Search

Motivated by Boston and Jones and Goksel, we propose a Markov model for the factorization of PCF cubic polynomials $f$. Using the information encoded in the critical orbits of cubic polynomials, we define a Markov model for PCF cubic polynomials with combined critical orbits of lengths one and two. A complete list of PCF cubic polynomials over $\mathbb{Q}$ is available thanks to the work of Anderson et al. Some of these polynomials have been previously studied -- for example, those with colliding critical orbits analyzed by Benedetto et al.; the results from these studies align with our model. We construct groups $M_n$ and prove that they follow our Markov model. These groups $M_n$ are conjectured to contain $\mathrm{Gal}(f^n)$.

Fault Trees represent an essential tool in the reliability and risk assessment of engineering systems. By decomposing the structure of the system into Boolean function, Fault Trees allow the quantitative and qualitative analysis of the system. One of the main important tasks in Fault Tree analysis is the identification of Minimal Cut Sets, defined as groups of components that present the least path of resistance toward a system's failure. Identifying them allows reliability engineers to enhance the reliability and safety of the system, making system failures less likely to occur. However, the minimal cut set identification problem is challenging to solve, due to the exponential growth experienced in the number of feasible configurations as the system's size grows linearly. Over the last few years, quantum computation has been heralded as a promising tool to tackle computational challenges of increased complexity. The reason for this is the promising prospects that the use of quantum effects has for challenging computational tasks. However, its application into Probabilistic Risk Assessment and reliability engineering, and in particular to challenges related to the Fault Tree model, is still uncharted territory. To fill this gap, the objective of the paper is to integrate quantum computation into the Fault Tree Model and present an assessment of their capabilities for the minimal cut set identification problem. To this end, this paper proposes a novel algorithm to encode a fault tree into a quantum computer and to perform the identification of minimal cut sets with increased efficiency via the application of the Quantum Amplitude Amplification protocol. For validation purposes, a series of theoretical and numerical results, the latter obtained using a quantum simulator, are presented in which the proposed algorithm is compared against traditional approaches, such as Monte Carlo sampling.

Over the last decade, concepts such as industry 4.0 and the Internet of Things (IoT) have contributed to the increase in the availability and affordability of sensing technology. In this context, Structural Health Monitoring (SHM) arises as an especially interesting field to integrate and develop these new sensing capabilities, given the criticality of structural application for human life and the elevated costs of manual monitoring. Due to the scale of structural systems, one of the main challenges when designing a modern monitoring system is the Optimal Sensor Placement (OSP) problem. The OSP problem is combinatorial in nature, making its exact solution infeasible in most practical cases, usually requiring the use of meta-heuristic optimization techniques. While approaches such as genetic algorithms (GA) have been able to produce significant results in many practical case studies, their ability to scale up to more complex structures is still an area of open research. This study proposes a novel quantum-based combinatorial optimization approach to solve the OSP problem approximately, within the context of SHM. For this purpose, a Quadratic Unconstrained Binary Optimization (QUBO) model formulation is developed, taking as a starting point the modal strain energy (MSE) of the structure. The framework is tested using numerical simulations of Warren truss bridges of varying scale. The results obtained using the proposed framework are compared against exhaustive search approaches to verify their performance. More importantly, a detailed discussion of the current limitations of the technology and the future paths of research in the area is presented to the reader.

A subresiduated lattice ordered commutative monoid (or srl-monoid for short) is a pair $(\textbf{A},Q)$ where $\textbf{A}=(A,\wedge,\vee,\cdot,e)$ is an algebra of type $(2,2,2,0)$ such that $(A,\wedge,\vee)$ is a lattice, $(A,\cdot,e)$ is a commutative monoid, $(a\vee b)\cdot c = (a\cdot c) \vee (b\cdot c)$ for every $a,b,c\in A$ and $Q$ is a subalgebra of \textbf{A} such that for each $a,b\in A$ there exists $c\in Q$ with the property that for all $q\in Q$, $a\cdot q \leq b$ if and only if $q\leq c$. This $c$ is denoted by $a\rightarrow_Q b$, or simply by $a\rightarrow b$. The srl-monoids $(\textbf{A},Q)$ can be regarded as algebras $(A,\wedge,\vee,\cdot,\rightarrow, e)$ of type $(2,2,2,2,0)$. These algebras are a generalization of subresiduated lattices and commutative residuated lattices respectively. In this paper we prove that the class of srl-monoids forms a variety. We show that the lattice of congruences of any srl-monoid is isomorphic to the lattice of its strongly convex subalgebras and we also give a description of the strongly convex subalgebra generated by a subset of the negative cone of any srl-monoid. We apply both results in order to study the lattice of congruences of any srl-monoid by giving as application alternative equational basis for the variety of srl-monoids generated by its totally ordered members., Comment: No comments

