Cubic rational expressions over a finite field

We classify the cubic rational expressions $g(x)/h(x)$ over a finite field, having at most three ramification points, under an equivalence relation given by pre- and post-composition with independent M\"obius transformations.Comment: 22 pages; minor update involving a choice of some simpler representatives in Theorems 19 and 2

Irreducible polynomials from a cubic transformation.

Let R(x)=g(x)/h(x) be a rational expression of degree three over the finite field F_q. We count the irreducible polynomials in F_q[x], of a given degree, that have the form h(x)^{\deg f}\cdot f\bigl(R(x)\bigr) for some f(x)\in\F_q[x]. As an example of application of our results, we recover the number of irreducible transformation shift registers of order three, which were computed by Jiang and Yang in 2017

Irreducible polynomials from a cubic transformation.

Let R(x)=g(x)/h(x) be a rational expression of degree three over the finite field F_q. We count the irreducible polynomials in F_q[x], of a given degree, that have the form h(x)^{\deg f}\cdot f\bigl(R(x)\bigr) for some f(x)\in\F_q[x]. As an example of application of our results, we recover the number of irreducible transformation shift registers of order three, which were computed by Jiang and Yang in 2017

Strain wave acquisition by a fiber optic coherent sensor for impact monitoring

A novel fiber optic sensing technology for high frequency dynamics detection is proposed in this paper, specifically tailored for structural health monitoring applications based on strain wave analysis, for both passive impact identification and active Lamb wave monitoring. The sensing solution relies on a fiber optic-based interferometric architecture associated to an innovative coherent detection scheme, which retrieves in a completely passive way the high-frequency phase information of the received optical signal. The sensing fiber can be arranged into different layouts, depending on the requirement of the specific application, in order to enhance the sensor sensitivity while still ensuring a limited gauge length if punctual measures are required. For active Lamb wave monitoring, this results in a sensing fiber arranged in multiple loops glued on an aluminum thin panel in order to increase the phase signal only in correspondence to the sensing points of interest. Instead, for passive impact identification, the required sensitivity is guaranteed by simply exploiting a longer gauge length glued to the structure. The fiber optic coherent (FOC) sensor is exploited to detect the strain waves emitted by a piezoelectric transducer placed on the aluminum panel or generated by an impulse hammer, respectively. The FOC sensor measurements have been compared with both a numerical model based on Finite Elements and traditional piezoelectric sensors, confirming a good agreement between experimental and simulated results for both active and passive impact monitoring scenarios

Symbolic Model Checking and Safety Assessment of Altarica models

Altarica is a language used to describe critical systems. In this paper we present a novel approach to the analysis of Altarica models, based on a translation into an extended version of NuSMV. This approach opens up the possibility to carry out functional verification and safety assessment with symbolic techniques. An experimental evaluation on a set of industrial case studies demonstrates the advantages of the approach over currently available tools.

Model Checking at Scale: Automated Air Traffic Control Design Space Exploration

Many possible solutions, differing in the assumptions and implementations of the components in use, are usually in competition during early design stages. Deciding which solution to adopt requires considering several trade-offs. Model checking represents a possible way of comparing such designs, however, when the number of designs is large, building and validating so many models may be intractable. During our collaboration with NASA, we faced the challenge of considering a design space with more than 20,000 designs for the NextGen air traffic control system. To deal with this problem, we introduce a compositional, modular, parameterized approach combining model checking with contract-based design to automatically generate large numbers of models from a possible set of components and their implementations. Our approach is fully automated, enabling the generation and validation of all target designs. The 1,620 designs that were most relevant to NASA were analyzed exhaustively. To deal with the massive amount of data generated, we apply novel data-analysis techniques that enable a rich comparison of the designs, including safety aspects. Our results were validated by NASA system designers, and helped to identify novel as well as known problematic configurations

Generalizations of self-reciprocal polynomials

A formula for the number of monic irreducible self-reciprocal polynomials, of a given degree over a finite field, was given by Carlitz in 1967. In 2011 Ahmadi showed that Carlitz's formula extends, essentially without change, to a count of irreducible polynomials arising through an arbitrary quadratic transformation. In the present paper we provide an explanation for this extension, and a simpler proof of Ahmadi's result, by a reduction to the known special case of self-reciprocal polynomials and a minor variation. We also prove further results on polynomials arising through a quadratic transformation, and through some special transformations of higher degree

A novel inhibitor prevents the peripheral neuroparalysis of Botulinum neurotoxins

Botulinum neurotoxins (BoNTs) form a large class of potent and deadly neurotoxins. Given their growing number, it is of paramount importance to discover novel inhibitors targeting common steps of their intoxication process. Recently, EGA was shown to inhibit the action of bacterial toxins and viruses exhibiting a pH-dependent translocation step in mammalian cells, by interfering with their entry route. As BoNTs act in the cytosol of nerve terminals, the entry into an appropriate compartment wherefrom they translocate the catalytic moiety is essential for toxicity. Herein we propose an optimized procedure to synthesize EGA and we show that, in vitro, it prevents the neurotoxicity of different BoNT serotypes by interfering with their trafficking. Furthermore, in mice, EGA mitigates botulism symptoms induced by BoNT/A and significantly decreases the lethality of BoNT/B and BoNT/D. This opens the possibility of using EGA as a lead compound to develop novel inhibitors of botulinum neurotoxins

Automated Analysis of Reliability Architectures

The development of complex and critical systems calls for a rigorous and thorough the evaluation of reliability aspects. Over the years, several methodologies have been introduced in order to aid the verification and analysis of such systems. Despite this fact, current technologies are still limited to specific architectures, without providing a generic evaluation of redundant system definitions. In this paper we present a novel approach able to assess the reliability of an arbitrary combinatorial redundant system. We rely on an expressive modeling language to represent a wide class of architectural solutions to be assessed. On such models, we provide a portfolio of automatic analysis techniques: we can produce a fault tree, that represents the conditions under which the system fails to produce a correct output; based on it, we can provide a function over the components reliability, which represents the failure probability of the system. At its core, the approach relies on the logical formalism of equality and uninterpreted functions; it relies on automated reasoning techniques, in particular Satisfiability Modulo Theories decision procedures, to achieve efficiency. We carried out an extensiver experimental evaluation of the proposed approach on a wide class of multi-stage redunded systems. On the one hand, we are able to automatically obtain all the results that are manually obtained in [1]; on the other, we provide results for a much wider class of architectures, including the cases of non-uniform probabilities and of two voters per stage