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Landgrebe and Smith (2022) have recently offered an important mathematical argument against the possibility of Artificial General Intelligence (AGI): human intelligence is a complex system; complex systems have some properties that cannot be modelled mathematically; hence we have no viable way to build an AI that would be able to emulate human intelligence. The issue of complexity is thus at the heart of the Landgrebe and Smith approach, and they tackle this issue by postulating a set of conditions, derived from mathematics, for a system to be complex. I argue that Hayek's "Theory of Complex Phenomena" offers an interesting alternative path to understanding what makes complex systems complex. This offers an argument complementary to that of Landgrebe and Smith, which approaches the issue of complexity from an ontological angle, and which is designed to show that AI systems are not the right kind of entity that may interact meaningfully with complex systems. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the strong product of the pentagonal networks. Let $ R_{n} $ be a pentagonal network composed of $ 2n $ pentagons and $ n $ quadrilaterals. Let $ P_{n}^{2} $ denote the graph formed by the strong product of $ R_{n} $ and its copy $ R_{n}^{\prime} $. By utilizing the decomposition theorem of the normalized Laplacian characteristics polynomial, we characterize the explicit formula of the multiplicative degree-Kirchhoff index completely. Moreover, the complexity of $ P_{n}^{2} $ is determined.

As a powerful tool for describing and studying the properties of networks, the graph spectrum analyses and calculations have attracted substantial attention from the scientific community. Let $ C_{n} $ represent linear crossed phenylenes. Based on the Laplacian (normalized Laplacian, resp.) polynomial of $ C_{n} $, we first investigated the Laplacian (normalized Laplacian, resp) spectrum of $ C_{n} $ in this paper. Furthermore, the Kirchhoff index, multiplicative degree-Kirchhoff, index and complexity of $ C_{n} $ were obtained through the relationship between the roots and the coefficients of the characteristic polynomials. Finally, it was found that the Kirchhoff index and multiplicative degree-Kirchhoff index of $ C_{n} $ were approximately one quarter of their Wiener index and Gutman index, respectively.

This paper reports fractal patterns identified in the complex musical composition DIAPHONIES by Michael Paouris via power-law fractal analysis with sliding-windows of size 1024. From 7,647,232 analysed musical segments of DIAPHONIES, 3,222,832 (42.4%) are fractional Brownian motion (fBm) fractal segments and 4,424,400 (57.6%) are fractional Gaussian noise (fGn) stochastic ones. From the fBm fractal segments 295,294 (9.1%) exhibit strong persistency-P with power-law segments in the range of 2.3≤b≤3. These are the very strong fractal areas in DIAPHONIES. Numerous segments with strong antipersistency 1.7≤b<2 are reported together with segments with AP changes (1.7≤b<2.3). In DIAPHONIES continuous fractal fBm areas are dipped in non-fractal fGn areas of deterministic music. The results are within the fBm fractal areas reported in existing papers. Very importantly, the simple composition called Nocturnal-Angel by Michael Paouris, exhibited limited fBm areas of average b¯=1.98 (σ=0.3), namely of pure statistical, deterministic music, while simultaneously, the fractal analysis profile was completely different from the profiles of DIAPHONIES, hence reinforcing, the fractal findings of DIAPHONIES in relation to trivial music harmony.

Jump dynamics in financial markets exhibit significant complexity, often resulting in increased probabilities of subsequent jumps, akin to earthquake aftershocks. This study aims to understand these complexities within a multifractal framework. To do this, we employed the high-frequency intraday data from six major cryptocurrencies (Bitcoin, Ethereum, Litecoin, Dashcoin, EOS, and Ripple) and six major forex markets (Euro, British pound, Canadian dollar, Australian dollar, Swiss franc, and Japanese yen) between 4 August 2019 and 4 October 2023, at 5 min intervals. We began by extracting daily jumps from realized volatility using a MinRV-based approach and then applying Multifractal Detrended Fluctuation Analysis (MFDFA) to those jumps to explore their multifractal characteristics. The results of the MFDFA—especially the fluctuation function, the varying Hurst exponent, and the Renyi exponent—confirm that all of these jump series exhibit significant multifractal properties. However, the range of the Hurst exponent values indicates that Dashcoin has the highest and Litecoin has the lowest multifractal strength. Moreover, all of the jump series show significant persistent behavior and a positive autocorrelation, indicating a higher probability of a positive/negative jump being followed by another positive/negative jump. Additionally, the findings of rolling-window MFDFA with a window length of 250 days reveal persistent behavior most of the time. These findings are useful for market participants, investors, and policymakers in developing portfolio diversification strategies and making important investment decisions, and they could enhance market efficiency and stability.

The study investigates the nonlinear contagion, tail dependence, and Granger causality relations with TAR-TR-GARCH–copula causality methods for daily Bitcoin, Fintech, energy consumption, and CO2 emissions in addition to examining these series for entropy, long-range dependence, fractionality, complexity, chaos, and nonlinearity with a dataset spanning from 25 June 2012 to 22 June 2024. Empirical results from Shannon, Rényi, and Tsallis entropy measures; Kolmogorov–Sinai complexity; Hurst–Mandelbrot and Lo’s R/S tests; and Phillips’ and Geweke and Porter-Hudak’s fractionality tests confirm the presence of entropy, complexity, fractionality, and long-range dependence. Further, the largest Lyapunov exponents and Hurst exponents confirm chaos across all series. The BDS test confirms nonlinearity, and ARCH-type heteroskedasticity test results support the basis for the use of novel TAR-TR-GARCH–copula causality. The model estimation results indicate moderate to strong levels of positive and asymmetric tail dependence and contagion under distinct regimes. The novel method captures nonlinear causality dynamics from Bitcoin and Fintech to energy consumption and CO2 emissions as well as causality from energy consumption to CO2 emissions and bidirectional feedback between Bitcoin and Fintech. These findings underscore the need to take the chaotic and complex dynamics seriously in policy and decision formulation and the necessity of eco-friendly technologies for Bitcoin and Fintech.

