Recursiveness Research Articles

3-D Multi-Component Reverse Time Migration Method for Tunnel Seismic Data.

Migration imaging is a key step in tunnel seismic data processing. Due to the limitation of tunnel space, tunnel seismic data are small-quantity, multi-component, and have a small offset. Kirchhoff migration based on the ray theory is limited to the migration aperture and has low migration imaging accuracy. Kirchhoff migration can no longer meet the requirements of high-precision migration imaging. The reverse time migration (RTM) method is used to realize cross-correlation imaging by reverse-time recursion principle of the wave equation. The 3-D RTM method cannot only overcome the effect of small offset, but also realize multi-component data imaging, which is the most accurate migration method for tunnel seismic data. In this paper, we will study the 3-D RTM method for multi-component tunnel seismic data. Combined with the modeled data and the measured data, the imaging accuracy of the 3-D Kirchhoff migration and 3-D RTM is analyzed in detail. By comparing single-component and multi-component Kirchhoff migration and RTM profile, the advantages of the multi-component RTM method are summarized. Compared with the Kirchhoff migration method, the 3-D RTM method has the following advantages: (1) it can overcome the effect of small offset and expand the range of migration imaging; (2) multi-component data can be realized to improve the energy of anomalous interface; (3) it can make full use of multiple waves to realize migration imaging and improve the resolution of the anomalous interface. The modeled data and the measured data prove the advantages of the 3-D multi-component RTM method.

Co-design of mini games for learning computational thinking in an online environment.

Understanding the principles of computational thinking (CT), e.g., problem abstraction, decomposition, and recursion, is vital for computer science (CS) students. Unfortunately, these concepts can be difficult for novice students to understand. One way students can develop CT skills is to involve them in the design of an application to teach CT. This study focuses on co-designing mini games to support teaching and learning CT principles and concepts in an online environment. Online co-design (OCD) of mini games enhances students’ understanding of problem-solving through a rigorous process of designing contextual educational games to aid their own learning. Given the current COVID-19 pandemic, where face-to-face co-designing between researchers and stakeholders could be difficult, OCD is a suitable option. CS students in a Nigerian higher education institution were recruited to co-design mini games with researchers. Mixed research methods comprising qualitative and quantitative strategies were employed in this study. Findings show that the participants gained relevant knowledge, for example, how to (i) create game scenarios and game elements related to CT, (ii) connect contextual storyline to mini games, (iii) collaborate in a group to create contextual low-fidelity mini game prototypes, and (iv) peer review each other’s mini game concepts. In addition, students were motivated toward designing educational mini games in their future studies. This study also demonstrates how to conduct OCD with students, presents lesson learned, and provides recommendations based on the authors’ experience.

A Recursive Model of the Spread of COVID-19: Modelling Study.

BackgroundThe major medical and social challenge of the 21st century is COVID-19, caused by the novel coronavirus SARS-CoV-2. Critical issues include the rate at which the coronavirus spreads and the effect of quarantine measures and population vaccination on this rate. Knowledge of the laws of the spread of COVID-19 will enable assessment of the effectiveness and reasonableness of the quarantine measures used, as well as determination of the necessary level of vaccination needed to overcome this crisis.ObjectiveThis study aims to establish the laws of the spread of COVID-19 and to use them to develop a mathematical model to predict changes in the number of active cases over time, possible human losses, and the rate of recovery of patients, to make informed decisions about the number of necessary beds in hospitals, the introduction and type of quarantine measures, and the required threshold of vaccination of the population.MethodsThis study analyzed the onset of COVID-19 spread in countries such as China, Italy, Spain, the United States, the United Kingdom, Japan, France, and Germany based on publicly available statistical data. The change in the number of COVID-19 cases, deaths, and recovered persons over time was examined, considering the possible introduction of quarantine measures and isolation of infected people in these countries. Based on the data, the virus transmissibility and the average duration of the disease at different stages were evaluated, and a model based on the principle of recursion was developed. Its key features are the separation of active (nonisolated) infected persons into a distinct category and the prediction of their number based on the average duration of the disease in the inactive phase and the concentration of these persons in the population in the preceding days.ResultsSpecific values for SARS-CoV-2 transmissibility and COVID-19 duration were estimated for different countries. In China, the viral transmissibility was 3.12 before quarantine measures were implemented and 0.36 after these measures were lifted. For the other countries, the viral transmissibility was 2.28-2.76 initially, and it then decreased to 0.87-1.29 as a result of quarantine measures. Therefore, it can be expected that the spread of SARS-CoV-2 will be suppressed if 56%-64% of the total population becomes vaccinated or survives COVID-19.ConclusionsThe quarantine measures adopted in most countries are too weak compared to those previously used in China. Therefore, it is not expected that the spread of COVID-19 will stop and the disease will cease to exist naturally or owing to quarantine measures. Active vaccination of the population is needed to prevent the spread of COVID-19. Furthermore, the required specific percentage of vaccinated individuals depends on the magnitude of viral transmissibility, which can be evaluated using the proposed model and statistical data for the country of interest.

