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Systems of oscillators whose internal phases and spatial dynamics are coupled, swarmalators, present diverse collective behaviors which in some cases lead to explosive synchronization in a finite population as a function of the coupling parameter between internal phases. Near the synchronization transition, the phase energy of the particles is represented by the XY model, and they undergo a transition which can be of the first order or second depending on the distribution of natural frequencies of their internal dynamics. The first order transition is obtained after an intermediate state (Static Wings Phase Wave state (SWPW)) from which the nodes, in cascade over time, achieve complete phase synchronization at a precise value of the coupling constant. For a particular case of natural frequencies distribution, a new phenomenon of Rotational Splintered Phase Wave state (RSpPW) is observed and leads progressively to synchronization through clusters switching alternatively from one to two and for which the frequency decreases as the phase coupling increases.

This paper presents the optimal control and synchronization problem of a multilevel network of R\"ossler chaotic oscillators. Using the Hamilton-Jacobi-Bellman (HJB) technique, the optimal control law with three-state variables feedback is designed such that the trajectories of all the R\"ossler oscillators in the network are optimally synchronized in each level. Furthermore, we provide numerical simulations to demonstrate the effectiveness of the proposed approach for the cases of one and three networks. A perfect correlation between the MATLAB and the PSPICE results was obtained, thus allowing the experimental validation of our designed controller and shows the effectiveness of the theoretical results.

The dynamics of competing opinions in social network play an important role in society, with many applications in diverse social contexts as consensus, elections, morality and so on. Here we study a model of interacting agents connected in networks to analyze their decision stochastic process. We consider a first-neighbor interaction between agents in a one-dimensional network with a shape of ring topology. Moreover, some agents are also connected to a hub, or master node, that has preferential choice or bias. Such connections are quenched. As the main results, we observed a continuous non-equilibrium phase transition to an absorbing state as a function of control parameters. By using the finite size scaling method, we analyzed the static and dynamic critical exponents to show that this model probably cannot match any universality class already known., Comment: 14 pages, 5 tables, 4 figures

A magma (or groupoid) is a set with a binary operation $(A,f)$. Roughly speaking, a magma is said to be lazy if compositions such as $f(x,f(f(y,z),u))$ depend on at most two variables. Recently, Kaprinai, Machida and Waldhauser described the lattice of all the varieties of lazy groupoids. A forbidden structure theorem is one that charcaterizes a smaller class $A$ inside a larger class $B$ as all the elements in $B$ that avoid some substructures. For example, a lattice is distributive (smaller class $A$) if and only if it is a lattice (larger class $B$) and avoids the pentagon and the diamond. In this paper we provide a characterization of all pairs of lazy groupoid varieties $A\le B$ by forbidden substructure theorems. Some of the results are straightforward, but some other are very involved. All of these results and proofs were found using a computational tool that proves theorems of this type (for many different classes of relational algebras) and that we make available to every mathematician.

Classical swine fever (CSF) in Ecuador is prevalent since 1940, pig farming represents an important economic and cultural sector. Recently, the National Veterinary Service (NVS) has implemented individual identification of pigs, movement control and mandatory vaccination against CSF, looking for a future eradication. Our aim was to characterise the pig premises according to risk criteria, analyse the effect of random and targeted strategies to control CSF and consider the temporal development of the network. We used social network analysis (SNA), SIRS (susceptible, infected, recovered, susceptible) network modelling and temporal network analysis. The data set contained 751,003 shipments and 6 million pigs from 2017 to 2019. 165,593 premises were involved: 144,118 farms, 138 industrials, 21,337 traders, and 51 markets. On annual average, 124,976 premises (75%) received or sent one movement with 1.5 pigs, in contrast, 166 (0.01%) with 1,372 movements and 11,607 pigs. Simulations resulted in CSF mean prevalence of 29.93%; Targeted selection strategy reduced the prevalence to 3.3%, while 24% with random selection. Selection of high-risk premises in every province was the best strategy using available surveillance infrastructure. Notably, selecting 10 traders/markets reduced the CSF prevalence to 4%, evidencing their prime influence over the network. Temporal analysis showed an overestimation of 38% (causal fidelity) in the number of transmission paths; The steps to cross the network were 4.3 (average path length), but take approximately 233 days. In conclusion, surveillance strategies applied by the NVS could be more efficient to find cases, reduce the spread of diseases and enable the implementation of risk-based surveillance. To focus the efforts on target selection of high-risk premises, special attention should be given to markets/traders which proved similar disease spread potential.

