Since its original publication 1 in 1978, Lozi’s chaotic map has been thoroughly explored and continues to be. Hundreds of publications analyze its particular structure or apply its properties in many fields (electronic devices like memristor, A.I. with swarm intelligence, etc.). Several generalizations have been proposed, transforming the initial two-dimensional map into multidimensional one. However, they do not respect the original constraint that allows this map to be one of the few strictly hyperbolic: a constant Jacobian. In this paper we introduce a three-dimensional piece-wise linear extension respecting this constraint and we explore a special property never highlighted for chaotic mappings: the coexistence of thread-chaotic attractors (i.e., attractors which are formed by collection of lines) and sheet-chaotic attractors (i.e., attractors which are formed by collection of planes). This new 3-dimensional mapping can generate a large variety of chaotic and hyperchaotic attractors. We give five examples of such behavior in this article. In the first three examples, there is coexistence of thread and sheet-chaotic attractors. However, their shape are different and they are constituted by a different number of pieces. In the two last examples, the blow up of the attractors with respect to parameter a and b is highlighted.

We present a novel method for interpolating univariate time series data. The proposed method combines multi-point fractional Brownian bridges, a genetic algorithm, and Takens’ theorem for reconstructing a phase space from univariate time series data. The basic idea is to first generate a population of different stochastically interpolated time series data, and secondly, to use a genetic algorithm to find the pieces in the population which generate the smoothest reconstructed phase space trajectory. A smooth trajectory curve is hereby found to have a low variance of second derivatives along the curve. For simplicity, we refer to the developed method as PhaSpaSto-interpolation, which is an abbreviation for phase-space-trajectory-smoothing stochastic interpolation. The proposed approach is tested and validated with a univariate time series of the Lorenz system, five non-model data sets and tested against a cubic spline interpolation and a linear linear interpolation. We find that the criterion for smoothness guarantees low errors on known model and non-model data. Finally, we interpolate the discussed non-model data sets, and show the corresponding improved phase space portraits. The proposed method is useful for interpolating low-sampled time series data sets for, e.g., machine learning, regression analysis, or time series prediction approaches.

In this research, we developed a wearable temperature-sensing element by dip dyeing threads in poly (3, 4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) (p-type conducting polymer) solution. The PEDOT:PSS was used to dye the textile and it exhibited negative temperature coefficient characteristics in which the resistance decreases as the temperature increases. The fabricated temperature-detection thread achieved a sensitivity of 167.1 W/°C with 99.8% linearity in the temperature range of -50 to 80 °C. We anticipate that temperature sensors that apply our technology will be made as stitch- or textile-type for wearable devices, and they will be widely adopted for different applications such as in fitness, leisure, healthcare, medical treatment, infotainment, industry, and military applications, among others.

Low-Level Virtual Machine (LLVM) compiler infrastructure is a useful tool for building Just-in-time (JIT) compilers, besides its reliable front-end represented by clang compiler and its elaborated middle-end containing different optimizations that improve the runtime performance. This paper addresses specifically the part of building a JIT compiler using LLVM with the scope of getting the hardware architecture details of the underlying machine such as the number of cores and the number of logical cores per processing unit and providing them to NUMA-BTLP static thread classification algorithm and to NUMA-BTDM static thread mapping algorithm. Afterwards, the hardware-aware algorithms are run by the JIT compiler within an optimization pass. JIT compiler in this paper is designed to run on a parallel C/C++ application (which creates threads using Pthreads), before the first time the application is executed on a machine. To do that, the JIT compiler takes the native code of the application, gets the corresponding LLVM IR (Intermediate Representation) for the native code and executes the hardware-aware thread classification and the thread mapping algorithms on the IR. The NUMA-Balanced Task and Loop Parallelism (NUMA-BTLP) and NUMA-Balanced Thread and Data Mapping (NUMA-BTDM) are expected to optimize the energy consumption up to 15%, on NUMA systems.

This paper provides an overview of the current state-of-the-art digital twin and digital thread technology in industrial operations. Both are transformational technologies that have the advantage of improving the efficiency of current design and manufacturing. Digital twin is an important element of the Industry 4.0 digitalization process; however, the huge amount of data that are generated and collected by digital twin offer challenges in handling, processing and storage. The paper aims to report on the development of a new framework that combines the digital twin and digital thread for better data management in order to drive innovation, improve the production process and performance, and to ensure continuity and traceability of information. The digital twin/thread framework incorporated behavior simulation and physical control components, in which these two components rely on the connectivity between the twin and thread for information flow and exchange to drive innovation. The twin/thread framework encompasses specifications that include organizational architecture layout, security, user access, cloud computing set-up, and hardware and software requirements. It is envisaged that the framework will be applicable to enhancing optimization of operational processes and traceability of information in the physical world, especially in Industry Shipyard 4.0.

