Lecture 2 - Rabie A. Ramadan
... • Determine how long the algorithm will run for each of these groups. n is the size of the input, m is the number of groups, pi is the probability that the input will be from ...
... • Determine how long the algorithm will run for each of these groups. n is the size of the input, m is the number of groups, pi is the probability that the input will be from ...
APPLICATION OF ORDER STATISTICS TO TERMINATION
... This scheme is the same for different Stochastic Approximation algorithms whose distinguish only by approach to stochastic gradient estimation. The minimizing sequence converges a.s. to solution of the optimization problem under conditions typical for SA algorithms (Ermolyev (1976), Mikhalevitch et ...
... This scheme is the same for different Stochastic Approximation algorithms whose distinguish only by approach to stochastic gradient estimation. The minimizing sequence converges a.s. to solution of the optimization problem under conditions typical for SA algorithms (Ermolyev (1976), Mikhalevitch et ...
Terminology: Lecture 1 Name:_____________________
... n: 7 (number of elements) algorithm - step-by-step procedure for producing a solution basic operation - fundamental operation in the algorithm (i.e., operation done the most) Generally, we want to derive a function for the number of times that the basic operation is performed related to the problem ...
... n: 7 (number of elements) algorithm - step-by-step procedure for producing a solution basic operation - fundamental operation in the algorithm (i.e., operation done the most) Generally, we want to derive a function for the number of times that the basic operation is performed related to the problem ...
here
... Problem 6. Find the global minimum and maximum of the function f (x, y) = 2x3 + 4y 3 on the set S = {x2 + y 2 ≤ 1}. (The maximum theorem tells us that there is a global max/min on S. If the min or max occurs in the interior of S, we can find it by looking at the gradient of f . If the min/max doesn’ ...
... Problem 6. Find the global minimum and maximum of the function f (x, y) = 2x3 + 4y 3 on the set S = {x2 + y 2 ≤ 1}. (The maximum theorem tells us that there is a global max/min on S. If the min or max occurs in the interior of S, we can find it by looking at the gradient of f . If the min/max doesn’ ...
Lecture Notes for Section 2.7
... Euler’s Method: A technique for obtaining a numerical approximation to points on the curve of the solution of a differential equation. We start by thinking about sub-dividing a region of x-values from a to b into n equal subdivisions, and integrating the differential equation using a left-endpoint n ...
... Euler’s Method: A technique for obtaining a numerical approximation to points on the curve of the solution of a differential equation. We start by thinking about sub-dividing a region of x-values from a to b into n equal subdivisions, and integrating the differential equation using a left-endpoint n ...
PATTERNS, CONTINUED: VERIFYING FORMULAS
... MATHEMATICAL INDUCTION A technique called Mathematic al Induction can be used to verify a formula or expression for the nth term in a pattern. This method is particularly useful when it is easy to describe the pattern recursively; that is, whenever it is easy to describe the procedure for going from ...
... MATHEMATICAL INDUCTION A technique called Mathematic al Induction can be used to verify a formula or expression for the nth term in a pattern. This method is particularly useful when it is easy to describe the pattern recursively; that is, whenever it is easy to describe the procedure for going from ...
Mineral Chemistry Calculations
... minerals as well as the determination of the chemical formula of the mineral • Determination of the weight % of elements in a mineral • this portion does not include oxygen based minerals--we will treat this later • need formula of mineral • need atomic weights of individual elements in mineral • ch ...
... minerals as well as the determination of the chemical formula of the mineral • Determination of the weight % of elements in a mineral • this portion does not include oxygen based minerals--we will treat this later • need formula of mineral • need atomic weights of individual elements in mineral • ch ...
Terminology: Lecture 1 Name:_____________________
... start = time.time() sum = sumList(aList) end = time.time() print "Time to sum the list was %.3f seconds" % (end-start) def sumList(myList): """Returns the sum of all items in myList""" total = 0 for item in myList: total = total + item return total main() ...
... start = time.time() sum = sumList(aList) end = time.time() print "Time to sum the list was %.3f seconds" % (end-start) def sumList(myList): """Returns the sum of all items in myList""" total = 0 for item in myList: total = total + item return total main() ...
A Simple Formula to Calculate Azimuth without a Two
... of the distance increments (changes in eastings and changes in northings) to corrections applied to the angle returned by the ATAN function available on hand calculators and in programming languages, but this approach is difficult to remember and awkward to implement because of the four-case logic. ...
... of the distance increments (changes in eastings and changes in northings) to corrections applied to the angle returned by the ATAN function available on hand calculators and in programming languages, but this approach is difficult to remember and awkward to implement because of the four-case logic. ...
B. Quadratic Formula
... Where the value of b 2 4ac is know as the discriminant. (NOTE: There is a typographical error in the text on pg 185 which lists the discriminant as b 2 4ac ) x ...
... Where the value of b 2 4ac is know as the discriminant. (NOTE: There is a typographical error in the text on pg 185 which lists the discriminant as b 2 4ac ) x ...
Common Trigonometry Mistakes Example: Simplifying a
... Common Trigonometry Mistakes Example: Simplifying a trigonometric expression Some problems provide the opportunity for more than one mistake. ...
... Common Trigonometry Mistakes Example: Simplifying a trigonometric expression Some problems provide the opportunity for more than one mistake. ...
Max Weight Learning Algorithms for Scheduling in Unknown
... and in [6][7] using fluid limits. The problem can be partly addressed using these prior techniques in the following special cases: • (Special Case 1) There is no “stage-1” control action k(t), so that the revealed randomness ω(t) does not depend on any control decision. • (Special Case 2) The distri ...
