Chebyshev polynomials and the Frohman-Gelca formula

Using Chebyshev polynomials, C. Frohman and R. Gelca introduce a basis of the Kauffman bracket skein module of the torus. This basis is especially useful because the Jones-Kauffman product can be described via a very simple Product-to-Sum formula. Presented in this work is a diagrammatic proof of this formula, which emphasizes and demystifies the role played by Chebyshev polynomials.Comment: 13 page

Fractal Spectrum of a Quasi_periodically Driven Spin System

We numerically perform a spectral analysis of a quasi-periodically driven spin 1/2 system, the spectrum of which is Singular Continuous. We compute fractal dimensions of spectral measures and discuss their connections with the time behaviour of various dynamical quantities, such as the moments of the distribution of the wave packet. Our data suggest a close similarity between the information dimension of the spectrum and the exponent ruling the algebraic growth of the 'entropic width' of wavepackets.Comment: 17 pages, RevTex, 5 figs. available on request from [email protected]

Aperiodic Ising Quantum Chains

Some years ago, Luck proposed a relevance criterion for the effect of aperiodic disorder on the critical behaviour of ferromagnetic Ising systems. In this article, we show how Luck's criterion can be derived within an exact renormalisation scheme for Ising quantum chains with coupling constants modulated according to substitution rules. Luck's conjectures for this case are confirmed and refined. Among other outcomes, we give an exact formula for the correlation length critical exponent for arbitrary two-letter substitution sequences with marginal fluctuations of the coupling constants.Comment: 27 pages, LaTeX, 1 Postscript figure included, using epsf.sty and amssymb.sty (one error corrected, some minor changes

Limit-(quasi)periodic point sets as quasicrystals with p-adic internal spaces

Model sets (or cut and project sets) provide a familiar and commonly used method of constructing and studying nonperiodic point sets. Here we extend this method to situations where the internal spaces are no longer Euclidean, but instead spaces with p-adic topologies or even with mixed Euclidean/p-adic topologies. We show that a number of well known tilings precisely fit this form, including the chair tiling and the Robinson square tilings. Thus the scope of the cut and project formalism is considerably larger than is usually supposed. Applying the powerful consequences of model sets we derive the diffractive nature of these tilings.Comment: 11 pages, 2 figures; dedicated to Peter Kramer on the occasion of his 65th birthda

Production of betalain-rich Opuntia ficus-indica peel flour microparticles using spray-dryer: A holist approach

This study aimed to obtain a betalain-rich extract (BRE) from Opuntia ficus-indica peels and protect them through a holistic approach involving microencapsulation via spray-drying. To enhance the stability of the microencapsulated betalains, an antioxidant-rich extract (ARE) obtained through hydrothermal extraction from the residual material remaining after the conventional extraction of betalains was used as a stabilizer during the spray-drying process. The antioxidant activity of the ARE was evaluated by measuring its IC50 value for 2,2-Diphenyl-1-picrylhydrazyl (DPPH) of 65.8 μg/mL, its Trolox equivalent antioxidant capacity (TEAC) of 60.4 gTrolox eq./100 g, and its reducing power of 16.6 g butylated hydroxytoluene (BHT) eq./100 g. Spray-drying parameters were optimized using a Box-Behnken design to enhance the total betalain content and minimize by-product formation. The results demonstrated that the addition of the ARE significantly improved the stability of betalains during spray-drying, leading to the formation of microparticles with high betalain content and enhanced stability. The optimal conditions (0.72% starch, 1.50% BRE and 0.25% ARE) resulted in microparticles with a maximum concentration of 6.74 ± 0.09 mgBetalains/g. The predictive model exhibited high accuracy in estimating experimental values. This research provides a natural and sustainable solution for food coloring by effectively utilizing discarded Opuntia ficus-indica peel. Moreover, it offers new scientific understanding on the production of betalain-rich microparticles as a possible substitute for food coloring, with considerable benefits in terms of sustainability and high antioxidant capacity.Agencia Estatal de Investigación | Ref. RYC2018-024454-IXunta de Galicia | Ref. ED431F 2020/01Xunta de Galicia | Ref. ED481D-2022/01

Was sind Territorien in der Urgeschichte? Netzwerkanalysen als Annäherung an den Begriff des Raumes im Jungpaläolithikum

