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Memetic algorithms are techniques that orchestrate the interplay between population-based and trajectory-based algorithmic components. In particular, some memetic models can be regarded under this broad interpretation as a group of autonomous basic optimization algorithms that interact among them in a cooperative way in order to deal with a specific optimization problem, aiming to obtain better results than the algorithms that constitute it separately. Going one step beyond this traditional view of cooperative optimization algorithms, this work tackles deep meta-cooperation, namely the use of cooperative optimization algorithms in which some components can in turn be cooperative methods themselves, thus exhibiting a deep algorithmic architecture. The objective of this paper is to demonstrate that such models can be considered as an efficient alternative to other traditional forms of cooperative algorithms. To validate this claim, different structural parameters, such as the communication topology between the agents, or the parameter that influences the depth of the cooperative effort (the depth of meta-cooperation), have been analyzed. To do this, a comparison with the state-of-the-art cooperative methods to solve a specific combinatorial problem, the Tool Switching Problem, has been performed. Results show that deep models are effective to solve this problem, outperforming metaheuristics proposed in the literature., Comment: 32 pages, 5 figures

Digital collectible card games are not only a growing part of the video game industry, but also an interesting research area for the field of computational intelligence. This game genre allows researchers to deal with hidden information, uncertainty and planning, among other aspects. This paper proposes the use of evolutionary algorithms (EAs) to develop agents who play a card game, Hearthstone, by optimizing a data-driven decision-making mechanism that takes into account all the elements currently in play. Agents feature self-learning by means of a competitive coevolutionary training approach, whereby no external sparring element defined by the user is required for the optimization process. One of the agents developed through the proposed approach was runner-up (best 6%) in an international Hearthstone Artificial Intelligence (AI) competition. Our proposal performed remarkably well, even when it faced state-of-the-art techniques that attempted to take into account future game states, such as Monte-Carlo Tree search. This outcome shows how evolutionary computation could represent a considerable advantage in developing AIs for collectible card games such as Hearthstone., Comment: 43 pages, 11 figures

Let $H$ be a monoid (written multiplicatively). We call $H$ Archimedean if, for all $a, b \in H$ such that $b$ is a non-unit, there is an integer $k \ge 1$ with $b^k \in HaH$; strongly Archimedean if, for each $a \in H$, there is an integer $k \ge 1$ such that $HaH$ contains any product of any $k$ non-units of $H$; and duo if $aH = Ha$ for all $a \in H$. We prove that the ideals of two strongly Archimedean, cancellative, duo monoids make up isomorphic semigroups under the induced operation of setwise multiplication if and only if the monoids themselves are isomorphic up to units; and the same holds upon restriction to finitely generated ideals in Archimedean, cancellative, duo monoids. Then we use the previous results to tackle a new case of a problem of Tamura and Shafer from the late 1960s., Comment: 12 pp., to appear in Proceedings of the Amer. Math. Soc

Every numerical semigroup can be expressed as an intersection of irreducible numerical semigroups. We show that the unions of sets of lengths of factorizations of numerical semigroups into irreducible numerical semigroups are all equal to $\mathbb{N}_{\ge 2}$.

We study the poset of normalized ideals of a numerical semigroup with multiplicity three. We show that this poset is always a lattice, and that two different numerical semigroups with multiplicity three have non-isomorphic posets of normalized ideals.

Domain wall (DW) devices have garnered recent interest for diverse applications including memory, logic, and neuromorphic primitives; fast, accurate device models are therefore imperative for large-scale system design and verification. Extant DW motion models are sub-optimal for large-scale system design either over-consuming compute resources with physics-heavy equations or oversimplifying the physics, drastically reducing model accuracy. We propose a DW model inspired by the phenomenological similarities between motions of a DW and a classical object being acted on by forces like air resistance or static friction. Our proposed phenomenological model predicts DW motion within 1.2% on average compared with micromagnetic simulations that are 400 times slower. Additionally our model is seven times faster than extant collective coordinate models and 14 times more accurate than extant hyper-reduced models making it an essential tool for large-scale DW circuit design and simulation. The model is publicly posted along with scripts that automatically extract model parameters from user-provided simulation or experimental data to extend the model to alternative micromagnetic parameters.

