Analysis of the Niching Particle Swarm Optimization Algorithm

Multimodal optimization (MMO) techniques have been researched and developed over the years to track multiple global optima concurrently. MMO algorithms extend traditional unimodal optimization algorithms by using search strategies built around forming niches for multiple possible solutions. NichePSO was one of the first approaches to utilize particle swarm optimization (PSO) for MMO problems, using several small subswarms of agents working concurrently to form niches within the search space. Despite its promising performance NichePSO does suffer from some problems, and very little research has been done to study and improve upon the algorithm over the years. A main goal of this thesis is to analyze the NichePSO algorithm, gaining insight into the strengths and weaknesses of the algorithm. Empirical analyses were performed to study the NichePSO’s ability to maintain niches within complex problem domains, as well as methods for improving the overall performance and effectiveness of the algorithm. Two variants of the NichePSO algorithm are proposed, and experimental results show that they both significantly improve the performance of the NichePSO algorithm across several benchmark functions

Off-critical lattice models and massive SLEs

We suggest how versions of Schramm’s SLE can be used to describe the scaling limit of some off-critical 2D lattice models. Many open questions remain

Mixed-mode oscillations and slow manifolds in the self-coupled FitzHugh Nagumo system

We investigate the organization of mixed-mode oscillations in the self-coupled FitzHugh-Nagumo system. These types of oscillations can be explained as a combination of relaxation oscillations and small-amplitude oscillations controlled by canard solutions that are associated with a folded singularity on a critical manifold. The self-coupled FitzHugh-Nagumo system has a cubic critical manifold for a range of parameters, and an associated folded singularity of node-type. Hence, there exist corresponding attracting and repelling slow manifolds that intersect in canard solutions. We present a general technique for the computation of two-dimensional slow manifolds (smooth surfaces). It is based on a boundary value problem approach where the manifolds are computed as one-parameter families of orbit segments. Visualization of the computed surfaces gives unprecedented insight into the geometry of the system. In particular, our techniques allow us to find and visualize canard solutions as the intersection curves of the attracting and repelling slow manifolds. © 2008 American Institute of Physics

Mixed mode oscillations in a conceptual climate model

Much work has been done on relaxation oscillations and other simple oscillators in conceptual climate models. However, the oscillatory patterns in climate data are often more complicated than what can be described by such mechanisms. This paper examines complex oscillatory behavior in climate data through the lens of mixed-mode oscillations. As a case study, a conceptual climate model with governing equations for global mean temperature, atmospheric carbon, and oceanic carbon is analyzed. The nondimensionalized model is a fast/slow system with one fast variable (corresponding to ice volume) and two slow variables (corresponding to the two carbon stores). Geometric singular perturbation theory is used to demonstrate the existence of a folded node singularity. A parameter regime is found in which (singular) trajectories that pass through the folded node are returned to the singular funnel in the limiting case where $\epsilon = 0$. In this parameter regime, the model has a stable periodic orbit of type $1^s$ for some $s>0$. To our knowledge, it is the first conceptual climate model demonstrated to have the capability to produce an MMO pattern.Comment: 28 pages, 11 figure

A similarity-based community detection method with multiple prototype representation

Communities are of great importance for understanding graph structures in social networks. Some existing community detection algorithms use a single prototype to represent each group. In real applications, this may not adequately model the different types of communities and hence limits the clustering performance on social networks. To address this problem, a Similarity-based Multi-Prototype (SMP) community detection approach is proposed in this paper. In SMP, vertices in each community carry various weights to describe their degree of representativeness. This mechanism enables each community to be represented by more than one node. The centrality of nodes is used to calculate prototype weights, while similarity is utilized to guide us to partitioning the graph. Experimental results on computer generated and real-world networks clearly show that SMP performs well for detecting communities. Moreover, the method could provide richer information for the inner structure of the detected communities with the help of prototype weights compared with the existing community detection models