Search

The purpose of this paper is twofold. Firstly, to emphasise that the class of Lie algebras with chain lattices of ideals are elementary blocks in the embedding or decomposition of Lie algebras with finite lattice of ideals. Secondly, to show that the number of Lie algebras of this class is large and they support other types of Lie structures. Beginning with general examples and algebraic decompositions, we focus on computational algorithms to build Lie algebras in which the lattice of ideals is a chain. The chain condition forces gradings on the nilradicals of this class of algebras. Our algorithms yield to several positive naturally graded parametric families of Lie algebras. Further generalizations and other kind of structures will also be discussed., Comment: 33 pages, 4 figures, 4 tables, 3 algorithms

We report results on the analysis of eleven new Milky Way open cluster candidates, recently discovered from the detection of stellar overdensities in the Vector Point diagram, by employing extreme deconvolution Gaussian mixture models. We treated these objects as real open clusters and derived their fundamental properties with their associated intrinsic dispersions by exploring the parameter space through the minimization of likelihood functions on generated synthetic colour-magnitude diagrams (CMDs). The intrinsic dispersions of the resulting ages turned out to be much larger than those usually obtained for open clusters. Indeed, they resemble those of ages and metallicities of composite star field populations. We also traced their stellar number density profiles and mass functions, derived their total masses, Jacobi and tidal radii, which helped us as criteria while assessing their physical nature as real open clusters. Because the eleven candidates show a clear gathering of stars in the proper motion plane and some hint for similar distances, we concluded that they are possibly sparse groups of stars., Comment: 9 pages, 6 figures. Accepted for publication in MNRAS

We study different domination problems of attacking and non-attacking rooks and queens on polyominoes and polycubes of all dimensions. Our main result proves that maximal domination is NP-complete for non-attacking queens and for non-attacking rooks on polycubes of dimension three and higher. We also analyse these problems for polyominoes and convex polyominoes, conjecture the complexity classes and provide a computer tool for investigation. We have also computed new values for classical queen domination problems on chessboards (square polyominoes). For our computations, we have translated the problem into an integer linear programming instance. Finally, using this computational implementation and the game engine Godot, we have developed a video game of minimal domination of queens and rooks on randomly generated polyominoes., Comment: 19 pages, 20 figures, 4 tables. Theorem 1 now for d>2, added results on approximation, fixed typos, reorganised some proofs

We study the heat transfer between two nanoparticles held at different temperatures that interact through nonreciprocal forces, by combining molecular dynamics simulations with stochastic thermodynamics. Our simulations reveal that it is possible to construct nano refrigerators that generate a net heat transfer from a cold to a hot reservoir at the expense of power exerted by the nonreciprocal forces. Applying concepts from stochastic thermodynamics to a minimal under-damped Langevin model, we derive exact analytical expressions predictions for the fluctuations of work, heat, and efficiency, which reproduce thermodynamic quantities extracted from the molecular dynamics simulations. The theory only involves a single unknown parameter, namely an effective friction coefficient, which we estimate fitting the results of the molecular dynamics simulation to our theoretical predictions. Using this framework, we also establish design principles which identify the minimal amount of entropy production that is needed to achieve a certain amount of uncertainty in the power fluctuations of our nano refrigerator. Taken together, our results shed light on how the direction and fluctuations of heat flows in natural and artificial nano machines can be accurately quantified and controlled by using nonreciprocal forces., Comment: Single PDF comprising the Main Text (first 11 pages), and the Supplemental Material (8 pages, at the end of the PDF)

The demonstrated success of transfer learning has popularized approaches that involve pretraining models from massive data sources and subsequent finetuning towards a specific task. While such approaches have become the norm in fields such as natural language processing, implementation and evaluation of transfer learning approaches for chemistry are in the early stages. In this work, we demonstrate finetuning for downstream tasks on a graph neural network (GNN) trained over a molecular database containing 2.7 million water clusters. The use of Graphcore IPUs as an AI accelerator for training molecular GNNs reduces training time from a reported 2.7 days on 0.5M clusters to 1.2 hours on 2.7M clusters. Finetuning the pretrained model for downstream tasks of molecular dynamics and transfer to a different potential energy surface took only 8.3 hours and 28 minutes, respectively, on a single GPU., Comment: Machine Learning and the Physical Sciences Workshop at the 36th conference on Neural Information Processing Systems (NeurIPS)

