Complex Classical Fields: A Framework for Reflection Positivity

We explore a framework for complex classical fields, appropriate for describing quantum field theories. Our fields are linear transformations on a Hilbert space, so they are more general than random variables for a probability measure. Our method generalizes Osterwalder and Schrader’s construction of Euclidean fields. We allow complex-valued classical fields in the case of quantum field theories that describe neutral particles. From an analytic point-of-view, the key to using our method is reflection positivity. We investigate conditions on the Fourier representation of the fields to ensure that reflection positivity holds. We also show how reflection positivity is preserved by various spacetime compactifications of ${\mathbb{R}^{d}}$ in different coordinate directions.     

Transients and Evolution in NiTi

Many of the applications that seek to utilize shape memory alloys for their unique set of properties inevitably must deal, on some level, with the dimensional instability that is inherent to these materials under cyclic thermomechanical loading conditions. As a result, a better understanding of the transient and evolutionary behavior of a shape memory alloy is critical to both the successful design of useful actuation systems and development of accurate material models that can adequately capture the types of dimensional instability that can arise during component design. To this end, a set of experiments were conducted wherein the temperature cycling excursion was held fixed while the applied stress was varied. The results indicated that the extent of strain evolution produced under the initially applied stress has a significant impact on both the amount of transient that is observed as well as the rate of evolution observed under subsequent stress levels. In particular, lowering the applied stress to 50 MPa after cycling under an initial stress of 75 MPa did not stabilize the strain. However, lowering the applied stress to 50 MPa after cycling under an initial stress of 150 MPa produced a nearly saturated strain/temperature response. The thermomechanical observations are discussed in terms of the nature of strain evolution and its connection to the concept of a local/global minimization of the energy of the system, however, the exact mechanisms associated with these strain evolutions were not determined.     

Application of a Near-Optimal Reinforcement Learning Controller to a Robotics Problem in Manufacturing: A Hybrid Approach

Optimization theory provides a framework for determining the best decisions or actions with respect to some mathematical model of a process. This paper focuses on learning to act in a near-optimal manner through reinforcement learning for problems that either have no model or the model is too complex. One approach to solving this class of problems is via approximate dynamic programming. The application of these methods are established primarily for the case of discrete state and action spaces. In this paper we develop efficient methods of learning which act in complex systems with continuous state and action spaces. Monte-Carlo approaches are employed to estimate function values in an iterative, incremental procedure. Derivative-free line search methods are used to obtain a near-optimal action in the continuous action space for a discrete subset of the state space. This near-optimal control policy is then extended to the entire continuous state space via a fuzzy additive model. To compensate for approximation errors, a modified procedure for perturbing the generated control policy is developed. Convergence results under moderate assumptions and stopping criteria are established.     

A proposition on memes and meta-memes in computing for higher-order learning

In computational intelligence, the term ‘memetic algorithm’ has come to be associated with the algorithmic pairing of a global search method with a local search method. In a sociological context, a ‘meme’ has been loosely defined as a unit of cultural information, the social analog of genes for individuals. Both of these definitions are inadequate, as ‘memetic algorithm’ is too specific, and ultimately a misnomer, as much as a ‘meme’ is defined too generally to be of scientific use. In this paper, we extend the notion of memes from a computational viewpoint and explore the purpose, definitions, design guidelines and architecture for effective memetic computing. Utilizing two conceptual case studies, we illustrate the power of high-order meme-based learning. With applications ranging from cognitive science to machine learning, memetic computing has the potential to provide much-needed stimulation to the field of computational intelligence by providing a framework for higher order learning.