On the average box dimensions of graphs of typical continuous functions

Let X be a bounded subset of Rd and write Cu(X) for the set of uniformly continuous functions on X equipped with the uniform norm. The lower and upper box dimensions, denoted by dim̲B(graph(f)) and dim ¯ B(graph (f)) , of the graph graph (f) of a function f∈ Cu(X) are defined by dim̲B(graph(f))=limδ↘0inflogNδ(graph(f))-logδ,dim¯B(graph(f))=limδ↘0suplogNδ(graph(f))-logδ,where Nδ(graph (f)) denotes the number of δ-mesh cubes that intersect graph (f). Hyde et al. have recently proved that the box counting function(∗)logNδ(graph(f))-logδof the graph of a typical function f∈ Cu(X) diverges in the worst possible way as δ↘ 0. More precisely, Hyde et al. showed that for a typical function f∈ Cu(X) , the lower box dimension of the graph of f is as small as possible and if X has only finitely many isolated points, then the upper box dimension of the graph of f is as big as possible. In this paper we will prove that the box counting function (*) of the graph of a typical function f∈ Cu(X) is spectacularly more irregular than suggested by the result due to Hyde et al. Namely, we show the following surprising result: not only is the box counting function in (*) divergent as δ↘ 0 , but it is so irregular that it remains spectacularly divergent as δ↘ 0 even after being “averaged" or “smoothened out" using exceptionally powerful averaging methods including all higher order Hölder and Cesàro averages and all higher order Riesz–Hardy logarithmic averages. For example, if the box dimension of X exists, then we show that for a typical function f∈ Cu(X) , all the higher order lower Hölder and Cesàro averages of the box counting function (*) are as small as possible, namely, equal to the box dimension of X, and if, in addition, X has only finitely many isolated points, then all the higher order upper Hölder and Cesàro averages of the box counting function (*) are as big as possible, namely, equal to the box dimension of X plus 1.PostprintPeer reviewe

Age estimation of Calliphora (Diptera: Calliphoridae) larvae using cuticular hydrocarbon analysis and Artificial Neural Networks

Cuticular hydrocarbons were extracted daily from the larvae of two closely related blowflies Calliphora vicina and Calliphora vomitoria (Diptera: Calliphoridae). The hydrocarbons were then analysed using Gas Chromatography–Mass Spectrometry (GC–MS), with the aim of observing changes within their chemical profiles in order to determine the larval age. The hydrocarbons were examined daily for each species from 1 day old larvae until pupariation. The results show significant chemical changes occurring from the younger larvae to the post-feeding larvae. With the aid of a multivariate statistical method (Principal Component Analysis and Artificial Neural Networks), samples were clustered and classified, allowing for the larval age to be established. Results from this study allowed larvae to be aged to the day with at worst, 87% accuracy, which suggests there is great potential for the use of cuticular hydrocarbons present on larvae to give an indication of their age and hence potentially a valuable tool for minimum PMI estimations

Age estimation of Calliphora (Diptera: Calliphoridae) larvae using cuticular hydrocarbon analysis and Artificial Neural Networks.

Cuticular hydrocarbons were extracted daily from the larvae of two closely related blowflies Calliphora vicina and Calliphora vomitoria (Diptera: Calliphoridae). The hydrocarbons were then analysed using Gas Chromatography-Mass Spectrometry (GC-MS), with the aim of observing changes within their chemical profiles in order to determine the larval age. The hydrocarbons were examined daily for each species from 1day old larvae until pupariation. The results show significant chemical changes occurring from the younger larvae to the post-feeding larvae. With the aid of a multivariate statistical method (Principal Component Analysis and Artificial Neural Networks), samples were clustered and classified, allowing for the larval age to be established. Results from this study allowed larvae to be aged to the day with at worst, 87% accuracy, which suggests there is great potential for the use of cuticular hydrocarbons present on larvae to give an indication of their age and hence potentially a valuable tool for minimum PMI estimations

Relativistic Effects in the Electromagnetic Current at GeV Energies

We employ a recent approach to the non-relativistic reduction of the electromagnetic current operator in calculations of electronuclear reactions. In contrast to the traditional scheme, where approximations are made for the transferred momentum, transferred energy and initial momentum of the struck nucleon in obtaining an on-shell inspired form for the current, we treat the problem exactly for the transferred energy and transferred momentum. We calculate response functions for the reaction $^2H(e,e'p)n$ at CEBAF (TJNAF) energies and find large relativistic corrections. We also show that in Plane Wave Impulse Approximation, it is always possible to use the full operator, and we present a comparison of such a limiting case with the results incorporating relativistic effects to the first order in the initial momentum of the struck nucleon.Comment: 31 pages, 8 figures, Revte