This paper proposes a recursive, virtual admittance based, secondary controller for DG units that improves the voltage profile in distribution networks. First, the adaptation of the virtual admittance concept for the goal of voltage regulation is explained. Then, a recursive secondary controller is developed to periodically update the virtual admittance gains. The controller is formulated as an optimization problem with current and stability limitations as constraints. Measurements across the grid, transmitted through low-bandwidth communications, are used to simplify the calculations, resulting in a recursive algorithm. Weight vectors are included in the objective function to allow participation flexibility of each converter. Results show that the primary virtual admittance controller is able to mitigate over- and under-voltages in steady state and under transient conditions. Subsequently, the secondary controller is shown to further improve the voltage profiles across the grid. Experimental results obtained from a laboratory environment, comprising three DG units and a grid emulator, validate the functionality of the complete control structure., Comment: in IEEE Transactions on Smart Grid

We review the theory of martingales as applied to stochastic thermodynamics and stochastic processes in physics more generally., Comment: 324 pages, 68 figures, submitted to Advances in Physics

A Lie algebra is said to be quadratic if it admits a symmetric invariant and non-degenerated bilinear form. Semisimple algebras with the Killing form are examples of these algebras, while orthogonal subspaces provide abelian quadatric algebras. The class of quadratic algebras is outsize, but at first sight it is not clear weather an algebra is quadratic. Some necessary structural conditions appear due to the existence of an invariant form forces elemental patterns. Along the paper we overview classical features and constructions on this topic and focus on the existence and constructions of local quadratic.

The future developments of three-dimensional magnetic nanotechnology require the control of domain wall dynamics by means of current pulses. While this has been extensively studied in planar magnetic strips (planar nanowires), few reports exist in cylindrical geometry, where Bloch point domain walls are expected to have intriguing properties. Here we report this investigation in cylindrical magnetic Ni nanowires with geometrical notches. Experimental work based on synchrotron X-ray magnetic circular dichroism (XMCD) combined with photoemission electron microscopy (PEEM) indicates that large current densities induce domain wall nucleation while smaller currents move domain walls preferably against the current direction. In the region where no pinning centers are present we found domain wall velocity of about 1 km/s. The domain wall motion along current was also detected in the vicinity of the notch region. Pinning of domain walls has been observed not only at geometrical constrictions but also outside of them. Thermal modelling indicates that large current densities temporarily raise the temperature in the nanowire above the Curie temperature leading to nucleation of domain walls during the system cooling. Micromagnetic modelling with spin-torque effect shows that for intermediate current densities Bloch point domain walls with chirality parallel to the Oersted field propagate antiparallel to the current direction. In other cases, domain walls can be bounced from the notches and/or get pinned outside their positions. We thus find that current is not only responsible for the domain wall propagation but is also a source of pinning due to the Oersted field action.

End-to-end reinforcement learning techniques are among the most successful methods for robotic manipulation tasks. However, the training time required to find a good policy capable of solving complex tasks is prohibitively large. Therefore, depending on the computing resources available, it might not be feasible to use such techniques. The use of domain knowledge to decompose manipulation tasks into primitive skills, to be performed in sequence, could reduce the overall complexity of the learning problem, and hence reduce the amount of training required to achieve dexterity. In this paper, we propose the use of Davenport chained rotations to decompose complex 3D rotation goals into a concatenation of a smaller set of more simple rotation skills. State-of-the-art reinforcement-learning-based methods can then be trained using less overall simulated experience. We compare its performance with the popular Hindsight Experience Replay method, trained in an end-to-end fashion using the same amount of experience in a simulated robotic hand environment. Despite a general decrease in performance of the primitive skills when being sequentially executed, we find that decomposing arbitrary 3D rotations into elementary rotations is beneficial when computing resources are limited, obtaining increases of success rates of approximately 10% on the most complex 3D rotations with respect to the success rates obtained by HER trained in an end-to-end fashion, and increases of success rates between 20% and 40% on the most simple rotations., Comment: 5 pages, 3 figures, 3 tables, submitted to ICARA 2023

