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This publication is an abstracted compilation of 15 investigations selected from other journals. The information includes purpose, rationale, research design and procedures, findings, interpretations, abstractor's comments, and references. This journal includes the following reports: (1) "A Constructivist Approach to Numeration in Primary School: Results of a Three Year Intervention with the Same Group of Children"; (2) "Identifying Fractions on Number Lines"; (3) "Teachers' Pedagogical Content Knowledge of Students' Problem Solving in Elementary Arithmetic"; (4) "Representation of Addition and Subtraction Word Problems"; (5) "Effect of Cognitive Entry Behavior, Mastery Level, and Information about Criterion on Third Graders' Mastery of Number Concepts"; (6) "The Effects of Computer-Assisted and Traditional Mastery Methods on Computation Accuracy and Attitudes"; (7) "An Investigation into the Use of Microcomputers to Teach Mathematical Problem-Solving Skills to 13 Year Olds"; (8) "Differences among Women Intending to Major in Quantitative Fields of Study"; (9) "Characteristics of Unskilled and Skilled Mental Calculators"; (10) "Intrinsic Orientation Profiles and Learning Mathematics in CAI Settings"; (11) "Putting the Student into the Word Problem: Microcomputer-Based Strategies that Personalize Math Instruction"; (12) "The Mathematics of Child Street Venders"; (13) "A Cognitive Approach to Meaningful Mathematics Instruction: Testing a Local Theory Using Decimal Numbers"; (14) "Teaching Children to Use Schematic Drawings to Solve Addition and Subtraction Word Problems"; and (15) "Effect of Assignment Projects on Students' Mathematical Activity." The titles and sources of mathematics education research studies reported in CIJE and RIE, April-June 1988, are listed. (YP)

Once the numerals are included, Boney and his colleagues hope to create a programming language using Cherokee script and numbers. In the remote Arctic almost 30 years ago, a group of Inuit middle school students and their teacher invented the Western Hemisphere's first new numeral system in more than a century. At first, students would convert their assigned math problems into Kaktovik numerals to do calculations, but middle school math classes in Kaktovik began teaching the numerals in equal measure with their Hindu-Arabic counterparts in 1997. [Extracted from the article]

The article focuses on learning to count like a computer, exploring the binary system's representation of numbers and its application in computing. Topics include the simplicity of the binary system compared to the decimal system, arithmetic operations using binary values, and methods for converting decimal numbers into binary.

Translating our theories of physics into an eight-dimensional number system might just give us a way to make sense of the laws of nature, says Michael Brooks [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to develop an algorithm to pretest an industrial portfolio on a new scale. Portfolios include complex and uncertain projects at the front-end phase. The study, therefore, proposes a procedure that helps decision-makers to handle various complex projects and defines a common scale applicable to various kinds of industrial projects. Design/methodology/approach: Decision-makers can employ the preference algorithm to reach a common understanding. To this end, the current paper posits the organization of criteria in various project sets. A sexagesimal scale is developed based on project complexity and its ability to achieve broad impact, both these factors being gauged on a five-point scale of user-friendly numberings. Findings: The proposed algorithm shows the equivalence of industrial projects in different fields. Also, the algorithm articulates the status in terms of uncertainty, complexity, risk, and value of projects. The connections between decision-makers and criteria operate on the basis of the foreseen complexity, risk, and value. It can be said that this study exemplifies and visualizes the portfolio and criteria relationship. Research limitations/implications: The procedure covers contingency exercises at the front-end phase of a portfolio and supports decisions. However, updated information can change support positions. Originality/value: The paper presents original scoring guidance for portfolio complexity on a new scale. The scaling and scoring are adjustable and calibrated using the proposed sexagesimal system. It presents an original classification of project risk and value. The main contribution is the presented algorithm which can be used to pretest industrial portfolios composed of projects that vary in both size and context. [ABSTRACT FROM AUTHOR]

Since the recent destruction of the Arecibo telescope in Puerto Rico, these are the world's only radio telescopes actively courting SETI researchers. After an initial transmission of a prime number to mark the broadcast as artificial, Jiang's message uses this alien alphabet to introduce our base-10 numeral system and basic mathematics. An international team of researchers, led by Jonathan H. Jiang of the nasa Jet Propulsion Laboratory, recently detailed a new missive intended for reaching out to extraterrestrial recipients. [Extracted from the article]

The article presents Single Option Correct Type questions for time trap-based examination.

