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For educational institutions in STEM areas, the provision of practical learning scenarios is, traditionally, a major concern. In the 21st century, the explosion of ICTs, as well as the universalization of low-cost hardware, have allowed the proliferation of technical solutions for any field; in the case of experimentation, encouraging the emergence and proliferation of non-traditional experimentation platforms. This movement has resulted in enriched practical environments, with wider adaptability for both students and teachers. In this paper, the evolution of scholar production has been analyzed at the global level from 2000 to 2020. Current and emerging experimentation scenarios have been identified, specifying the scope and boundaries between them., Comment: Transaction on learning Technologies, 20 pages

In this work, a recently introduced general framework for trajectory statistical solutions is considered, and the question of convergence of families of such solutions is addressed. Conditions for the convergence are given which rely on natural assumptions related to a priori estimates for the individual solutions of typical approximating problems. The first main result is based on the assumption that the superior limit of suitable families of compact subsets of carriers of the family of trajectory statistical solutions be included in the set of solutions of the limit problem. The second main result is a version of the former in the case in which the approximating family is associated with a well-posed system. These two results are then applied to the inviscid limit of incompressible Navier-Stokes system in two and three spatial dimensions, showing, in particular, the existence of trajectory statistical solutions to the two- and three-dimensional Euler equations, in the context of weak and dissipative solutions, respectively. Another application of the second main result is on the Galerkin approximations of statistical solutions of the three-dimensional Navier-Stokes equations.

This paper presents the Random-Key Optimizer (RKO), a versatile and efficient stochastic local search method tailored for combinatorial optimization problems. Using the random-key concept, RKO encodes solutions as vectors of random keys that are subsequently decoded into feasible solutions via problem-specific decoders. The RKO framework is able to combine a plethora of classic metaheuristics, each capable of operating independently or in parallel, with solution sharing facilitated through an elite solution pool. This modular approach allows for the adaptation of various metaheuristics, including simulated annealing, iterated local search, and greedy randomized adaptive search procedures, among others. The efficacy of the RKO framework, implemented in C++, is demonstrated through its application to three NP-hard combinatorial optimization problems: the alpha-neighborhood p-median problem, the tree of hubs location problem, and the node-capacitated graph partitioning problem. The results highlight the framework's ability to produce high-quality solutions across diverse problem domains, underscoring its potential as a robust tool for combinatorial optimization., Comment: 54 pages, 16 figures, 8 tables

Digital Twin (DT) technologies promise to remove cyber-physical barriers in systems and services and provide seamless management of distributed resources effectively. Ideally, full-fledged instantiations of DT offer bi-directional features for physical-virtual representations, tackling data governance, risk assessment, security and privacy protections, resilience, and performance, to name a few characteristics. More broadly, Federated Digital Twins (FDT) are distributed physical-virtual counterparts that collaborate for enacting synchronisation and accurate mapping of multiple DT instances. In this work we focus on understanding and conceptualising the cyber-physical and business perspectives using FDT in multinational and multimodal transportation systems. These settings enforce a plethora of regulations, compliance, standards in the physical counterpart that must be carefully considered in the virtual mirroring. Our aim is to discuss the regulatory and technical underpinnings and, consequently, the existing operational and budgetary overheads to factor in when designing or operating FDT.

DevOps (development and operations), has significantly changed the way to overcome deficiencies for delivering high-quality software to production environments. Past years witnessed an increased interest in embedding DevOps with cybersecurity in an approach dubbed secure DevOps. However, as the practices and guidance mature, teams must consider them within a broader risk context. We argue here how secure DevOps could profit from engaging with risk related activities within organisations. We focus on combining Risk Assessment (RA), particularly Threat Modelling (TM) and apply security considerations early in the software life-cycle. Our contribution provides a roadmap for enacting secure DevOps alongside risk objectives, devising informed ways to improve TM and establishing effective security underpinnings in organisations focusing on software products and services. We aim to outline proven methods over the literature on the subject discussing case studies, technologies, and tools. It presents a case study for a real-world inspired organisation employing the proposed approach with a discussion. Enforcing these novel mechanisms centred on security requires investment, training, and stakeholder engagement. It requires understanding the actual benefits of automation in light of Continuous Integration/Continuous Delivery settings that improve the overall quality of software solutions reaching the market.

This paper proposes a problem-independent GRASP metaheuristic using the random-key optimizer (RKO) paradigm. GRASP (greedy randomized adaptive search procedure) is a metaheuristic for combinatorial optimization that repeatedly applies a semi-greedy construction procedure followed by a local search procedure. The best solution found over all iterations is returned as the solution of the GRASP. Continuous GRASP (C-GRASP) is an extension of GRASP for continuous optimization in the unit hypercube. A random-key optimizer (RKO) uses a vector of random keys to encode a solution to a combinatorial optimization problem. It uses a decoder to evaluate a solution encoded by the vector of random keys. A random-key GRASP is a C-GRASP where points in the unit hypercube are evaluated employing a decoder. We describe random key GRASP consisting of a problem-independent component and a problem-dependent decoder. As a proof of concept, the random-key GRASP is tested on five NP-hard combinatorial optimization problems: traveling salesman problem, tree of hubs location problem, Steiner triple covering problem, node capacitated graph partitioning problem, and job sequencing and tool switching problem., Comment: 24 pages, 8 figures