The Sixth Assessment Report (AR6) of the Intergovernmental Panel on Climate Change (IPCC) has adopted the FAIR Guiding Principles. The Atlas chapter of Working Group I (WGI) is presented as a test case. Here, we describe the application of these principles in the Atlas, the challenges faced during its implementation, and those that remain for the future. We present the open source repository resulting from this process, which collects the code (including annotated Jupyter notebooks), data provenance, and some aggregated datasets underpinning the key figures in the Atlas chapter and its interactive companion (the Interactive Atlas), open to scrutiny by the scientific community and the general public. We describe the informal pilot review conducted on this repository to gather recommendations that led to significant improvements. Finally, a working example illustrates the use of the repository to produce customized regional information, extending the Interactive Atlas products and running the code interactively in a web browser using Jupyter notebooks. Atlas repository: doi:10.5281/zenodo.5171760., Comment: 18 pages, 3 figures and 1 table. Submitted to Scientific Data; currently under peer review

Fault tree analysis is a technique widely used in risk and reliability analysis of complex engineering systems given its deductive nature and relatively simple interpretation. In a fault tree, events are usually represented by a binary variable that indicates whether an event occurs or not, traditionally associated with the values 1 and 0, respectively. Different events are linked together using logical gates, modelling the dependencies that a subsystem or system may have over its basic components. In this study, quantum computing is leveraged to propose a novel approach to encode a traditional fault tree into a quantum algorithm. This quantum fault tree method uses quantum bits to represent basic events, effectively encoding the original fault tree into a quantum circuit. The execution of the resulting quantum circuit represents a full simulation of the fault tree, and multiple executions can be utilized to compute the failure probability of the whole system. The proposed approach is tested on a case study portraying a dynamic positioning system. Results verify that the quantum-based proposed approach is able to effectively obtain the dynamic positioning failure probability through simulation, opening promising opportunities for future investigations in the area., Comment: 12 pages, 7 figures, 2 tables

Small corrections in the argument of the latitude can be used to improve the accuracy of the SGP4 orbit propagator. These corrections have been obtained by applying the hybrid methodology for orbit propagation to SGP4, therefore yielding a hybrid version of this propagator. The forecasting part of the hybrid method is based on a state-space formulation of the exponential smoothing method. If the error terms that have to be considered during the model fitting process are taken as Gaussian noise, then the maximum-likelihood method can be applied so as to estimate the parameters of the exponential-smoothing model, as well as to compute the forecast together with its confidence interval. Finally, this hybrid SGP4 orbit propagator has been applied to data from Galileo-type orbits. This new propagator improves the accuracy of the classical SGP4, especially for short forecasting horizons., Comment: 9 pages, 5 figures

Astrometric Science and Technology Roadmap for Astrophysics (ASTRA) is a bilateral cooperation between China and Italy with the goal of consolidating astrometric measurement concepts and technologies. In particular, the objectives include critical analysis of the Gaia methodology and performance, as well as principle demonstration experiments aimed at future innovative astrometric applications requiring high precision over large angular separations (one to 180 degrees). Such measurement technologies will be the building blocks for future instrumentation focused on the "great questions" of modern cosmology, like General Relativity validity (including Dark Matter and Dark Energy behavior), formation and evolution of structure like proto-galaxies, and planetary systems formation in bio compatibles environments. We describe three principle demonstration tests designed to address some of the potential showstoppers for high astrometric precision experiments. The three tests are focused on the key concepts of multiple fields telescopes, astrometric metrology and very fine sub-pixel precision (goal: <1/2000 pixel) in white light., Comment: 12 pages, 12 figures; SPIE Astronomical Telescopes + Instrumentation, 2020, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation IV

