Fast algorithm for border bases of Artinian Gorenstein algebras

Given a multi-index sequence $$\sigma$$, we present a new efficient algorithm to compute generators of the linear recurrence relations between the terms of $$\sigma$$. We transform this problem into an algebraic one, by identifying multi-index sequences, multivariate formal power series and linear functionals on the ring of multivariate polynomials. In this setting, the recurrence relations are the elements of the kerne l$I$\sigma of the Hankel operator $H$\sigma associated to $$\sigma$$. We describe the correspondence between multi-index sequences with a Hankel operator of finite rank and Artinian Gorenstein Algebras. We show how the algebraic structure of the Artinian Gorenstein algebra $A$\sigma$$associated to the sequence$$\sigma yields the structure of the terms $\sigma\alpha$for all$$\alpha$ $\in$ N n$. This structure is explicitly given by a border basis of$A$\sigma$$, which is presented as a quotient of the polynomial ring$K[x 1 ,. .. , xn$] by the kernel$I$\sigma$$of the Hankel operator$H$\sigma$$. The algorithm provides generators of$I$\sigma$$constituting a border basis, pairwise orthogonal bases of$A$\sigma$$ and the tables of multiplication by the variables in these bases. It is an extension of Berlekamp-Massey-Sakata (BMS) algorithm, with improved complexity bounds. We present applications of the method to different problems such as the decomposition of functions into weighted sums of exponential functions, sparse interpolation, fast decoding of algebraic codes, computing the vanishing ideal of points, and tensor decomposition. Some benchmarks illustrate the practical behavior of the algorithm

Hard sphere-like dynamics in a non hard sphere liquid

The collective dynamics of liquid Gallium close to the melting point has been studied using Inelastic X-ray Scattering to probe lengthscales smaller than the size of the first coordination shell. %(momentum transfers, $Q$, $>$15 nm$^{-1}$). Although the structural properties of this partially covalent liquid strongly deviate from a simple hard-sphere model, the dynamics, as reflected in the quasi-elastic scattering, are beautifully described within the framework of the extended heat mode approximation of Enskog's kinetic theory, analytically derived for a hard spheres system. The present work demonstrates the applicability of Enskog's theory to non hard- sphere and non simple liquids.Comment: 5 pages, 2 figures, accepted in Phys. Rev. Let

Twisted mass chiral perturbation theory for 2+1+1 quark flavours

We present results for the masses of pseudoscalar mesons in twisted mass lattice QCD with a degenerate doublet of u and d quarks and a non-degenerate doublet of s and c quarks in the framework of next-to-leading order chiral perturbation theory, including lattice effects up to O(a^2). The masses depend on the two twist angles for the light and heavy sectors. For maximal twist in both sectors, O(a)-improvement is explicitly exhibited. The mixing of flavour-neutral mesons is also discussed, and results in the literature for the case of degenerate s and c quarks are corrected.Comment: LaTeX2e, 12 pages, corrected typo

Whispering Gallery States of Antihydrogen

We study theoretically interference of the long-living quasistationary quantum states of antihydrogen atoms, localized near a concave material surface. Such states are an antimatter analog of the whispering gallery states of neutrons and matter atoms, and similar to the whispering gallery modes of sound and electro-magnetic waves. Quantum states of antihydrogen are formed by the combined effect of quantum reflection from van der Waals/Casimir-Polder (vdW/CP) potential of the surface and the centrifugal potential. We point out a method for precision studies of quantum reflection of antiatoms from vdW/CP potential; this method uses interference of the whispering gallery states of antihydrogen.Comment: 13 pages 7 figure

A gravimetric assessment of the Gotthard Base Tunnel geological model: insights from a novel gravity terrain-adaptation correction and rock physics data.

The Gotthard Base Tunnel (GBT) is a 57 km long railway tunnel, constructed in the Central Alps in Switzerland and extending mainly North-South across numerous geological units. We acquired 80 new gravity data points at the surface along the GBT profile and used 77 gravity measurements in the tunnel to test and constrain the shallow crustal, km-scale geological model established during the tunnel construction. To this end, we developed a novel processing scheme, which computes a fully 3D, density-dependent gravity terrain-adaptation correction (TAC), to consistently compare the gravity observations with the 2D geological model structure; the latter converted into a density model. This approach allowed to explore and quantify candidate rock density distributions along the GBT modelled profile in a computationally-efficient manner, and to test whether a reasonable fit can be found without structural modification of the geological model. The tested density data for the various lithologies were compiled from the SAPHYR rock physical property database. The tested models were evaluated both in terms of misfit between observed and synthetic gravity data, and also in terms of correlation between misfit trend and topography of the target profile. The results indicate that the locally sampled densities provide a better fit to the data for the considered lithologies, rather than density data averaged over a wider set of Alpine rock samples for the same lithology. Furthermore, using one homogeneous and constant density value for all the topographic corrections does not provide an optimal fit to the data, which instead confirms density variations along the profile. Structurally, a satisfactory fit could be found without modifying the 2D geological model, which thus can be considered gravimetry-proof. From a more general perspective, the gravity data processing routines and the density-dependent corrections developed in this case study represent a remarkable potential for further high-resolution gravity investigations of geological structures. The online version contains supplementary material available at 10.1186/s00015-022-00422-z