... and in [6][7] using fluid limits. The problem can be partly addressed using these prior techniques in the following special cases: • (Special Case 1) There is no “stage-1” control action k(t), so that the revealed randomness ω(t) does not depend on any control decision. • (Special Case 2) The distri ...
Learning Algorithms for Solving MDPs References: Barto, Bradtke
... 2. Asynchronous stochastic approximation: Only update or “back up” some of the components of at time . Let be an infinite sequence of times at which state is updated. Then ...
... 2. Asynchronous stochastic approximation: Only update or “back up” some of the components of at time . Let be an infinite sequence of times at which state is updated. Then ...
mecce 101 analytical foundations for communication engineering
... at least 2 arrivals in the first 20 minutes (iii) Probability of ( at least one arrival in the first 15 minutes / there are exactly 2 arrivals in the first 15 minutes) ...
... at least 2 arrivals in the first 20 minutes (iii) Probability of ( at least one arrival in the first 15 minutes / there are exactly 2 arrivals in the first 15 minutes) ...
Body Surface Area Activity
... usually described as covering a percentage of the body surface area. Some chemotherapy drug dosages are based on body surface area. ...
... usually described as covering a percentage of the body surface area. Some chemotherapy drug dosages are based on body surface area. ...
12:2: Applications of Maxima and Minima
... 3. Identify the constraints (if any). At most 500 jerseys can be manufactured in a run. Also, is not defined. Thus, x is constrained by 0 < x ≤ 500. Put another way, the domain of the objective function is (0, 500]. ...
... 3. Identify the constraints (if any). At most 500 jerseys can be manufactured in a run. Also, is not defined. Thus, x is constrained by 0 < x ≤ 500. Put another way, the domain of the objective function is (0, 500]. ...
COURSE CONTENT MATHEMATICAL ECONOMICS
... Classical programming: the optimization of an objective function subject to equality constraints. The Lagrange method, first and second order conditions, the economic interpretation of Lagrange multipliers, comparative static analysis in classical programming. Applications in economics: utility maxi ...
... Classical programming: the optimization of an objective function subject to equality constraints. The Lagrange method, first and second order conditions, the economic interpretation of Lagrange multipliers, comparative static analysis in classical programming. Applications in economics: utility maxi ...
COS 511: Theoretical Machine Learning Problem 1
... [10] Suppose, in the usual boosting set-up, that the weak learning condition is guaranteed to hold so that t ≤ 12 − γ for some γ > 0 which is not known before boosting begins. And suppose AdaBoost is run in the usual fashion, except that the algorithm is modified to halt and output the combined cla ...
... [10] Suppose, in the usual boosting set-up, that the weak learning condition is guaranteed to hold so that t ≤ 12 − γ for some γ > 0 which is not known before boosting begins. And suppose AdaBoost is run in the usual fashion, except that the algorithm is modified to halt and output the combined cla ...
2008
... Let ABC be an acute triangle with vertices A,B,C and corresponding opposite sides of lengths a,b,c. (See the figure below). Let P be a point on the side AB, and d the length of the segment CP. (a) If P is the midpoint of the side AB find a formula for the measure of angle C ( = CB) in terms of a,b ...
... Let ABC be an acute triangle with vertices A,B,C and corresponding opposite sides of lengths a,b,c. (See the figure below). Let P be a point on the side AB, and d the length of the segment CP. (a) If P is the midpoint of the side AB find a formula for the measure of angle C ( = CB) in terms of a,b ...
Homework 4 Solutions, CS 321, Fall 2002 Due Tuesday, 1 October
... As discussed in section, a minimization algorithm cannot solve the constrained minimization problem in a straightforward way. In other words, if we wish to minimize a function f subject to some constraint , then the method of Lagrange multipliers says that the solution will be a stationary point ...
... As discussed in section, a minimization algorithm cannot solve the constrained minimization problem in a straightforward way. In other words, if we wish to minimize a function f subject to some constraint , then the method of Lagrange multipliers says that the solution will be a stationary point ...
Euler`s Even Zeta Formula
... A clever scheme due to Max Woon (1997) computes the Bernoulli numbers using the binary tree defined above, starting with root 1/2! and growing the tree to left and right as indicated: the left child reverses the sign and increases the left-most factorial argument by 1; the right child preserves sign ...
... A clever scheme due to Max Woon (1997) computes the Bernoulli numbers using the binary tree defined above, starting with root 1/2! and growing the tree to left and right as indicated: the left child reverses the sign and increases the left-most factorial argument by 1; the right child preserves sign ...
Finding Empirical and Molecular Formulas (1A)
... 1. Convert all masses to moles of each element. If %-mass are given, assume 100 g of the sample (so that % = massing) and then convert to number of moles using the respective atomic masses. 2. Find which number of moles is the smallest and divide all the different numbers of moles by that smallest n ...
... 1. Convert all masses to moles of each element. If %-mass are given, assume 100 g of the sample (so that % = massing) and then convert to number of moles using the respective atomic masses. 2. Find which number of moles is the smallest and divide all the different numbers of moles by that smallest n ...
A Bundle Method to Solve Multivalued Variational Inequalities
... di®erentiable and strongly convex and f¸k gk2IN be a sequence of positive numbers. The problem considered at iteration k is the following: k ...
... di®erentiable and strongly convex and f¸k gk2IN be a sequence of positive numbers. The problem considered at iteration k is the following: k ...