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Vibration-based energy harvesting is of increasing importance and there is a current challenge to improve energy harvesting capacity exploiting nonlinear and random effects. This article investigates random effects in a nonlinear energy harvesting system. The system is represented by a magnetoelastic structure with two piezoceramic layers attached to the root of a cantilever beam, obtaining a bimorph generator. The energy harvesting system is subjected to three excitation conditions: pure harmonic, pure random and a combination of harmonic and random excitations. Noise-to-Signal Ratio (NSR) is employed to quantify different combinations of the forcing terms, establishing a procedure to evaluate the system performance. This approach is based on Power Spectral Density (PSD) of input and output signals. Numerical simulations are carried out, identifying the better combinations of harmonic and random excitations for energy harvesting purposes. Discussions about the influence of the kind of response are carried out evaluating the differences between periodic and chaotic motions. Conclusions show that both random and nonlinear effects can be tuned in order to enhance energy harvesting capacity.

While wealth distribution in the world is highly skewed and heavy-tailed, human talent — as the majority of individual features — is normally distributed. In a recent computational study by Pluchino et al. [Talent vs luck: The role of randomness in success and failure, Adv. Complex Syst. 21(03–04) (2018) 1850014], it has been shown that the combined effects of both random external factors (lucky and unlucky events) and multiplicative dynamics in capital accumulation are able to clarify this apparent contradiction. We introduce here a simplified version (STvL) of the original Talent versus Luck (TvL) model, where only lucky events are present, and verify that its dynamical rules lead to the same very large wealth inequality. We also derive some analytical approximations aimed to capture the mechanism responsible for the creation of such wealth inequality from a Gaussian-distributed talent. Under these approximations, our analysis is able to reproduce quite well the results of the numerical simulations of the simplified model in special cases. On the other hand, it also shows that the complexity of the model lies in the fact that lucky events are transformed into an increase of capital with heterogeneous rates, which yields a nontrivial generalization of the role of multiplicative processes in generating wealth inequality, whose fully generic case is still not amenable to analytical computations.

In order to deal with stochasticity in center node selection and instability in community detection of label propagation algorithm, this paper proposes an improved label propagation algorithm named label propagation algorithm based on community belonging degree (LPA-CBD) that employs community belonging degree to determine the number and the center of community. The general process of LPA-CBD is that the initial community is identified by the nodes with the maximum degree, and then it is optimized or expanded by community belonging degree. After getting the rough structure of network community, the remaining nodes are labeled by using label propagation algorithm. The experimental results on 10 real-world networks and three synthetic networks show that LPA-CBD achieves reasonable community number, better algorithm accuracy and higher modularity compared with other four prominent algorithms. Moreover, the proposed algorithm not only has lower algorithm complexity and higher community detection quality, but also improves the stability of the original label propagation algorithm.

We consider effective versions of two classical theorems, the Lebesgue density theorem and the Denjoy–Young–Saks theorem. For the first, we show that a Martin-Löf random real z ∈ [0, 1] is Turing incomplete if and only if every effectively closed class 𝒞 ⊆ [0, 1] containing z has positive density at z. Under the stronger assumption that z is not LR-hard, we show that every such class has density one at z. These results have since been applied to solve two open problems on the interaction between the Turing degrees of Martin-Löf random reals and K-trivial sets: the noncupping and covering problems. We say that f : [0, 1] → ℝ satisfies the Denjoy alternative at z ∈ [0, 1] if either the derivative f′(z) exists, or the upper and lower derivatives at z are +∞ and -∞, respectively. The Denjoy–Young–Saks theorem states that every function f : [0, 1] → ℝ satisfies the Denjoy alternative at almost every z ∈ [0, 1]. We answer a question posed by Kučera in 2004 by showing that a real z is computably random if and only if every computable function f satisfies the Denjoy alternative at z. For Markov computable functions, which are only defined on computable reals, we can formulate the Denjoy alternative using pseudo-derivatives. Call a real zDA-random if every Markov computable function satisfies the Denjoy alternative at z. We considerably strengthen a result of Demuth (Comment. Math. Univ. Carolin.24(3) (1983) 391–406) by showing that every Turing incomplete Martin-Löf random real is DA-random. The proof involves the notion of nonporosity, a variant of density, which is the bridge between the two themes of this paper. We finish by showing that DA-randomness is incomparable with Martin-Löf randomness.

