can I do?

Last edited: Sep 28, 2011
4. Sep 28, 2011

### dynamicsolo

Do you know about L'Hopital's Rule?

5. Sep 28, 2011

### SithsNGiggles

Does differentiation work in the same manner with sequences? If they do I'll try that.

6. Sep 28, 2011

### dynamicsolo

You can treat the points xn as discrete points on the curve of a function f(x), but I don't know if they'll fuss at you about not having established this in your course. As an alternative, you can use the "divide numerator and denominator of the rational function by the highest power of x " approach, so you will have a constant leading term "above and below" and the rest are terms which are reciprocals of positive powers of x.

(I take it this is an analysis course and not just multivariate calculus.)


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## Mathematicians Of The Day

### 25th September

On this day in 1988, Faà di Bruno was beatified by Pope John Paul II in St Peter's Square in Rome.

Click on for a poster.

#### Quotation of the day

##### From Johann Heinrich Lambert
I am undecided whether or not the Milky Way is but one of countless others all of which form an entire system. Perhaps the light from these infinitely distant galaxies is so faint that we cannot see them.
Quoted in E Maor, To infinity and beyond (Princeton 1991)