AbstractFor a graph [Formula: see text] with [Formula: see text] and [Formula: see text], a perfect double Italian dominating function is a function [Formula: see text] having the property that [Formula: see text], for every vertex [Formula: see text] with [Formula: see text]. The weight of a perfect double Italian dominating function f is the sum [Formula: see text] and the minimum weight of a perfect double Italian dominating function on G is the perfect double Italian domination number [Formula: see text] of G. We initiate the study of perfect double Italian dominating functions. We check the [Formula: see text] of some standard graphs and evaluate with γdI of such graphs. The perfect double Italian dominating functions versus perfect double Roman dominating functions are perused. The NP-completeness of this parameter is verified even when it is restricted to bipartite graphs. Finally, we characterize the graphs G of order n with [Formula: see text].

This paper is concerned with the mathematical modeling of complex living systems whose element microscopic state contains variables which can attain discrete values. Specifically, the main mathematical frameworks of the discrete thermostatted kinetic theory for active particles are reviewed and generalized. In the generalized thermostatted frameworks, which are based on nonlinear ordinary or partial differential equations, the elements of the system are viewed as active particles that are able to perform certain strategies modeled by introducing a functional-state variable called activity. Interactions, which are responsible of the evolution of the system, are modeled using the fundamentals of stochastic game theory and may be influenced by the action of an external force field coupled to a Gaussian-type thermostat. In particular, the interaction domain is modeled by introducing a weighted function and different non-homogeneous discrete frameworks are proposed and coupled with a specific thermostat. Two recent models derived within this approach are reviewed and refer to vehicular and pedestrian dynamics. Future research perspectives are discussed in the whole paper from theoretical and modeling viewpoints.

This paper introduces a new symmetric fractional-order discrete system. The dynamics and symmetry of the suggested model are studied under two initial conditions, mainly a comparison of the commensurate order and incommensurate order maps, which highlights their effect on symmetry-breaking bifurcations. In addition, a theoretical analysis examines the stability of the zero equilibrium point. It proves that the map generates typical nonlinear features, including chaos, which is confirmed numerically: phase attractors are plotted in a two-dimensional (2D) and three-dimensional (3D) space, bifurcation diagrams are drawn with variations in the derivative fractional values and in the system parameters, and we calculate the Maximum Lyapunov Exponents (MLEs) associated with the bifurcation diagram. Additionally, we use the C0 algorithm and entropy approach to measure the complexity of the chaotic symmetric fractional map. Finally, nonlinear 3D controllers are revealed to stabilize the symmetric fractional order map’s states in commensurate and incommensurate cases.

In this paper, we consider a robust combinatorial optimization problem with uncertain weights and propose an uncertainty set that generalizes interval uncertainty by imposing lower and upper bounds on deviations of subsets of items. We prove that if the number of such subsets is fixed and the family of these subsets is laminar, then the robust combinatorial optimization problem can be solved by solving a fixed number of nominal problems. This result generalizes a previous similar result for the case where the family of these subsets is a partition of the set of items.

This article enters the debate about the complex and dynamical nature of second language acquisition (SLA) by discussing and commenting on Pallotti's critique of Complex Dynamic Systems Theory (CDST). Pallotti's critique brings to the fore the argument that, due to its anti-reductionist stance, CDST research fails to observe three fundamental research criteria, namely that research should (1) construct models, (2) make generalizations and falsifiable predictions and (3) adopt clear empirical approaches. While Pallotti does not explore research already moving SLA beyond anti-reductionist approaches to complexity and dynamism, the debate can be advanced by examining research doing exactly this. This article aims to evaluate the extent to which Processability Theory (PT) – a theory of second language (L2) processing that advocates reductionism for the sake of theory construction – meets Pallotti's criteria for researching L2 complexity and dynamics. By discussing Pallotti's – and PT's – criticisms of CDST, the article outlines the implied research criteria and delineates how PT meets these criteria by (1) its bidimensional design, (2) its generalizations and falsifiable predictions for development and variation, and (3) its operationalization of constructs. Findings from a longitudinal study of L2 English are presented. These findings elucidate that, by meeting the criteria, PT can reveal the predictable, implicational development of processing complexity in eight learners and the patterned, dynamical interaction between development and variation in the trajectories of two of these learners. The article concludes that PT fulfils Pallotti's (2022) criteria and, by a reductionist approach which models SLA as multidimensional, it can generate what CDST cannot; dynamical and complex L2 systems which progress in predictable stages, with well-defined constraints on variation, including DST-defined constraints. The article closes by discussing the implications of PT's approach for future research on L2 complexity and dynamics. [ABSTRACT FROM AUTHOR]

The intricacy and fractal properties of human DNA sequences are examined in this work. The core of this study is to discern whether complete DNA sequences present distinct complexity and fractal attributes compared with sequences containing exclusively exon regions. In this regard, the entire base pair sequences of DNA are extracted from the NCBI (National Center for Biotechnology Information) database. In order to create a time series representation for the base pair sequence {G,C,T,A}, we use the Chaos Game Representation (CGR) approach and a mapping rule f, which enables us to apply the metric known as the Complexity–Entropy Plane (CEP) and multifractal detrended fluctuation analysis (MF-DFA). To carry out our investigation, we divided human DNA into two groups: the first is composed of the 24 chromosomes, which comprises all the base pairs that form the DNA sequence, and another group that also includes the 24 chromosomes, but the DNA sequences rely only on the exons’ presence. The results show that both sets provide fractal patterns in their structure, as obtained by the CGR approach. Complete DNA sequences show a sharper visual fractal pattern than sequences composed only of exons. Moreover, the sequences occupy distinct areas of the complexity–entropy plane, and the complete DNA sequences lead to greater statistical complexity and lower entropy than the exon sequences. Also, we observed that different fractal parameters between chromosomes indicate diversity in genomic sequences. All these results occur in different scales for all chromosomes.