The compound 2-mercaptobenzothizaole (MBT) has been frequently detected in wastewater and surface water and is a potential threat to both aquatic organisms and human health (its mutagenic potential has been demonstrated). This study investigated the degradation routes of MBT in the anode of a microbial electrolysis cell (MEC) and the involved microbial communities. The results indicated that graphene-modified anodes promoted the presence of more enriched, developed, and specific communities compared to bare anodes. Moreover, consecutive additions of the OH substituent to the benzene ring of MBT were only detected in the reactor equipped with the graphene-treated electrode. Both phenomena, together with the application of an external voltage, may be related to the larger reduction of biotoxicity observed in the MEC equipped with graphene-modified anodes (46.2 eqtox/m3 to 27.9 eqtox/m3).

A hybrid orbit propagator based on the analytical integration of the Kepler problem is designed to determine the future position and velocity of any orbiter, usually an artificial satellite or space debris fragment, in two steps: an initial approximation generated by means of an integration method, followed by a forecast of its error, determined by a prediction technique that models and reproduces the missing dynamics. In this study we analyze the effect of slightly changing the initial conditions for which a hybrid propagator was developed. We explore the possibility of generating a new hybrid propagator from others previously developed for nearby initial conditions. We find that the interpolation of the parameters of the prediction technique, which in this case is an additive Holt-Winters method, yields similarly accurate results to a non-interpolated hybrid propagator when modeling the J2 effect in the main problem propagation., Comment: 12 pages, 3 figures

Two-Line Elements (TLEs) continue to be the sole public source of orbiter observations. The accuracy of TLE propagations through the Simplified General Perturbations-4 (SGP4) software decreases dramatically as the propagation horizon increases, and thus the period of validity of TLEs is very limited. As a result, TLEs are gradually becoming insufficient for the growing demands of Space Situational Awareness (SSA). We propose a technique, based on the hybrid propagation methodology, aimed at extending TLE validity with minimal changes to the current TLE-SGP4 system in a non-intrusive way. It requires that the institution in possession of the osculating elements distributes hybrid TLEs, HTLEs, which encapsulate the standard TLE and the model of its propagation error. The validity extension can be accomplished when the end user processes HTLEs through the hybrid SGP4 propagator, HSGP4, which comprises the standard SGP4 and an error corrector., Comment: 18 pages, 4 figures

In this work we present a new methodology for orbit propagation, the hybrid perturbation theory, based on the combination of an integration method and a prediction technique. The former, which can be a numerical, analytical or semianalytical theory, generates an initial approximation that contains some inaccuracies derived from the fact that, in order to simplify the expressions and subsequent computations, not all the involved forces are taken into account and only low-order terms are considered, not to mention the fact that mathematical models of perturbations not always reproduce physical phenomena with absolute precision. The prediction technique, which can be based on either statistical time series models or computational intelligence methods, is aimed at modelling and reproducing missing dynamics in the previously integrated approximation. This combination results in the precision improvement of conventional numerical, analytical and semianalytical theories for determining the position and velocity of any artificial satellite or space debris object. In order to validate this methodology, we present a family of three hybrid orbit propagators formed by the combination of three different orders of approximation of an analytical theory and a statistical time series model, and analyse their capability to process the effect produced by the flattening of the Earth. The three considered analytical components are the integration of the Kepler problem, a first-order and a second-order analytical theories, whereas the prediction technique is the same in the three cases, namely an additive Holt-Winters method., Comment: 27 pages, 8 figures

One of the methodologies based on group dynamics is Role Playing (RP). This method consists on the simulation of a real situation, allowing its study and understanding. Knowledge and technical skills are not the only prerequisites for proper practice in health sciences. RP has been used as Communication Skills Training (CST) amongst health professionals. In the teaching of odontology and stomatology, object of our research, dental assistance brings up situations where the professional must develop transversal skills, which improve the interaction with the patient and the dental treatment itself. The aim of this study is to evaluate the efficacy of the proposed RP methodology through the students' opinion. The study sample is made out of dental students (n=80), all of them on the 4th year at the College of Dentistry (University of Seville, Spain). The students who took part in the activity considered the incorporation of RP in the syllabus as relevant, though further study should be considered in order to analyze the efficacy of this teaching methodology in depth., Comment: 17 pages, 11 figures