Sequences of binary irreducible polynomials

In this paper we construct an infinite sequence of binary irreducible polynomials starting from any irreducible polynomial f_0 \in \F_2 [x]. If $f_0$ is of degree $n = 2^l \cdot m$, where $m$ is odd and $l$ is a non-negative integer, after an initial finite sequence of polynomials $f_0, f_1, ..., f_{s}$ with $s \leq l+3$, the degree of $f_{i+1}$ is twice the degree of $f_i$ for any $i \geq s$.Comment: 7 pages, minor adjustment

Graphs associated with the map x↦x+x−1x \mapsto x + x^{-1} in finite fields of characteristic three

In this paper we study the structure of the graphs associated with the iterations of the map $x \mapsto x+x^{-1}$ over finite fields of characteristic three.Comment: The definitions of the maps $s$ and $\psi$ have been slightly modified in order to simplify the following discussion. 6 page

Symmetries of stochastic differential equations using Girsanov transformations

Aiming at enlarging the class of symmetries of an SDE, we introduce a family of stochastic transformations able to change also the underlying probability measure exploiting Girsanov Theorem and we provide new determining equations for the infinitesimal symmetries of the SDE. The well-defined subset of the previous class of measure transformations given by Doob transformations allows us to recover all the Lie point symmetries of the Kolmogorov equation associated with the SDE. This gives the first stochastic interpretation of all the deterministic symmetries of the Kolmogorov equation. The general theory is applied to some relevant stochastic models

Weak symmetries of stochastic differential equations driven by semimartingales with jumps

Stochastic symmetries and related invariance properties of \ufb01nite dimensional SDEs driven by general c`adl`ag semimartingales taking values in Lie groups are de\ufb01ned and investigated. The considered set of SDEs, \ufb01rst introduced by S. Cohen, includes a\ufb03ne and Marcus type SDEs as well as smooth SDEs driven by L\ub4evy processes and iterated random maps. A natural extension to this general setting of reduction and reconstruction theory for symmetric SDEs is provided. Our theorems imply as special cases non trivial invariance results concerning a class of a\ufb03ne iterated random maps as well as (weak) symmetries for numerical schemes (of Euler and Milstein type) for Brownian motion driven SDEs

Architectures and Key Technical Challenges for 5G Systems Incorporating Satellites

Satellite Communication systems are a promising solution to extend and complement terrestrial networks in unserved or under-served areas. This aspect is reflected by recent commercial and standardisation endeavours. In particular, 3GPP recently initiated a Study Item for New Radio-based, i.e., 5G, Non-Terrestrial Networks aimed at deploying satellite systems either as a stand-alone solution or as an integration to terrestrial networks in mobile broadband and machine-type communication scenarios. However, typical satellite channel impairments, as large path losses, delays, and Doppler shifts, pose severe challenges to the realisation of a satellite-based NR network. In this paper, based on the architecture options currently being discussed in the standardisation fora, we discuss and assess the impact of the satellite channel characteristics on the physical and Medium Access Control layers, both in terms of transmitted waveforms and procedures for enhanced Mobile BroadBand (eMBB) and NarrowBand-Internet of Things (NB-IoT) applications. The proposed analysis shows that the main technical challenges are related to the PHY/MAC procedures, in particular Random Access (RA), Timing Advance (TA), and Hybrid Automatic Repeat reQuest (HARQ) and, depending on the considered service and architecture, different solutions are proposed.Comment: Submitted to Transactions on Vehicular Technologies, April 201

Current surgical concepts and indications in the management of the short bowel state: A call for the use of multidisciplinary intestinal rehabilitation programs

The mainstay of management for short bowel syndrome (SBS) is to promote access to the best quality of care provided by the intestinal rehabilitation program (IRP) in specialized centres. When treating SBS patients, the main goal is to minimize disease-associated complications, as well as achieve enteral autonomy. Surgical strategies should be selected cautiously upon the actual state of the bowel with respect to what it is clinically relevant for that specific patient. To this aim, a personalized and multidisciplinary approach for such a complex syndrome is needed