To accurately depict inventory management over time, this paper introduces a fractional inventory management model that builds upon the existing classical inventory management framework. According to the definition of fractional difference equation, the numerical solution and phase diagram of an inventory management system are obtained by MATLAB simulation. The influence of parameters on the nonlinear behavior of the system is analyzed by a bifurcation diagram and largest Lyapunov exponent (LLE). Combined with the related indexes of time series, the complex characteristics of a quantization system are analyzed using spectral entropy and C0. This study concluded that the changing law of system complexity is consistent with the LLE of the system. By analyzing the influence of order on the system, it is found that the inventory changes will be periodic in some areas when the system is fractional, which is close to the actual conditions of the company’s inventory situation. The research results of this paper provide useful information for inventory managers to implement inventory and facility management strategies.

The canonical decomposition of a bipartite graph is a new decomposition method that involves three operators: parallel, series, and K⨁ S. The class of weak-bisplit graphs is the class of totally decomposable graphs with respect to these operators, and the class of bicographs is the class of totally decomposable graphs with respect to parallel and series operators. We prove in this paper that the class of bipartite (P6,C6)-free graphs is the class of bipartite graphs that are totally decomposable with respect to parallel and K⨁S operators. We present a linear time recognition algorithm for (P6,C6)-free graphs that is symmetrical to the linear recognition algorithms of weak-bisplit graphs and star1,2,3-free bipartite graphs. As a result of this algorithm, we present efficient solutions in this class of graphs for two optimization graph problems: the maximum balanced biclique problem and the maximum independent set problem.

The trade distance is an important constraining factor underpinning the emergence of social and economic interactions of complex systems. However, agent-based studies supported by the granular analysis of distances are limited. Here, we present a complexity method that places the actual geographical locations of individual firms in Japan at the epicentre of our research. By combining methods derived from network science together with information theory measures, and by using a comprehensive dataset of Japanese inter-firm business transactions, we evaluate the effects of spatial features on the structural patterns of the economy. We find that the normalised probability distributions of the distances between interacting firms obey a power law like decay concomitant with the sizes of firms and regions. Furthermore, small firms would reach large distances to become customers of large firms, while trading between either only small firms or only large firms tends to be at smaller distances. Furthermore, a time evolution analysis suggests a reduction in the overall average trading distances in last 20 years. Lastly, our analysis concerning the trading dynamics among prefectures indicates that the preference to trade with neighbouring prefectures tends to be more pronounced at rural regions as opposed to the larger central conurbations.

In general, the problem of building optimal convolutional codes under a certain criteria is hard, especially when size field restrictions are applied. In this paper, we confront the challenge of constructing an optimal 2D convolutional code when communicating over an erasure channel. We propose a general construction method for these codes. Specifically, we provide an optimal construction where the decoding method presented in the bibliography is considered.

For positive integers j and k, an efficient (j, k)-dominating function of a graph G = (V, E) is a function f : V → {0, 1, 2, . . ., j} such that the sum of function values in the closed neighbourhood of every vertex equals k. The relationship between the existence of efficient (j, k)-dominating functions and various kinds of efficient dominating sets is explored. It is shown that if a strongly chordal graph has an efficient (j, k)-dominating function, then it has an efficient dominating set. Further, every efficient (j, k)-dominating function of a strongly chordal graph can be expressed as a sum of characteristic functions of efficient dominating sets. For j < k there are strongly chordal graphs with an efficient dominating set but no efficient (j, k)-dominating function. The problem of deciding whether a given graph has an efficient (j, k)-dominating function is shown to be NP-complete for all positive integers j and k, and solvable in polynomial time for strongly chordal graphs when j = k. By taking j = 1 we obtain NP-completeness of the problem of deciding whether a given graph has an efficient k-tuple dominating set for any fixed positive integer k. Finally, we consider efficient (2, 2)-dominating functions of trees. We describe a new constructive characterization of the trees with an efficient dominating set and a constructive characterization of the trees with two different efficient dominating sets. A number of open problems and questions are stated throughout the work.

AbstractA quasi-total Roman dominating function (QTRD-function) on [Formula: see text] is a function [Formula: see text] such that (i) every vertex x for which f(x) = 0 is adjacent to at least one vertex v for which f(v) = 2, and (ii) if x is an isolated vertex in the subgraph induced by the set of vertices with non-zero values, then f(x) = 1. The weight of a QTRD-function is the sum of its function values over the whole set of vertices, and the quasi-total Roman domination number is the minimum weight of a QTRD-function on G. The quasi-total Roman reinforcement number [Formula: see text] of a graph G is the minimum number of edges that have to be added to G in order to decrease the quasi-total Roman domination number. In this paper, we initiate the study of quasi-total Roman reinforcement in graphs. We first show that the decision problem associated with the quasi-total Roman reinforcement problem is NP-hard even when restricted to bipartite graphs. Then basic properties of the quasi-total Roman reinforcement number are provided. Finally, some sharp bounds for [Formula: see text] are also presented.

Let G be a nontrivial edge-colored connected graph. An edge-cut R of G is called a rainbow-cut if no two of its edges are colored the same. An edge-colored graph G is rainbow disconnected if for every two vertices u and v of G, there exists a u-v-rainbow-cut separating them. For a connected graph G, the rainbow disconnection number of G, denoted by rd(G), is defined as the smallest number of colors that are needed in order to make G rainbow disconnected. In this paper, we first determine the maximum size of a connected graph G of order n with rd(G) = k for any given integers k and n with 1 ≤ k ≤ n − 1, which solves a conjecture posed only for n odd in [G. Chartrand, S. Devereaux, T.W. Haynes, S.T. Hedetniemi and P. Zhang, Rainbow disconnection in graphs, Discuss. Math. Graph Theory 38 (2018) 1007–1021]. From this result and a result in their paper, we obtain Erdős-Gallai type results for rd(G). Secondly, we discuss bounds on rd(G) for complete multipartite graphs, critical graphs with respect to the chromatic number, minimal graphs with respect to the chromatic index, and regular graphs, and we also give the values of rd(G) for several special graphs. Thirdly, we get Nordhaus-Gaddum type bounds for rd(G), and examples are given to show that the upper and lower bounds are sharp. Finally, we show that for a connected graph G, to compute rd(G) is NP-hard. In particular, we show that it is already NP-complete to decide if rd(G) = 3 for a connected cubic graph. Moreover, we show that for a given edge-colored (with an unbounded number of colors) connected graph G it is NP-complete to decide whether G is rainbow disconnected.

