Graphical and mechanical computation,

"Embodies a course given by the writer for a number of years in the mathematical laboratory of the Massachusetts Institute of Technology."

An investigation of the laws of thought, on which are founded the mathematical theories of logic and probabilities.

Mode of access: Internet.

The mathematical review

No title-page

An investigation of the laws of thought, on which are founded mathematical theories of logic and probabilities.

Mode of access: Internet.

Operations and Planning in Sustainable Power Systems

Thesis (Ph.D.)--University of Washington, 2016-06

Optimization and Machine Learning Frameworks for Complex Network Analysis

Thesis (Ph.D.)--University of Washington, 2016-06

Optics and Optoelectronics of Two-dimensional Semiconducting Monolayers and Heterostructures

Thesis (Ph.D.)--University of Washington, 2016-06

Breadth-first search and the Andrews-Curtis conjecture

Andrews and Curtis conjectured in 1965 that every balanced presentation of the trivial group can be transformed into a standard presentation by a finite sequence of elementary transformations. Recent computational work by Miasnikov and Myasnikov on this problem has been based on genetic algorithms. We show that a computational attack based on a breadth-first search of the tree of equivalent presentations is also viable, and seems to outperform that based on genetic algorithms. It allows us to extract shorter proofs (in some cases, provably shortest) and to consider the length thirteen case for two generators. We prove that, up to equivalence, there is a unique minimum potential counterexample.

Numerical simulation of stochastic ordinary differential equations in biomathematical modelling

In this work we discuss the effects of white and coloured noise perturbations on the parameters of a mathematical model of bacteriophage infection introduced by Beretta and Kuang in [Math. Biosc. 149 (1998) 57]. We numerically simulate the strong solutions of the resulting systems of stochastic ordinary differential equations (SDEs), with respect to the global error, by means of numerical methods of both Euler-Taylor expansion and stochastic Runge-Kutta type. (C) 2003 IMACS. Published by Elsevier B.V. All rights reserved.

A multi-scaled approach for simulating chemical reaction systems

In this paper we give an overview of some very recent work, as well as presenting a new approach, on the stochastic simulation of multi-scaled systems involving chemical reactions. In many biological systems (such as genetic regulation and cellular dynamics) there is a mix between small numbers of key regulatory proteins, and medium and large numbers of molecules. In addition, it is important to be able to follow the trajectories of individual molecules by taking proper account of the randomness inherent in such a system. We describe different types of simulation techniques (including the stochastic simulation algorithm, Poisson Runge–Kutta methods and the balanced Euler method) for treating simulations in the three different reaction regimes: slow, medium and fast. We then review some recent techniques on the treatment of coupled slow and fast reactions for stochastic chemical kinetics and present a new approach which couples the three regimes mentioned above. We then apply this approach to a biologically inspired problem involving the expression and activity of LacZ and LacY proteins in E. coli, and conclude with a discussion on the significance of this work.

International evaluation of current and future requirements for environmental engineering education

The field of environmental engineering is developing as a result of changing environmental requirements. In response, environmental engineering education (E3) needs to ensure that it provides students with the necessary tools to address these challenges. In this paper the current status and future development of E3 is evaluated based on a questionnaire sent to universities and potential employers of E3 graduates. With increasing demands on environmental quality, the complexity of environmental engineering problems to be solved can be expected to increase. To find solutions environmental engineers will need to work in interdisciplinary teams. Based on the questionnaire there was a broad agreement that the best way to prepare students for these future challenges is to provide them with a fundamental education in basic sciences and related engineering fields. Many exciting developments in the environmental engineering profession will be located at the interface between engineering, science, and society. Aspects of all three areas need to be included in E3 and the student needs to be exposed to the tensions associated with linking the three.

The development of retinotectal maps: A review of models based on molecular gradients

Information about the world is often represented in the brain in the form of topographic maps. A paradigm example is the topographic representation of the visual world in the optic tectum/superior colliculus. This map initially forms during neural development using activity-independent molecular cues, most notably some type of chemospecific matching between molecular gradients in the retina and corresponding gradients in the tectum/superior colliculus. Exactly how this process might work has been studied both experimentally and theoretically for several decades. This review discusses the experimental data briefly, and then in more detail the theoretical models proposed. The principal conclusions are that (1) theoretical models have helped clarify several important ideas in the field, (2) earlier models were often more sophisticated than more recent models, and (3) substantial revisions to current modelling approaches are probably required to account for more than isolated subsets of the experimental data.