In the present study, we have derived the Lorentz factor using a coordinate system with antiparallel X-axes. Using a thought experiment, common in relativistic literature, we have used the case of a pulse of light moving along the X-axis. Next, we have argued that, consequently with the isotropy of space, the result must be the same if the trajectory of the light pulse is any angle $\alpha>0^{\circ}$, thus obtaining an alternative transformation factor that generates the same results as the Lorenz factor at any angle of the trajectory of the light pulse, therefore confirming the relativistic isotropy of space in the context of the Minkowski spacetime. Nevertheless, a particularly important novelty is that the derived alternative transformation factor allows the reference frames involved to move at speeds greater than that of light., Comment: arXiv admin note: text overlap with arXiv:2104.01492

Through documentary research and interviews with nutrition experts, we found that all nutrients have two thresholds, the Recommended Daily Allowance (RDA) and the Tolerable Upper Intake Level (UL). Intake less than the RDA or more than the UL negatively affects health. Intake quantities of nutrients within these limits covers 100% of the objective physiological needs without negative repercussions. These characteristics, and others, are common knowledge among nutrition experts; however, these are not adequately reflected in the microeconomics models that study these needs. We conclude that the generalized presence of these thresholds determines the existence of significant indifference areas that should be added to the microeconomics models of the indifference curves, thus improving the modelling of reality.

This paper proposes a taxonomy of power converter control schemes based on the recently proposed concept of complex frequency. This quantity captures local frequency variations due to the change of both the phase angle and amplitude of bus voltages and current injections. The paper derives the analytical expressions of the link between complex power variations and complex frequency of each converter controller as well as the identification of critical control parameters. The main contribution of this work is to provide a general framework that allows classifying converters synchronization mechanisms and controllers. This framework also allows comparing converters with synchronous machines. To validate the theoretical results, extensive simulations are performed using a modified version of the WSCC 9-bus system. Examples of how the theoretical formulations of the paper can be used to improve power converter control in power system applications are showcased., Comment: 10 pages, 22 figures

Robotic manipulation and control has increased in importance in recent years. However, state of the art techniques still have limitations when required to operate in real world applications. This paper explores Hindsight Experience Replay both in simulated and real environments, highlighting its weaknesses and proposing reinforcement-learning based alternatives based on reward and goal shaping. Additionally, several research questions are identified along with potential research directions that could be explored to tackle those questions., Comment: 4 pages, 1 figure, Submitted to PhD Workshop submission at IRC 2022. Updated figure 1

In the present work we revise a transformation that links generalized Lozi maps with max-type difference equations. In this view, according to the technique of topological conjugation, we relate the dynamics of a concrete Lozi map with a complete uniparametric family of max-equations, and we apply this fact to investigate the dynamics of two particular families. Moreover, we present some numerical simulations related to the topic and, finally, we propose some open problems that look into the relationship established between generalized Lozi maps and max-equations., Comment: 30 pages and 12 figures. The final version of the paper will be published in the Journal of Difference Equations and Applications

The evolution of asymptotic giant branch stars from the spherical symmetry into the diverse shapes of planetary nebulae (PNe) is a topic of intensive research. Young PNe provide a unique opportunity to characterize the onset of this transitional phase. In particular, OH maser-emitting PNe (OHPNe) are considered nascent PNe. In fact, only 6 OHPNe have been confirmed to date. In order to identify and characterize more OHPNe, we processed the unpublished continuum data of the interferometric follow-up of the Southern Parkes Large-Area Survey in Hydroxyl (SPLASH). We then matched the interferometric positions of OH maser and radio continuum emission, considering the latter as a possible tracer of free-free emission from photoionized gas, characteristic of PNe. We report 8 objects with a positive coincidence, 4 of which are classified as candidate OHPNe here for the first time (IRAS 16372-4808, IRAS 17494-2645, IRAS 18019-2216 and OH 341.6811+00.2634). Available evidence strongly indicates that they are evolved stars, while the comparison with confirmed OHPNe indicates that they are likely to be PNe. Their final confirmation as bona fide PNe, however, requires optical/infrared spectroscopy. The obtained spectral indices of the radio continuum emission (between $\simeq$ 0.4 - 1.3) are consistent with partially optically thick free-free emission from photoionized gas. Also, they cluster in the same region of a WISE colour-colour diagram as that of the confirmed OHPNe ($9.5 \lesssim [3.4]-[22] \lesssim 13.5$, and $4.0 \lesssim [4.6]-[12] \lesssim 7.0$), thus this diagram could help to identify more OHPNe candidates in the future., Comment: 17 pages, 7 figures, 5 tables. Accepted for publication in MNRAS