In this paper, we study the link between finite-dimensional Zinbiel algebras and combinatorial structures or (pseudo)digraphs determining which configurations are associated with those algebras. Some properties of Zinbiel algebras that can be read from their associated combinatorial structures are studied. We also analyze the isomorphism classes for each configuration associated with these algebras providing a new method to classify them and we compare our results with the current classifications of 2- and 3-dimensional Zinbiel algebras. We also obtain the 3-vertices combinatorial structures associated with such algebras. In order to complement the theoretical study, we have designed and performed the implementation of an algorithm which constructs and draws the (pseudo)digraph associated with a given Zinbiel algebra and, conversely, another procedure to test if a given combinatorial structure is associated with some Zinbiel algebra.

AbstractA quasi-total Roman dominating function (QTRD-function) on [Formula: see text] is a function [Formula: see text] such that (i) every vertex x for which f(x) = 0 is adjacent to at least one vertex v for which f(v) = 2, and (ii) if x is an isolated vertex in the subgraph induced by the set of vertices with non-zero values, then f(x) = 1. The weight of a QTRD-function is the sum of its function values over the whole set of vertices, and the quasi-total Roman domination number is the minimum weight of a QTRD-function on G. The quasi-total Roman bondage number [Formula: see text] of a graph G is the minimum number of edges that have to be deleted to G in order to increase the quasi-total Roman domination number. In this paper, we start the study of quasi-total Roman bondage in graphs. We first show that the decision problem associated with the quasi-total Roman bondage problem is NP-hard even when restricted to bipartite graphs. Then basic properties of the quasi-total Roman bondage number are provided. Finally, some sharp bounds for [Formula: see text] are also presented.

Metaverse (MV) technology introduces new tools for users each day. MV companies have a significant share in the total stock markets today, and their size is increasing. However, MV technologies are questioned as to whether they contribute to environmental pollution with their increasing energy consumption (EC). This study explores complex nonlinear contagion with tail dependence and causality between MV stocks, EC, and environmental pollution proxied with carbon dioxide emissions (CO2) with a decade-long daily dataset covering 18 May 2012–16 March 2023. The Mandelbrot–Wallis and Lo’s rescaled range (R/S) tests confirm long-term dependence and fractionality, and the largest Lyapunov exponents, Shannon and Havrda, Charvât, and Tsallis (HCT) entropy tests followed by the Kolmogorov–Sinai (KS) complexity measure confirm chaos, entropy, and complexity. The Brock, Dechert, and Scheinkman (BDS) test of independence test confirms nonlinearity, and White‘s test of heteroskedasticity of nonlinear forms and Engle’s autoregressive conditional heteroskedasticity test confirm heteroskedasticity, in addition to fractionality and chaos. In modeling, the marginal distributions are modeled with Markov-Switching Generalized Autoregressive Conditional Heteroskedasticity Copula (MS-GARCH–Copula) processes with two regimes for low and high volatility and asymmetric tail dependence between MV, EC, and CO2 in all regimes. The findings indicate relatively higher contagion with larger copula parameters in high-volatility regimes. Nonlinear causality is modeled under regime-switching heteroskedasticity, and the results indicate unidirectional causality from MV to EC, from MV to CO2, and from EC to CO2, in addition to bidirectional causality among MV and EC, which amplifies the effects on air pollution. The findings of this paper offer vital insights into the MV, EC, and CO2 nexus under chaos, fractionality, and nonlinearity. Important policy recommendations are generated.

This paper presents a survey of advanced concepts and research perspectives, of a philosophical-mathematical approach to describe the dynamics of systems of many interacting living entities. The first part introduces the general conceptual framework. Then, a critical analysis of the existing literature is developed and referred to a multiscale view of a mathematics of living organisms. This paper attempts to understand how far the present state-of-the-art is far from the achievement of such challenging objective. The overall study leads to identify research perspectives and possible hints to deal with them. [ABSTRACT FROM AUTHOR]

Executing loosely structured processes generate unstructured behaviours. Thus, an Unstructured Business Process (UBP) still has more issues that are difficult to be analysed and to be understood due to its complexity and variability. Moreover, the need of an instantiate response is clearly appeared in operational systems. Therefore, it is required to study related challenges that can be acquired during the transition from the structured BP to the unstructured one. In this context, process mining plays a dominant role to understand business process complexity using event data resulted from business process execution. Mainly, this paper treats three challenges related to unstructured BPs. The first challenge is how to support UBPs at runtime using process mining techniques. The second challenge is how to manage UBP variability taking into consideration variant conditions. The third challenge is how to adapt dynamically UBPs according to the company business rules and conditions.

In this paper, we study the nonlinear dynamics of a multiplex system consisting of neuronal networks each with an arbitrary number of FitzHugh-Nagumo neurons and intra-connections and delayed couplings. The network contains an autaptic connection formed by the axon of a neuron on its own soma or dendrites. The stability and instability of the network are determined and the existence of bifurcation is discussed. Then, the study turns to validate the theoretical analysis through numerical simulations. Abundant dynamical phenomena of the network are explored, such as coexisting multi-period oscillations and chaotic responses.

