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On Correspondences Between Feedforward Artificial Neural Networks On Finite Memory Automata And Classes Of Primitive Recursive Functions, Vladimir A. Kulyukin
On Correspondences Between Feedforward Artificial Neural Networks On Finite Memory Automata And Classes Of Primitive Recursive Functions, Vladimir A. Kulyukin
Computer Science Faculty and Staff Publications
When realized on computational devices with finite quantities of memory, feedforward artificial neural networks and the functions they compute cease being abstract mathematical objects and turn into executable programs generating concrete computations. To differentiate between feedforward artificial neural networks and their functions as abstract mathematical objects and the realizations of these networks and functions on finite memory devices, we introduce the categories of general and actual computabilities and show that there exist correspondences, i.e., bijections, between functions computable by trained feedforward artificial neural networks on finite memory automata and classes of primitive recursive functions.
The Generalized Riemann Hypothesis And Applications To Primality Testing, Peter Hall
The Generalized Riemann Hypothesis And Applications To Primality Testing, Peter Hall
University Scholar Projects
The Riemann Hypothesis, posed in 1859 by Bernhard Riemann, is about zeros
of the Riemann zeta-function in the complex plane. The zeta-function can be repre-
sented as a sum over positive integers n of terms 1/ns when s is a complex number
with real part greater than 1. It may also be represented in this region as a prod-
uct over the primes called an Euler product. These definitions of the zeta-function
allow us to find other representations that are valid in more of the complex plane,
including a product representation over its zeros. The Riemann Hypothesis says that
all …
On Conway's Generalization Of The 3x + 1 Problem, Robin M. Givens
On Conway's Generalization Of The 3x + 1 Problem, Robin M. Givens
Honors Theses
This thesis considers a variation of the 3x+1, or Collatz, Problem involving a function we call the Conway function. The Conway function is defined by letting C3(n)=2k for n=3k and C3(n)=4k±1 for n=3k±1, where n is an integer. The iterates of this function generate a few 'short' cycles, but the s' tructural dynamics are otherwise unknown. We investigate properties of the Conway function and other related functions. We also discuss the possibility of using the Conway function to generate keys for cryptographic use based on a fast, efficient binary implemenation of the function. Questions related to the conjectured tree-like structure …
New Graph Model For Channel Assignment In Ad Hoc Wireless Networks, Maggie Xiaoyan Cheng, S. C. Huang, X. Huang, Weili Wu
New Graph Model For Channel Assignment In Ad Hoc Wireless Networks, Maggie Xiaoyan Cheng, S. C. Huang, X. Huang, Weili Wu
Computer Science Faculty Research & Creative Works
The channel assignment problem in ad hoc wireless networks is investigated. The problem is to assign channels to hosts in such a way that interference among hosts is eliminated and the total number of channels is minimised. Interference is caused by direct collisions from hosts that can hear each other or indirect collisions from hosts that cannot hear each other, but simultaneously transmit to the same destination. A new class of disk graphs (FDD: interFerence Double Disk graphs) is proposed that include both kinds of interference edges. Channel assignment in wireless networks is a vertex colouring problem in FDD graphs. …