Environmental Education and Complexity

The purpose of this study is to identify and analyze meanings that the term complexity assumes in Brazilian theses and dissertations in the field of environmental education, especially when addressing socio-environmental issues. The studies were selected from the database Theses and Dissertations of EArte ( http://earte.net/ ), which is a repository for Brazilian theses and dissertations in the field of environmental education. Twenty theses and dissertations were selected to compose the documental corpus of this investigation. For the investigation, content analysis was used. Three a priori categories were defined to analyze the meanings of Complexity: (1) complex thinking: organized from Morin’s ideas of Dialogical Principle, Organizational Recursion Principle, Holographic Principle, and Scienza Nuova; (2) complex systems: organized from uncertainty, dynamics, and open systems groupings; and (3) complexification organized from the environmental complexity grouping. The complex thinking category was the most frequent in the analyses, identified in fifteen of the twenty theses and dissertations. In twelve of the twenty dissertations, the category of complex systems was identified, while in four of the twenty, the category complexification was referenced. These studies show a greater inclination towards the ideas of Edgar Morin and Enrique Leff.

Formalization of metatheory of the Lambda Calculus in constructive type theory using the Barendregt variable convention

AbstarctWe formalize in Constructive Type Theory the Lambda Calculus in its classical first-order syntax, employing only one sort of names for both bound and free variables, and with α-conversion based upon name swapping. As a fundamental part of the formalization, we introduce principles of induction and recursion on terms which provide a framework for reproducing the use of the Barendregt Variable Convention as in pen-and-paper proofs within the rigorous formal setting of a proof assistant. The principles in question are all formally derivable from the simple principle of structural induction/recursion on concrete terms. We work out applications to some fundamental meta-theoretical results, such as the Church–Rosser Theorem and Weak Normalization for the Simply Typed Lambda Calculus. The whole development has been machine checked using the system Agda.

Backstepping Nonsingular Terminal Sliding Mode Control for PMSM With Finite-Time Disturbance Observer

Aiming at the speed regulation problem of permanent magnet synchronous motor (PMSM) drives, a novel backstepping nonsingular terminal sliding mode control (BNTSMC) method with finite-time disturbance observer (FTDO) is proposed. In order to ensure excellent tracking and anti-disturbance performance, the backstepping nonsingular terminal sliding mode speed controller based on equivalent motor model and the recursive principle is designed for PMSM. The benefits of this approach are that the controller has asymptotic stability based on backstepping design and strong robustness for the matched disturbance based on sliding mode control. Then, to further improve the anti-disturbance performance, a finite-time disturbance observer is designed, and it is used to estimate the mismatched external disturbance in motor drive system. The stability of the system is also proved with Lyapunov criterion. Finally, the experimental results show that the proposed method has the advantages of fast convergence and strong robustness against parameter variations and external disturbance.

ORA FROM TEMPORALITY TO TEXTUALITY: A CASE OF GRAMMATICALIZATION

ORA FROM TEMPORALITY TO TEXTUALITY: A CASE OF GRAMMATICALIZATION

Research on Solving Mathematical Model of Itinerary Problem Based on Recursive Method

A special type of itinerary problem is introduced in this paper, and by using the principle of recursion, the mathematical model is established under two conditions. The results obtained by MATLAB software: if all passengers wait for the car to pick them up and then they are sent to the railway station directly, the time calculated by model (1) is about 3.3 hours; in the process of each car sending passengers to the railway station, at the same time other passengers who have not reached the station should walk to the station, and the time calculated by model (2) - (4) is about 2.85 hours, 2.718 hours and 2.602 hours respectively. In the latter case, the time is less than 3 hours, which means that the model is feasible. An extended discussion is carried out on the itinerary problem at last.

