A power permutation of a finite field F is a permutation of F whose functional form is x -> x^d for some exponent d. Power permutations are used in cryptography, and the exponent d must be chosen so that the permutation is highly nonlinear, that is, not easily approximated by linear functions. The Walsh spectrum […]
Title: Exploiting metric structure for more accurate classification Speaker: Mike Izbicki, Department of Mathematical Sciences, Claremont McKenna College Abstract: Classification problems often have many semantically similar classes. For example, the famous ImageNet dataset contains classes for 80 different dog breeds, 40 different bird species, and 25 types of vehicles. This semantic structure can be formalized using a metric […]
Title: Modern techniques to approach the invariant subspace problem Abstract: The invariant subspace problem is by far one of the most important problems in operator theory. It has been open for more than half a century, and there are many significant contributions with a huge variety of techniques, making this challenging problem so interesting; however […]
A frame in a Euclidean space is a spanning set, which can be overdetermined. Large frames are used for redundant signal transmission, which allows for error correction. An important parameter of frames is coherence, which is maximal absolute value of the cosine of the angle between two frame vectors: the smaller it is, the closer […]
In this talk I will recount the history of my knot theory-based music project and show an example of my method for creating music from knot homsets.
Title: Modeling the waning and boosting of immunity Speaker: Dr. Lauren Childs Assistant Professor and the Cliff and Agnes Lilly Faculty Fellow Virgina Tech Abstract: Infectious disease often leads to significant loss of life and burden on society. Understanding disease dynamics is essential to the development and implementation of earlier and more effective interventions. Traditionally, perfect, […]
One of the most important axioms in analyzing voting systems is that of "neutrality", which stipulates that the system should treat all candidates symmetrically. Even though this doesn't always directly apply (such as in primary systems or those with intentional incumbent protection), it is extremely important both in theory and practice.If the voting systems in […]
M. Niebrzydowski and J. H. Przytycki defined a Kauffman bracket magma and constructed the invariant P of framed links in 3-space. The invariant is closely related to the Kauffman bracket polynomial. The normalized bracket polynomial is obtained from the Kauffman bracket polynomial by the multiplication of indeterminate and it is an ambient isotopy invariant for […]
Title: Solving the Race in Backgammon Speaker: Prof. Arthur Benjamin Smallwood Family Professor of Mathematics Harvey Mudd College Abstract: Backgammon is perhaps the oldest game that is still played today. It is a game that combines luck with skill, where two players take turns rolling dice and decide how to move their checkers […]
Title: Modeling Zoonotic Infectious Diseases from Wildlife to Humans Speaker: Prof. Linda J. S. Allen, P. W. Horn Distinguished Professor Emeritus Texas Tech University Abstract: Zoonotic infectious diseases are diseases transmitted from animals to humans. It is estimated that over 60% of human infectious diseases are zoonotic. The Centers for Disease Control and Prevention has identified eight priority zoonoses […]
Title: Pareto optimization of resonances and optimal control methods Abstract: First successes in fabrication of high-Q optical cavities two decades ago led to active applied physics and numerical studies of optimization problems involving resonances. The questions is how to design an open resonator that has an eigenvalue as close as possible to the real line […]