This article studies examines the relationship of literature, ideology, and reading through a study of language, or la langue, as explored by De Man, Derrida, and Lacan. It attempts to show that structure, assumed to be the given of language, even within deconstruction, is, as structure, that which undoes structure. Literature explores this possibility of language, which is that it be and not be at the same time. The article finishes by studying the connection between this idea of literature as the possibility of language and the possibility of man, an important theme of the above three thinkers.

The diameter of a H13 steel tool with M6 threads and a pin diameter of 5.9 mm and a pin length of 5 mm was measured after each 25.4 mm length of friction stir processing (FSP) of 6061-T6 extrusions. The change in pin diameter with FSP time or distance did not exhibit any steady state and was found to have two distinct regions. Metallographic analysis of two tools subjected to FSP for 60 and 120 seconds showed that (i) threads fractured in early stages of FSP, (ii) a built-up layer formed between the threads, and (iii) threads progressively wore with processing time. The metallographic analysis of an embedded tool showed the presence of a fractured piece of the tool in the stir zone. These points are discussed in detail in the paper.

Hybrid reinforcement in a composite material (CM), in many situations, allows better govern material mechanical properties. Polymer matrix CM plate is reinforced with small particles and macro-fibers. Particles are oil shale ash (OSA) powder, macro-fibers – basalt fiber threads im-pregnated by matrix material. With the goal to find out elastic properties of the matrix- polymer with OSA, samples with its different concentrations were experimentally fabricated and their elastic properties were experimentally measured. Obtained data were used in numerical model-ling. Was observed polymer matrix composite slab, reinforced with OSA and three-dimensional (3D) basalt fiber fabric. Fabric are forming threads impregnated by matrix (polymer resin mixed with OSA particles). Damage accumulation in the stretched slab was modelled. Impregnated thread, in the modelling, is observed as a macro-fiber (MF) with averaged elastic properties. With the load increase MF in the material began to break. At first, appeared isolated single breaks. A probabilistic sequential MF rupture accumulation model was accepted and numerical-ly realized. The geometry of the reinforcing knitted fabric was modeled using the Leaf and Glaskin approach. In the knitted fabric highly, stressed MF cross-sections are observed as po-tential location where thread breakage can occur. If one thread breaks, the cross-sections of the adjacent threads experience the overload caused by this rupture. More overloaded crossection in the adjacent overloaded thread breaks and we obtain two adjacent broken MF designated as a defect with the size j=2. The probabilities of obtaining defect consisting of at least 2, 3, … j adjacent broken MF in the plate were calculated. The calculations continued until the rupture process becomes unstable (j→∞). The overstresses on adjacent threads in the CM were calculat-ed using the FEM three-dimensional numerical approach. Analytical and stochastic methods were used for the load-carrying capacity determination and different size defects accumulation in the hybrid composite material (HCM) plate. Also, was calculated the probability of the plate rupture.

This work presents a new type of chaotic dynamical system originated from Dirichlet Eta function. Although the exposition describes only a bidimensional instance, it is certainly possible to construct higher dimensional such models. The novelty resides in the multitude of interesting characteristics concentrated in only one kind of dynamical system, mainly because of its simple abstract definition - it provokes dissipative, chaotic and itinerant behavior, and its paths typically display nonrecurring quasi-attractors and associate regions of ruin. In addition, it is discrete and nonautonomous, being additively driven by a simple real vector sequence. Also, the defining formulas have parameters which permit to activate bifurcatory effects, mainly related to setting the number of quasi-attractors and overall geometric complexity and diversity. In this fashion, it holds a certain similarity with classical itinerant chaotic systems, but it is a completely different object. One of its parameters is very influential and may be intuitively compared to a type of "potential energy", capable of changing the duration of sojourns etc. In this fashion, there is a potential opportunity to employ artificial inference techniques for designing specific structures on paths. Of course, the other parameters are also relevant, but not necessarily in the control of the number of quasi-attractors and the permanence periods near them. It is important to state that the described system was found during a previous investigation about certain features of the Riemann hypothesis, using the Dirichlet Eta function instead of the Riemann Zeta function - the components of the system under study here were part of certain series whose convergence had to be established, and that scenario produced this very positive side effect. The text also suggests an atypical, but important, potential application in philosophy: the representation of the Hindu concepts of Samsara and Moksha.