THE EXACT STRENGTH OF THE CLASS FORCING THEOREM

AbstractThe class forcing theorem, which asserts that every class forcing notion ${\mathbb {P}}$ admits a forcing relation $\Vdash _{\mathbb {P}}$ , that is, a relation satisfying the forcing relation recursion—it follows that statements true in the corresponding forcing extensions are forced and forced statements are true—is equivalent over Gödel–Bernays set theory $\text {GBC}$ to the principle of elementary transfinite recursion $\text {ETR}_{\text {Ord}}$ for class recursions of length $\text {Ord}$ . It is also equivalent to the existence of truth predicates for the infinitary languages $\mathcal {L}_{\text {Ord},\omega }(\in ,A)$ , allowing any class parameter A; to the existence of truth predicates for the language $\mathcal {L}_{\text {Ord},\text {Ord}}(\in ,A)$ ; to the existence of $\text {Ord}$ -iterated truth predicates for first-order set theory $\mathcal {L}_{\omega ,\omega }(\in ,A)$ ; to the assertion that every separative class partial order ${\mathbb {P}}$ has a set-complete class Boolean completion; to a class-join separation principle; and to the principle of determinacy for clopen class games of rank at most $\text {Ord}+1$ . Unlike set forcing, if every class forcing notion ${\mathbb {P}}$ has a forcing relation merely for atomic formulas, then every such ${\mathbb {P}}$ has a uniform forcing relation applicable simultaneously to all formulas. Our results situate the class forcing theorem in the rich hierarchy of theories between $\text {GBC}$ and Kelley–Morse set theory $\text {KM}$ .

‘A new normative architecture’ – risk and resilience as routines of un-governance

ABSTRACT Our contribution describes a reorientation in the intelligibility of governance practices authorised under international law. Observing the World Bank, we narrate new managerial attitudes and organisational routines that exhibit heightened ‘risk appetites’. Risk and complexity are no longer seen as limiting conditions on the institutional project, but as co-constitutive elements and constructive tools, including new sets of heuristics aimed at governing with and through contingency and unknowability. The practices that we observe are characterised by adaptive, iterative and recursive routines, flexibly attuned to immanent possibilities and aims of resilience. We situate these changes in a genealogy of governmentality, focusing on the relation to a ‘surplus of life’, or unruly elements of populations that persistently escape productive incorporation into the closure of institutional programmes. The World Bank’s turn to resilience as a particular rationality of reform signals an institutional attempt to enrol what has escaped prior efforts at determinate institutional intervention.

Biological Recursion and Digital Systems: Conceptual Tools for Analysing Man-Machine Interaction

The theory of numbers, the theory of computation and well-known biological and neurological studies on cognition and consciousness all indicate the concept of recursion as their common denominator. Mathematical recursion owes its meaning and properties to a dual relationship between its results, which always constitute a sequence, and the operator that generated them, which is instead invariant. This article proposes that this duality in recursion originates from the duality between the biological homeostatic equilibrium in living systems and the adaptive physico-chemical changes required to sustain such equilibria. Such duality gives order and meaning to the experiences of a living system. One of the many implications of this innovative perspective is that this duality can decouple computational results from our intuitive order relations, and that this can cause a rarefaction of the capacity of digital systems to convey communication and favour adaptation to the environment.