In this paper, we provide an infinite metric space $M$ such that the set $\mbox{SNA}(M)$ of strongly norm-attaining Lipschitz functions does not contain a subspace which is isometric to $c_0$. This answers a question posed by Antonio Avil\'es, Gonzalo Mart\'inez Cervantes, Abraham Rueda Zoca, and Pedro Tradacete. On the other hand, we prove that $\mbox{SNA}(M)$ contains an isometric copy of $c_0$ whenever $M$ is a metric space which is not uniformly discrete. In particular, the latter holds true for infinite compact metric spaces while it does not for proper metric spaces. Some positive results in the non-separable setting are also given.

An animal is a planar shape formed by attaching congruent regular polygons along their edges. In 1976, Harary and Harborth gave closed isoperimetric formulas for Euclidean animals. Here, we provide analogous formulas for hyperbolic animals. We do this by proving a connection between Sturmian words and the parameters of a discrete analogue of balls in the graph determined by hyperbolic tessellations. This reveals a complexity in hyperbolic animals that is not present in Euclidean animals., Comment: 16 pages, 2 figures, 3 tables

Accessibility percolation is a new type of percolation problem inspired by evolutionary biology: a random number, called its fitness, is assigned to each vertex of a graph, then a path in the graph is accessible if fitnesses are strictly increasing through it. In the Rough Mount Fuji (RMF) model the fitness function is defined on the graph as $\omega(v)=\eta(v)+\theta\cdot d(v)$, where $\theta$ is a positive number called the drift, $d$ is the distance to the source of the graph and $\eta(v)$ are i.i.d. random variables. In this paper we determine values of $\theta$ for having RMF accessibility percolation on the hypercube and the two-dimensional lattices $\mathbb{L}^2$ and $\mathbb{L}^2_{alt}$.

The recent success of neural networks in natural language processing has drawn renewed attention to learning sequence-to-sequence (seq2seq) tasks. While there exists a rich literature that studies classification and regression tasks using solvable models of neural networks, seq2seq tasks have not yet been studied from this perspective. Here, we propose a simple model for a seq2seq task that has the advantage of providing explicit control over the degree of memory, or non-Markovianity, in the sequences -- the stochastic switching-Ornstein-Uhlenbeck (SSOU) model. We introduce a measure of non-Markovianity to quantify the amount of memory in the sequences. For a minimal auto-regressive (AR) learning model trained on this task, we identify two learning regimes corresponding to distinct phases in the stationary state of the SSOU process. These phases emerge from the interplay between two different time scales that govern the sequence statistics. Moreover, we observe that while increasing the integration window of the AR model always improves performance, albeit with diminishing returns, increasing the non-Markovianity of the input sequences can improve or degrade its performance. Finally, we perform experiments with recurrent and convolutional neural networks that show that our observations carry over to more complicated neural network architectures., Comment: Code to reproduce our experiments available at https://github.com/alirezaseif/nonmarkovian_learning

Automatic Speech Recognition (ASR) systems typically produce unpunctuated transcripts that have poor readability. In addition, building a punctuation restoration system is challenging for low-resource languages, especially for domain-specific applications. In this paper, we propose a Spanish punctuation restoration system designed for a real-time customer support transcription service. To address the data sparsity of Spanish transcripts in the customer support domain, we introduce two transfer-learning-based strategies: 1) domain adaptation using out-of-domain Spanish text data; 2) cross-lingual transfer learning leveraging in-domain English transcript data. Our experiment results show that these strategies improve the accuracy of the Spanish punctuation restoration system., Comment: Accepted to DeepLo 2022 at NAACL 2022