Objective: Autism spectrum disorder (ASD) is usually characterised by altered social skills, repetitive behaviours, and difficulties in verbal/nonverbal communication. It has been reported that electroencephalograms (EEGs) in ASD are characterised by atypical complexity. The most commonly applied method in studies of ASD EEG complexity is multiscale entropy (MSE), where the sample entropy is evaluated across several scales. However, the accuracy of MSE-based classifications between ASD and neurotypical EEG activities is poor owing to several shortcomings in scale extraction and length, the overlap between amplitude and frequency information, and sensitivity to frequency. The present study proposes a novel, nonlinear, non-stationary, adaptive, data-driven, and accurate method for the classification of ASD and neurotypical groups based on EEG complexity and entropy without the shortcomings of MSE. Approach: The proposed method is as follows: (a) each ASD and neurotypical EEG (122 subjects × 64 channels) is decomposed using empirical mode decomposition (EMD) to obtain the intrinsic components (intrinsic mode functions). (b) The extracted components are normalised through the direct quadrature procedure. (c) The Hilbert transforms of the components are computed. (d) The analytic counterparts of components (and normalised components) are found. (e) The instantaneous frequency function of each analytic normalised component is calculated. (f) The instantaneous amplitude function of each analytic component is calculated. (g) The Shannon entropy values of the instantaneous frequency and amplitude vectors are computed. (h) The entropy values are classified using a neural network (NN). (i) The achieved accuracy is compared to that obtained with MSE-based classification. (j) The consistency of the results of entropy 3D mapping with clinical data is assessed. Main results: The results demonstrate that the proposed method outperforms MSE (accuracy: 66.4%), with an accuracy of 93.5%. Moreover, the entropy 3D mapping results are more consistent with the available clinical data regarding brain topography in ASD. Significance: This study presents a more robust alternative to MSE, which can be used for accurate classification of ASD/neurotypical as well as for the examination of EEG entropy across brain zones in ASD.

In the process of rational development and utilisation of nuclear energy, people often face nuclear accidents such as lost and stolen radioactive sources; so, the means of searching for these sources quickly in highly radioactive environments is an important security challenge. In the past, these jobs were limited to workers specialising in nuclear technology. They used gamma-ray detection equipment to search for radioactive sources, but the search efficiency was low. The main purpose of this article is to design a meta-heuristic algorithm based on imitating professional technicians to locate radioactive sources in a computer-aided manner. At the same time, due to the complexity that may characterise the actual search, the search strategy must be optimised. The article established an intelligent random search model with human thinking. Finally, it was proved based on the mathematical theory that the complexity of the model search algorithm is linear, and the simulation experiment results show that the optimisation algorithm has good efficiency and fault tolerance.

In this study, we expand a 2D sine map via adding the discrete memristor to introduce a new 3D fractional-order sine-based memristor map. Under commensurate and incommensurate orders, we conduct an extensive exploration and analysis of its nonlinear dynamic behaviors, employing diverse numerical techniques, such as analyzing Lyapunov exponents, visualizing phase portraits, and plotting bifurcation diagrams. The results emphasize the sine-based memristor map’s sensitivity to fractional-order parameters, resulting in the emergence of distinct and diverse dynamic patterns. In addition, we employ the sample entropy (SampEn) method and C0 complexity to quantitatively measure complexity, and we also utilize the 0–1 test to validate the presence of chaos in the proposed fractional-order sine-based memristor map. Finally, MATLAB simulations are be executed to confirm the results provided.

Cellular automata are mathematical models that represent systems with complex behavior through simple interactions between their individual elements. These models can be used to study unconventional computational systems and complexity. One notable aspect of cellular automata is their ability to create structures known as gliders, which move in a regular pattern to represent the manipulation of information. This paper introduces the modification of mean-field theory applied to cellular automata, using random perturbations based on the system’s evolution rule. The original aspect of this approach is that the perturbation factor is tailored to the nature of the rule, altering the behavior of the mean-field polynomials. By combining the properties of both the original and perturbed polynomials, it is possible to detect when a cellular automaton is more likely to generate gliders without having to run evolutions of the system. This methodology is a useful approach to finding more examples of cellular automata that exhibit complex behavior. We start by examining elementary cellular automata, then move on to examples of automata that can generate gliders with more states. To illustrate the results of this methodology, we provide evolution examples of the detected automata.

In this study, galeite, Na15(SO4)5ClF4 and schairerite, Na21(SO4)7ClF6 were investigated via in situ single-crystal X-ray diffraction in the temperature range of 300–750 K. Galeite and schairerite are trigonal, P31m, a = 12.1903(2), c = 13.9454(2) Å, V = 1794.69(6) Å3, and Z = 3 (R1 = 0.0273, 300 K) for galeite and a = 12.1859(3), c = 19.3080(6) Å, V = 2483.04(14) Å3, and Z = 3 (R1 = 0.0334, 300 K) for schairerite. The crystal structures of galeite and schairerite are based upon frameworks consisting of alternating face- and corner-sharing fluorine- and chlorine-centered octahedra. Galeite and schairerite can be attributed to 5H (galeite) and 7H (schairerite) antiperovskite polytypes, respectively. It was observed that schairerite undergoes at least one reversible phase transition before it starts to lose its crystallinity at 750 K. This phase transition occurs in the temperature range of 550–600 K. The high-temperature modification of schairerite is trigonal, with the centrosymmetric space group P-3m1 and the unit-cell parameters a = 7.0714(2), c = 19.5972(7) Å, V = 848.66(6) Å3, and Z = 1. Galeite is stable up to 600 K. The crystal structures of minerals expand anisotropically, and, in both cases, the strongest thermal expansion was parallel to the modules of face-sharing anion-centered octahedra. The structural complexity analysis showed that galeite is complex (695.175 bits/cell) and that the LT-modification of schairerite is very complex (1064.990 bits/cell), whereas its HT-modification is intermediate in complexity (256.755 bits/cell). The complexities of LT- and HT-polymorphs of schairerite are consistent with the general observations regarding structures with positional disorder: complexity decreases with increasing temperature, and simpler polymorphs have lower physical density.

