Spherical functions and local densities on the space of p-adic quaternion Hermitian forms

We introduce the space [Formula: see text] of quaternion Hermitian forms of size [Formula: see text] on a [Formula: see text]-adic field with odd residual characteristic, and define typical spherical functions [Formula: see text] on [Formula: see text] and give their induction formula on sizes by using local densities of quaternion Hermitian forms. Then, we give functional equation of spherical functions with respect to [Formula: see text], and define a spherical Fourier transform on the Schwartz space [Formula: see text] which is Hecke algebra [Formula: see text]-injective map into the symmetric Laurent polynomial ring of size [Formula: see text]. Then, we determine the explicit formulas of [Formula: see text] by a method of the author’s former result. In the last section, we give precise generators of [Formula: see text] and determine all the spherical functions for [Formula: see text], and give the Plancherel formula for [Formula: see text].

Mass occurrence of small isopodan crustaceans in 100-million-year-old amber: an extraordinary view on behaviour of extinct organisms

Within Isopoda (woodlice and relatives), there are lineages characterised by a parasitic lifestyle that all belong to Cymothoida and likely form a monophyletic group. Representatives of Epicaridea (ingroup of Cymothoida) are parasitic on crustaceans and usually go through three distinct larval stages. The fossil record of Epicaridea is sparse and thus little is known about the palaeoecology and the origin of the complex life cycle of modern epicarideans. We present an assemblage of over 100 epicarideans preserved in a single piece of Late Cretaceous Myanmar amber. All individuals are morphologically similar to cryptoniscium stage larvae. The cryptoniscium stage usually constitutes the third and last larval stage. In modern representatives of Epicaridea, the cryptoniscium larvae are planktic and search for suitable host animals or adult females. These fossil specimens, though similar to some extant species, differ from other fossil epicaridean larvae in many aspects. Thus, a new species (and a new genus), Cryptolacruma nidis, is erected. Several factors can favour the preservation of multiple conspecific animals in a single piece of amber. However, the enormous density of epicarideans in the herein presented amber piece can only be explained by circumstances that result in high local densities of individuals, close to the resin-producing tree.

Clustering using kernel entropy principal component analysis and variable kernel estimator

Clustering as unsupervised learning method is the mission of dividing data objects into clusters with common characteristics. In the present paper, we introduce an enhanced technique of the existing EPCA data transformation method. Incorporating the kernel function into the EPCA, the input space can be mapped implicitly into a high-dimensional of feature space. Then, the Shannon’s entropy estimated via the inertia provided by the contribution of every mapped object in data is the key measure to determine the optimal extracted features space. Our proposed method performs very well the clustering algorithm of the fast search of clusters’ centers based on the local densities’ computing. Experimental results disclose that the approach is feasible and efficient on the performance query.

Efficiency Parameterization with Neural Networks

Multidimensional efficiency maps are commonly used in high-energy physics experiments to mitigate the limitations in the generation of large samples of simulated events. Binned efficiency maps are however strongly limited by statistics. We propose a neural network approach to learn ratios of local densities to estimate in an optimal fashion efficiencies as a function of a set of parameters. Graph neural network techniques are used to account for the high dimensional correlations between different physics objects in the event. We show in a specific toy model how this method is applicable to produce accurate multidimensional efficiency maps for heavy-flavor tagging classifiers in HEP experiments, including for processes on which it was not trained.

Extreme boundary conditions and random tilings

Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as illustrated by the famous 'arctic circle theorem' for dimer coverings in two dimensions. In these notes, I discuss such examples in the context of critical phenomena, and their relation to 1+1d quantum particle models. All those turn out to share a common feature: they are inhomogeneous, in the sense that local densities now depend on position in the bulk. I explain how such problems may be understood using variational (or hydrodynamic) arguments, how to treat long range correlations, and how non trivial edge behavior can occur. While all this is done on the example of the dimer model, the results presented here have much greater generality. In that sense the dimer model serves as an opportunity to discuss broader methods and results. [These notes require only a basic knowledge of statistical mechanics.]