In systems theory and science, emergence is the way complex systems and patterns arise out of a multiplicity of relatively simple interactions. Emergence is central to the theories of integrative levels and of complex systems [Aziz-Alaoui & Bertelle, 2009]. In this paper, we use the emergent property of the ultra weak multidimensional coupling of p 1-dimensional dynamical chaotic systems which leads from chaos to randomness.

Generation of random or pseudorandom numbers, nowadays, is a key feature of industrial mathematics. Pseudorandom or chaotic numbers are used in many areas of contemporary technology such as modern communication systems and engineering applications. More and more European or US patents using discrete mappings for this purpose are obtained by researchers of discrete dynamical systems [Petersen & Sorensen, 2007; Ruggiero et al., 2006]. Efficient Chaotic Pseudo Random Number Generators (CPRNG) have been recently introduced. They use the ultra weak multidimensional coupling of p 1-dimensional dynamical systems which preserve the chaotic properties of the continuous models in numerical experiments. Together with chaotic sampling and mixing processes, ultra weak coupling leads to families of (CPRNG) which are noteworthy [Hénaff et al., 2009a, 2009b, 2009c, 2010].

In this paper we improve again these families using a double threshold chaotic sampling instead of a single one.

We analyze numerically the properties of these new families and underline their very high qualities and usefulness as CPRNG when very long series are computed. Moreover, a determining property of such improved CPRNG is the high number of parameters used and the high sensitivity to the parameters value which allows choosing it as cipher-keys. It is why we call these families multiparameter chaotic pseudo-random number generators (M-p CPRNG).

Regression testing is a very time-consuming and expensive testing activity. Many test case prioritization techniques have been proposed to speed up regression testing. Previous studies show that no one technique is always best. Random strategy, as the simplest strategy, is not always so bad. Particularly, when a test suite has higher fault detection capability, the strategy can generate a better result. Nevertheless, due to the randomness, the strategy is not always as satisfactory as expected. In this context, we present a test case prioritization approach using fixed size candidate set adaptive random testing algorithm to reduce the effect of randomness and improve fault detection effectiveness. The distance between pair-wise test cases is assessed by exclusive OR. We designed and conducted empirical studies on eight C programs to validate the effectiveness of the proposed approach. The experimental results, confirmed by a statistical analysis, indicate that the approach we proposed is more effective than random and the total greedy prioritization techniques in terms of fault detection effectiveness. Although the presented approach has comparable fault detection effectiveness to ART-based and the additional greedy techniques, the time cost is much lower. Consequently, the proposed approach is much more cost-effective.

In belief functions, there is a total measure of uncertainty that quantify the lack of knowledge and verifies a set of important properties. It is based on two measures: maximum of entropy and non-specificity. In this paper, we prove that the maximum of entropy verifies the same set of properties in a more general theory as credal sets and we present an algorithm that finds the probability distribution of maximum entropy for another interesting type of credal sets as probability intervals.

Although noise-based logic shows potential advantages of reduced power dissipation and the ability of large parallel operations with low hardware and time complexity the question still persist: Is randomness really needed out of orthogonality? In this Letter, after some general thermodynamical considerations, we show relevant examples where we compare the computational complexity of logic systems based on orthogonal noise and sinusoidal signals, respectively. The conclusion is that in certain special-purpose applications noise-based logic is exponentially better than its sinusoidal version: Its computational complexity can be exponentially smaller to perform the same task.

In this study, the multiscale stochastic finite element method (MsSFEM) was developed based on a novel digital image kernel to make analysis for chloride diffusion in recycled aggregate concrete (RAC). It is significant to study the chloride diffusivity in RAC, because when RAC was applied in coastal areas, chloride-induced rebar corrosion became a common problem for concrete infrastructures. The MsSFEM was an efficient tool to examine the effect of microscopic randomness of RAC on the chloride diffusivity. Based on the proposed digital image kernel, the Karhunen–Loeve expansion and the polynomial chaos were used in the stochastic homogenization process. To investigate advantages and disadvantages of both generation and application of the proposed digital image kernel, it was compared with many other kernels. The comparisons were made between the method to develop the digital image kernel, which is called the pixel-matrix method, and other methods, and between the application of the kernel and various other kernels. It was shown that the proposed digital image kernel is superior to other kernels in many aspects.