One of the most recent advancements in graph theory is the use of a multidisciplinary approach to the investigation of specific structural dependent features, such as physico-chemical properties, biological activity and the entropy measure of a graph representing objects like a network or a chemical compound. The ability of entropy measures to determine both the certainty and uncertainty about objects makes them one of the most investigated topics in science along with its multidisciplinary nature. As a result, many formulae, based on vertices, edges and symmetry, for determining the entropy of graphs have been developed and investigated in the field of graph theory. These measures assist in understanding the characteristics of graphs, such as the complexity of the networks or graphs, which may be determined using entropy measures. In this paper, we derive formulae of entropy measures of an extensively studied family of the interconnection networks and classify them in terms of complexity. This is accomplished by utilizing all three tools, including analytical formulae, graphical methods and numerical tables.

Let $G$ be a simple graph with finite vertex set $V(G)$ and $S=\{-1,1,2\}$. A signed total Roman $k$-dominating function (STRkDF) on a graph $G$ is a function $f:V(G)\to S$ such that (i) any vertex $y$ with $f(y)=-1$ is adjacent to at least one vertex $t$ with $f(t)=2,$ (ii) $\sum_{t\in N(y)}f(t)\geq k$ holds for any vertex $y$. The $weight$ of an STRkDF $f$, denoted by $\omega(f)$, is $\sum_{y\in V(G)}f(y)$, and the minimum weight of an STRkDF is the signed total Roman k-domination number,$\gamma_{stR}^k(G),$ of $G$. In this article, we prove that the decision problem for the signed total Roman $k$-domination is NP-complete on bipartite and chordal graphs for $k\in\{1, 2\}$.

A total Roman dominating function on a graph G is a function satisfying the conditions: (i) every vertex u with f(u) = 0 is adjacent to at least one vertex v of G for which f(v) = 2; (ii) the subgraph induced by the vertices assigned non-zero values has no isolated vertices. The minimum of over all such functions is called the total Roman domination number The total Roman domination stability number of a graph G with no isolated vertex, denoted by is the minimum number of vertices whose removal does not produce isolated vertices and changes the total Roman domination number of G. In this paper we present some bounds for the total Roman domination stability number of a graph, and prove that the associated decision problem is NP-hard even when restricted to bipartite graphs or planar graphs.

For a graph a double Roman dominating function is a function having the property that if f(v) = 0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor w with f(w) = 3, and if f(v) = 1, then vertex v must have at least one neighbor w with The weight of a double Roman dominating function f is the value The double Roman domination number of a graph G, denoted by equals the minimum weight of a double Roman dominating function on G. The double Roman reinforcement number of a graph G is the minimum number of edges that have to be added to G in order to decrease the double Roman domination number. In this paper, we first show that the decision problem associated to the double Roman reinforcement problem is NP-hard even when restricted to bipartite graphs and then we investigate the properties of double Roman reinforcement number in graphs, and we present some sharp bounds for Next we characterize trees with double Roman reinforcement number greater than one.

The purpose of this study was to assess the effects of transverse friction massage (TFM) on the electromechanical delay components and complexity of the surface electromechanical activity in the rectus femoris (RF) and vastus medialis (VM) muscles and to identify possible mechanisms behind TFM-induced alterations in the dynamics of RF and VM activity. Seven female and five male healthy subjects participated in this study. The subjects generated five maximal voluntary isometric contractions (MVICs) consecutively before and after TFM. Meanwhile, electromyography (EMG), mechanomyography (MMG), and force were recorded. The onset times of the recorded signals were detected offline by setting the threshold to three times the SD of the baseline. The delays between EMG and MMG (Δt(EMG–MMG)), MMG and force (Δt(MMG–Force)), and EMG and force (Δt(EMG–Force)) were computed from the detected onsets. The fractal dimension (FD) of the EMG time series was computed using the correlation dimension method. TFM increased Δt(MMG–Force) and Δt(EMG–Force) significantly in the RF but decreased Δt(EMG–MMG) and increased Δt(MMG–Force) in the VM. TFM decreased the FD in the RF and increased it in the VM. The results imply that TFM decreased the stiffness of both the RF and VM and decreased the duration of the electrochemical processes in the VM. It is proposed that the decrease in EMG complexity in the RF may be associated with the decreased stiffness of the RF, and the increase in EMG complexity in the VM may be associated with the decreased electrochemical processes in this muscle. It is also suggested that the opposite changes in EMG complexity in the RF and VM can be used as a discriminating parameter to search for the effects of an intervention in the quadriceps muscles. The present study also demonstrates how to discriminate the nonlinear dynamics of a complex muscle system from a noisy time series.

The whole world has entered the era of the Vuca. Some traditional methods of problem analysis begin to fail. Complexity science is needed to study and solve problems from the perspective of complex systems. As a complex system full of volatility and uncertainty, price fluctuations have attracted wide attention from researchers. Therefore, through a literature review, this paper analyzes the research on complex theories on price prediction. The following conclusions are drawn: (1) The price forecast receives widespread attention year by year, and the number of published articles also shows a rapid rising trend. (2) The hybrid model can achieve higher prediction accuracy than the single model. (3) The complexity of models is increasing. In the future, the more complex methods will be applied to price forecast, including AI technologies such as LLM. (4) Crude-oil prices and stock prices will continue to be the focus of research, with carbon prices, gold prices, Bitcoin, and others becoming new research hotspots. The innovation of this research mainly includes the following three aspects: (1) The whole analysis of all the articles on price prediction using mathematical models in the past 10 years rather than the analysis of a single field such as oil price or stock price. (2) Classify the research methods of price forecasting in different fields, and found the common problems of price forecasting in different fields (including data processing methods and model selection, etc.), which provide references for different researchers to select price forecasting models. (3) Use VOSviewer to analyze the hot words appearing in recent years according to the timeline, find the research trend, and provide references for researchers to choose the future research direction.

