Graph Theory

Highlights of this workshop on structural graph theory included new developments on graph and matroid minors, continuous structures arising as limits of finite graphs, and new approaches to higher graph connectivity via tree structures

A novel method to rapidly fit conductance-based models to individual neurons

In this thesis, I present a new method of model optimisation that allows the calibration of conductance-based models of neuronal membrane potential to data from just a single neuron, and achieves good correspondence with the reference data in mere minutes. These properties are desirable because they allow investigations of individual variability among neurons of a given type, of homoeostatic processes and non-synaptic plasticity events, as well as of the contribution of particular neuronal properties to the dynamics of small circuits. In the first chapter, the thesis introduces in detail the working principle of the method, which can be summed up as model optimisation using stimuli to isolate parameter subsets (“MOSTIPS”), and represents a major part of the work and novelty of this project. The second chapter focusses on the construction of accurate models of two mammalian potassium channels which, being ectopically expressed in Xenopus laevis oocytes, served as a validation tool for the new method. In the third chapter, I evaluate the new method, presenting results from fitting models to data from synthetic sources as well as the above-mentioned oocytes. Finally, the fourth chapter contains a number of related results from closed-loop electrophysiology approaches, including extensions to the dynamic clamp protocol for both single neurons and hybrid circuits composed of live and simulated neurons, as well as preliminary results from a closed-loop model fitting approach closely related to the main work presented above. The thesis concludes that the newly developed approaches to model fitting constitute valuable additions to existing methods. The MOSTIPS method achieves tightly constrained parametrisations using both less data and less processing time than classical methods, while the related closed-loop fitting approach produces results that closely follow ongoing changes in evoked activity patterns in real time. Conversely, some issues have been left unanswered, including the contribution of the stimulus generation and selection algorithm, the success of which I have been unable to establish, as well as whether the methods developed herein can reliably identify relevant properties of individual cells. Nevertheless, both the particular methods and the general approach of using prior estimates of the model and its parameter values to propose stimulus patterns represent major advances in the field of neuron model optimisation

Recent Advances in Industrial and Applied Mathematics

This open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress

Bibliography of Lewis Research Center technical publications announced in 1992

This compilation of abstracts describes and indexes the technical reporting that resulted from the scientific and engineering work performed and managed by the Lewis Research Center in 1992. All the publications were announced in the 1992 issues of STAR (Scientific and Technical Aerospace Reports) and/or IAA (International Aerospace Abstracts). Included are research reports, journal articles, conference presentations, patents and patent applications, and theses

Recent Advances in Industrial and Applied Mathematics

This open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress

Tensor lattice field theory with applications to the renormalization group and quantum computing

We discuss the successes and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution. We show that these lattice models can be reformulated using tensorial methods where the field integrations in the path-integral formalism are replaced by discrete sums. These formulations involve various types of duality and provide exact coarse-graining formulas which can be combined with truncations to obtain practical implementations of the Wilson renormalization group program. Tensor reformulations are naturally discrete and provide manageable transfer matrices. Combining truncations with the time continuum limit, we derive Hamiltonians suitable to perform quantum simulation experiments, for instance using cold atoms, or to be programmed on existing quantum computers. We review recent progress concerning the tensor field theory treatment of non-compact scalar models, supersymmetric models, economical four-dimensional algorithms, noise-robust enforcement of Gauss's law, symmetry preserving truncations and topological considerations. We discuss connections with other tensor network approaches.Comment: Review article, 71 pages, 47 figures, connections to other tensor network approaches and references adde