Let $S$ be the numerical semigroup generated by three consecutive numbers $a,a+1,a+2$, where $a\in\mathbb{N}$, $a\geq 3$. We describe the elements of $S$ whose factorizations have all the same length, as well as the set of factorizations of each of these elements. We give natural partitions of this subset of $S$ in terms of the length and the denumerant. By using Ap\'ery sets and Betti elements we are able to extend some results, first obtained by elementary means.

The antisymmetric interlayer exchange interaction, i.e., interlayer Dzyaloshinskii-Moriya interaction (IL-DMI) has attracted significant interest since this long-range chiral spin interaction provides a new dimension for controlling spin textures and dynamics. However, the role of IL-DMI in the field induced and spin-orbit torque (SOT) induced switching of synthetic ferrimagnets (SFi) has not been uncovered. Here, we exploit interlayer chiral exchange bias fields in SFi to address both the sign and magnitude of the IL-DMI. Depending on the degree of imbalance between the two magnetic moments of the SFi, the amount of asymmetry, addressed via loop shifts of the hysteresis loops under an in-plane field reveals a unidirectional and chiral nature of the IL-DMI. The devices are then tested with SOT switching experiments and the process is examined via both transient state and steady state detection. In addition to field-free SOT switching, we find that the combination of IL-DMI and SOT give rise to multi-resistance states, which provides a possible direction for the future design of neuromorphic computing devices based on SOT. This work is a step towards characterizing and understanding the IL-DMI for spintronic applications., Comment: no

We study the free Banach lattice $FBL^{(p,\infty)}[E]$ with upper $p$-estimates generated by a Banach space $E$. Using a classical result of Pisier on factorization through $L^{p,\infty}(\mu)$ together with a finite dimensional reduction, it is shown that the spaces $\ell^{p,\infty}(n)$ witness the universal property of $FBL^{(p,\infty)}[E]$ isomorphically. As a consequence, we obtain a functional representation for $FBL^{(p,\infty)}[E]$. More generally, our proof allows us to identify the norm of any free Banach lattice over $E$ associated with a rearrangement invariant function space. After obtaining the above functional representation, we take the first steps towards analyzing the fine structure of $FBL^{(p,\infty)}[E]$. Notably, we prove that the norm for $FBL^{(p,\infty)}[E]$ cannot be isometrically witnessed by $L^{p,\infty}(\mu)$ and settle the question of characterizing when an embedding between Banach spaces extends to a lattice embedding between the corresponding free Banach lattices with upper $p$-estimates. To prove this latter result, we introduce a novel push-out argument, which when combined with the injectivity of $\ell^p$ allows us to give an alternative proof of the subspace problem for free $p$-convex Banach lattices. On the other hand, we prove that $\ell^{p,\infty}$ is not injective in the class of Banach lattices with upper $p$-estimates, elucidating one of many difficulties arising in the study of $FBL^{(p,\infty)}[E]$., Comment: 37 pages

The transient high-frequency noise response of two-dimensional MoS2 under abrupt large signal switching field conditions is studied by means of an ensemble Monte Carlo simulator. Low-to-high and high-to-low transitions are analyzed at low (77 K) and room temperature, considering several underlying substrates. The incorporation of stochastic individual scattering events allows capturing the transient collective phonon-electron coupling, which is shown to be responsible for the appearance of an oscillatory behaviour in the average velocity and energy at low temperature in the case of MoS2 on SiO2, hBN and Al2O3. Activation and deactivation of surface polar phonon emissions in the low-to-high field switching process yield to the appearance of a relevant peak in the power spectral density of velocity fluctuations in the THz range. The results show the important influence of the substrate type in the noise behaviour of MoS2 at very high frequencies, which is critical for the design of future FET devices based on 2D TMD technology., Comment: 6 pages, 5 figures. Published in Appl. Phys. Lett. 123, 052105 (2023)

When search methods are being designed it is very important to know which parameters have the greatest influence on the behaviour and performance of the algorithm. To this end, algorithm parameters are commonly calibrated by means of either theoretic analysis or intensive experimentation. When undertaking a detailed statistical analysis of the influence of each parameter, the designer should pay attention mostly to the parameters that are statistically significant. In this paper the ANOVA (ANalysis Of the VAriance) method is used to carry out an exhaustive analysis of a simulated annealing based method and the different parameters it requires. Following this idea, the significance and relative importance of the parameters regarding the obtained results, as well as suitable values for each of these, were obtained using ANOVA and post-hoc Tukey HSD test, on four well known function optimization problems and the likelihood function that is used to estimate the parameters involved in the lognormal diffusion process. Through this statistical study we have verified the adequacy of parameter values available in the bibliography using parametric hypothesis tests.