In this paper, a three tier mathematical model describing the interactions between susceptible population, Covid-19 infected, diabetic population and Covid-19 infected, non diabetic population is proposed. Basic properties of such a dynamic model, namely, non negativity, boundedness of solutions, existence of disease-free and disease equilibria are studied and sufficient conditions are obtained. Basic reproduction number for the system is derived. Sufficient conditions on functionals and parameters of the system are obtained for the local as well as global stability of equilibria, thus, establishing the conditions for eventual prevalence of disease free or disease environment, as the case may be. The stability aspects are discussed in the context of basic reproduction number and vice versa. An important contribution of this article is that a novel technique is presented to estimate some key, influencing parameters of the system so that a pre-specified, assumed equilibrium state is approached eventually. This enables the society to prepare itself with the help of these key, influencing parameters so estimated. Several examples are provided to illustrate the results established and simulations are provided to visualize the examples. [ABSTRACT FROM AUTHOR]

This paper presents a novel framework for generating new chaotic signals for image encryption that is based on the finite precision of computers. First, we select a system from a number of chaotic systems. Next, we obtain a trajectory of this system. Then, another trajectory is obtained by perturbing the initial values of the same chaotic system. Finally, we calculate the evolution error of two trajectories to obtain a new chaotic signal. Our method is successfully applied to simulate three new chaotic signals for image encryption. A novel image cryptography algorithm based on new chaotic signals and true random numbers is developed. These circular diffusion and local versus global scrambling methods are designed. The results show that the proposed method is effective and exhibits a higher level of security than other sophisticated methods. [ABSTRACT FROM AUTHOR]

The article shares reflections about activities that offer opportunities for teachers to develop epistemic empathy. The base 7 and T-numeration activities are described which allow teachers to construct, communicate and critique knowledge about ideas related to number sense. It discusses the critique of knowledge experienced by teachers as a result of an investigation into an unfamiliar topic in mathematics and its implication for teacher education.

A study conducted by researchers at Monash University in Melbourne, Australia, explored the language and cognitive processes of Pitjantjatjara-English bilinguals when making comparisons of magnitude. Pitjantjatjara, an indigenous language of Australia, uses contextually driven comparators rather than dedicated comparative constructions. The study found that participants were less accurate when making comparisons of extent using Pitjantjatjara, suggesting that linguistic comparison strategies may influence comparison behavior. The research provides insights into the relationship between language and cognition in bilingual individuals. [Extracted from the article]

Super Grub2 Disk is a live CD that allows users to boot into virtually any operating system. It is a lightweight tool that cannot write to the system partition or MBR, but it can rescue booting of a number of systems. The latest version of Super Grub2 Disk supports various operating systems and file systems, and it offers a navigable text interface for easy use. It is available in multiple languages and is primarily used for recovering unbootable operating systems. However, it lacks the ability to repair corrupted or boot partitions. [Extracted from the article]

A patent application titled "Systems and Methods for Performing Progressive Mesh Compression" has been published by the US Patent and Trademark Office. The application, filed by Sherry Ignatchenko, describes techniques for compressing and decompressing computer-generated 3D models using progressive mesh compression. The methods involve encoding initial meshes into an intermediate symbol stream and applying operators to subsequent meshes to create a progressive mesh. The application also includes techniques for compressing skinned meshes and using algebraic surface prediction. The patent application provides detailed descriptions and claims for the computer-implemented methods and systems. The assignee for this patent application is Six Impossible Things Before Breakfast Limited. [Extracted from the article]

In this study, we have explored the effect of time-varying parameters in a forced Liénard system. The system exhibits extreme events that manifest occasional large deviations from the bounded motion. In the absence of time-varying parameters, the system shows either a chaotic or periodic state. However, with the influence of parametric perturbation, the system elucidates rare large amplitude dynamics that appear at irregular time intervals. The emergence of extreme events and their transitions are characterized using various dynamical and statistical measures. The parametric perturbation is also applied to different parameters in the system, and their relevant dynamics are evaluated. We extended our study into a network of Liénard systems that exemplify the impact of time-varying parameters in the emergence of extreme events in the oscillatory network. • The advent of extreme events in the Liénard systems with time-varying parameters. • Formation of unexpected events when system parameters are far from transition points. • Extreme events are commonly identified regardless of the number of systems involved. [ABSTRACT FROM AUTHOR]