A behavioral comparison of male and female adults with high functioning autism spectrum conditions

Autism spectrum conditions (ASC) affect more males than females in the general population. However, within ASC it is unclear if there are phenotypic sex differences. Testing for similarities and differences between the sexes is important not only for clinical assessment but also has implications for theories of typical sex differences and of autism. Using cognitive and behavioral measures, we investigated similarities and differences between the sexes in age- and IQ-matched adults with ASC (high-functioning autism or Asperger syndrome). Of the 83 (45 males and 38 females) participants, 62 (33 males and 29 females) met Autism Diagnostic Interview-Revised (ADI-R) cut-off criteria for autism in childhood and were included in all subsequent analyses. The severity of childhood core autism symptoms did not differ between the sexes. Males and females also did not differ in self-reported empathy, systemizing, anxiety, depression, and obsessive-compulsive traits/symptoms or mentalizing performance. However, adult females with ASC showed more lifetime sensory symptoms (p = 0.036), fewer current socio-communication difficulties (p = 0.001), and more self-reported autistic traits (p = 0.012) than males. In addition, females with ASC who also had developmental language delay had lower current performance IQ than those without developmental language delay (p<0.001), a pattern not seen in males. The absence of typical sex differences in empathizing-systemizing profiles within the autism spectrum confirms a prediction from the extreme male brain theory. Behavioral sex differences within ASC may also reflect different developmental mechanisms between males and females with ASC. We discuss the importance of the superficially better socio-communication ability in adult females with ASC in terms of why females with ASC may more often go under-recognized, and receive their diagnosis later, than males

The 3-D structure of the Somma-Vesuvius volcanic complex (Italy) inferred from new and historic gravimetric data

Existing 3-D density models of the Somma-Vesuvius volcanic complex (SVVC), Italy, largely disagree. Despite the scientific and socioeconomic importance of Vesuvius, there is no reliable 3-D density model of the SVVC. A considerable uncertainty prevails concerning the presence (or absence) of a dense body underlying the Vesuvius crater (1944 eruption) that is implied from extensive seismic investigations. We have acquired relative gravity measurements at 297 stations, including measurements in difficult-to-access areas (e.g., the first-ever measurements in the crater). In agreement with seismic investigations, the simultaneous inversion of these and historic data resolves a high-density body that extends from the surface of the Vesuvius crater down to depths that exceed 2 km. A 1.5-km radius horseshoe-shaped dense feature (open in the southwestern sector) enforces the existing model of groundwater circulation within the SVVC. Based on its volcano-tectonic evolution, we interpret volcanic structures that have never been imaged before

Definition of a Solvent System for Spherical Crystallization of Salbutamol Sulfate by Quasi-Emulsion Solvent Diffusion (QESD) Method

International audienceIn this paper we describe how the spherical crystallization process by QESD method can be applied to a water-soluble drug, salbutamol sulfate. The type of solvent, antisolvent, and emulsi®er and the concentration of emulsi®er to be used for the production of spherical particles with a size range 80±500 mm are determined. Furthermore, the solvent/antisolvent ratio and the temperature difference between them (DT) are studied. It was observed that, in the case of salbutamol sulfate, the DT value has no in¯uence on the formation of spherical particles. A very large metastable zone of salbutamol sulfate in water could explain this phenomenon. Finally, the in¯uence of emulsi®er concentration and of maturation time on the size of spherical particles is studied. The results show that these two parameters must be ®xed to control the size of the recovered particles

Development of a direct ESI-MS method for measuring the tannin precipitation effect of proline-rich peptides and in silico studies on the proline role in tannin-protein interactions

Tannins are a heterogeneous class of polyphenols that are present in several plants and foods. Their ability to interact and precipitate proline-rich proteins leads to different effects such as astringency or antidiarrheal activity. Thus, evaluation of the tannin content in plant extracts plays a key role in understanding their potential use as pharmaceuticals and nutraceuticals. Several methods have been proposed to study tannin-protein interactions but few of them are focused on quantification. The purpose of the present work is to set up a suitable and time efficient method able to quantify the extent of tannin protein precipitation. Bradykinin, chosen as a model, was incubated with increasing concentrations of 1,2,3,4,6-penta-O-galloyl-\u3b2-D-glucose and tannic acid selected as reference of tannic compounds. Bradykinin not precipitated was determined by a mass spectrometer TSQ Quantum Ultra Triple Quadrupole (direct infusion analysis). The results were expressed as PC 50 , which is the concentration able to precipitate 50% of the protein. The type of tannin-protein interaction was evaluated also after precipitate solubilisation. The involvement of proline residues in tannin-protein interactions was confirmed by repeating the experiment using a synthesized peptide (RR-9) characterized by the same bradykinin sequence, but having proline residues replaced by glycine residues: no interaction occurred between the peptide and the tannins. Moreover, modelling studies on PGG-BK and PGG-RR-9 were performed to deeply investigate the involvement of prolines: a balance of hydrophobic and H-bond contacts stabilizes the PGG-BK cluster and the proline residues exert a crucial role thus allowing the PGG molecules to elicit a sticking effect