The spiral of applied research: A methodological view on integrated design research

Abstract not available

Randomized Extended Kaczmarz for Solving Least-Squares

We present a randomized iterative algorithm that exponentially converges in expectation to the minimum Euclidean norm least squares solution of a given linear system of equations. The expected number of arithmetic operations required to obtain an estimate of given accuracy is proportional to the square condition number of the system multiplied by the number of non-zeros entries of the input matrix. The proposed algorithm is an extension of the randomized Kaczmarz method that was analyzed by Strohmer and Vershynin.Comment: 19 Pages, 5 figures; code is available at https://github.com/zouzias/RE

Solving the riddle of codon usage preferences: a test for translational selection

Translational selection is responsible for the unequal usage of synonymous codons in protein coding genes in a wide variety of organisms. It is one of the most subtle and pervasive forces of molecular evolution, yet, establishing the underlying causes for its idiosyncratic behaviour across living kingdoms has proven elusive to researchers over the past 20 years. In this study, a statistical model for measuring translational selection in any given genome is developed, and the test is applied to 126 fully sequenced genomes, ranging from archaea to eukaryotes. It is shown that tRNA gene redundancy and genome size are interacting forces that ultimately determine the action of translational selection, and that an optimal genome size exists for which this kind of selection is maximal. Accordingly, genome size also presents upper and lower boundaries beyond which selection on codon usage is not possible. We propose a model where the coevolution of genome size and tRNA genes explains the observed patterns in translational selection in all living organisms. This model finally unifies our understanding of codon usage across prokaryotes and eukaryotes. Helicobacter pylori, Saccharomyces cerevisiae and Homo sapiens are codon usage paradigms that can be better understood under the proposed model

The application of reliability methods in the design of stiffened FRP composite panels for marine vessels

The use of composite laminate materials has increased rapidly in recent years due to their excellent strength to weight ratio and resistance to corrosion. In the construction of marine vessels, stiffened plates are the most commonly used structural elements, forming the deck, bottom hull, side shells and bulkheads. This paper presents the use of a stochastic approach to the design of stiffened marine composite panels as part of a current research programme into developing stochastic methods for composite ship structures, accounting for variations in material properties, geometric indices and processing techniques, from the component level to the full system level. An analytical model for the solution of a stiffened isotropic plate using a grillage analogy is extended by the use of equivalent elastic properties for composite modelling. This methodology is applied in a reliability analysis of an isotropic (steel) stiffened plate before the final application for a reliability analysis for a FRP composite stiffened plate

Encoded

ENCODED is an immersive aerial dance performance and installation that uses the latest interactive technologies to build a projected digital environment that responds to the movements of the performers

Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation

The Yablonskii-Vorob'ev polynomials $y_{n}(t)$, which are defined by a second order bilinear differential-difference equation, provide rational solutions of the Toda lattice. They are also polynomial tau-functions for the rational solutions of the second Painlev\'{e} equation ($P_{II}$). Here we define two-variable polynomials $Y_{n}(t,h)$ on a lattice with spacing $h$, by considering rational solutions of the discrete time Toda lattice as introduced by Suris. These polynomials are shown to have many properties that are analogous to those of the Yablonskii-Vorob'ev polynomials, to which they reduce when $h=0$. They also provide rational solutions for a particular discretisation of $P_{II}$, namely the so called {\it alternate discrete} $P_{II}$, and this connection leads to an expression in terms of the Umemura polynomials for the third Painlev\'{e} equation ($P_{III}$). It is shown that B\"{a}cklund transformation for the alternate discrete Painlev\'{e} equation is a symplectic map, and the shift in time is also symplectic. Finally we present a Lax pair for the alternate discrete $P_{II}$, which recovers Jimbo and Miwa's Lax pair for $P_{II}$ in the continuum limit $h\to 0$.Comment: 23 pages, IOP style. Title changed, and connection with Umemura polynomials adde

The Hamiltonian Structure of the Second Painleve Hierarchy

In this paper we study the Hamiltonian structure of the second Painleve hierarchy, an infinite sequence of nonlinear ordinary differential equations containing PII as its simplest equation. The n-th element of the hierarchy is a non linear ODE of order 2n in the independent variable $z$ depending on n parameters denoted by ${t}_1,...,{t}_{n-1}$ and $\alpha_n$. We introduce new canonical coordinates and obtain Hamiltonians for the $z$ and $t_1,...,t_{n-1}$ evolutions. We give explicit formulae for these Hamiltonians showing that they are polynomials in our canonical coordinates

Dynamics of a lattice Universe

We find a solution to Einstein field equations for a regular toroidal lattice of size L with equal masses M at the centre of each cell; this solution is exact at order M/L. Such a solution is convenient to study the dynamics of an assembly of galaxy-like objects. We find that the solution is expanding (or contracting) in exactly the same way as the solution of a Friedman-Lema\^itre-Robertson-Walker Universe with dust having the same average density as our model. This points towards the absence of backreaction in a Universe filled with an infinite number of objects, and this validates the fluid approximation, as far as dynamics is concerned, and at the level of approximation considered in this work.Comment: 14 pages. No figure. Accepted version for Classical and Quantum Gravit