• Obtaining the optimal discounting weights of BPAs is proposed using the BWM method by considering consistency ratio. • A new way to determine the best and worst BPA is presented based on the distance of evidences. • Partially decrease the computing cost of fusion system by decreasing the number of comparisons using the BWM method. • More reasonable results in decision making are obtained by the proposed methodology. Dempster-Shafer evidence theory (DST) could show its advantages during the process of data fusion. In DST, the determination of the weight of evidence in conflict management is attracting growing interest. Limited work has been done based on the discount model, the consistency of the weight is still virgin and may become a fascinating question. In this paper, a novel strategy about how to ascertain the optimal weight of basic probability assignment (BPA) using BWM method is proposed, which provides a promising way to ascertain the best BPA and the worst BPA. Then, a consistency ratio is utilized for BPA, which has the ability of inspecting the reliability of the comparisons and producing more rational results. Some numerical experiments and application examples are used to illustrate the effectiveness and practicability of the proposed methodology. [ABSTRACT FROM AUTHOR]

Copyright of Changement is the property of Solutions by HANDELSBLATT MEDIA GROUP GmbH and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

• For a linear periodic coupled system with arbitrary number of subsystems, a new method for constructing a Lyapunov function is proposed. Contrast to the classical version of the Lyapunov vector function method the stability property of independent subsystems is not assumed a priori. The proposed approach makes it possible to establish new conditions for the asymptotic stability of a linear large-scale system. This article proposes an approach to construct a Lyapunov function for a linear large-scale periodic system. In this case, in contrast to various variants of small-gain stability conditions for large-scale systems, the presence of the asymptotic stability property of independent subsystems is not assumed. To analyze the asymptotic stability of a large-scale system, the direct Lyapunov method is used in combination with the discretization method and identities of the commutator calculus. The main results are illustrated by means of examples. [ABSTRACT FROM AUTHOR]

Animals, including cats, chimpanzees, dogs, cows, crows, fish, and chickens, have the ability to understand patterns and quantities, which are fundamental math concepts. A study conducted by a university professor in Padua, Italy compared the abilities of his students and angelfish to identify patterns with a large quantity of dots. The angelfish performed nearly as accurately as humans in the same test. These studies are conducted to better understand evolution and determine if math is instinctive rather than a learned skill. Additionally, crickets can accurately calculate the temperature based on the frequency of their chirps, and dogs like Elvis can calculate angles correctly without fail. Babies and animals have similar processes in assessing quantities, as observed in studies with monkeys, salamanders, dogs, cats, and human babies. The results consistently show that confusion arises when the quantity exceeds two. [Extracted from the article]

In this article, we are interested in the problem of synthesizing a partial observation supervisor for a discrete-event system such that it enforces a desired property. We introduce a compact and uniform approach to the problem of synthesizing state-based property-enforcing supervisors. A state-based property is a property that only depends on the current estimate of the past behavior of the system and does not depend on its future behavior. Previous work has introduced a uniform methodology to solve this problem through the construction of a finite structure called the all enforcement structure (AES), which captures a game between the supervisor and the environment. Although the AES is a powerful structure that includes all possible property-enforcing supervisors, its construction is computationally challenging since the number of states grows exponentially in the number of states and the number of events of the system. Our contribution is the definition of a compact AES that is equivalent to but computationally more efficient than the original AES. Specifically, the compact AES enjoys the same properties as the original AES with respect to synthesizing maximally permissive supervisors under the assumption of incomparable sets of controllable and observable events. We also provide experimental results to show the benefits of the compact AES over the original AES. [ABSTRACT FROM AUTHOR]

There, Gerbert met the Pope and many others who would change his life - the most important being the Holy Roman Emperor Otto the Great (912-973), ruler of Germany and much of Italy. Gerbert of Aurillac also learned about politics and diplomacy in Andalusia. While Gerbert of Aurillac's personal history was misrepresented in this process, he and many other likeminded scholars reinvigorated European scholarship with Greek and Arabic texts and new knowledge of mathematics and astronomy. FEATURES In the year 999 CE, it was rumored that Pope Sylvester II kept a mechanical head in a box, a brass creation that came from the Moors in Islamic Spain. [Extracted from the article]