Magnetic anisotropy and low-energy spin waves in the Dzyaloshinskii-Moriya spiral magnet Ba_2 Cu Ge_2 O_7

New neutron diffraction and inelastic scattering experiments are used to investigate in detail the field dependence of the magnetic structure and low-energy spin wave spectrum of the Dzyaloshinskii-Moriya helimagnet Ba_2 Cu Ge_2 O_7. The results suggest that the previously proposed model for the magnetism of this compound (an ideal sinusoidal spin spiral, stabilized by isotropic exchange and Dzyaloshinskii-Moriya interactions) needs to be refined. Both new and previously published data can be quantitatively explained by taking into account the Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) term, a special magnetic anisotropy term that was predicted to always accompany Dzyaloshinskii-Moriya interactions in insulators.Comment: 30 pages, 10 figures, submitted to PR

Adult fly age estimations using cuticular hydrocarbons and Artificial Neural Networks in forensically important Calliphoridae species

Blowflies (Diptera: Calliphoridae) are forensically important as they are known to be one of the first to colonise human remains. The larval stage is typically used to assist a forensic entomologists with adult flies rarely used as they are difficult to age because they remain morphologically similar once they have gone through the initial transformation upon hatching. However, being able to age them is of interest and importance within the field. This study examined the cuticular hydrocarbons (CHC) of Diptera: Calliphoridae species Lucilia sericata, Calliphora vicina and Calliphora vomitoria. The CHCs were extracted from the cuticles of adult flies and analysed using Gas Chromatography–Mass Spectrometry (GC–MS). The chemical profiles were examined for the two Calliphora species at intervals of day 1, 5, 10, 20 and 30 and up to day 10 for L. sericata. The results show significant chemical changes occurring between the immature and mature adult flies over the extraction period examined in this study. With the aid of a Principal Component Analysis (PCA) and Artificial Neural Networks (ANN), samples were seen to cluster, allowing for the age to be established within the aforementioned time frames. The use of ANNs allowed for the automatic classification of novel samples with very good performance. This was a proof of concept study, which developed a method allowing to age post-emergence adults by using their chemical profiles

The NIKA2 large-field-of-view millimetre continuum camera for the 30 m IRAM telescope

Context. Millimetre-wave continuum astronomy is today an indispensable tool for both general astrophysics studies (e.g. star formation, nearby galaxies) and cosmology (e.g. cosmic microwave background and high-redshift galaxies). General purpose, large-field-of-view instruments are needed to map the sky at intermediate angular scales not accessible by the high-resolution interferometers (e.g. ALMA in Chile, NOEMA in the French Alps) and by the coarse angular resolution space-borne or ground-based surveys (e.g. Planck, ACT, SPT). These instruments have to be installed at the focal plane of the largest single-dish telescopes, which are placed at high altitude on selected dry observing sites. In this context, we have constructed and deployed a three-thousand-pixel dual-band (150 GHz and 260 GHz, respectively 2 mm and 1.15 mm wavelengths) camera to image an instantaneous circular field-of-view of 6.5 arcmin in diameter, and configurable to map the linear polarisation at 260 GHz. Aims. First, we are providing a detailed description of this instrument, named NIKA2 (New IRAM KID Arrays 2), in particular focussing on the cryogenics, optics, focal plane arrays based on Kinetic Inductance Detectors, and the readout electronics. The focal planes and part of the optics are cooled down to the nominal 150 mK operating temperature by means of an adhoc dilution refrigerator. Secondly, we are presenting the performance measured on the sky during the commissioning runs that took place between October 2015 and April 2017 at the 30-m IRAM telescope at Pico Veleta, near Granada (Spain). Methods. We have targeted a number of astronomical sources. Starting from beam-maps on primary and secondary calibrators we have then gone to extended sources and faint objects. Both internal (electronic) and on-the-sky calibrations are applied. The general methods are described in the present paper. Results. NIKA2 has been successfully deployed and commissioned, performing in-line with expectations. In particular, NIKA2 exhibits full width at half maximum angular resolutions of around 11 and 17.5 arcsec at respectively 260 and 150 GHz. The noise equivalent flux densities are, at these two respective frequencies, 33±2 and 8±1 mJy s1/2. A first successful science verification run was achieved in April 2017. The instrument is currently offered to the astronomy community and will remain available for at least the following ten years