This paper describes a deep reinforcement learning (DRL) approach that won Phase 1 of the Real Robot Challenge (RRC) 2021, and then extends this method to a more difficult manipulation task. The RRC consisted of using a TriFinger robot to manipulate a cube along a specified positional trajectory, but with no requirement for the cube to have any specific orientation. We used a relatively simple reward function, a combination of goal-based sparse reward and distance reward, in conjunction with Hindsight Experience Replay (HER) to guide the learning of the DRL agent (Deep Deterministic Policy Gradient (DDPG)). Our approach allowed our agents to acquire dexterous robotic manipulation strategies in simulation. These strategies were then applied to the real robot and outperformed all other competition submissions, including those using more traditional robotic control techniques, in the final evaluation stage of the RRC. Here we extend this method, by modifying the task of Phase 1 of the RRC to require the robot to maintain the cube in a particular orientation, while the cube is moved along the required positional trajectory. The requirement to also orient the cube makes the agent unable to learn the task through blind exploration due to increased problem complexity. To circumvent this issue, we make novel use of a Knowledge Transfer (KT) technique that allows the strategies learned by the agent in the original task (which was agnostic to cube orientation) to be transferred to this task (where orientation matters). KT allowed the agent to learn and perform the extended task in the simulator, which improved the average positional deviation from 0.134 m to 0.02 m, and average orientation deviation from 142{\deg} to 76{\deg} during evaluation. This KT concept shows good generalisation properties and could be applied to any actor-critic learning algorithm., Comment: This paper has been summited to Expert Systems: the Journal of Knowledge Engineering for reviewing. arXiv admin note: text overlap with arXiv:2109.15233

In this article we provide a splitting method for solving monotone inclusions in a real Hilbert space involving four operators: a maximally monotone, a monotone-Lipschitzian, a cocoercive, and a monotone-continuous operator. The proposed method takes advantage of the intrinsic properties of each operator, generalizing the forward-back-half forward splitting and the Tseng's algorithm with line-search. At each iteration, our algorithm defines the step-size by using a line search in which the monotone-Lipschitzian and the cocoercive operators need only one activation. We also derive a method for solving non-linearly constrained composite convex optimization problems in real Hilbert spaces. Finally, we implement our algorithm in a non-linearly constrained least-square problem, and we compare its performance with available methods in the literature., Comment: 17 pages

In the present study, we analyze in combination the principles of special relativity and the phenomenon of the aberration of light, deriving a system of equations that allows establishing the relationship between the angles commonly involved in this phenomenon. As a consequence, a transformation factor is obtained that generates two solutions, one of them with the same values as the Lorentz factor. This suggests that due to relativistic aberration, an apparent double image of celestial objects could be obtained. On the other hand, its functional form does not establish a limit to the speed of the reference frames with inertial movement., Comment: 10 pages, 3 figures

The double extension and the T*-extension are classical methods for constructing finite dimensional quadratic Lie algebras. The first one gives an inductive classification in characteristic zero, while the latest produces quadratic non-associative algebras (not only Lie) out of arbitrary ones in characteristic different from 2. The classification of quadratic nilpotent Lie algebras can also be reduced to the study of free nilpotent Lie algebras and their invariant forms. In this work we will establish an equivalent characterization among these three construction methods. This equivalence reduces the classification of quadratic 2-step nilpotent to that of trivectors in a natural way. In addition, theoretical results will provide simple rules for switching among them., Comment: 27 pages, preprint