In networked control systems, impairments of the communication channel can be disruptive to stability and performance. In this article, we consider the problem of scheduling the access to limited communication resources for a number of decoupled systems subject to state and input constraints, whose loops need to be closed over the network. The schedule must be designed to robustly preserve the invariance property of each system, which, in turn, guarantees constraint satisfaction. To that end, we first focus on systematic offline scheduling design to preserve robust invariance and afterward on online scheduling design with the aim of improving performance and compensating for packet losses while guaranteeing recursive schedulability. [ABSTRACT FROM AUTHOR]

A study conducted by researchers at Huanghe Jiaotong University in Henan, China, focused on the development of an intelligent real-time classification and recognition system for food packaging images. The researchers introduced a recurrent neural network algorithm to meet the needs of edge computing in the Internet of Things. They used a memristor as the research object to construct the mapping layer of a parallel array reserve pool neural network. The system achieved a high classification accuracy of 98.59% for the food packaging data set. The research concluded that the system reduces the number of traditional neural network layers, lowers training costs, and enables high-precision real-time online recognition of time series signals. [Extracted from the article]

REGULARS AT A GLANCEEuroLinux is designed for enterprise environments and incorporates large amounts of RHEL code, making it compatible with its parent OS and other distros like Oracle Linux. Version 8.10 was released on 27th May, preceded by version 9.4 on 13th May. The eccentric numbering system aside, version 8.10 (code name Bucharest) includes a number of new modules, such as MariaDB, Nginx and PostgreSQL. Critical packages such as GCC have also been upgraded. You can discover more at https://euro-linux.com.PHOTO (COLOR): EuroLinux is compatible with RHEL and derivatives. [Extracted from the article]

This paper solves the group consensus problem of incremental quadratic constraints nonlinear multi-agent systems with semi-Markov switching parameters via a quantity limited controller. The quantity limited controller is designed according to the stationary probability distribution of the system modes, and the number of controllers can be selected from 1 to the number of system modes. Therefore, the controller can be applied in cases where there is a mismatch between the number of system modes and the number of controllers. Next, the more general incremental quadratic constraint is used to handle the nonlinear terms. Finally, in the simulation section, the method of adding topology links is used to implement external equitable partitions of arbitrary topologies, and the validity of the proposed method is verified by a spring damping system. [ABSTRACT FROM AUTHOR]

Copyright of AutomotiveIT is the property of Media-Manufaktur GmbH and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The G-Skyline query aims to return the best groups that are not g-dominated by any other group of equal size; this approach plays an important role in many fields, such as multiobjective decision-making. The top- k G-Skyline query has important implications since the output size of the G-Skyline query is often too large to make decisions. Due to the massive number of candidate groups and the high index construction consumption, the existing top- k G-Skyline algorithms cannot handle large-scale databases well. In this paper, an efficient algorithm is proposed called the TGPE (T op- k G -Skyline algorithm based on P resorting and E numeration) to rapidly compute the top- k G-Skyline groups for large-scale databases. TGPE proposes an efficient scanning method based on a presorted table to obtain tuples making up G-Skyline groups and their dominant relationships. TGPE does not need to repeatedly reconstruct the index for different skyline criteria. Three computational lemmas are presented based on sorting information and monotonicity, and they are utilized to reduce the number of candidate groups to obtain results rapidly. Finally, extensive experiments on synthetic and real datasets verify that TGPE has significant performance advantages over those of the existing algorithms. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to show the applicability of a discrete Hodge operator in the context of the De Rham cohomology to bicomplex-valued electromagnetic wave propagation problems. It was applied in the finite element method (FEM) to get a higher accuracy through conformal discretization. Therewith, merely the primal mesh is needed to discretize the full system of Maxwell equations. Design/methodology/approach: At the beginning, the theoretical background is presented. The bicomplex number system is used as a geometrical algebra to describe three-dimensional electromagnetic problems. Because we treat rotational field problems, Whitney edge elements are chosen in the FEM to realize a conformal discretization. Next, numerical simulations regarding practical wave propagation problems are performed and compared with the common FEM approach using the Helmholtz equation. Findings: Different field problems of three-dimensional electromagnetic wave propagation are treated to present the merits and shortcomings of the method, which calculates the electric and magnetic field at the same spatial location on a primal mesh. A significant improvement in accuracy is achieved, whereas fewer essential boundary conditions are necessary. Furthermore, no numerical dispersion is observed. Originality/value: A novel Hodge operator, which acts on bicomplex-valued cotangential spaces, is constructed and discretized as an edge-based finite element matrix. The interpretation of the proposed geometrical algebra in the language of the De Rham cohomology leads to a more comprehensive viewpoint than the classical treatment in FEM. The presented paper may motivate researchers to interpret the form of number system as a degree of freedom when modeling physical effects. Several relationships between physical quantities might be inherently implemented in such an algebra. [ABSTRACT FROM AUTHOR]