First passage percolation with recovery is a process aimed at modeling the spread of epidemics. On a graph $G$ place a red particle at a reference vertex $o$ and colorless particles (seeds) at all other vertices. The red particle starts spreading a \emph{red first passage percolation} of rate $1$, while all seeds are dormant. As soon as a seed is reached by the process, it turns red and starts spreading {red first passage percolation}. All vertices are equipped with independent exponential clocks ringing at rate $\gamma>0$, when a clock rings the corresponding \emph{red vertex turns black}. For $t\geq 0$, let $H_t$ and $M_t$ denote the size of the longest red path and of the largest red cluster present at time $t$. %, respectively. If $G$ is the semi-line, then for all $\gamma>0$ almost surely $\limsup_{t}\frac{H_t\log\log t}{\log t}=1 $ and $\liminf_{t}H_t=0$. In contrast, if $G$ is an infinite Galton-Watson tree with offspring mean $\mathbf{m}>1$ then, for all $\gamma>0$, almost surely $\liminf_{t}\frac{H_t\log t}{t}\geq\mathbf{m}-1 $ and $\liminf_{t}\frac{M_t\log\log t}{t}\geq \mathbf{m}-1$, while $\limsup_{t} \frac{M_t}{e^{c t}}\leq 1$, for all $c>\mathbf{m} -1$. Also, almost surely as $t\to \infty$, for all $\gamma>0$ $H_t$ is of order at most $t$. Furthermore, if we restrict our attention to bounded-degree graphs, then for any $\varepsilon>0$ there is a critical value $\gamma_c>0$ so that for all $\gamma>\gamma_c$, almost surely $\limsup_{t}\frac{M_t}{t}\leq \varepsilon $., Comment: 7 figures, 25 pages

This research paper presents an analysis of the propagation of the SARS-CoV-2, or other similar pathogens, in a hospital isolation room using computational fluid dynamics (CFD) and Lagrangian Coherent Structures (LCS). The study investigates the airflow dispersion and droplets in the room under air conditioning vent and sanitizer conditions. The CFD simulation results show that both the air conditioner and sanitizer systems significantly influence the dispersion of the virus in the room. The use of LCS enables acquiring a deep understanding of the dispersion of suspended particles, providing insights into the mechanisms of virus transmission. The findings of this study could help in developing strategies for improving the design and operation of isolation rooms to minimize the likelihood of virus dissemination within hospitals., Comment: 17 pages

This paper proposes a new uncertainty measure, appropriate for quantifying the performance of transport models in assessing the origin or source of a given observation. It is found that in a neighbourhood of the observation the proposed uncertainty measure is related to the invariant dynamical structures of the model. The paper illustrates the implementation of the proposed definition to quantify the performance of ocean data sets in the context of a real oil spill event in the Eastern Mediterranean in 2021., Comment: 13 pages

We report the dynamic characterization of the spin-torque-driven in-plane precession modes of a spin-torque nano-oscillator based on two different synthetic ferrimagnets: a pinned one characterized by a strong RKKY interaction which is exchange coupled to an antiferromagnetic layer; and a second one, non-pinned characterized by weak RKKY coupling. The microwave properties associated with the steady-state precession of both SyFs are characterized by high spectral purity and power spectral density. However, frequency dispersion diagrams of the damped and spin transfer torque modes reveal drastically different dynamical behavior and microwave emission properties in both SyFs. In particular, the weak coupling between the magnetic layers of the non-pinned SyF raises discontinuous dispersion diagrams suggesting a strong influence of mode crossing. An interpretation of the different dynamical features observed in the damped and spin torque modes of both SyF systems was obtained by solving simultaneously, in a macrospin approach, a linearized version of the Landau-Lifshitz-Gilbert equation including the spin transfer torque term., Comment: 16 pages, 8 figures

From any poset isomorphic to the poset of gaps of a numerical semigroup $S$ with the order induced by $S$, one can recover $S$. As an application, we prove that two different numerical semigroups cannot have isomorphic posets (with respect to set inclusion) of ideals whose minimum is zero. We also show that given two numerical semigroups $S$ and $T$, if their ideal class monoids are isomorphic, then $S$ must be equal to $T$.

