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(Swarthmore College)

Swarthmore College is a private, independent, liberal arts college in the United States with an enrollment of about 1,500 students. The college is located in the borough of Swarthmore, Pennsylvania, 11 miles (17.7 km) southwest of Philadelphia.

More information: http://en.wikipedia.org/wiki/Swarthmore_College

Neuromancer, Mona Lisa Overdrive and

Neuromancer, Mona Lisa Overdrive and
Online Gaming

Online Gaming
Sebor Absinth Ltd

Sebor Absinth Ltd

Presentation By Jeremy Hill

The Model Following these assumptions, I propose a hierarchical model with these characteristics: where is the number of goals scored by a team’s offense or allowed by a team’s defense, represent the strength of offense and defense for each individual team, is the total number of games played by each team, is the shape parameter, and is the scale parameter. Also, in this model it is assumed that any observed score can be split into offensive ‘scores’, and defensive ‘allowed scores’. In other words, For simplicity’s sake, in this model I assume and I use a data-set in which the number of games for each team is equal (pool play). The expanded forms of this model that relax these assumptions are explored further in my paper. What is a Hierarchical Model, and why use it? A hierarchical model is a model that is useful when a distributions parameters are assumed to have been drawn from a common underlying distribution: in this case, we assume that different teams offense and defense are defined by a common underlying Gamma distribution. The parameters that define this underlying distribution are known as the hyperparameters for the model. In this model’s case, the hyperparameters are and . Having a team’s strength come from an underlying distribution also makes sense, since all teams tend to draw from the same pool of players. While strength may vary between teams, there should be an underlying average skill level on which most players an...

Solving Dynamic Stochastic General Equilibrium Models Eric Zwick ’07 Swarthmore College, Department of Mathematics & Statistics References Boyd and Smith. “The Evolution of debt and equity markets in economic development.” Economic Theory. Vol. 12, pp. 519-560, 1998. Marimon, Ramon and Andrew Scott, eds. Computational Methods for the Study of Dynamic Economies. New York: Oxford UP, 1999. Sargent, Thomas J. Dynamic Macroeconomic Theroy. Cambridge, MA: Harvard UP, 1987. Sumru, Jagjit and Charles Nolan, eds. Dynamic Macroeconomic Analysis. New York: Cambridge UP, 2003. Walsh, Carl E. Monetary Theory and Policy. Cambridge, MA: MIT Press, 2003. Acknowledgements I want to thank Professors Jefferson and Stromquist for their guidance. Additionally, I want to thank Dan Hammer for inspiring my poster template and Nick Groh for sharing. Introduction Many economic models begin with the simple idea of maximizing a utility function subject to a budget constraint over time. However, the task of solving for an intertemporal equilibrium is not always an easy one. In particular, it can be extremely difficult to solve a nonlinear system of equations, especially when the variables are themselves functions and even more so when these functions are stochastic processes. Fortunately, certain types of models can be simplified by approximating the stochastics of the system about a time- invariant equilibrium. The resulting linear system can be solved using difference equations for a recurs...

Abstract Though previous explorations of equilibria in game theory have incorporated the concept of error-making, most do not consider the possibility of anticipation of errors. Instead of treating them as inherently unpredictable, I allow the awareness of error-making to directly affect a player's choice of strategy before any errors actually occur. I explore the consequences of allowing players to be estimate their opponent's error rate and incorporate this information into an expected payoff function. I show that if both players are aware of a high error rate of their opponent, a new, stable, non-Nash equilibrium can be achieved. The General n × n Game Matrix Any normal form game can, by definition, be represented as a matrix like the one below. The a- and b-values, S’s and T’s, and q’s and p’s are the payoffs, strategies, and probabilities of playing those strategies of Players I and II, respectively. Background Information Nash Equilibrium The Nash Equilibrium (NE) is the equilibrium concept in game theory. It is defined as a set of strategies such that no player has an incentive to make a unilateral change of strategy. That is, each player is playing the best response to his opponent’s choice of strategy. Expected Payoff Functions As can be inferred from the n x n game matrix, the expected payoff to Player I of playing Si and to Player II of playing Tj are as follows: That is, the payoff depends on the opponent’s probability distribution. Deceptive Error Rates. ...
E-Commerce and the Copyright Conundrum By: JAMES DALTON and SUE WESTON

E-Commerce and the Copyright Conundrum By: JAMES DALTON and SUE WESTON
Coronal Polarization Measurements and Associated Observations from the June, 2001, Solar Eclipse Roban H. Kramer (roban@sccs.swarthmore.edu) Swarthmore College 2003 Dr. Jay M. Pasachoff, Williams College

Coronal Polarization Measurements and Associated Observations from the June, 2001, Solar Eclipse Roban H. Kramer (roban@sccs.swarthmore.edu) Swarthmore College 2003 Dr. Jay M. Pasachoff, Williams College

On June 21 of this year, the Earth briefly passed through the Moon’s cone of shadow. For those of us in the right place at the right time, the Sun’s disk was blotted from the sky, revealing the diffuse streamers of light referred to as the Solar Corona.
Biology How Does Information/Entropy/ Complexity fit in?