Formulations of an extra-degree-of-freedom (DOF) free extended isogeometric analysis (IGA) are presented in this study. The idea is achieved by reconstruction of the coefficients through a mesh-free-based local approximation, based on the framework of a generalized finite-element method. The enrichment functions are embedded in the mesh-free basis implicitly, resulting in an identical number of DOFs. Moreover, the system condition number is of the same level between the enriched IGA and non-enriched version. The approach to handling the blending issues is discussed. Numerical examples with a solution containing sharp features/singularities are designed and studied in terms of accuracy and convergence. [ABSTRACT FROM AUTHOR]

Multiagent distributed optimal coordination (DOC) involves the motion conflicts of a large numbers of physical systems, which lead to significant safety challenges in terms of collision avoidance. This article studies the problem of secure DOC for multiple uncertain Euler–Lagrangian (EL) systems. The objective is to steer each EL agent to achieve the optimization task while avoiding collisions with other agents. The main challenge focuses on the co-design of optimal coordination strategy and collision avoidance mechanism. The safety barrier certificates in the closed form of path integrals are constructed, which generate provably collisions-free behaviors. With convex optimization and adaptive nonlinear control, a fully distributed protocol is proposed. Based on Lyapunov method and boundedness analysis for the barrier functions, it is proved that the protocol simultaneously guarantees the global convergence and collision avoidance of the EL systems in the presence of parametric uncertainties. [ABSTRACT FROM AUTHOR]

The $\mathcal {H}_2$ norm of an exponentially stable system described by delay differential algebraic equations (DDAEs) might be infinite due to the existence of hidden feedthrough terms and, as shown in this article, it might become infinite as a result of infinitesimal changes to the delay parameters. We introduce the notion of strong $\mathcal {H}_2$ norm of semi-explicit DDAEs, a robustified measure that considers delay perturbations, and we analyze its properties. We derive necessary and sufficient finiteness criteria for the strong $\mathcal {H}_2$ norm in terms of a finite number of equalities involving multidimensional powers of a finite set of matrices. As the main contribution, we present a strengthened, sufficient, condition for finiteness of the strong $\mathcal {H}_2$ norm, along with an algorithm for checking it, which has significantly better scalability properties in terms of both the system dimension and the number of delays. We show that the satisfaction of the novel condition is equivalent to the existence of a simultaneous block triangularization of the matrices of the delay difference equation associated with the DDAE. The latter is instrumental to a novel regularization procedure that allows us to transform the DDAE to a neutral-type system with the same transfer matrix, without any need for differentiation of inputs or outputs. This transformation enables computing of the strong $\mathcal {H}_2$ norm using Lyapunov matrices. Finally, we show by a counterexample that the strengthened condition is, in general, not necessary, inducing open problems, but we also list several classes of DDAEs for which it is necessary and sufficient. [ABSTRACT FROM AUTHOR]

With fast developments in communication technologies, a large number of practical systems adopt the networked control structure. For this structure, the fading problem is an emerging issue among other network problems. It has not been extensively investigated how to guarantee superior control performance in the presence of unknown fading channels. This article presents a learning strategy for gradually improving the tracking performance. To this end, an iterative estimation mechanism is first introduced to provide necessary statistical information such that the biased signals after transmission can be corrected before being utilized. Then, learning control algorithms incorporating with a decreasing step-size sequence are designed for both output and input fading cases. The convergence in both mean-square and almost-sure senses of the proposed schemes is strictly proved under mild conditions. Illustrative simulations verify the effectiveness of the entire learning framework. [ABSTRACT FROM AUTHOR]