The paper introduces a novel two-dimensional fractional discrete-time predator–prey Leslie–Gower model with an Allee effect on the predator population. The model’s nonlinear dynamics are explored using various numerical techniques, including phase portraits, bifurcations and maximum Lyapunov exponent, with consideration given to both commensurate and incommensurate fractional orders. These techniques reveal that the fractional-order predator–prey Leslie–Gower model exhibits intricate and diverse dynamical characteristics, including stable trajectories, periodic motion, and chaotic attractors, which are affected by the variance of the system parameters, the commensurate fractional order, and the incommensurate fractional order. Finally, we employ the 0–1 method, the approximate entropy test and the C0 algorithm to measure complexity and confirm chaos in the proposed system.

Background: Incorporating variability within gait rehabilitation offers a promising approach to restore functional capacity. However, it's success requires adequate synchronization, a parameter that lacks report in most of the literature regarding cued gait training.Research Question: How changes to synchronization performance during fractal-like and isochronous cueing impacts gait variability measures?Methods: We asked twelve young male participants to walk in synchronization to two different temporally structure cueing (isochronous [ISO] and fractal [FRC]). We have also manipulated the cueing's tempo by increasing and decreasing it by 5% to manipulate synchronization, resulting in six conditions (stimuli [ISO,FRC] x tempo [SLOW, NORMAL, FAST]). The normal condition was set from an uncued trial through the participant's self-paced stride time. Synchronization performance (ASYNC) and gait variability (fractal scaling and coefficient of variation) were calculated from stride time data ( -ISIs,CV-ISIs). Repeated measures analysis of variance or Aligned Rank Transform were conducted to determine significant differences between metronome tempo and stimuli for the dependent variables RESULTS: Our results showed a FAST tempo decreases synchronization performance (ASYNC) and leads to lower -ISIs, for both ISO and FRC stimuli. This indicates that when an individual exhibits poor synchronization during cued gait training, his/her gait variability patterns will not follow the temporal structure of the presented metronome. Specifically, if the individual poorly synchronizes to the cues, the gait patterns become more random, a condition typically observed in older adults and neurological patients, which runs contrary to the hypothesis when using fractal-like metronomes.Significance: This study provides supporting evidence that measuring synchronization performance in cued training is fundamental for a proper clinical interpretation of its effects. This is particularly relevant for the recent and ongoing clinical research using fractal-like metronomes since the expected gait patterns are dependent on the synchronization performance. Randomized control trials must incorporate synchronization performance related measures. [ABSTRACT FROM AUTHOR]

This study uses fractal analysis to measure the detailed intensity of well-known Classical and Renaissance façades. The study develops a method to understand their interrelated design principles more comprehensively. With this evaluation tool, one can observe intrinsic connections that support the historical continuity and point out balancing composition protocols, such as the ‘compensation rule’, that regulated design for centuries. The calculations offer mathematical constants to identify Classical and Renaissance details by plasticity rates. Finally, we base this method on spatial evaluation. Our calculations involve depth, which connects planar front views with the haptic reality of the façades’ tectonic layers. The article also discusses the cultural and urban implications of our results.

In this paper, we study the directed multicut and directed multimultiway cut problems. The input to the directed multi-multiway cut problem is a weighted directed graph $G=(V,E)$ and $k$ sets $S_1, S_2,\cdots, S_k$ of vertices. The goal is to find a subset of edges of minimum total weight whose removal will disconnect all the connections between the vertices in each set $S_i$, for $1\leq i\leq k$. A special case of this problem is the directed multicut problem whose input consists of a weighted directed graph $G=(V,E)$ and a set of ordered pairs of vertices $(s_1,t_1),\cdots,(s_k,t_k)$. The goal is to find a subset of edges of minimum total weight whose removal will make for any $i, 1\leq i\leq k$, there is no directed path from si to ti . In this paper, we present two approximation algorithms for these problems. The so called region growing paradigm is modified and used for these two cut problems on directed graphs. using this paradigm, we give an approximation algorithm for each problem such that both algorithms have the approximation factor of $O(k)$ the same as the previous works done on these problems. However, the previous works need to solve $k$ linear programming, whereas our algorithms require only one linear programming. Therefore, our algorithms improve the running time of the previous algorithms.

A partition of the vertex set V of a graph G into k color classes with is called a quorum coloring if for every vertex at least half of the vertices in the closed neighborhood of v have the same color as v. The maximum order of a quorum coloring of G is called the quorum coloring number of G and is denoted In this paper, we give answers to two open problems stated in 2013 by Hedetniemi, Hedetniemi, Laskar and Mulder. In fact, we prove that the decision problem associated with is NP-complete when the input graph is a 4-regular graph. We also show that the decision problem asks whether a given graph G has a quorum coloring of order at least 2 is NP-complete too.

An important paradigm in modeling the complexity of mathematical tasks relies on computational complexity theory, in which complexity is measured through the resources (time, space) taken by a Turing machine to carry out the task. These complexity measures, however, are asymptotic and as such potentially a problematic fit when descriptively modeling mathematical tasks that involve small inputs. In this paper, we argue that empirical data on human arithmetical cognition implies that a more fine-grained complexity measure is needed to accurately study mental arithmetic tasks. We propose a computational model of mental integer addition that is sensitive to the relevant aspects of human arithmetical ability. We show that this model necessitates a two-part complexity measure, since the addition tasks consists of two qualitatively different stages: retrieval of addition facts and the (de)composition of multidigit numbers. Finally, we argue that the two-part complexity measure can be developed into a single response-time measure with the help of empirical study of the two stages.

