Breaking the habit: measuring and predicting departures from routine in individual human mobility

Researchers studying daily life mobility patterns have recently shown that humans are typically highly predictable in their movements. However, no existing work has examined the boundaries of this predictability, where human behaviour transitions temporarily from routine patterns to highly unpredictable states. To address this shortcoming, we tackle two interrelated challenges. First, we develop a novel information-theoretic metric, called instantaneous entropy, to analyse an individual’s mobility patterns and identify temporary departures from routine. Second, to predict such departures in the future, we propose the first Bayesian framework that explicitly models breaks from routine, showing that it outperforms current state-of-the-art predictor

Optimising superoscillatory spots for far-field super-resolution imaging

Optical superoscillatory imaging, allowing unlabelled far-field super-resolution, has in recent years become reality. Instruments have been built and their super-resolution imaging capabilities demonstrated. The question is no longer whether this can be done, but how well: what resolution is practically achievable? Numerous works have optimised various particular features of superoscillatory spots, but in order to probe the limits of superoscillatory imaging we need to simultaneously optimise all the important spot features: those that define the resolution of the system. We simultaneously optimise spot size and its intensity relative to the sidebands for various fields of view, giving a set of best compromises for use in different imaging scenarios. Our technique uses the circular prolate spheroidal wave functions as a basis set on the field of view, and the optimal combination of these, representing the optimal spot, is found using a multi-objective genetic algorithm. We then introduce a less computationally demanding approach suitable for real-time use in the laboratory which, crucially, allows independent control of spot size and field of view. Imaging simulations demonstrate the resolution achievable with these spots. We show a three-order-of-magnitude improvement in the efficiency of focusing to achieve the same resolution as previously reported results, or a 26 % increase in resolution for the same efficiency of focusing

Old and New Fields on Super Riemann Surfaces

The ``new fields" or ``superconformal functions" on $N=1$ super Riemann surfaces introduced recently by Rogers and Langer are shown to coincide with the Abelian differentials (plus constants), viewed as a subset of the functions on the associated $N=2$ super Riemann surface. We confirm that, as originally defined, they do not form a super vector space.Comment: 9 pages, LaTex. Published version: minor changes for clarity, two new reference

Nonlinear self-adjointness and conservation laws

The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self-adjointness and quasi self-adjointness introduced earlier by the author. It is shown that the equations possessing the nonlinear self-adjointness can be written equivalently in a strictly self-adjoint form by using appropriate multipliers. All linear equations possess the property of nonlinear self-adjointness, and hence can be rewritten in a nonlinear strictly self-adjoint. For example, the heat equation $u_t - \Delta u = 0$ becomes strictly self-adjoint after multiplying by $u^{-1}.$ Conservation laws associated with symmetries can be constructed for all differential equations and systems having the property of nonlinear self-adjointness

Gauge fixing and equivariant cohomology

The supersymmetric model developed by Witten to study the equivariant cohomology of a manifold with an isometric circle action is derived from the BRST quantization of a simple classical model. The gauge-fixing process is carefully analysed, and demonstrates that different choices of gauge-fixing fermion can lead to different quantum theories.Comment: 18 pages LaTe

Current-Voltage Characteristics of Long-Channel Nanobundle Thin-Film Transistors: A Bottom-up Perspective

By generalizing the classical linear response theory of stick percolation to nonlinear regime, we find that the drain current of a Nanobundle Thin Film Transistor (NB-TFT) is described under a rather general set of conditions by a universal scaling formula ID = A/LS g(LS/LC, rho_S * LS * LS) f(VG, VD), where A is a technology-specific constant, g is function of geometrical factors like stick length (LS), channel length (LC), and stick density (rho_S) and f is a function of drain (VD) and gate (VG) biasing conditions. This scaling formula implies that the measurement of full I-V characteristics of a single NB-TFT is sufficient to predict the performance characteristics of any other transistor with arbitrary geometrical parameters and biasing conditions