Biology How Does Information/Entropy/ Complexity fit in?

“The object is a wonderful example of rigourous beauty, the big wealth of natural laws: it is a perfect example of the human mind possibilities to test their scientific rigour and to dominate them. It represents the unity of real and beautiful, which means for me the same thing.” - Ernö Rubik Notation: Name the faces of the cube according to their relative orientation to you. So they can be called Front, Back, Right, Left, Up and Down (abbreviate as F,B,R,L,U,D). Furthermore, use the same abbreviation to symbolise the process of rotating that face. Thus rotating the front face clockwise by 90° is described with F (refer to the figure below). Thus F-1 corresponds to a counter clock-wise rotation. The same notation applies to the other moves as well. The F-subgroup: All the possible processes that are the result of turning the F face only. Its only elements are E (the identity), F, F-1 and F2. The SLICE SQUARED subgroup: The name comes from the fact that the moves in this group are equivalent to rotating one of the central slices by 180 °. The group has the following moves: X=(R2L2), Y=(U2D2) and Z=(F2B2). This group is of order 8. Applying XYZ to a solved cube results in a “checkerboard” pattern (refer to the figure below). SOLVING THE CUBE: There are many methods of solving the cube, including speed cubing. However, the method I am describing below is a more ‘group theoretical’ approach to solving the cube. Place the UP edge cubelets 2. Place the UP corner cubelet...
Ever wonder how they made STAR WARS or TOY STORY?

Ever wonder how they made STAR WARS or TOY STORY?

The development of Computer Graphics is responsible for a revolution in art and media. Starting with the pixel (the smallest discrete unit of color inherent in almost all common electronic displays today), Computer Graphics progressed through 2D manipulation to creation of imagery and onto the illusion of 3D scenes. 2D image manipulation demonstrated here involved transformations of images (arrays of pixels) and fractal sets. Fractal patterns were generated using julia and mandelbrot sets which mapped colors determined by complex quadratic polynomials to pixels. 2D image creation from primitives such as lines, splines, and circles is deceivingly difficult. The primary difficulty is choosing which pixels to color, an issue of aliasing. Aliasing occurs when trying to map something of high resolution (in this case a mathematical line) to a discrete (low resolution) system. The result is jagged edges. The other issue is rendering speed. For instance, when drawing a circle, traditional mathematical methods such as x = cos(theta) are not practical. Splines which were used to create the curves in my name on the left were created by specifying points, joining them with lines, and then recursively subdiving those lines. Filled shapes (especially filled polygons) provide yet another hurdle. Polygons are filled by stepping through an image row by row and filling between edges. The difficulty comes with the many exceptions relevant to scanline filling such as image boundary ...
Evolutionary Fitness

Evolutionary Fitness
Self Organized Criticality Benjamin Good March 21, 2008

Self Organized Criticality Benjamin Good March 21, 2008
Volvox “THE FIERCE ROLLER”

Volvox “THE FIERCE ROLLER”
How closely do real biological systems fit these ideal fractal networks of West, Brown, and Enquist? or… great moments in scientific discourse as read by children

How closely do real biological systems fit these ideal fractal networks of West, Brown, and Enquist? or… great moments in scientific discourse as read by children
Power Laws Otherwise known as any semi-straight line on a log-log plot

Power Laws Otherwise known as any semi-straight line on a log-log plot

What are permutation statistics? Let’s write [n] for the set {1, 2, 3, …, n}. A permutation of size n is a bijection :[n] [n]. We usually write permutations as sequences, and denote their entries using subscripts. For example,  = 2413 is a permutation of size 4, and its last entry is 4 = 3. An inversion in  is a pair of entries (not necessarily consecutive) that appear in decreasing order; that is, i < j but i > j . If the entries are consecutive it is also called a descent. The permutation 2413 has two inversions (41 and 43) but it only has one descent (41). Let: A ( n, k ) = # of permutations of size n with k descents B ( n, k ) = # of permutations of size n with k inversions The inversion number and the descent number are examples of permutation statistics. The functions A(n,k) and B(n,k) are called the distributions of these statistics. Factorial Functions A factorial function of size n is a function from [n] to [n] that satisfies ai <= i for every i. We write factorial functions like permutations, but the generally aren’t permutations. For example, 1132 is a factorial function (but 1312 isn’t, because 3 > 2). Every factorial function has a1=1. The image of a is the set of distinct values of a: Im a = { j | for some i, ai = j }. The image size, |Im a|, is always an integer from 1 to n. It turns out that the image size is an Eulerian statistic. Theorem 1. The number of factorial functions of size n with |Im a| = k is exa...
As a result of activities in grades 9-12, all students should develop:

As a result of activities in grades 9-12, all students should develop:

National Standards on Science abilities necessary to do scientific inquiry. understandings about science inquiry.
Words vs. Terms Taken from Jason Eisner’s NLP class slides: www.cs.jhu.edu/~eisner

Words vs. Terms Taken from Jason Eisner’s NLP class slides: www.cs.jhu.edu/~eisner
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