We introduce a new family of monoids, which we call gap absorbing monoids. Every gap absorbing monoid is an ideal extension of a free commutative monoid. For a gap absorbing monoid $S$ we study its set of atoms and Betti elements, which allows us to show that the catenary degree of $S$ is at most four and that the set of lengths of any element in $S$ is an interval. We also give bounds for the $\omega$-primality of any ideal extension of a free commutative monoid. For ideal extensions $S$ of $\mathbb{N}^d$, with $d$ a positive integer, we show that $\omega(S)$ is finite if and only if $S$ has finitely many gaps.

Controlled creation of stable chiral spin textures is required to use them as an energy-efficient information carrier in spintronics. Here we have studied the stable creation of isolated chiral spin texture (skyrmion and antiskyrmion) and its pair through the magnetization reversal of a rectangular nanostructure using spin-polarized currents. An isolated spin texture is created through a negative current pulse. Dynamics of the stable spin texture are explored under external magnetic fields, and the resonant frequencies are calculated. A stable skyrmion pair is created using an asymmetric current pulse, and their interaction is studied using the Thiele equation. The stability of isolated or paired spin texture depends on the DMI strength, spin-polarized current density, and pulse duration. In addition, the stability of the skyrmion pair depends on their initial separation, and a threshold for the separation between skyrmions of 78 nm is observed., Comment: 29 pages, 11 figures, 2 extra figures

Accurate information on waves and storm surges is essential to understand coastal hazards that are expected to increase in view of global warming and rising sea levels. Despite the recent advancement in development and application of large-scale coastal models, nearshore processes are still not sufficiently resolved due to coarse resolutions, transferring errors to coastal risk assessments and other large-scale applications. Here we developed a 50-year hindcast of waves and storm surges on an unstructured mesh of >650,000 nodes with an unprecedented resolution of 2-4 km at the global coast. Our modelling system is based on the circulation model SCHISM that is fully coupled with the WWM-V (WindWaveModel) and is forced by surface winds, pressure, and ice coverage from the ERA5 reanalysis. Results are compared with observations from satellite altimeters, tidal gauges and buoys, and show good skill for both Sea Surface Height (SSH) and Significant Wave Height (Hs), and a much-improved ability to reproduce the nearshore dynamics compared with previous, lower-resolution studies. Besides SSH, the modelling system also produces a range of other wave-related fields at each node of the mesh with a time step of 3 hours, including the spectral parameters of the first three largest energy peaks. This dataset offers the potential for more accurate global-scale applications on coastal hazard and risk

A numerical semigroup is said to be universally free if it is free for any possible arrangement of its minimal generating set. In this work, we establish that toric ideals associated with universally free numerical semigroups can be generated by their set of circuits. Additionally, we provide a characterization of universally free numerical semigroups in terms of Gr\"obner bases. Specifically, a numerical semigroup is universally free if and only if all initial ideals of its corresponding toric ideal are complete intersections. Furthermore, we establish several equalities among the toric bases of a universally free numerical semigroup. We provide a complete characterization of $3$-generated universally free numerical semigroups in terms of their minimal generating sets, and by proving the equality of certain toric bases. We compute exactly all the toric bases of a toric ideal defined by a 3-generated universally free numerical semigroup. Notably, we answer some questions posed by Tatakis and Thoma by demonstrating that toric ideals defined by $3$-generated universally free numerical semigroups have a set of circuits and a universal Gr\"obner basis of size 3, while the universal Markov basis and the Graver basis can be arbitrarily large. We present partial results and propose several conjectures regarding universally free numerical semigroups with more than three generators.