Numeral recognition plays a crucial role in creating automated systems such as posting address sorting and license plate recognition. Nowadays, numeral recognition systems which have the capability of recognising multiple languages are highly beneficial due to growing international correspondence and transactions, especially in multilingual countries where several languages are used simultaneously. Therefore, handwritten numeral recognition is more challenging than printed numeral recognition due to having different and complex handwriting styles. Hence, developing a multilingual handwritten system is considered as an important and debatable issue. We address this issue by proposing a language-independent model based on a robust CNN. Our proposed model is composed of language recognition and digit recognition, which aims to handle the recognition of multi-script images. We used transfer-learning in the proposed system to enhance the image quality and consequently the recognition performance. Extensive experiments were conducted to verify the effectiveness of both language and digit recognition procedures. The proposed system was tested with six different languages. The results showed an average accuracy of up to 99.8% for recognising various languages and the associated digits. The robustness and design procedure of the proposed model created a cost-effective extension for recognition of handwritten numerals in other languages. [ABSTRACT FROM AUTHOR]

Copyright of Der Handel is the property of dfv Mediengruppe and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, a fractional-order model for HIV with drug-resistance and CTL immune response is established. Two cases (subsystem with drug-sensitive and subsystem with drug-resistant) are considered. For both subsystems: firstly, the existence and uniqueness of the positive solution is proved; secondly, the sufficient conditions for the stability of the disease-free equilibrium are obtained; finally, some numerical simulations are performed to verify the theoretical results. After that, the main system is analyzed in a similar way. Calculation indicates that the basic reproduction number of the main system is the maximum value of the basic reproduction numbers of the corresponding subsystems. In addition, through numerical simulation, we know that the drug efficacy plays an important role in the treatment of HIV. • A fractional-order model for HIV with drug-resistance and CTL immune response is constructed. • The basic reproduction number of the main model is the maximum value of the corresponding two subsystems. • Through numerical simulations, the relationship of basic reproduction number with respect to fractional order was found. [ABSTRACT FROM AUTHOR]

A new fast multipole boundary element method (FM-BEM) is proposed to analyze 2-D elastostatic problems by using linear and three-node quadratic elements. The use of higher-order elements in BEM analysis results in more complex forms of the integrands, in which the direct Gaussian quadrature is difficult to calculate the singular and nearly singular integrals. Herein, the complex notation is first introduced to simplify all integral formulations (including the near-field integrals) in FM-BEM for 2-D elasticity. In direct evaluation of the near-field integrals, the nearly singular integrals on linear elements are calculated by the analytic scheme, and those on quadratic elements are evaluated by a robust semi-analytical algorithm. Numerical examples show that the present method possesses higher accuracy than the FM-BEM with constant elements. The computed efficiency of FM-BEM with higher order elements for analyzing large scale problems is still O (N), where N is the number of linear system of equations. In particular, the proposed FM-BEM is available for solving thin structures. [ABSTRACT FROM AUTHOR]

The article explores how to bridge the gap between a written curriculum and the activities in a mathematics lessons. Topics discussed include suggestion to give children images of the number system involving number lines, number squares and Gattegno tens charts; suggestion to talks about the hard work and persistence needed to achieve success; and needs to encourage children to acquire mathematical habits.

• Present SN P systems with autapses as a new variant of SN P systems by introducing autapses. • Prove SN P systems with autapses are Turing universal as natural number generators. • Construct an SN P systems with autapses with 53 neurons for computing functions. • A simulator is developed and used to check the correctness of universal SNP-AU systems. Inspired by the structure and communication method of neural systems, a parallel computing model, spiking neural P systems (SN P systems, for short), was proposed in 2006. A new class of SN P systems, SN P systems with autapses (SNP-AU systems), is presented in this work. Autapses are a special kind of synapses, connecting the axon of a neuron onto itself. We prove that SNP-AU systems can generate Turing-computable numbers, through the simulation of the modules of universal register machines. This result improves significantly the results given by classical SN P systems in terms of the number of neurons and rules, while preserving simplicity and power to a reasonable extent. Moreover, we construct an SNP-AU system using 53 neurons, proving its universality for computing functions. Finally, going beyond the design of the building blocks of register machines, a whole universal machine is provided. Thus, a simulator is developed and used to check the correctness of two universal SNP-AU systems proposed in this paper, complementing the theoretical proof with the experimental validation of our systems with respect to the reference example appearing in the foundational paper of small register machines. [ABSTRACT FROM AUTHOR]

