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In the modern world of electronic devices, a person can bring to life any projects that make their life more comfortable and safe. The basis for such solutions is robotics. Creating and programming a robot today is quite simple. We offer the experience of conducting long-term projects that can take place in summer camps, scientific studios, and extracurricular clubs. The uniqueness of such activities lies in the combination of various types of work that help explore the topic and conduct scientific and technological research. Mastering robotics technology and understanding the principles of their operation is an important aspect of preparing modern children for a safe life in a high-tech world and successful self-realization. The foundation for the study and effective application of these technologies is mathematics, physics, engineering, and programming. Therefore, STEM education, aimed at developing competencies demanded in society, increasing motivation to study traditionally challenging subjects of the natural-mathematical cycle, is of particular importance. The peculiarity of this approach to education is project activity and transdisciplinarity, contributing to the formation of teamwork skills, critical thinking, and a comprehensive understanding of the researched problem. The article presents the experience of a volunteer project to teach robotics to children from Ukraine. Organizational conditions for conducting classes, typical difficulties, examples of projects, and the lesson scenario are provided. The proposed approach to organizing education is based on years of practical experience and can be used by educational institutions and non-profit organizations.

We present the first generalization of Navier-Stokes theory to relativity that satisfies all of the following properties: (a) the system coupled to Einstein’s equations is causal and strongly hyperbolic; (b) equilibrium states are stable; (c) all leading dissipative contributions are present, i.e., shear viscosity, bulk viscosity, and thermal conductivity; (d) nonzero baryon number is included; (e) entropy production is non-negative in the regime of validity of the theory; (f) all of the above hold in the nonlinear regime without any simplifying symmetry assumptions. These properties are accomplished using a generalization of Eckart’s theory containing only the hydrodynamic variables, so that no new extended degrees of freedom are needed as in Müller-Israel-Stewart theories. Property (b), in particular, follows from a more general result that we also establish, namely, sufficient conditions that when added to stability in the fluid’s rest frame imply stability in any reference frame obtained via a Lorentz transformation All of our results are mathematically rigorously established. The framework presented here provides the starting point for systematic investigations of general-relativistic viscous phenomena in neutron star mergers.

Bayesian Networks (BNs) have become increasingly popular over the last few decades as a tool for reasoning under uncertainty in fields as diverse as medicine, biology, epidemiology, economics and the social sciences. This is especially true in real-world areas where we seek to answer complex questions based on hypothetical evidence to determine actions for intervention. However, determining the graphical structure of a BN remains a major challenge, especially when modelling a problem under causal assumptions. Solutions to this problem include the automated discovery of BN graphs from data, constructing them based on expert knowledge, or a combination of the two. This paper provides a comprehensive review of combinatoric algorithms proposed for learning BN structure from data, describing 74 algorithms including prototypical, well-established and state-of-the-art approaches. The basic approach of each algorithm is described in consistent terms, and the similarities and differences between them highlighted. Methods of evaluating algorithms and their comparative performance are discussed including the consistency of claims made in the literature. Approaches for dealing with data noise in real-world datasets and incorporating expert knowledge into the learning process are also covered.

A mechanistic understanding of catalytic organic reactions is crucial for the design of new catalysts, modes of reactivity and the development of greener and more sustainable chemical processes 1 – 13 . Kinetic analysis lies at the core of mechanistic elucidation by facilitating direct testing of mechanistic hypotheses from experimental data. Traditionally, kinetic analysis has relied on the use of initial rates 14 , logarithmic plots and, more recently, visual kinetic methods 15 – 18 , in combination with mathematical rate law derivations. However, the derivation of rate laws and their interpretation require numerous mathematical approximations and, as a result, they are prone to human error and are limited to reaction networks with only a few steps operating under steady state. Here we show that a deep neural network model can be trained to analyse ordinary kinetic data and automatically elucidate the corresponding mechanism class, without any additional user input. The model identifies a wide variety of classes of mechanism with outstanding accuracy, including mechanisms out of steady state such as those involving catalyst activation and deactivation steps, and performs excellently even when the kinetic data contain substantial error or only a few time points. Our results demonstrate that artificial-intelligence-guided mechanism classification is a powerful new tool that can streamline and automate mechanistic elucidation. We are making this model freely available to the community and we anticipate that this work will lead to further advances in the development of fully automated organic reaction discovery and development. Mechanistic elucidation through currently available kinetic analysis is limited by mathematical approximations and human interpretation, here a deep neural network model has been trained to analyse ordinary kinetic data and automatically elucidate the corresponding mechanism class.

A subset A of a group G is called product-free if there is no solution to a=bc with a,b,c all in A. It is easy to see that the largest product-free subset of the symmetric group Sn is obtained by taking the set of all odd permutations, i.e. Sn∖An, where An is the alternating group. In 1985 Babai and Sós (Eur. J. Comb. 6(2):101–114, 1985) conjectured that the group An also contains a product-free set of constant density. This conjecture was refuted by Gowers (whose result was subsequently improved by Eberhard), still leaving the long-standing problem of determining the largest product-free subset of An wide open. We solve this problem for large n, showing that the maximum size is achieved by the previously conjectured extremal examples, namely families of the form {π:π(x)∈I,π(I)∩I=∅} and their inverses. Moreover, we show that the maximum size is only achieved by these extremal examples, and we have stability: any product-free subset of An of nearly maximum size is structurally close to an extremal example. Our proof uses a combination of tools from Combinatorics and Non-abelian Fourier Analysis, including a crucial new ingredient exploiting some recent theory developed by Filmus, Kindler, Lifshitz and Minzer for global hypercontractivity on the symmetric group.