In this paper, we study global well-posedness and long-time asymptotic behavior of solutions to the nonlinear heat equation with absorption, ut-Δ⁢u+|u|α⁢u=0{u_{t}-\Delta u+\lvert u\rvert^{\alpha}u=0}, where u=u⁢(t,x)∈ℝ{u=u(t,x)\in\mathbb{R}}, (t,x)∈(0,∞)×ℝN{(t,x)\in(0,\infty)\times\mathbb{R}^{N}} and α>0{\alpha>0}. We focus particularly on highly singular initial values which are antisymmetric with respect to the variables x1,x2,…,xm{x_{1},x_{2},\ldots,x_{m}} for some m∈{1,2,…,N}{m\in\{1,2,\ldots,N\}}, such as u0=(-1)m∂1∂2⋯∂m|⋅|-γ∈𝒮′(ℝN){u_{0}=(-1)^{m}\partial_{1}\partial_{2}\cdots\partial_{m}\lvert\,{\cdot}\,% \rvert^{-\gamma}\in\mathcal{S}^{\prime}(\mathbb{R}^{N})}, 00{\alpha>0}. Our approach is to study well-posedness and large time behavior on sectorial domains of the form Ωm={x∈ℝN:x1,…,xm>0}{\Omega_{m}=\{x\in\mathbb{R}^{N}:x_{1},\ldots,x_{m}>0\}}, and then to extend the results by reflection to solutions on ℝN{\mathbb{R}^{N}} which are antisymmetric. We show that the large time behavior depends on the relationship between α and 2γ+m{\frac{2}{\gamma+m}}, and we consider all three cases, α equal to, greater than, and less than 2γ+m{\frac{2}{\gamma+m}}. Our results include, among others, new examples of self-similar and asymptotically self-similar solutions.

This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes a bounded number of state changes in any orbit, and finally cellular automata where each orbit converges to some fixed point. Many examples studied in the literature fit into these definitions, in particular the works on cristal growth started by S. Ulam in the 60s. The central question addressed here is how the computational power and computational hardness of basic properties is affected by the constraints of convergence, bounded number of change, or local decreasing of states in each cell. By studying various benchmark problems (short-term prediction, long term reachability, limits) and considering various complexity measures and scales (LOGSPACE vs. PTIME, communication complexity, Turing computability and arithmetical hierarchy) we give a rich and nuanced answer: the overall computational complexity of such cellular automata depends on the class considered (among the three above), the dimension, and the precise problem studied. In particular, we show that all settings can achieve universality in the sense of Blondel-Delvenne-K\r{u}rka, although short term predictability varies from NLOGSPACE to P-complete. Besides, the computability of limit configurations starting from computable initial configurations separates bounded-change from convergent cellular automata in dimension~1, but also dimension~1 versus higher dimensions for freezing cellular automata. Another surprising dimension-sensitive result obtained is that nilpotency becomes decidable in dimension~ 1 for all the three classes, while it stays undecidable even for freezing cellular automata in higher dimension.

Diseases, natural disasters, and other emergencies force the economy and management system to confront nonlinear and random changes. In recent years, complexity science has attracted much attention. Complex economics believes that economic models are dynamic, stochastic, and unpredictable, and that equilibrium and stability are temporary. It is changing traditional economic theory. Based on complexity theory, bibliometric theory, nonlinear theory, and game theory, combined with knowledge graph methods, the article analyzed 200 papers from the Web of Science, covering the period 1998–2022. This research presents the research structure and theoretical evolution of complex economic games through visualization techniques. The clusters of keywords and the logical relationships between them are discussed. Then, the analysis of hot keywords and co-occurrence keywords is carried out. Finally, future research directions for complex economic games are given: (1) the market complexity that comes with intelligent expectations, (2) complex characteristics of the data trading market, and (3) complex risk control for emergencies. The innovation lies in the use of data analysis software combined with manual knowledge to overcome the shortcomings of inflexible software analysis, as well as weak manual storage and computation. This research builds a theoretical foundation for grasping the research direction and selecting advanced topics.

This paper presents a survey of advanced concepts and research perspectives, of a philosophical-mathematical approach to describe the dynamics of systems of many interacting living entities. The first part introduces the general conceptual framework. Then, a critical analysis of the existing literature is developed and referred to a multiscale view of a mathematics of living organisms. This paper attempts to understand how far the present state-of-the-art is far from the achievement of such challenging objective. The overall study leads to identify research perspectives and possible hints to deal with them.

Fractional order maps are a hot research topic; many new mathematical models are suitable for developing new applications in different areas of science and engineering. In this paper, a new class of a 2D fractional hyperchaotic map is introduced using the Caputo-like difference operator. The hyperchaotic map has no equilibrium and lines of equilibrium points, depending on the values of the system parameters. All of the chaotic attractors generated by the proposed fractional map are hidden. The system dynamics are analyzed via bifurcation diagrams, Lyapunov exponents, and phase portraits for different values of the fractional order. The results show that the fractional map has rich dynamical behavior, including hidden homogeneous multistability and offset boosting. The paper also illustrates a novel theorem, which assures that two hyperchaotic fractional discrete systems achieve synchronized dynamics using very simple linear control laws. Finally, the chaotic dynamics of the proposed system are stabilized at the origin via a suitable controller.

Today, aircraft demand is exceeding the capacity of the Air Traffic Control (ATC) system. As a result, airspace is becoming a very complex environment to control. The complexity of airspace is thus closely related to the workload of controllers and is a topic of great interest. The major concern is that variables that are related to complexity are currently recognised, but there is still a debate about how to define complexity. This paper attempts to define which variables determine airspace complexity. To do so, a novel methodology based on the use of machine learning models is used. In this way, it tries to overcome one of the main disadvantages of the current complexity models: the subjectivity of the models based on expert opinion. This study has determined that the main indicator that defines complexity is the number of aircraft in the sector, together with the occupancy of the traffic flows and the vertical distribution of aircraft. This research can help numerous studies on both air traffic complexity assessment and Air Traffic Controller (ATCO) workload studies. This model can also help to study the behaviour of air traffic and to verify that there is symmetry in structure and the origin of the complexity in the different ATC sectors. This would have a great benefit on ATM, as it would allow progress to be made in solving the existing capacity problem.