Nonlocal First-Order Hamilton-Jacobi Equations Modelling Dislocations Dynamics

We study nonlocal first-order equations arising in the theory of dislocations. We prove the existence and uniqueness of the solutions of these equations in the case of positive and negative velocities, under suitable regularity assumptions on the initial data and the velocity. These results are based on new $L^1$-type estimates on the viscosity solutions of first-order Hamilton-Jacobi Equations appearing in the so-called ``level-sets approach''. Our work is inspired by and simplifies a recent work of Alvarez, Cardaliaguet and Monneau

How Researchers Use Diagrams in Communicating Neural Network Systems

Neural networks are a prevalent and effective machine learning component, and their application is leading to significant scientific progress in many domains. As the field of neural network systems is fast growing, it is important to understand how advances are communicated. Diagrams are key to this, appearing in almost all papers describing novel systems. This paper reports on a study into the use of neural network system diagrams, through interviews, card sorting, and qualitative feedback structured around ecologically-derived examples. We find high diversity of usage, perception and preference in both creation and interpretation of diagrams, examining this in the context of existing design, information visualisation, and user experience guidelines. Considering the interview data alongside existing guidance, we propose guidelines aiming to improve the way in which neural network system diagrams are constructed.Comment: 19 pages, 6 tables, 3 figure

The large gender gap in Trump’s support threatens his reelection. Here’s what’s driving it.

While women have tended to be more supportive of Democrats than Republicans in recent years, the gender gap in support for Donald Trump between men and women is exceptionally large, write Harold Clarke, Marianne Stewart, Paul Whiteley and Guy D. Whitten

Dermal Absorption of Pesticide Residues

Current guidance for dermal exposure assessment of plant protection products typically uses in vitro skin penetration data for the active ingredient when applied as both the concentrated product and relevant spray dilutions thereof. However, typical re-entry scenarios involve potential skin exposure to a "dried residue" of the spray dilution, from which the absorption of a pesticide may be quite different. The research reported in this paper has shown: (1) The method to assess the transfer of dried pesticide residues from a surface to the skin is reproducible for four active ingredients of diverse physicochemical properties, after their application in commercially relevant formulations. (2) Skin absorption of all four pesticides examined was significantly less from a dried residue than from a spray dilution; the difference, in general, was of the order of a factor of 2. (3) Decontamination experiments with one of the active ingredients tested (trinexapac-ethyl) showed that, post-exposure to a spray dilution, skin surface cleaning must be performed within 1 h to significantly reduce potential systemic exposure (relative to continual contact for 24 h); in contrast, after contact with a dried residue, the sooner decontamination was performed, the greater the decrease in exposure achieved, even when the time of contact was as long as 8 h.</p

Uniqueness Results for Nonlocal Hamilton-Jacobi Equations

We are interested in nonlocal Eikonal Equations describing the evolution of interfaces moving with a nonlocal, non monotone velocity. For these equations, only the existence of global-in-time weak solutions is available in some particular cases. In this paper, we propose a new approach for proving uniqueness of the solution when the front is expanding. This approach simplifies and extends existing results for dislocation dynamics. It also provides the first uniqueness result for a Fitzhugh-Nagumo system. The key ingredients are some new perimeter estimates for the evolving fronts as well as some uniform interior cone property for these fronts

Lagrange formalism of memory circuit elements: classical and quantum formulations

The general Lagrange-Euler formalism for the three memory circuit elements, namely, memristive, memcapacitive, and meminductive systems, is introduced. In addition, {\it mutual meminductance}, i.e. mutual inductance with a state depending on the past evolution of the system, is defined. The Lagrange-Euler formalism for a general circuit network, the related work-energy theorem, and the generalized Joule's first law are also obtained. Examples of this formalism applied to specific circuits are provided, and the corresponding Hamiltonian and its quantization for the case of non-dissipative elements are discussed. The notion of {\it memory quanta}, the quantum excitations of the memory degrees of freedom, is presented. Specific examples are used to show that the coupling between these quanta and the well-known charge quanta can lead to a splitting of degenerate levels and to other experimentally observable quantum effects

Investigating the origins of ivory recovered in the United Kingdom

Over recent years, mounting pressure has been placed on countries to assess their role in the ivory trade, with a view to tackling the rapidly declining numbers of elephants, due to poaching. The United Kingdom has been identified as a large re-exporter of ivory. Despite much of this trade being reported as legal or antique ivory, such provision of ivory to meet demand is known to fuel illegal markets and provide trade routes for modern ivory sales. Aside from ivory species and age, further analysis to evaluate geographic provenance, can inform where an elephant had lived, and so identify a source region or population where poaching occurred. The purpose of this study was to determine the age and species of ivory objects surrendered or seized in the UK and assess their likely geographic provenance through comparison of results from mitochondrial DNA and stable isotope analysis to publicly accessible georeferenced African elephant databases. The results demonstrated that the objects tested from an airport seizure were modern and matched existing haplotypes allowing for regional geographic inferences (supported by both techniques) to be obtained for most of these objects. In contrast, antique and modern ivory was detected amongst the amnesty objects, and several new mtDNA haplotypes were identified. Regional geographic inferences were achieved for some but not all of the objects tested. Our findings show this combination of methods provides a wealth of information which, could provide insight into targeted elephant populations and assist in disrupting international wildlife trade networks