Interpreting partial information collected from systems subject to noise is a key problem across scientific disciplines. Theoretical frameworks often focus on the dynamics of variables that result from coarse-graining the internal states of a physical system. However, most experimental apparatuses can only detect a partial set of transitions, while internal states are inaccessible. Here, we consider an observer who records a time series of occurrences of one or several transitions performed by a system, under the assumption that its underlying dynamics is Markovian. We pose the question of how one can use the transitions' information to make inferences of dynamical, thermodynamical, and biochemical properties. First, elaborating on first-passage time techniques, we derive analytical expressions for the probabilities of consecutive transitions and the time elapsed between them. Second, we derive a lower bound for the entropy production rate that equals the sum of two non-negative contributions, one due to the statistics of transitions and a second due to the statistics of inter-transition times. We also show that when only one current is measured, our estimate still detects irreversibility even in the absence of net currents. We illustrate the developed framework in experimentally-validated biophysical models of kinesin and dynein molecular motors, and in a minimal model for template-directed polymerization. Our results reveal that while entropy production is entailed in the statistics of two successive transitions of the same type, the statistics of two different successive transitions can probe the existence of an underlying disorder in the motion of a molecular motor. Taken all together, our results highlight the power of inference from transition statistics ranging from thermodynamic quantities to network-topology properties of Markov processes.

Given a pointed metric space $M$, we study when there exist $n$-dimensional linear subspaces of $\operatorname{Lip}_0(M)$ consisting of strongly norm-attaining Lipschitz functionals, for $n\in\mathbb{N}$. We show that this is always the case for infinite metric spaces, providing a definitive answer to the question. We also study the possible sizes of such infinite-dimensional closed linear subspaces $Y$, as well as the inverse question, that is, the possible sizes of the metric space $M$ given that such a subspace $Y$ exists. We also show that if the metric space $M$ is $\sigma$-precompact, then the aforementioned subspaces $Y$ need to be always separable and isomorphically polyhedral, and we show that for spaces containing $[0,1]$ isometrically, they can be infinite-dimensional., Comment: Some of the results (mostly Section 2) have been improved since the first version of the preprint (arXiv:2202.06855v1) thanks to a comment that Mikhail Ostrovskii kindly made to us. The new version has 12 pages

Modelling noisy oscillations of active systems is one of the current challenges in physics and biology. Because the physical mechanisms of such processes are often difficult to identify, we propose a linear stochastic model driven by a non-Markovian bistable noise that is capable of generating self-sustained periodic oscillation. We derive analytical predictions for most relevant dynamical and thermodynamic properties of the model. This minimal model turns out to describe accurately bistable-like oscillatory motion of hair bundles in bullfrog sacculus, extracted from experimental data. Based on and in agreement with these data, we estimate the power required to sustain such active oscillations to be of the order of one hundred $k_B T$ per oscillation cycle., Comment: 29 pages, 13 figures

We study the puzzle graphs of hexagonal sliding puzzles of various shapes and with various numbers of holes. The puzzle graph is a combinatorial model which captures the solvability and the complexity of sequential mechanical puzzles. Questions relating to the puzzle graph have been previously studied and resolved for the 15 Puzzle which is the most famous, and unsolvable, square sliding puzzle of all time. It is known that for square puzzles such as the 15 Puzzle, solvability depends on a parity property that splits the puzzle graph into two components. In the case of hexagonal sliding puzzles, we get more interesting parity properties that depend on the shape of the boards and on the missing tiles or holes on the board. We show that for large-enough hexagonal, triangular, or parallelogram-shaped boards with hexagonal tiles, all puzzles with three or more holes are solvable. For puzzles with two or more holes, we give a solvability criterion involving both a parity property and the placement of tiles in tight corners of the board. The puzzle graph is a discrete model for the configuration space of hard tiles (hexagons or squares) moving on different tessellation-based domains. Understanding the combinatorics of the puzzle graph could lead to understanding some aspects of the topology of these configuration spaces., Comment: 20 pages, 11 figures, 3 tables

