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Department of Mathematics and Computer Science

Department of Mathematics and Computer Science

Recent Submissions

  • Schrum, Jacob; Rollins, Alex C. (GECCO '17 Proceedings of the Genetic and Evolutionary Computation Conference Companion, 2017-07)
    Previous research using evolutionary computation in Multi-Agent Systems indicates that assigning fitness based on team vs. individual behavior has a strong impact on the ability of evolved teams of artificial agents to ...
  • Schrum, Jacob; Gillespie, Lauren E.; Gonzalez, Gabriela R. (Proceedings of the Genetic and Evolutionary Computation Conference, 2017-07)
    Intelligent agents have a wide range of applications in robotics, video games, and computer simulations. However, fully general agents should function with as little human guidance as possible. Specifically, agents should ...
  • Schrum, Jacob; McDonnell, Tyler; Andoni, Sari; Bonab, Elmira; Cheng, Sheila; Goode, Jimmie; Moore, Keith; Sellers, Gavin; Choi, Jun-Hwan (GECCO '18 Proceedings of the Genetic and Evolutionary Computation Conference, 2018-07)
    Neuroevolution is a powerful and general technique for evolving the structure and weights of artificial neural networks. Though neuroevolutionary approaches such as NeuroEvolution of Augmenting Topologies (NEAT) have been ...
  • Schrum, Jacob; Volz, Vanessa; Lucas, Simon M.; Smith, Adam; Liu, Jialin; Risi, Sebastian (Proceedings of the Genetic and Evolutionary Computation Conference, 2018-07)
    Generative Adversarial Networks (GANs) are a machine learning approach capable of generating novel example outputs across a space of provided training examples. Procedural Content Generation (PCG) of levels for video games ...
  • Schrum, Jacob; Tweraser, Isabel; Gillespie, Lauren E. (Proceedings of the Genetic and Evolutionary Computation Conference, 2018-07)
    Compositional Pattern Producing Networks (CPPNs) are a generative encoding that has been used to evolve a variety of novel artifacts, such as 2D images, 3D shapes, audio timbres, soft robots, and neural networks. This paper ...
  • Schrum, Jacob (Proceedings of the Genetic and Evolutionary Computation Conference, 2018-07)
    Tetris is a challenging puzzle game that has received much attention from the AI community, but much of this work relies on intelligent high-level features. Recently, agents played the game using low-level features (10 X ...
  • Richards, Kendall C. (Proceedings of the American Mathematical Society, 1993)
    Let f and g be functions analytic on the unit disk and let I* denote the Bergman norm. Conditions are identified under which there exists an absolute constant c, with 0 < c < 1, such that the relationship Ig(z)I < ...
  • Richards, Kendall C. (Transactions of the American Mathematical Society, 1993)
    Using a theorem of S. Bernstein [1] we prove a special case of the following maximum principle for the Bergman space conjectured by B. Koren- blum [3]: There exists a number S e (0, 1) such that if / and g are ...
  • Richards, Kendall C. (Mathematics Magazine, 1993)
  • Richards, Kendall C. (Transactions of the American Mathematical Society, 1995)
    The authors study certain monotoneity and convexity properties of the Gaussian hypergeometric function and those of the Euler gamma function.
  • Richards, Kendall C. (Journal of Approximation Theory, 1998)
    Let {φk}n k=0, n<m, be a family of polynomials orthogonal with respect to the positive semi-definite bilinear form (g, h)d := 1 m Xm j=1 g(xj )h(xj ), xj := −1 + (2j − 1)/m. These polynomials are known as Gram ...
  • Richards, Kendall C. (Siam Journal on Mathematical Analysis, 2000)
    In this paper we verify a conjecture of M. Vuorinen that the Muir approxima- tion is a lower approximation to the arc length of an ellipse. Vuorinen conjectured that f(x) = 2F1( 1 2 , − 1 2 ; 1; x) − [(1 + (1 − ...
  • Richards, Kendall C. (Siam Journal on Mathematical Analysis, 2001)
    Conditions are determined under which 3F2 (−n, a, b; a + b + 2, ε − n + 1; 1) is a monotone function of n satisfying ab· 3F2 (−n, a, b; a + b + 2, ε − n + 1; 1) ≥ ab· 2F1 (a, b; a + b + 2; 1) . Motivated by a conjecture ...
  • Richards, Kendall C. (Computational Methods and Function Theory, 2001)
    Recent efforts to obtain bounds for the complete elliptic integral π 2 · 2F1 −1 2 , 1 2 ; 1; r2 in terms of power means and other related means have precipitated the search for similar bounds for the more ...
  • Richards, Kendall C. (Journal of Mathematical Analysis and Applications, 2005)
    Sharp inequalities are established between the Gaussian hypergeometric function and the power mean. These results extend known inequalities involving the complete elliptic integral and the hyper- geometric mean.
  • Richards, Kendall C. (Journal of Inequalities in Pure and Applied Mathematics, 2006)
    Recently obtained inequalities [12] between the Gaussian hypergeometric func- tion and the power mean are applied to establish new sharp inequalities involv- ing the weighted identric, logartithmic, and power means.
  • Richards, Kendall C. (Journal of Inequalities in Pure and Applied Mathematics, 2007)
    In this note, we present sharp inequalities relating hypergeometric analogues of the arithmetic-geometric mean discussed in [5] and the power mean. The main result generalizes the corresponding sharp inequality for the ...
  • Richards, Kendall C. (Journal of Mathematical Analysis and Applications, 2009)
    Turán-type inequalities for combinations of Kummer functions involving Φ(a ± ν, c ± ν, x) and Φ(a, c ± ν, x) have been recently investigated in [Á. Baricz, Functional inequalities involving Bessel and modified Bessel ...
  • Richards, Kendall C. (Journal of Mathematical Inequalities, 2010)
    We give an expository summary of a collection of inequalities involving Gauss’ hyper- geometric function 2F1 and the closely-related power mean (and certain other bivariate means). Two conjectures involving simultaneous ...
  • Richards, Kendall C.; Denman, Richard T.; Futamura, Fumiko (Linear Algebra and Its Applications, 2013)
    It was recently shown that if M = 1 ⊕ ··· ⊕ k ∈ Cn×n is a Jordan matrix with k nontrivial Jordan blocks i, then M can be frame diagonalized by embedding M into a diagonalizable matrix in C(n+)×(n+) with = k. This ...

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