Under certain conditions, a neural network may be trained to perform a
specific task by altering the weights of only a portion of the synapses.
Specifically, it has been noted that certain three layer feed-forward networks may
be trained to certain tasks by adjusting only the synapses to the output...
Product densities have been widely used in the literature to give a
concrete description of the distribution of a point process. A rigorous
description of properties of product densities is presented with examples to
show that in some sense these results are the best possible. Product
densities are then used...
In this thesis, the reduction of neural networks is studied. A new, largely automatic method is developed for reducing a neural network, and its capabilities are analyzed and compared with current methods. An example is presented that is irreducible via existing techniques, but is reducible by the new method. Factors...
For a certain class of Z²-actions, we provide a proof of a conjecture that the ratio of the Perron eigenvalues of the transfer matrices of the free boundary restrictions converge to the entropy of that action. Also, a novel method for computing the entropy of Z²-actions is conjectured.
Factorization of integers is an important aspect of cryptography since it can be used as an
attack against some of the common cryptographic methods being used. There are
numerous methods in existence for factoring integers. Some of these are faster than
others for general numbers, while others work best on...
The notion of a normal number and the Normal Number Theorem date back over 100 years. Émile Borel first stated his Normal Number Theorem in 1909. Despite their seemingly basic nature, normal numbers are still engaging many mathematicians to this day. In this paper, we provide a reinterpretation of the...
There has been a lot of work done in recent decades in the field of symbolic dynamics.
Much attention has been paid to the so-called "complexity" function, which gives a sense
of the rate at which the number of words in the system grow. In this paper, we explore this...
Neural networks are models which have been developed to simulate the anatomy
of the nervous system. The connection between the elements of these networks,
the so called artificial neurons, is similar to the connection between the biological
neurons. In developing neural networks people are trying to create systems which
have...
The LA Book is a free-to-students Linear Algebra textbook written at the introductory
level and suitable for teaching MTH341 at Oregon State University. It functions both as
a traditional, printed book (rendered via LaTeX) and as an online textbook (rendered via
HTML), viewable via any modern web-browser. It is built...