The family of invariant Riemannian manifolds in the Wallach flag manifold $\mathrm{SU}(3)/\mathrm{T}^2$ is described by three parameters $(x,y,z)$ of positive real numbers. By restricting such a family of metrics in the \emph{tetrahedron} $\cal{T}:= x+y+z = 1$, in this paper, we describe all regions $\cal R \subset \cal T$ admitting metrics with curvature properties varying from positive sectional curvature to positive scalar curvature, including positive intermediate curvature notion's. We study the dynamics of such regions under the \emph{projected Ricci flow} in the plane $(x,y)$, concluding sign curvature maintenance and escaping. In addition, we obtain some results for positive intermediate Ricci curvature for a path of metrics on fiber bundles over $\mathrm{SU}(3)/\mathrm{T}^2$, further studying its evolution under the Ricci flow on the base., Comment: 15 pages, 12 figures. arXiv admin note: text overlap with arXiv:2305.06119

It is well known that the Euler method for a random ordinary differential equation $\mathrm{d}X_t/\mathrm{d}t = f(t, X_t, Y_t)$ driven by a stochastic process $\{Y_t\}_t$ with $\theta$-H\"older sample paths is estimated to be of strong order $\theta$ with respect to the time step, provided $f=f(t, x, y)$ is sufficiently regular and with suitable bounds. This order is known to increase to $1$ in some special cases. Here, it is proved that, in many more typical cases, further structures on the noise can be exploited so that the strong convergence is of order 1. More precisely, we prove so for any semi-martingale noise. This includes It\^o diffusion processes, point-process noises, transport-type processes with sample paths of bounded variation, and time-changed Brownian motion. The result follows from estimating the global error as an iterated integral over both large and small mesh scales, and by switching the order of integration to move the critical regularity to the large scale. The work is complemented with numerical simulations showing the optimality of the strong order 1 convergence in those cases, and with an example with fractional Brownian motion noise with Hurst parameter $0 < H < 1/2,$ which is not a semi-martingale and for which the order of convergence is $H + 1/2$, hence lower than the attained order 1 in the semi-martingale case, but still higher than the order $H$ of convergence expected from previous works., Comment: 16 figures; v2) fixed stability condition in the Fisher-KPP example; v3) adjust mesh points to N+1 and add references; v4) add missing jumps for FV process; v5) generalize to any semi-martingale noise; v6) focus only on the strong-convergence, simplify some proofs, update the numerical experiments, and reorganize the paper (23 figures) (version 6 submitted for publication)

In this note, we show that the classical Wallach manifold $\mathrm{SU}(3)/\mathrm{T}^2$-admits metrics of positive intermediate Ricci curvature $(\mathrm{Ric}_d >0)$ for $d = 1, 2, 3, 4, 5$ that lose these properties under the homogeneous Ricci flow for $d=1, 2, 3, 5$. We make the same analyses to the family of Riemannian flag manifolds $\mathrm{SU}(m+2p)/\mathrm{S}(\mathrm{U}(m)\times\mathrm{U}(p)\times \mathrm{U}(p))$, concluding similar results. These explicitly verify some claims expected to be true among experts (see \cite{BW}) for positive Ricci curvature and intermediate positive Ricci curvature. Our technique is only possible due to the global behavior understanding of the homogeneous Ricci flow for invariant metrics on these manifolds., Comment: Accepted version. To appear in the Special Issue of the Workshop on Geometric Structures and Moduli Spaces (WGSMS). Revista Matem\'atica Contempor\^anea

The Poincar\'e-Hopf Theorem relates the Euler characteristic of a 2-dimensional compact manifold to the local behavior of smooth vector fields defined on it. However, despite the importance of Filippov vector fields, concerning both their theoretical and applied aspects, until now, it was not known whether this theorem extends to Filippov vector fields. In this paper, we demonstrate that the Poincar\'e-Hopf Theorem applies to Filippov vector fields defined on 2-dimensional compact manifolds with smooth switching manifolds. As a result, we establish a variant of the Hairy Ball Theorem, asserting that "any Filippov vector field on a sphere with smooth switching manifolds must have at least one singularity (in the Filippov sense) with positive index". This extension is achieved by introducing a new index definition that includes the singularities of Filippov vector fields, such as pseudo-equilibria and tangential singularities. Our work extends the classical index definition for singularities of smooth vector fields to encompass those of Filippov vector fields with smooth switching manifolds. This extension is based on an invariance property under a regularization process, allowing us to establish all classical index properties. We also compute the indices of all generic $\Sigma$-singularities and some codimension-1 $\Sigma$-singularities, including fold-fold tangential singularities, regular-cusp tangential singularities, and saddle-node pseudo-equilibria., Comment: 27 pages, 4 figures