A dispersive wave pattern on Jupiter's fastest retrograde jet at 20∘20^\circS

A compact wave pattern has been identified on Jupiter's fastest retrograding jet at 20S (the SEBs) on the southern edge of the South Equatorial Belt. The wave has been identified in both reflected sunlight from amateur observations between 2010 and 2015, thermal infrared imaging from the Very Large Telescope and near infrared imaging from the Infrared Telescope Facility. The wave pattern is present when the SEB is relatively quiescent and lacking large-scale disturbances, and is particularly notable when the belt has undergone a fade (whitening). It is generally not present when the SEB exhibits its usual large-scale convective activity ('rifts'). Tracking of the wave pattern and associated white ovals on its southern edge over several epochs have permitted a measure of the dispersion relationship, showing a strong correlation between the phase speed (-43.2 to -21.2 m/s) and the longitudinal wavelength, which varied from 4.4-10.0 deg. longitude over the course of the observations. Infrared imaging sensing low pressures in the upper troposphere suggest that the wave is confined to near the cloud tops. The wave is moving westward at a phase speed slower (i.e., less negative) than the peak retrograde wind speed (-62 m/s), and is therefore moving east with respect to the SEBs jet peak. Unlike the retrograde NEBn jet near 17N, which is a location of strong vertical wind shear that sometimes hosts Rossby wave activity, the SEBs jet remains retrograde throughout the upper troposphere, suggesting the SEBs pattern cannot be interpreted as a classical Rossby wave. Cassini-derived windspeeds and temperatures reveal that the vorticity gradient is dominated by the baroclinic term and becomes negative (changes sign) in a region near the cloud-top level (400-700 mbar) associated with the SEBs, suggesting a baroclinic origin for this meandering wave pattern. [Abr]Comment: 19 pages, 11 figures, article accepted for publication in Icaru

Product renovation and shared ownership: sustainable routes to satisfying the world's growing demand for goods

It has been estimated that by 2030 the number of people who are wealthy enough to be considered as middle class consumers will have tripled. This will have a dramatic impact on the demands for primary materials and energy. Much work has been carried out on sustainable ways of meeting the World’s energy demands and some work has been carried out on the sustainable production and consumption of goods. It has been estimated that with improvements in design and manufacturing it is possible to reduce the primary material requirements by 30% to produce the current demand for goods. Whilst this is a crucial step on the production side, there will still be a doubling of primary material requirements by the end of the century because of an absolute rise in demand for goods and services. It is therefore clear that the consumption of products must also be explored. This is a key areas of research for the UK INDEMAND centre, which is investigating ways of reducing the UK’s industrial energy demand and demand for energy intensive materials. Our ongoing work shows that two strategies would result in considerable reductions in the demand for primary materials: product longevity and using goods more intensively (which may requires increased durability). Product longevity and durability are not new ideas, but ones that can be applied across a raft of goods as methods of reducing the consumption of materials. With long life products there is a potential risk of outdated design and obsolescence, consequently there is a need to ensure upgradability and adaptability are incorporated at the design stage. If products last longer, then the production of new products can be diverted to emerging markets rather than the market for replacement goods. There are many goods which are only used occasionally; these goods do not normally wear out. The total demand for such could be drastically reduced if they were shared with other people. Sharing of goods has traditionally been conducted between friends or by hiring equipment. The use of modern communication systems and social media could enable the development of sharing co-ops and swap spaces that will increase the utilisation of goods and hence reduce the demand for new goods. This could also increase access to a range of goods for those on low incomes. From a series of workshops it has been found that the principal challenges are sociological rather than technological. This paper contains a discussion of these challenges and explores possible futures where these two strategies have been adopted. In addition, the barriers and opportunities that these strategies offer for consumers and businesses are identified, and areas where government policy could be instigated to bring about change are highlighted

A Dirac-type Characterization of k-chordal Graphs

Characterization of k-chordal graphs based on the existence of a "simplicial path" was shown in [Chv{\'a}tal et al. Note: Dirac-type characterizations of graphs without long chordless cycles. Discrete Mathematics, 256, 445-448, 2002]. We give a characterization of k-chordal graphs which is a generalization of the known characterization of chordal graphs due to [G. A. Dirac. On rigid circuit graphs. Abh. Math. Sem. Univ. Hamburg, 25, 71-76, 1961] that use notions of a "simplicial vertex" and a "simplicial ordering".Comment: 3 page

Marketing Percolation

A percolation model is presented, with computer simulations for illustrations, to show how the sales of a new product may penetrate the consumer market. We review the traditional approach in the marketing literature, which is based on differential or difference equations similar to the logistic equation (Bass 1969). This mean field approach is contrasted with the discrete percolation on a lattice, with simulations of "social percolation" (Solomon et al 2000) in two to five dimensions giving power laws instead of exponential growth, and strong fluctuations right at the percolation threshold.Comment: to appear in Physica