In this paper, we study the existence of the random -pullback attractor of a non-autonomous local modified stochastic Swift-Hohenberg equation with multiplicative noise in stratonovich sense. It is shown that a random -pullback attractor exists in when its external force has exponential growth. Due to the stochastic term, the estimate are delicate, we overcome this difficulty by using the Ornstein-Uhlenbeck(O-U) transformation and its properties.

A statistical analysis of semantic memory should reflect the complex, multifactorial structure of the relations among its items. Still, a dominant paradigm in the study of semantic memory has been the idea that the mental representation of concepts is structured along a simple branching tree spanned by superordinate and subordinate categories. We propose a generative model of item representation with correlations that overcomes the limitations of a tree structure. The items are generated through "factors" that represent semantic features or real-world attributes. The correlation between items has its source in the extent to which items share such factors and the strength of such factors: if many factors are balanced, correlations are overall low; whereas if a few factors dominate, they become strong. Our model allows for correlations that are neither trivial nor hierarchical, but may reproduce the general spectrum of correlations present in a data-set of nouns. We provide an estimate of the number of concepts that can be stored and retrieved by a large-scale cortical network, the Potts network, which is perhaps approximately 10⁷ with human cortical parameters. When this storage capacity is exceeded, however, retrieval fails completely only for balanced factors; above a critical degree of imbalance, a phase transition leads to a regime where the network still extracts considerable information about the cued item, even if not recovering its detailed representation: partial categorization seems to emerge spontaneously as a consequence of the dominance of particular factors, rather than being imposed ad hoc. We argue this to be a relevant model of semantic memory resilience in Tulving’s remember/know paradigms.

In this paper the D 3 dihedral logistic map of fractional order is introduced. The map 1 presents a dihedral symmetry D 3 . It is numerically shown that the construction and interpretation 2 of the bifurcation diagram versus the fractional order require special attention. The system stability 3 is determined and the problem of hidden attractors is analyzed. Also, analytical and numerical 4 results show that the chaotic attractor of integer order, with D 3 symmetries, looses its symmetry 5 in the fractional-order variant.

At present paper, we aim to study the long-time behavior of a stochastic semi-linear degenerate parabolic equation on bounded or unbounded domain and driven by a nonlinear noise and defined. Since the theory of pathwise random dynamical systems can not be applied directly to the equation with nonlinear noise, first, we establish the existence of weak pullback mean random attractors for the equation by applying the theory of mean-square random dynamical systems; then, we prove the existence of (pathwise) pullback random attractors for the Wong-Zakai approximate system of the equation. In addition, we establish the upper semicontinuity of pullback random attractors for the Wong-Zakai approximate system of the equation under consideration driven by a linear multiplicative noise.

A probabilistic description is essential for understanding the dynamics of stochastic systems far from equilibrium. To compare different Probability Density Functions (PDFs), it is extremely useful to quantify the difference among different PDFs by assigning an appropriate metric to probability such that the distance increases with the difference between the two PDFs. This metric structure then provides a key link between stochastic processes and geometry. For a non-equilibrium process, we define an infinitesimal distance at any time by comparing two PDFs at times infinitesimally apart and sum these distances in time. The total distance along the trajectory of the system quantifies the total number of different states that the system undergoes in time and is called the information length. By using this concept, we investigate classical and quantum systems and demonstrate the utility of the information length as a unique Lagrangian diagnostic to quantify the information change as a system continuously evolves in time and to map out attractor structure. We further elucidate quantum effects (uncertainty relation) and the dual role of the width of PDF in quantum systems.

Process mining offers significant services in the development of digital threads and digital twin applications for healthcare. One of the sub-emerging case studies is the use of patients’ location data in process mining analyses. While the streamlining of published works is focused on introducing process discovery algorithms, there is a necessity to address challenges beyond that. Literature analysis indicates that explainability, reasoning, and characterizing the root causes of process drifts in healthcare processes is an important but overlooked challenge. In addition, incorporating domain-specific knowledge into process discovery could be a significant contribution to process mining literature. To address this, we present the DIAG approach that consists of a meta-model and an algorithm that enables diagnosing in process mining through an ontology-driven approach. With DIAG, we modeled the healthcare semantics in a process mining application and diagnosed the causes of drifts in patients’ pathways. We performed an experiment in a hospital living lab to examine the effectiveness of the DIAG approach.

