418 research outputs found

### Tensor Products, Positive Linear Operators, and Delay-Differential Equations

We develop the theory of compound functional differential equations, which
are tensor and exterior products of linear functional differential equations.
Of particular interest is the equation $\dot
x(t)=-\alpha(t)x(t)-\beta(t)x(t-1)$ with a single delay, where the delay
coefficient is of one sign, say $\delta\beta(t)\ge 0$ with $\delta\in{-1,1}$.
Positivity properties are studied, with the result that if $(-1)^k=\delta$ then
the $k$-fold exterior product of the above system generates a linear process
which is positive with respect to a certain cone in the phase space.
Additionally, if the coefficients $\alpha(t)$ and $\beta(t)$ are periodic of
the same period, and $\beta(t)$ satisfies a uniform sign condition, then there
is an infinite set of Floquet multipliers which are complete with respect to an
associated lap number. Finally, the concept of $u_0$-positivity of the exterior
product is investigated when $\beta(t)$ satisfies a uniform sign condition.Comment: 84 page

### John Mallet: 'This is the way that life happened'

Article for festschrift publication in honour of V&A former Keeper of Ceramics, John Mallet, drawing on extracts of his life history recording with Linda Sandino for the V&A Curators Lives oral history project

### Snakes: Oriented families of periodic orbits, their sources, sinks, and continuation

AbstractPoincarĆ© observed that for a differential equation xā² = Ę(x, Ī±) depending on a parameter Ī±, each periodic orbit generally lies in a connected family of orbits in (x, Ī±)-space. In order to investigate certain large connected sets (denoted Q) of orbits containing a given orbit, we introduce two indices: an orbit index Ļ and a ācenterā index defined at certain stationary points. We show that genetically there are two types of Hopf bifurcation, those we call āsourcesā ( = 1) and āsinksā ( = ā1). Generically if the set Q is bounded in (x, Ī±)-space, and if there is an upper bound for periods of the orbits in Q, then Q must have as many source Hopf bifurcations as sink Hopf bifurcations and each source is connected to a sink by an oriented one-parameter āsnakeā of orbits. A āsnakeā is a maximal path of orbits that contains no orbits whose orbit index is 0. See Fig. 1.1

### Traveling Wave Solutions for Systems of ODEs on a Two-Dimensional Spatial Lattice

This is the published version, also available here: http://dx.doi.org/10.1137/S0036139996312703.We consider infinite systems of ODEs on the two-dimensional integer lattice, given by a bistable scalar ODE at each point, with a nearest neighbor coupling between lattice points. For a class of ideal nonlinearities, we obtain traveling wave solutions in each direction $e^{i\theta}$, and we explore the relation between the wave speed c, the angle $\theta$, and the detuning parameter a of the nonlinearity. Of particular interest is the phenomenon of "propagation failure," and we study how the critical value $a=a^*(\theta)$ depends on $\theta$, where $a^*(\theta)$ is defined as the value of the parameter a at which propagation failure (that is, wave speed c=0) occurs. We show that $a^*:\Bbb{R}\to\Bbb{R} is continuous at each point$\theta$where$\tan\theta$is irrational, and is discontinuous where$\tan\theta$ is rational or infinite

### A model of workplace safety incorporating worker interactions and simple interventions

Although there was substantial research into the occupational health and safety sector over the past forty years, this generally focused on statistical analyses of data related to costs and/or fatalities and injuries. There is a lack of mathematical modelling of the interactions between workers and the resulting safety dynamics of the workplace. There is also little work investigating the potential impact of different safety intervention programs prior to their implementation. In this article, we present a fundamental, differential equation-based model of workplace safety that treats worker safety habits similarly to an infectious disease in an epidemic model. Analytical results for the model, derived via phase plane and stability analysis, are discussed. The model is coupled with a model of a generic safety strategy aimed at minimising unsafe work habits, to produce an optimal control problem. The optimal control model is solved using the forward-backward sweep numerical scheme implemented in Matlab.
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### Noiseless nonreciprocity in a parametric active device

Nonreciprocal devices such as circulators and isolators belong to an
important class of microwave components employed in applications like the
measurement of mesoscopic circuits at cryogenic temperatures. The measurement
protocols usually involve an amplification chain which relies on circulators to
separate input and output channels and to suppress backaction from different
stages on the sample under test. In these devices the usual reciprocal symmetry
of circuits is broken by the phenomenon of Faraday rotation based on magnetic
materials and fields. However, magnets are averse to on-chip integration, and
magnetic fields are deleterious to delicate superconducting devices. Here we
present a new proposal combining two stages of parametric modulation emulating
the action of a circulator. It is devoid of magnetic components and suitable
for on-chip integration. As the design is free of any dissipative elements and
based on reversible operation, the device operates noiselessly, giving it an
important advantage over other nonreciprocal active devices for quantum
information processing applications.Comment: 17 pages, 4 figures + 12 pages Supplementary Informatio

### Major improvements to the Heliconius melpomene genome assembly used to confirm 10 chromosome fusion events in 6 million years of butterfly evolution

The Heliconius butterflies are a widely studied adaptive radiation of 46 species spread across Central and South America, several of which are known to hybridize in the wild. Here, we present a substantially improved assembly of the Heliconius melpomene genome, developed using novel methods that should be applicable to improving other genome assemblies produced using short read sequencing. First, we whole-genome-sequenced a pedigree to produce a linkage map incorporating 99% of the genome. Second, we incorporated haplotype scaffolds extensively to produce a more complete haploid version of the draft genome. Third, we incorporated ~20x coverage of Pacific Biosciences sequencing, and scaffolded the haploid genome using an assembly of this long-read sequence. These improvements result in a genome of 795 scaffolds, 275 Mb in length, with an N50 length of 2.1 Mb, an N50 number of 34, and with 99% of the genome placed, and 84% anchored on chromosomes. We use the new genome assembly to confirm that the Heliconius genome underwent 10 chromosome fusions since the split with its sister genus Eueides, over a period of about 6 million yr

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