Mathematical modelling of infectious diseases has shown that combinations of isolation, quarantine, vaccine and treatment are often necessary in order to eliminate most infectious diseases. However, if they are not administered at the right time and in the right amount, the disease elimination will remain a difficult task. Optimal control theory has proven to be a successful tool in understanding ways to curtail the spread of infectious diseases by devising the optimal diseases intervention strategies. The method consists of minimizing the cost of infection or the cost of implementing the control, or both. This paper reviews the available literature on mathematical models that use optimal control theory to deduce the optimal strategies aimed at curtailing the spread of an infectious disease.

Penetration depth of ultraviolet, visible light and infrared radiation in biological tissue has not previously been adequately measured. Risk assessment of typical intense pulsed light and laser intensities, spectral characteristics and the subsequent chemical, physiological and psychological effects of such outputs on vital organs as consequence of inappropriate output use are examined. This technical note focuses on wavelength, illumination geometry and skin tone and their effect on the energy density (fluence) distribution within tissue. Monte Carlo modelling is one of the most widely used stochastic methods for the modelling of light transport in turbid biological media such as human skin. Using custom Monte Carlo simulation software of a multi-layered skin model, fluence distributions are produced for various non-ionising radiation combinations. Fluence distributions were analysed using Matlab mathematical software. Penetration depth increases with increasing wavelength with a maximum penetration depth of 5378 μm calculated. The calculations show that a 10-mm beam width produces a fluence level at target depths of 1–3 mm equal to 73–88% (depending on depth) of the fluence level at the same depths produced by an infinitely wide beam of equal incident fluence. Meaning little additional penetration is achieved with larger spot sizes. Fluence distribution within tissue and thus the treatment efficacy depends upon the illumination geometry and wavelength. To optimise therapeutic techniques, light-tissue interactions must be thoroughly understood and can be greatly supported by the use of mathematical modelling techniques.

Classical optimization algorithms are insufficient in large scale combinatorial problems and in nonlinear problems. Hence, metaheuristic optimization algorithms have been proposed. General purpose metaheuristic methods are evaluated in nine different groups: biology-based, physics-based, social-based, music-based, chemical-based, sport-based, mathematics-based, swarm-based, and hybrid methods which are combinations of these. Studies on plants in recent years have showed that plants exhibit intelligent behaviors. Accordingly, it is thought that plants have nervous system. In this work, all of the algorithms and applications about plant intelligence have been firstly collected and searched. Information is given about plant intelligence algorithms such as Flower Pollination Algorithm, Invasive Weed Optimization, Paddy Field Algorithm, Root Mass Optimization Algorithm, Artificial Plant Optimization Algorithm, Sapling Growing up Algorithm, Photosynthetic Algorithm, Plant Growth Optimization, Root Growth Algorithm, Strawberry Algorithm as Plant Propagation Algorithm, Runner Root Algorithm, Path Planning Algorithm, and Rooted Tree Optimization.

We prove that quantum information encoded in some topological excitations, including certain Majorana zero modes, is protected in closed systems for a time scale exponentially long in system parameters. This protection holds even at infinite temperature. At lower temperatures, the decay time becomes even longer, with a temperature dependence controlled by an effective gap that is parametrically larger than the actual energy gap of the system. This nonequilibrium dynamical phenomenon is a form of prethermalization and occurs because of obstructions to the equilibration of edge or defect degrees of freedom with the bulk. We analyze the ramifications for ordered and topological phases in one, two, and three dimensions, with examples including Majorana and parafermionic zero modes in interacting spin chains. Our results are based on a nonperturbative analysis valid in any dimension, and they are illustrated by numerical simulations in one dimension. We discuss the implications for experiments on quantum-dot chains tuned into a regime supporting end Majorana zero modes and on trapped ion chains.

Mathematical word problem solving is influenced by various characteristics of the task and the person solving it. Yet, previous research has rarely related these characteristics to holistically answer which word problem requires which set of individual cognitive skills. In the present study, we conducted a secondary data analysis on a dataset of N = 1282 undergraduate students solving six mathematical word problems from the Programme for International Student Assessment (PISA). Previous results had indicated substantial variability in the contribution of individual cognitive skills to the correct solution of the different tasks. Here, we exploratively reanalyzed the data to investigate which task characteristics may account for this variability, considering verbal, arithmetic, spatial, and general reasoning skills simultaneously. Results indicate that verbal skills were the most consistent predictor of successful word problem solving in these tasks, arithmetic skills only predicted the correct solution of word problems containing calculations, spatial skills predicted solution rates in the presence of a visual representation, and general reasoning skills were more relevant in simpler problems that could be easily solved using heuristics. We discuss possible implications, emphasizing how word problems may differ with regard to the cognitive skills required to solve them correctly.