Polarizations and differential calculus in affine spaces

Within the framework of mappings between affine spaces, the notion of $n$-th polarization of a function will lead to an intrinsic characterization of polynomial functions. We prove that the characteristic features of derivations, such as linearity, iterability, Leibniz and chain rules, are shared -- at the finite level -- by the polarization operators. We give these results by means of explicit general formulae, which are valid at any order $n$, and are based on combinatorial identities. The infinitesimal limits of the $n$-th polarizations of a function will yield its $n$-th derivatives (without resorting to the usual recursive definition), and the above mentioned properties will be recovered directly in the limit. Polynomial functions will allow us to produce a coordinate free version of Taylor's formula

Multi Bands Network Performance Assessment for Different System Upgrades

We investigate the capacity of a reference German network when employing band-division multiplexing (BDM) using C+L+S-bands and spatial-division multiplexing (SDM) in case of different nodes distribution scenarios. We show that BDM enables increasing the network capacity by up to almost 3 x with respect to C-band transmission only

Power control strategies and network performance assessment for C+L+S multiband optical transport

Spatial-division multiplexing (SDM) and band-division multiplexing (BDM) have emerged as solutions to expand the capacity of existing C-band wavelength-division multiplexing (WDM) optical systems and to deal with increasing traffic demands. An important difference between these two approaches is that BDM solutions enable data transmission over unused spectral bands of already-deployed optical fibers, whereas SDM solutions require the availability of additional fibers to replicate C-band WDM transmission. On the other hand, to properly design a multiband optical line system (OLS), the following fiber propagation effects have been taken into account in the analysis: (i) stimulated Raman scattering (SRS), which induces considerable power transfer among bands; (ii) frequency dependence of fiber parameters such as attenuation, dispersion, and nonlinear coefficients; and (iii) utilization of optical amplifiers with different doping materials, thus leading to different characteristics, e.g., in terms of noise figures. This work follows a two-step approach: First, we aim at maximizing and flattening the quality of transmission (QoT) when adding L-and rm L +rm S-bands to a traditional WDM OLS where only the C-band is deployed. This is achieved by applying a multiband optimized optical power control for BDM upgrades, which consists of setting a pre-tilt and power offset in the line amplifiers, thus achieving a considerable increase in QoT, both in average value and flatness. Second, the SDM approach is used as a benchmark for the BDM approach by assessing network performance on three network topologies with different geographical footprints. We show that, with optical power properly optimized, BDM may enable an increase in network traffic, slightly less than an SDM upgrade but still comparable, without requiring additional fiber cables

New psychoactive substance use among regular psychostimulant users in Australia, 2010-2015

Objective: To examine the rates and patterns of new psychoactive substance (NPS) use amongst regular psychostimulant users (RPU) in Australia. Method: Data were obtained from the 2010-2015 Ecstasy and related Drugs Reporting System (EDRS), which comprised a total cross-sectional sample of 4122. RPU. Results: Recent use of 'any' NPS increased from 33% in 2010 to 40% in 2015, although trends of use differed significantly across NPS classes. The correlates associated with NPS use also varied across NPS classes: frequent (i.e. weekly or more) ecstasy users were more likely to report recent phenethylamine use; LSD users were more likely to report recent phenethylamine and tryptamine use; and daily cannabis users were more likely to report recent synthetic cannabinoid use than RPU who had not used NPS. 'Poly' NPS consumers were found to be a particularly high risk group and were significantly more likely to be younger, male, report daily cannabis use, report weekly or more ecstasy use, report recent LSD use, have higher levels of poly drug use, have overdosed on any drug in the past year, and to have engaged in past month criminal activity. Conclusion: NPS use has been established as a significant and ongoing practice amongst our sample of RPU. It appears that RPU seek out NPS with similar properties to the illicit drugs that they are already consuming, with poly NPS consumers found to be a particularly high risk group