Characterization of composite materials, whose properties vary in space over microscopic scales, has become a problem of broad interdisciplinary interest. In particular, estimation of the inhomogeneous transport coefficients, e.g. the diffusion coefficient or the heat conductivity which shape important processes in biology and engineering, is a challenging task. The analysis of such systems is further complicated, because two alternative formulations of the inhomogeneous transport equations exist in the literature -- the Smoluchowski and Fokker-Planck equations, which are also related to the so-called Ito-Stratonovich dilemma. Using the theory of statistical physics, we show that the two formulations, usually regarded as distinct models, are physically equivalent. From this result we develop efficient estimates for the transverse space-dependent diffusion coefficient in fluids near a phase boundary. Our method requires only measurements of escape probabilities and mean exit times of molecules leaving a narrow spatial region. We test our estimates in three case studies: (i) a Langevin model of a Buettikker-Landauer ratchet; atomistic molecular-dynamics simulations of liquid-water molecules in contact with (ii) vapor and (iii) soap (surfactant) film which has promising applications in physical chemistry. Our analysis reveals that near the surfactant monolayer the mobility of water molecules is slowed down almost twice with respect to the bulk liquid. Moreover, the diffusion coefficient of water correlates with the transition from hydrophilic to hydrophobic parts of the film., Comment: 16 pages, 7 figures

Electronic phase transition in strongly correlated materials is extremely sensitive to the dimensionality and crystallographic orientations. Transition metal nitrides (TMNs) are seldom investigated due to the difficulty in fabricating the high-quality and stoichiometric single crystals. In this letter, we report the epitaxial growth and electronic properties of CrN films on different-oriented NdGaO3 (NGO) substrates. Astonishingly, the CrN films grown on (110)-oriented NGO substrates maintain a metallic phase, whereas the CrN films grown on (010)-oriented NGO substrates are semiconducting. We attribute the unconventional electronic transition in the CrN films to the strongly correlation with epitaxial strain. The effective modulation of bandgap by the anisotropic strain triggers the metal-to-insulator transition consequently. This work provides a convenient approach to modify the electronic ground states of functional materials using anisotropic strain and further stimulates the investigations of TMNs.

For a given positive integer $k$, the Sidon-Ramsey number $\SR(k)$ is defined as the minimum value of $n$ such that, in every partition of the set $[1, n]$ into $k$ parts, there exists a part that contains two distinct pairs of numbers with the same sum. In other words, there is a part that is not a Sidon set. In this paper, we investigate the asymptotic behavior of this parameter and two generalizations of it. The first generalization involves replacing pairs of numbers with $h$-tuples, such that in every partition of $[1, n]$ into $k$ parts, there exists a part that contains two distinct $h$-tuples with the same sum. Alternatively, there is a part that is not a $B_h$ set. The second generalization considers the scenario where the interval $[1, n]$ is substituted with a non-necessarily symmetric $d$-dimensional box of the form $\prod_{i=1}^d[1,n_i]$. For the general case of $h\geq 3$ and non-symmetric boxes, before applying our method to obtain the Ramsey-type result, we needed to establish an upper bound for the corresponding density parameter., Comment: 11 pages

The International Fusion Materials Irradiation Facility - Demo Oriented NEutron Source (IFMIF-DONES) is a single-sited novel Research Infrastructure for testing, validation and qualification of the materials to be used in a fusion reactor. The main purpose of IFMIF-DONES is related to fusion technology and neutron irradiation of the materials to be used in the future fusion power plants. However, there is an important effort to take advantage of the outstanding characteristics of the facility in terms of neutrons and deuterons. One of the applications could be radioisotopes production with deuterons and neutrons. We discuss here the possible production of radioisotopes with deuterons at DONES. In this work, we have focused on the production of 177Lu with deuterons. The study has been carried out through the design and simulation of a device as cooling system for the sample producing the radioisotope. The results show the viability of using DONES for such production. In addition, the study suggests that new nuclear energy data above 20 MeV for deuterons is mandatory for an accurate study in this field., Comment: 7 pages, 8 figures

We consider the max-type equation $$x_{n+4}=\max\{x_{n+3},x_{n+2},x_{n+1},0\}-x_n,$$ with arbitrary real initial conditions. We describe completely its set of periods $\mathrm{Per}(F_4)$, as well as its associate periodic orbits. We also prove that there exists a natural number $N\notin\mathrm{Per}(F_4)$ for which $$\left\{N+m:m\geq 1,m\in\mathbb N\right\}\subset\mathrm{Per}(F_4).$$, Comment: 39 pages, 1 figure; to be published in Journal of Difference Equations and Applications