The Les Pradelles hyena bone is potentially the earliest-known example of this type of mark making, says d'Errico. BONES OF CONTENTION But QUANTA researcher Núñez, along with some researchers who are not involved in the project, cautions that ancient artifacts such as the Les Pradelles bone are challenging to interpret. FEATURES Some 60,000 years ago, in what is now western France, a Neandertal picked up a chunk of hyena femur and a stone tool and began to work. In fact, although d'Errico and his colleagues have spent innumerable hours analyzing the bone, he says it's possible that the Neandertal who chipped away at that hyena femur some 60,000 years ago spent very little time using it before tossing the bone aside. [Extracted from the article]

A number of physical systems allow a complex-valued representation. This article extends the theory of sliding modes to a class of nonlinear systems described by complex-valued variables. Hence, states, parameters, control actions, and sliding manifolds belong, in general, to the complex field. In this article, it is also shown that the proposed design in the complex-valued framework provides shorter reaching times to the sliding manifold than the standard sliding-mode design at equal initial condition and control effort. Different implementation approaches are also evaluated, and numerical examples illustrate the proposal. [ABSTRACT FROM AUTHOR]

This article analyzes the sliding behavior of a Filippov-type epidemiological system in three dimensions. Initially, a smooth model is mentioned, which involves the transmission of a disease with variables being the average number of susceptible, infected and recovered individuals. The model is analyzed at steady state and then, after locating a switching boundary in the number of infected people, and considering the application of a treatment to a certain number of infected people, a piecewise smooth model is proposed and analyzed in sliding mode. In the steady state, a local stability analysis of the equilibrium points is carried out based on the basic number of reproduction and then, in the sliding mode, the behavior of the number of infected individuals is analyzed from the commutation threshold, determining the existence of pseudo-equilibria, tangent folds, limit equilibria and singular points in the slide zone. The variation of the basic reproduction number of the system leads to a discontinuity-induced bifurcation in the sliding model. The results show that the application of a control is more efficient when the first infected are detected, compared to when there is already a significant number of infections. [ABSTRACT FROM AUTHOR]

The novel propagation system submist, which applies water to the bases of cuttings rather than overhead, is a promising alternative. We developed and tested a commercial-scale submist system to make this propagation system more accessible to commercial propagators. Five species, including blue star flower (Amsonia tabernaemontana), faassen nepeta (Nepeta ·faassenii 'Six Hills Giant'), panicle hydrangea (Hydrangea paniculata 'Grandiflora'), sweetgale (Myrica gale), and sweetfern (Comptonia peregrina), were propagated from cuttings in commercial-scale submist and overhead mist systems. Blue star flower and faassen nepeta cuttings had greater root length, root rating, and root number with the submist system. Panicle hydrangea cuttings hadmore roots in submist, but longer roots in overhead mist. There were no differences in rooting between the systems for sweetgale and sweetfern cuttings. The comparable or superior rooting of these five species in a submist system compared with traditional overhead mist systems is evidence that submist is a viable alternative propagation system. Water use in submist systems was 98% less than that for overhead mist systems. [ABSTRACT FROM AUTHOR]

Muhammad ibn Mūsā al-Khwārizmī, a Persian scientist and polymath who lived during the Islamic Golden Age, is credited with inventing the concept of algorithms over 1,000 years ago. The word "algorithm" is derived from the Latinized version of his name, "algorithmi." Al-Khwārizmī made significant contributions to mathematics, geography, astronomy, and trigonometry, and is considered the "father of algebra." His most important work, "Al-Jabr," was the first definitive book on algebra and became the basis for algebra textbooks in European universities until the 16th century. Al-Khwārizmī's mathematical writings introduced the Hindu-Arabic numerals to Western mathematicians, which are the basis for modern computing technology. His systematic approach to solving mathematical problems laid the foundation for the concept of algorithms. [Extracted from the article]