This article proposes an artificial data generating algorithm that is simple and easy to customize. The fundamental concept is to perform random permutation of Monte Carlo generated random numbers which conform to the unconditional probability distribution of the original real time series. Similar to constraint surrogate methods, random permutations are only accepted if a given objective function is minimized. The objective function is selected in order to describe the most important features of the stochastic process. The algorithm is demonstrated by producing simulated log-returns of the S\&P 500 stock index., Comment: 2 columns, 6 pages, 6 figures

We study the dynamics of a multilayer network of chaotic oscillators subject to an amplification. Previous studies have proven that multilayer networks present phenomena such as synchronization, cluster and chimera states. Here we consider a network with two layers of Roessler chaotic oscillators as well as applications to multilayer networks of chaotic jerk and Lienard oscillators. Intralayer coupling is considered to be all to all in the case of Roessler oscillators, a ring for jerk oscillators and global mean field coupling in the case of Lienard, the interlayer coupling is unidirectional in all these three cases. The second layer has an amplification coefficient. An in depth study on the case of a network of Roessler oscillators using master stability function and order parameter leads to several phenomena such as complete synchronization, generalized, cluster and phase synchronization with amplification. For the case of Roessler oscillators, we note that there are also certain values of coupling parameters and amplification where the synchronization does not exist or the synchronization can exist but without amplification. Using other systems with different topologies, we obtain some interesting results such as chimera state with amplification, cluster state with amplification and complete synchronization with amplification., Comment: 13 pages, 8 figures. To appear in Chaos: An Interdisciplinary Journal of Nonlinear Science

Generally, carbohydrate-active enzymes are studied using chromogenic substrates that provide quick and easy color-based detection of enzyme-mediated hydrolysis. In the case of feruloyl esterases, commercially available chromogenic ferulate derivatives are both costly and limited in terms of their experimental application. In this study, we describe solutions for these two issues, using a chemoenzymatic approach to synthesize different ferulate compounds. The overall synthetic routes towards commercially available 5-bromo-4-chloro-3-indolyl and 4-nitrophenyl O-5-feruloyl-$\alpha$-l-arabinofuranosides 1a and 1b were significantly shortened (7-8 steps reduced to 4-6) and transesterification yields enhanced (from 46 to 73% for 1a and 47 to 86 % for 1b). This was achieved using enzymatic (immobilized Lipolase 100T from Thermomyces lanuginosus) transesterification of unprotected vinyl ferulate to the primary hydroxyl group of $\alpha$-l-arabinofuranosides. Moreover, a novel feruloylated-butanetriol 4-nitrocatechol-1-yl analog 12, containing a cleavable hydroxylated linker was also synthesized in 29% overall yield in 3 steps (convergent synthesis). The latter route combined regioselective functionalization of 4-nitrocatechol and enzymatic transferuloylation. The use of 12 as a substrate to characterize type A feruloyl esterase from Aspergillus niger reveals the advantages of this substrate for the characterizations of feruloyl esterases.

We present a detailed study of the performance of a trading rule that uses moving average of past returns to predict future returns on stock indexes. Our main goal is to link performance and the stochastic process of the traded asset. Our study reports short, medium and long term effects by looking at the Sharpe ratio (SR). We calculate the Sharpe ratio of our trading rule as a function of the probability distribution function of the underlying traded asset and compare it with data. We show that if the performance is mainly due to presence of autocorrelation in the returns of the traded assets, the SR as a function of the portfolio formation period (look-back) is very different from performance due to the drift (average return). The SR shows that for look-back periods of a few months the investor is more likely to tap into autocorrelation. However, for look-back larger than few months, the drift of the asset becomes progressively more important. Finally, our empirical work reports a new long-term effect, namely oscillation of the SR and propose a non-stationary model to account for such oscillations., Comment: 32 pages, 14 figures, accepted for publication in Quantitative Finance on 12/2017. Result of research initiated in 2013 which generated several conference presentations and working papers. This effort is substantially extended, edited and updated. arXiv admin note: substantial text overlap with arXiv:1402.3030

We consider a first neighbor interaction where agents are spread through a uni-dimensional network. Some agents are also connected to a hub, or master node, who has preferential values (or orientation). The role of master node is to persuade some individuals to follow a specific orientation, subject to a probability of successful persuasion. The connections between master node and the network society are quenched in disorder. Despite its simplicity, we found a phase transition from disorder to order for three different control parameters. We also discuss how this model may be useful as a framework to study the spread of morality, innovation, opinion formation and consensus. Is important to recall the route from disorder to order in social systems still a great challenge. We hope to contribute with a novel approach to model a this issues., Comment: 7 pages, 6 figures and 1 table