2+1 gravity and Doubly Special Relativity

It is shown that gravity in 2+1 dimensions coupled to point particles provides a nontrivial example of Doubly Special Relativity (DSR). This result is obtained by interpretation of previous results in the field and by exhibiting an explicit transformation between the phase space algebra for one particle in 2+1 gravity found by Matschull and Welling and the corresponding DSR algebra. The identification of 2+1 gravity as a $DSR$ system answers a number of questions concerning the latter, and resolves the ambiguity of the basis of the algebra of observables. Based on this observation a heuristic argument is made that the algebra of symmetries of ultra high energy particle kinematics in 3+1 dimensions is described by some DSR theory.Comment: 8 pages Latex, no figures, typos correcte

Attention on Weak Ties in Social and Communication Networks

Granovetter's weak tie theory of social networks is built around two central hypotheses. The first states that strong social ties carry the large majority of interaction events; the second maintains that weak social ties, although less active, are often relevant for the exchange of especially important information (e.g., about potential new jobs in Granovetter's work). While several empirical studies have provided support for the first hypothesis, the second has been the object of far less scrutiny. A possible reason is that it involves notions relative to the nature and importance of the information that are hard to quantify and measure, especially in large scale studies. Here, we search for empirical validation of both Granovetter's hypotheses. We find clear empirical support for the first. We also provide empirical evidence and a quantitative interpretation for the second. We show that attention, measured as the fraction of interactions devoted to a particular social connection, is high on weak ties --- possibly reflecting the postulated informational purposes of such ties --- but also on very strong ties. Data from online social media and mobile communication reveal network-dependent mixtures of these two effects on the basis of a platform's typical usage. Our results establish a clear relationships between attention, importance, and strength of social links, and could lead to improved algorithms to prioritize social media content

Numerical modeling and simulation of supersonic flows in propulsion systems by open-source solvers

Two open-source solvers, Eilmer and hyFoam, are here considered for their performance in simulating high-speed flows in different flow conditions and geometric configurations typical of propulsive systems at supersonic speeds. The goal is to identify the open-source platform providing the best compromise between accuracy, flexibility and computational cost to eventually simulate the flow fields inside ramjet and scramjet engines. The differences in terms of discretization and solution methods of the selected solvers are discussed in terms of their impact on solution accuracy and computational efficiency and in view of the aerothermodynamic analysis and design of future trans-atmospheric propulsive systems. In this work steady state problems are considered. Numerical results of two scramjet type engines demonstrated a similar predictive capability of both codes in non-reacting conditions. These results highlight their potential to be considered for further characterization of overall engine performance

New insights into the classification and nomenclature of cortical GABAergic interneurons.

A systematic classification and accepted nomenclature of neuron types is much needed but is currently lacking. This article describes a possible taxonomical solution for classifying GABAergic interneurons of the cerebral cortex based on a novel, web-based interactive system that allows experts to classify neurons with pre-determined criteria. Using Bayesian analysis and clustering algorithms on the resulting data, we investigated the suitability of several anatomical terms and neuron names for cortical GABAergic interneurons. Moreover, we show that supervised classification models could automatically categorize interneurons in agreement with experts' assignments. These results demonstrate a practical and objective approach to the naming, characterization and classification of neurons based on community consensus

Inferior vena cava filters: a review

Venous thromboembolism is an entity that ranges from deep vein thrombosis to pulmonary embolism, both are highly prevalent diseases in our environment and potentially fatal. The intention of this review is to compile information regarding the indications, contraindications, complications and comparison of different therapeutic methods in order to create an algorithm. An exhaustive review was performed with the available literature, using the PubMed, ScienceDirect, Scopus and Cochrane databases from 2004 to 2021. The search criteria were formulated to identify reports related to inferior vena cava filters. Venous thrombosis manifested as deep vein thrombosis or pulmonary embolism is a highly prevalent disease in our setting with high morbidity and mortality. Currently, different therapeutic options have been presented to address this pathology, in this review we focus on the developments regarding the use of vena cava filters. Reviewing the indications for the placement of a vena cava filter, we find absolute indications such as a contraindication to anticoagulation and high risk of massive pulmonary embolism. Pulmonary thromboembolism is a disease with high prevalence and mortality, we have highly effective and novel treatments such as the vena cava filter, patients should be selected carefully always taking into account the absolute and relative indications