The Schelling model of 1971 is a complicated version of a square-lattice Ising model at zero temperature, to explain urban segregation, based on the neighbor preferences of the residents, without external reasons. Various versions between Ising and Schelling models give about the same results. Inhomogeneous "temperatures" T do not change the results much, while a feedback between segregation and T leads to a self-organization of an average T.

Thanks to the simplicity and robustness of its calculation methods, algorithmic (or Kolmogorov) complexity appears as a useful tool to reveal chaotic dynamics when experimental time series are too short and noisy to apply Takens’ reconstruction theorem. We measure the complexity in chaotic regimes, with and without extreme events (sometimes called optical rogue waves), of three different all-solid-state lasers: Kerr lens mode locking femtosecond Ti:Sapphire (“fast” saturable absorber), Nd:YVO₄$+$ Cr:YAG (“slow” saturable absorber) and Nd:YVO₄ with modulated losses. We discuss how complexity characterizes the dynamics in an understandable way in all cases, and how it provides a correction factor of predictability given by Lyapunov exponents. This approach may be especially convenient to implement schemes of chaos control in real time.

We reinvestigate the model of Bonabeau et al.¹ of self-organizing social hierarchies by including a distribution of attractive sites. Agents move randomly except in the case where an attractive site is located in its neighborhood. We find that the transition between an egalitarian society at low population density and a hierarchical one at high population density strongly depends on the distribution and percolation of the valuable sites. We also show how agent diffusivity is closely related to social hierarchy.

Pseudo-random bit sequence have a wide range of applications in the field of cryptography and communications. For the good chaotic dynamical properties of chaotic systems sequence such as randomness and initial sensitivity, chaotic systems have a strong advantage in generating the pseudo-random bit sequence. However, in practical use, the dynamical properties of chaotic systems will be degraded because of the limited calculation accuracy and it even could cause a variety of security issues. To improve the security, in full analyses of the pseudo-random bit generator proposed in our former paper, we point out some problems in our former design and redesign a better pseudo-random bit generator base on it. At the same time, we make some relevant theoretical and experimental analyses on it. The experiments show that the design proposed in this paper has good statistical properties and security features.

The quaternary alloy (QA) is simulated on the Bethe lattice (BL) in the form of AB_pC_qD_r and its phase diagrams are calculated by using the exact recursion relations (ERR) for the coordination number z = 3. The QA is designed on the BL by placing A atoms (spin-1/2) on the odd shells and randomly placing B (spin-3/2), C (spin-5/2) or D (spin-1) atoms with probabilities p, q and r, respectively, on the even shells. A compact form of formulation for the QA is obtained in the standard-random approach which can easily be reduced to ternary alloy (TA) and mixed-spin models by the appropriate values of the random variables p, q and r. The phase diagrams are calculated on the temperature and ratio of bilinear interaction parameter planes for given values of probabilities.

Let $L$ be a simplicial complex. In this paper, we study random sub-hypergraphs and random sub-complexes of $L$. By considering the minimal complex that a sub-hypergraph can be embedded in and the maximal complex that can be embedded in a sub-hypergraph, we define some maps on the space of probability functions on sub-hypergraphs of $L$. We study the compositions of these maps as well as their actions on the space of probability functions.

We study the sets that are computable from both halves of some (Martin–Löf) random sequence, which we call $1/2$-bases. We show that the collection of such sets forms an ideal in the Turing degrees that is generated by its c.e. elements. It is a proper subideal of the $K$-trivial sets. We characterize $1/2$-bases as the sets computable from both halves of Chaitin’s $\mathrm{\Omega }$, and as the sets that obey the cost function $c(x,s)=\sqrt{{\mathrm{\Omega }}_s-{\mathrm{\Omega }}_x}$.