Addressed from the perspective of where they were obtained, lithic raw materials found in archaeological sites carry and contain data of geographical value. Thus, they are privileged witnesses to human movements in prehistoric times. By coupling the results of technological analyses with multi-scale diagnostic methodologies based on the principle of an evolutionary chain set up by some of us and recently optimised, today it is possible to evaluate the acquisition modes for raw materials, the manner of their introduction into sites, and better understand the prehistoric management of mineralogical resources. This techno-economic approach, becoming ever more precise, is being facilitated thanks to the results from a consortium of researchers interconnected in the ‘Réseau de lithothèques’ and ‘Silex’ projects.Detailed petro-archaeological studies of an archaeological series make it possible to identify litho-spaces that are not images of territories. Indeed, territories are not only shaped by economic constraints (where space is the basis of a society), but they are the way in which collectives build themselves by conferring meaning on places of singular use linked to each other by a complex network of values. Yet, the symbolic dimension of spaces is a central element in the cultural representations that societies have of it. Rather than limiting the analysis of the territories to the scale of a site, which in the context of nomadic societies is contradictory, it seems more efficient to analyse the relationships between places (i.e. networks of places). Taking as an example current or recently nomadic peoples – for whom networks in which materials circulate correspond to networks of places – we propose a method based on a concept of network analysis in order to escape the point of view based on single sites, and offer an approach to determining prehistoric territories. This side-step not only questions the spatial extent of archaeological records, but also their coherence as chrono-anthropological entities

Symbolic innovation at the onset of the Upper Paleolithic in Eurasia shown by the personal ornaments from Tolbor-21 (Mongolia)

Figurative depictions in art first occur ca. 50,000 years ago in Europe, Africa, and Southeast Asia. Considered by most as an advanced form of symbolic behavior, they are restricted to our species. Here, we report a piece of ornament interpreted as a phallus-like representation. It was found in a 42,000 ca.-year-old Upper Paleolithic archaeological layer at the open-air archaeological site of Tolbor-21, in Mongolia. Mineralogical, microscopic, and rugosimetric analyses points toward the allochthonous origin of the pendant and a complex functional history. Three-dimensional phallic pendants are unknown in the Paleolithic record, and this discovery predates the earliest known sexed anthropomorphic representation. It attests that hunter-gatherer communities used sex anatomical attributes as symbols at a very early stage of their dispersal in the region. The pendant was produced during a period that overlaps with age estimates for early introgression events between Homo sapiens and Denisovans, and in a region where such encounters are plausible

The origin of early Acheulean expansion in Europe 700 ka ago: new findings at Notarchirico (Italy)

Notarchirico (Southern Italy) has yielded the earliest evidence of Acheulean settlement in Italy and four older occupation levels have recently been unearthed, including one with bifaces, extending the roots of the Acheulean in Italy even further back in time. New 40Ar/39Ar on tephras and ESR dates on bleached quartz securely and accurately place these occupations between 695 and 670 ka (MIS 17), penecontemporaneous with the Moulin-Quignon and la Noira sites (France). These new data demonstrate a very rapid expansion of shared traditions over Western Europe during a period of highly variable climatic conditions, including interglacial and glacial episodes, between 670 and 650 (i.e., MIS17/MIS16 transition). The diversity of tools and activities observed in these three sites shows that Western Europe was populated by adaptable hominins during this time. These conclusions question the existence of refuge areas during intense glacial stages and raise questions concerning understudied migration pathways, such as the Sicilian route

The origin of early Acheulean expansion in Europe 700 ka ago: new findings at Notarchirico (Italy)

Notarchirico (Southern Italy) has yielded the earliest evidence of Acheulean settlement in Italy and four older occupation levels have recently been unearthed, including one with bifaces, extending the roots of the Acheulean in Italy even further back in time. New 40Ar/39Ar on tephras and ESR dates on bleached quartz securely and accurately place these occupations between 695 and 670 ka (MIS 17), penecontemporaneous with the Moulin-Quignon and la Noira sites (France). These new data demonstrate a very rapid expansion of shared traditions over Western Europe during a period of highly variable climatic conditions, including interglacial and glacial episodes, between 670 and 650 (i.e., MIS17/MIS16 transition). The diversity of tools and activities observed in these three sites shows that Western Europe was populated by adaptable hominins during this time. These conclusions question the existence of refuge areas during intense glacial stages and raise questions concerning understudied migration pathways, such as the Sicilian route