This article sets out to examine how digital twins have been used in a multi-national corporation, what technologies have been used, what benefits delivered and the significance of people and process related issues in achieving successful implementation. A qualitative, inductive research method is used, based on interviews provided by key personnel involved in three digital twin projects. The article concludes that digital twin projects are likely to involve incremental rather than disruptive change, and that successful implementation is usually underpinned by ensuring technology, people and process change factors are progressed in a balanced and integrated fashion. Building upon existing frameworks, three “properties” are identified as being of particular value in digital twin projects - workforce adaptability, technology manageability and process agility – and a related set of steps and actions is put forward as a template and point of reference for future digital twin implementations. The findings are a contribution to the developing theory around digital twins and digitalization in general, and are also of relevance to professionals embarking on DT projects.

Four discrete models using the exact spectral derivative discretization finite difference (ESDDFD) method are proposed for a chaotic five-dimensional, conformable fractional derivative financial system incorporating ethics and market confidence. Since the system considered was recently studied using the conformable Euler finite difference (CEFD) method and found to be hyperchaotic, and the CEFD method was recently shown to be valid only at fractional index , the source of the hyperchaos is in question. Through numerical experiments, illustration is presented that the hyperchaos previously detected is in part an artifact of the CEFD method as it is absent from the ESDDFD models.

In the context of the COVID-19 epidemic, and on the basis of the Theory of Dynamical Systems, we propose a simple model for the expansion of contagious diseases, with a particular focus on viral respiratory tracts. The infection develops through contacts between contagious and exposed people, with a rate proportional to contact duration and turnover, inversely proportional to the efficiency of protection measures, and balanced by the average immunological response. The obvious initial exponential increase is readily hindered by the size reduction of the exposed population. The system converges towards a stable attractor whose value is expressed in terms of the ratio C/D of contamination vs decay factors. Decreasing this ratio below a critical value leads to a tipping point beyond which the epidemic is over. By contrast, significant values of C/D may bring the system through a bifurcating hierarchy of stable cycles up to a chaotic behaviour.

Currently, the majority of industrial metal processing involves the use of taps for cutting. However, existing tap machines require relocation to specialized inspection stations and only assess the con-dition of the cutting edges for defects. They do not evaluate the quality of the cutting angles and the amount of removed material. Machine vision, a key component of smart manufacturing, is com-monly used for visual inspection. Taps are employed for processing various materials. Traditional tap replacement relies on the technician's accumulated empirical experience to determine the ser-vice life of the tap. Typically, inspecting tooth wear involves removing the tap and evaluating the degree of wear to determine if regrinding or replacement is necessary. Therefore, we propose the use of visual inspection of the tap's external features to determine whether replacement or regrinding is needed. We examined the bearing surface of the tap and utilized single images to identify the cutting angle, clearance angle, and cone angles. By inspecting the side of the tap, we calculated the wear of each cusp. We further investigated whether the cutting portion affected the length of the tool by measuring changes in tooth surface area and the amount of removed thread. This inspection process can facilitate the development of a tap life system, allowing for the estimation of the durability and wear of taps and nuts made of different materials. Statistical analysis can be employed to predict the lifespan of taps in production lines.

The phenomenon of dissipative self-organization is studied on the example of time-crystal networks. Particular attention was given to transient processes, attractor topologies, phase transitions, and asymptotic stability. New concepts were introduced, including topological phases, spinorial states, and bond flavors. Concepts such as ground states, chemical potentials, elastic forces, temperature, and statistical distributions were endowed with a new meaning associated with asymptotic stability. Phenomena usually attributed exclusively to quantum physics have been shown to occur in this essentially classical environment. They coexist with, and in some cases, such as charge quantization, are related to the phenomenon of time dilation. The approach was applied to model vacuum self-organization. We have shown that under the ac-tion of competing forces, such as gravity and antigravity, a cascade of phase transitions can transform an unorganized vacuum into phases in which interactions, fields and waves resemble electromagnetic, weak, and strong, and their elements can be used as building blocks for prototype particles. In addition, some interrelation field parameters and probabilities of particle transmutations were calculated, which are not predicted by the standard model. The results are consistent with the experiment. The presented material and methodology may be of interest for studying self-organization in different environments.