Ozone vertical profiles from TGO/NOMAD-UVIS: an inter-comparison of three retrieval schemes

<p>We will present the vertical distribution of <strong>ozone</strong> obtained from <strong>NOMAD-UVIS solar occultations</strong> and we will compare the results of three retrieval schemes.</p><p><strong>NOMAD</strong> (Nadir and Occultation for MArs Discovery) is a spectrometer composed of 3 channels: 1) a solar occultation channel (SO) operating in the infrared (2.3-4.3 μm); 2) a second infrared channel LNO (2.3-3.8 μm) capable of doing nadir, as well as solar occultation and limb; and 3) an ultraviolet/visible channel <strong>UVIS</strong> (200-650 nm) that can work in the three observation modes [1,2].</p><p>The UVIS channel has a spectral resolution <1.5 nm. In the solar occultation mode it is mainly devoted to study the climatology of <strong>ozone</strong> and <strong>aerosols</strong> content [3].</p><p>Since the beginning of operations, on 21 April 2018, NOMAD UVIS acquired more than 4000 solar occultations with an almost complete coverage of the planet.</p><p>NOMAD-UVIS spectra are simulated using three different retrieval scheme:</p><p>1) An onion peeling approach based on [4,5] deriving slant columns at the different altitudes sounded, from which local densities are obtained;</p><p>2) The line-by-line radiative transfer code ASIMUT-ALVL developed at IASB-BIRA [6] using the Optimal Estimation Method to derive the local density profile in one go (on all transmittances of one occultation observation);</p><p>3) A direct onion peeling method deriving sequentially from top to bottom the local densities in the different layers probed.</p><p>We will compare results obtained from the different retrieval methods as well as their uncertainties and we will discuss the advantages and difficulties of each method.</p><p><strong>References</strong></p><p>[1] Vandaele, A.C., et al., Planetary and Space Science, Vol. 119, pp. 233–249, 2015.</p><p>[2] Neefs, E., et al., Applied Optics, Vol. 54 (28), pp. 8494-8520, 2015.</p><p>[3] M.R. Patel et al., In: Appl. Opt. 56.10 (2017), pp. 2771–2782. DOI: 10.1364/AO.56.002771.</p><p>[4] Quémerais, E.,et al. J.Geophys. Res. (Planets)111, 9, 2006.</p><p>[5] Piccialli, A. et al., Planetary and Space Science, 113-114(2015) 321–335</p><p>[6] Vandaele, A.C., et al., JGR, 2008. 113 doi:10.1029/2008JE003140.</p>

Local densities of diagonal integral ternary quadratic forms at odd primes

We give formulas for local densities of diagonal integral ternary quadratic forms at odd primes. Exponential sums and quadratic Gauss sums are used to obtain these formulas. These formulas (along with 2-adic densities and Siegel’s mass formula) can be used to compute the representation numbers of certain ternary quadratic forms.

Substrate wettability guided oriented self assembly of Janus particles

Self-assembly of Janus particles with spatial inhomogeneous properties is of fundamental importance in diverse areas of sciences and has been extensively observed as a favorably functionalized fluidic interface or in a dilute solution. Interestingly, the unique and non-trivial role of surface wettability on oriented self-assembly of Janus particles has remained largely unexplored. Here, the exclusive role of substrate wettability in directing the orientation of amphiphilic metal-polymer Bifacial spherical Janus particles, obtained by topo-selective metal deposition on colloidal Polymestyere (PS) particles, is explored by drop casting a dilute dispersion of the Janus colloids. While all particles orient with their polymeric (hydrophobic) and metallic (hydrophilic) sides facing upwards on hydrophilic and hydrophobic substrates respectively, they exhibit random orientation on a neutral substrate. The substrate wettability guided orientation of the Janus particles is captured using molecular dynamic simulation, which highlights that the arrangement of water molecules and their local densities near the substrate guide the specific orientation. Finally, it is shown that by spin coating it becomes possible to create a hexagonal close-packed array of the Janus colloids with specific orientation on differential wettability substrates. The results reported here open up new possibilities of substrate-wettability driven functional coatings of Janus particles, which has hitherto remained unexplored.