La complejidad del lenguaje en los procesos de facilitación de grupos

This review article is a derivative of the author’s doctoral thesis on facilitation and complex thinking. From the analysis and synthesis, it is concluded that although there are already approaches and methods of facilitation that address complexity, these have not been sufficiently disseminated and understood, so a Cartesian facilitation approach that simplifies complex reality still predominates. Reality is presented in its simple, complicated and complex dimensions and Cartesian facilitation is more applicable to simple situations but has difficulties in addressing the complexity that presents critical, rare, uncertain, ambiguous, discontinuous and blurred phenomena. As much as facilitation has the purpose of making things easier, it faces multiple complexities such as that of the brain, mind, intelligence, consciousness, group, communication, language, among other complexities. In this concert of complexities the present article addresses the complexity of language as part of the communicational processes in dialogue group facilitation. It is found that language complexity can be approached from the complex adaptive systems characteristic of the complexity sciences and complex thought with its principles of organization, dialogicity, recursion and hologram. As such, it is understood that language is an organized system that presents a set of tangible and intangible elements that are interrelated and interdependent and that present the property of self-organization and emergence, a non-linear dynamic far from equilibrium with the capacity for adaptation and evolution. This allows the expansion of consciousness to be generated from the resignification of initial ideas resulting from inter-subjective dialogue. In this sense, group facilitation can be enriched by understanding the complexity of language.

Higher Prolongations of Control Affine Systems: Absolute Stability and Generalized Recurrence

This manuscript deals with higher prolongations and higher prolongational limit sets of control affine systems. The higher prolongations extend the positive semiorbit and determine a great number of stability concepts, indexed by the ordinal numbers. The highest stability is named absolute stability and can be characterized by a continuous Lyapunov functional. It is proved that compact positively invariant uniform attractors and positive semiorbits of dispersive control systems are absolutely stable sets. The higher prolongational limit sets determine the generalized recurrence, which extends the recursive concepts of Poincaré recurrence and nonwandering points. The notion of chain prolongation is introduced in order to discuss the generalized recurrence. The main result shows that the chain prolongation is the largest extension of the positive semiorbit, and then the chain recurrence is the more general concept of recurrence.

Image encryption by using a specific adaptation of Lehmer’s algorithm

A congruential generator is an algorithm that yields a sequence of integers, it is defined by an arbitrary first term (seed) x 0, and by a simple mathematical recursion relation which containing three parameters (a, c, m) which must satisfy the kunth criterias. The aim of this work is to propose a crypto system based on a new adaptation of the linear congruential generator in this case, it must be able to produce an indistinguishable output of a perfect randomly and, must withstand of different attacks. Also, it must be able to pass the test of the following bit, that is to say that there is no polynomial time algorithm such that knowing the first L bits of the sequence S, we can deduce the (L + 1)th bit from S with a probability greater than 0.5. There are several techniques for the construction of such a generator, we envisaged to use a linear combination of these linear congruential generators which are adapted to the cryptography.

CATEGORY «LEGAL PROCESS» AS A DEVELOPMENT OF THE CONCEPT «LEGAL RELATIONSHIP» IN THE CONTEXT OF RECURSIVE PARADIGM IN THE LEGAL REGULATION

In this article authors consider the possibility of developing the concept of legal relationship in the context of the recursive paradigm in the legal regulation, which was the result of an attempt to synthesize the general theory of law and the theory of formal systems. Synthesis of theories was carried out on the basis of the analysis of the sphere of legal regulation using the concept of recursion. The result of this study was the category of legal process which is a consequence of the development of relationship concept in the modern general theory of law. It is suggested that use of the category of legal process will allow more fully and accurately describe the modern procedure of legal regulation. A number of concepts have been defined, the application of which within the framework of the legal process will contribute to the solution of tasks aimed at a qualitative increase in the volume and in the degree of accuracy of the legal regulation. The authors present for discussion the questions, the solution of which will contribute to the creation of theoretical basis for immersion of modern law in the virtual space.

A Recursive General Regression Neural Network (R-GRNN) Oracle for classification problems