Generalizing these results yields a dense hierarchy of subideals in the $K$-trivial degrees: For $k<n$, let ${{ℬ}}_{k/n}$ be the collection of sets that are below any $k$ out of $n$ columns of some random sequence. As before, this is an ideal generated by its c.e. elements and the random sequence in the definition can always be taken to be $\mathrm{\Omega }$. Furthermore, the corresponding cost function characterization reveals that ${{ℬ}}_{k/n}$ is independent of the particular representation of the rational $k/n$, and that ${{ℬ}}_p$ is properly contained in ${{ℬ}}_q$ for rational numbers $p<q$. These results are proved using a generalization of the Loomis–Whitney inequality, which bounds the measure of an open set in terms of the measures of its projections. The generality allows us to analyze arbitrary families of orthogonal projections. As it turns out, these do not give us new subideals of the $K$-trivial sets; we can calculate from the family which ${{ℬ}}_p$ it characterizes.

We finish by studying the union of ${{ℬ}}_p$ for $p<1$; we prove that this ideal consists of the sets that are robustly computable from some random sequence. This class was previously studied by Hirschfeldt [D. R. Hirschfeldt, C. G. Jockusch, R. Kuyper and P. E. Schupp, Coarse reducibility and algorithmic randomness, J. Symbolic Logic81(3) (2016) 1028–1046], who showed that it is a proper subclass of the $K$-trivial sets. We prove that all such sets are robustly computable from $\mathrm{\Omega }$, and that they form a proper subideal of the sets computable from every (weakly) LR-hard random sequence. We also show that the ideal cannot be characterized by a cost function, giving the first such example of a ${\mathrm{\Sigma }}_3^0$ subideal of the $K$-trivial sets.

Among large-span bridges, arch bridges have relatively high stiffness, which may lead to large dynamic amplification factors (DAFs). The DAFs suggested by current codes mostly originate from common simply supported beam bridges. Previous DAF studies on dynamic vehicle–bridge solutions for arch bridges have mainly focused on one or two side-by-side vehicles. However, complex traffic flows with randomness rather than one or two vehicles act on bridges. DAFs that consider the effects of random traffic flows have not previously been reported. In this study, a random traffic–bridge vibration solution was established to explore the DAFs of arch bridge components. The randomness of the traffic parameters and road roughness was explored. The randomness of the external excitation, including traffic flow and road roughness, resulted in random dynamic responses and DAFs of the arch bridge components. Normal distributions could be used to fit the DAF distributions of each arch bridge component under random vehicle spacing, weight, speed, and road roughness. Under random traffic parameters, the coefficients of variation of the DAFs exceeded the 5% accepted level. The shortest suspenders were more sensitive to the randomness of the traffic flow parameters. Both the mean and coefficient of variation of the DAFs increased with worsening of the road conditions. The influence of the randomness of the road roughness on the DAFs of arch bridges must be considered, particularly for the shortest suspender. The 95% upper confidence limits of the DAFs for all components may be greater than the suggested values in the code.

This paper examines stochastic pairwise dependence structures in binary time series obtained from discretised versions of standard chaotic logistic maps. It is motivated by applications in communications modelling which make use of so-called chaotic binary sequences. The strength of non-linear stochastic dependence of the binary sequences is explored. In contrast to the original chaotic sequence, the binary version is non-chaotic with non-Markovian non-linear dependence, except in a special case. Marginal and joint probability distributions, and autocorrelation functions are elicited. Multivariate binary and more discretised time series from a single realisation of the logistic map are developed from the binary paradigm. Proposals for extension of the methodology to other cases of the general logistic map are developed. Finally, a brief illustration of the place of chaos-based binary processes in chaos communications is given.

Sol Golomb was my supervisor, mentor, and long-term collaborator, and played an important role in my life. This article is written according to my talks at various occasions in memory of Sol for describing some experiences when I worked with Sol.

Quantum counterparts of certain classical systems exhibit chaotic spectral statistics of their energy levels; eigenvalues of infinite random matrices model irregular spectra. Eigenvalue spacings for the Gaussian orthogonal ensemble (GOE) of infinite random real symmetric matrices admit a gamma distribution approximation, as do the hermitian unitary (GUE) and quaternionic symplectic (GSE) cases. Then chaotic and non-chaotic cases fit in the information geometric framework of the manifold of gamma distributions, which has been the subject of recent work on neighbourhoods of randomness for general stochastic systems.