Functional expansion representations of artificial neural networks

In the past few years, significant interest has developed in using artificial neural networks to model and control nonlinear dynamical systems. While there exists many proposed schemes for accomplishing this and a wealth of supporting empirical results, most approaches to date tend to be ad hoc in nature and rely mainly on heuristic justifications. The purpose of this project was to further develop some analytical tools for representing nonlinear discrete-time input-output systems, which when applied to neural networks would give insight on architecture selection, pruning strategies, and learning algorithms. A long term goal is to determine in what sense, if any, a neural network can be used as a universal approximator for nonliner input-output maps with memory (i.e., realized by a dynamical system). This property is well known for the case of static or memoryless input-output maps. The general architecture under consideration in this project was a single-input, single-output recurrent feedforward network

SISO Output Affine Feedback Transformation Group and Its Faa di Bruno Hopf Algebra

The general goal of this paper is to identify a transformation group that can be used to describe a class of feedback interconnections involving subsystems which are modeled solely in terms of Chen-Fliess functional expansions or Fliess operators and are independent of the existence of any state space models. This interconnection, called an output affine feedback connection, is distinguished from conventional output feedback by the presence of a multiplier in an outer loop. Once this transformation group is established, three basic questions are addressed. How can this transformation group be used to provide an explicit Fliess operator representation of such a closed-loop system? Is it possible to use this feedback scheme to do system inversion purely in an input-output setting? In particular, can feedback input-output linearization be posed and solved entirely in this framework, i.e., without the need for any state space realization? Lastly, what can be said about feedback invariants under this transformation group? A final objective of the paper is to describe the Lie algebra of infinitesimal characters associated with the group in terms of a pre-Lie product.Comment: revised manuscript; title and abstract changed; new material adde

Assembly and functionalization of phage onto substrates patterned by dip-pen nanolithography

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2006.Includes bibliographical references (leaves 25-26).Advances in nanochemistry will drive the development of technologies at the scale of 1 - 100 nm. Principles of biology are used for the self-assembly of structures and devices at this scale. The Ml 13 bacteriophage, a virus employed in phage-display libraries, serves as a scaffold for nanoscale structures. Phage are functionalized with inorganic materials, and controlled placement of phage at the nanoscale may lead to useful devices. Substrates patterned with dip-pen nanolithography (DPN) serve as templates for the deposition of phage. On gold substrates, 16-mercaptohexadecanoic acid (MHA) is deposited to form patterned lines. After surface passivation and activation chemistry, phage are deposited and adhere to the patterned substrate. Images from atomic force microscopy support that phage are covalently coupled to MHA lines and that cobalt precipitates on patterned phage.by David S. Gray.S.B

Dendriform-Tree Setting for Fully Non-commutative Fliess Operators

This paper provides a dendriform-tree setting for Fliess operators with matrix-valued inputs. This class of analytic nonlinear input-output systems is convenient, for example, in quantum control. In particular, a description of such Fliess operators is provided using planar binary trees. Sufficient conditions for convergence of the defining series are also given

A comparative analysis of two different analysers used for determination of the Total Organic Carbon in pharmaceutical grade water

Total Organic Carbon (TOC) is a routine test for pharmaceutical grade water. Several manufacturers supply equipment of different designs but there is a dearth of published, peer-reviewed, information evaluating the various analysers. In this study, we compared two TOC analysers, both validated to the same pharmacopoeial criteria, but with different oxidation and detection methods. The results in this paper show that there were no unexplained out-of-specification results and that both analysers operated equivalently in terms of the pharmacopoeial 500ppb pass/fail limits. However, significant differences between the TOC levels reported from paired samples were observed, two paired samples recorded a pass/fail conflict (albeit flagged with an overestimation warning), as well as differences in analyser responses between spiked samples that contained low levels of nitro- and chloro-carbon compounds