## Williams Hall, Room 202

## Abstract

The Sisyphus function is defined and we determine the smallest nonnegative integer $n$ requiring a specified number of iterations of the function that must be applied to $n$ until the sequence generated by the iterations of this function becomes stable or cycles.

## Abstract

Problems in algebraic graph theory provide a rich source of research projects for under-graduate students. In this talk, I will present some results obtained over the last couple of summers with SUNY Geneseo undergraduates on the study of the eigenvalues of threshold graphs. The main takeaway of the research is that there is a distinguished threshold graph that plays a prominent role in the study of the spectral properties of the entire class of threshold graphs.

## Abstract

We will discuss and investigate the positive integer solutions of some quadratic equations whose solutions have links to generalized Fibonacci and Lucas sequences.

## Abstract

We investigate an inverse time-dependent source problem for a parabolic partial differential equation with a Neumann boundary condition and subject to an integral constraint. We show the existence, uniqueness, and continuous dependence of solutions. The proof of the existence and uniqueness of solutions yields an algorithm that we used to approximate solutions of the inverse problem using a finite element discretization in space and the backward Euler scheme in time. The errors resulting from our experiments show that the proposed scheme approximates solutions of this inverse problem accurately.

## Abstract

In this work, we discuss the graph directed partitioning method, and its applications in complex systems science such as but not limited to coherent structures, computer vision, weather, complex networks analysis, and earth science. We introduce examples and applications from Jupiter, weather movies, network synchronization, and predicting ice shelf cracks in Antarctica’s Larsen Cice shelf.

## Abstract

In the recent decade, Particle Swarm Optimization (PSO) become a favorable global optimization method the fields of science and engineering. Moreover, PSO is a meta heuristic method, and it makes few or no assumptions about the problem being optimized and can search very large spaces of candidate solutions, which made it an efficient method in the field of machine learning, and training of neural networks. However, two main problems face the PSO which are the possibility to trap with local minima and the slow local convergence. This work introduces an efficient method to combine the Swarm Optimization with the Local optimization solvers, which goes beyond the parallel independent implementation to use dynamic internal connections that achieve robust results.