This research introduces the Recursive General Regression Neural Network Oracle (R-GRNN Oracle) and is demonstrated on several binary classification datasets. The traditional GRNN Oracle classifier (Masters et al., 1998) combines the predictive powers of several machine learning classifiers by weighing the amount of error each classifier has on the final predictions. Each classifier is assigned a weight based on the percentage of errors it contributes to the final predictions as the classifiers evaluate the dataset. The proposed R-GRNN Oracle is an enhancement to the GRNN Oracle in which the proposed algorithm consists of an oracle within an oracle – where the inner oracle acts as a classifier with its own predictions and error contribution. By combining the inner oracle with other classifiers, the R-GRNN Oracle produces superior results. The classifiers considered in this study are: Support Vector Machine (SVM), Multilayer Perceptron (MLP), Probabilistic Neural Network (PNN), Gaussian Naïve Bayes (GNB), K-Nearest Neighbor (KNN), and Random Forest (RF). To demonstrate the effectiveness of the proposed approach, several datasets were used, with the primary one being the publicly available Spambase dataset. The predictions of SVM, MLP, KNN, and RF were used to create the first GRNN Oracle, which was then enhanced with the high performances of SVM and RF to create the second oracle, the R-GRNN Oracle. The combined recursive model was 93.24% accurate using 10-fold cross validation, higher than the 91.94% of the inner GRNN Oracle and the 91.29% achieved by RF, the highest performance by a stand-alone classifier. The R-GRNN Oracle was not only the most accurate, but it also had the highest AUC, sensitivity, specificity, precision, and F1-score (97.99%, 91.86%, 94.40%, 93.28%, and 92.57%, respectively). The research contribution of this paper is introducing the concept of recursion (a concept not fully explored in machine learning models and applications) and testing this structure's ability on further enhancing the performance of the traditional oracle. The recursive model has also been applied to several other datasets: The Human Resources, Bank Marketing, and Monoclonal Gammopathy of Undetermined Significance (MGUS) datasets. The results of these implementations are summarized in this paper.

A Formalized General Theory of Syntax with Bindings: Extended Version

We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying numbers of inputs, quotiented to alpha-equivalence and sorted according to a binding signature. The theory contains a rich collection of properties of the standard operators on terms, including substitution, swapping and freshness—namely, there are lemmas showing how each of the operators interacts with all the others and with the syntactic constructors. The theory also features induction and recursion principles and support for semantic interpretation, all tailored for smooth interaction with the bindings and the standard operators.

Preservation of choice principles under realizability

AbstractEspecially nice models of intuitionistic set theories are realizability models $V({\mathcal A})$, where $\mathcal A$ is an applicative structure or partial combinatory algebra. This paper is concerned with the preservation of various choice principles in $V({\mathcal A})$ if assumed in the underlying universe $V$, adopting Constructive Zermelo–Fraenkel as background theory for all of these investigations. Examples of choice principles are the axiom schemes of countable choice, dependent choice, relativized dependent choice and the presentation axiom. It is shown that any of these axioms holds in $V(\mathcal{A})$ for every applicative structure $\mathcal A$ if it holds in the background universe.1 It is also shown that a weak form of the countable axiom of choice, $\textbf{AC}^{\boldsymbol{\omega , \omega }}$, is rendered true in any $V(\mathcal{A})$ regardless of whether it holds in the background universe. The paper extends work by McCarty (1984, Realizability and Recursive Mathematics, PhD Thesis) and Rathjen (2006, Realizability for constructive Zermelo–Fraenkel set theory. In Logic Colloquium 03, pp. 282–314).

Completeness: When Enough is Enough

We investigate the notion of a complete enough metric space that, while classically vacuous, in a constructive setting allows for the generalisation of many theorems to a much wider class of spaces. In doing so, this notion also brings the known body of constructive results significantly closer to that of classical mathematics. Most prominently, we generalise the Kreisel-Lacome-Shoenfield Theorem/Tseytin's Theorem on the continuity of functions in recursive mathematics.

On the Parzen Kernel-Based Probability Density Function Learning Procedures Over Time-Varying Streaming Data With Applications to Pattern Classification.

In this paper, we propose a recursive variant of the Parzen kernel density estimator (KDE) to track changes of dynamic density over data streams in a nonstationary environment. In stationary environments, well-established traditional KDE techniques have nice asymptotic properties. Their existing extensions to deal with stream data are mostly based on various heuristic concepts (losing convergence properties). In this paper, we study recursive KDEs, called recursive concept drift tracking KDEs, and prove their weak (in probability) and strong (with probability one) convergence, resulting in perfect tracking properties as the sample size approaches infinity. In three theorems and subsequent examples, we show how to choose the bandwidth and learning rate of a recursive KDE in order to ensure weak and strong convergence. The simulation results illustrate the effectiveness of our algorithm both for density estimation and classification over time-varying stream data.