Recursiveness Research Articles

Log Topological Recursion Through the Prism of x-y Swap

Abstract We introduce a new concept of logarithmic topological recursion that provides a patch to topological recursion in the presence of logarithmic singularities and prove that this new definition satisfies the universal $x-y$ swap relation. This result provides a vast generalization and a proof of a very recent conjecture of Hock. It also uniformly explains (and conceptually rectifies) an approach to the formulas for the $n$-point functions proposed by Hock.

Topological recursion on transalgebraic spectral curves and Atlantes Hurwitz numbers

Given a spectral curve with exponential singularities (which we call a “transalgebraic spectral curve”), we extend the definition of topological recursion to include contributions from the exponential singularities in a way that is compatible with limits of sequences of spectral curves. This allows us to prove the topological recursion/quantum curve correspondence for a large class of transalgebraic spectral curves. As an application, we find that Atlantes Hurwitz numbers, which were previously thought to fall outside the scope of topological recursion, satisfy (our extended version of) topological recursion, and we construct the corresponding quantum curve directly from topological recursion.

The Concept of Recursion in Cognitive Studies. Part I: From Mathematics to Cognition

The Concept of Recursion in Cognitive Studies. Part I: From Mathematics to Cognition

Numerical Study of Fluid Flow in a Gyroid-Shaped Heat Transfer Element

This paper deals with the design of porous geometry of a heat transfer element. The proposed geometry combines a gyroid triply periodic minimal surface with the recursive principle of geometric body creation. The designed geometry is based on an attempt to increase the heat transfer surface while eliminating negative impacts on the fluid characteristics in the form of pressure loss or increase of the friction coefficient. The proposed geometry of the heat transfer element was compared with a pair of geometries based on the basic gyroid shape but with different channel size parameters. A numerical simulation was performed in Ansys Fluent 2020 R1 using the SST k-omega turbulence model for flow velocities in the range of 0.01 m.s−1 to 0.5 m.s−1, which covered a wide range of the Reynolds number and thus also flow forms in terms of the turbulence intensity. The presented results clearly show lower values of pressure loss and friction coefficient of the proposed geometry compared to the evaluated porous structures. Also, at the same time, they describe the factors positively influencing the mixing process of the liquid in the proposed element, which leads to an increase in the efficiency of the heat transfer process.

Enhancing Symbolic Manipulation through Pairing Primitive Recursive String Functions and Interplay with Generalized Pairing PRSF

In earlier studies, the notion of generalized primitive recursive string functions has been presented, and their connections with abstract paring-based primitive recursive string functions have been investigated. Our study is centered around establishing a fundamental theorem that states a connection between these two distinct sorts of functions. The theorem specifically establishes that the universal definition of every generalized pairing primitive recursive string function is contingent upon its correspondence with a conventional(abstract) pairing primitive recursive string function. This article introduces innovative concept of Pairing Primitive Recursive String Functions (P-PRSF) for manipulating and interacting with word pairs. Based on the principles of primitive recursion and pairing functions, P-PRSF enables the extraction, transformation, and combination of word components. The proposed theorems validate the effectiveness of P-PRSF in capturing relationships within word pairs. Moreover, the interplay between P-PRSF and Generalized Pairing PRSF (GP-PRSF) extends the concept to involve more intricate interactions.

A Numerical Method for Solving Evolutionary Statistical Characteristics of Dynamic Responses of the Vehicle–Bridge Coupled System Based on the Recursion Principle

A Numerical Method for Solving Evolutionary Statistical Characteristics of Dynamic Responses of the Vehicle–Bridge Coupled System Based on the Recursion Principle

Experimental Study of a Room-Temperature Shimming Technology Employing Genetic Algorithm for NMR/MRI Superconducting Magnets

We present a recently developed shimming method that uses a system of room-temperature (RT) orthogonal shimming coils to improve the spatial field homogeneity of high-resolution nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) superconducting magnets. Conventional RT shimming methods require recursive routines of field mapping and RT shim coil current adjustments, which lead to a less effective and time-consuming process. In this paper, we introduce a new RT shimming method that utilizes a process of gradual and automatic search to find an optimal operating point with a genetic algorithm (GA), a type of optimization technique. The proposed algorithm is capable of determining the optimal set of currents for a system of shimming coils to create the best spatial field homogeneity by minimizing the NMR spectral linewidth. We used a commercial 600-MHz NMR magnet with a full NMR spectral linewidth at half maximum (FWHM) of 2.2 ppm, as determined by an NMR test sample contained in a cylindrical glass tube with a diameter of 5 mm to demonstrate that the shimming method can improve the FWHM to 0.15 ppm. The results demonstrate the strong potential of the proposed RT shimming methodology for the auto-shimming process of NMR/MRI applications.

Rensets and Renaming-Based Recursion for Syntax with Bindings Extended Version

We introduce renaming-enriched sets (rensets for short), which are algebraic structures axiomatizing fundamental properties of renaming (also known as variable-for-variable substitution) on syntax with bindings. Rensets compare favorably in some respects with the well-known foundation based on nominal sets. In particular, renaming is a more fundamental operator than the nominal swapping operator and enjoys a simpler, equationally expressed relationship with the variable-freshness predicate. Together with some natural axioms matching properties of the syntactic constructors, rensets yield a truly minimalistic characterization of lambda -calculus terms as an abstract datatype—one involving an infinite set of unconditional equations, referring only to the most fundamental term operators: the constructors and renaming. This characterization yields a recursion principle, which (similarly to the case of nominal sets) can be improved by incorporating Barendregt’s variable convention. When interpreting syntax in semantic domains, our renaming-based recursor is easier to deploy than the nominal recursor. Our results have been validated with the proof assistant Isabelle/HOL.

Enfoque lingüístico a la escritura creativa: un paseo por los lugares donde se manifiesta la creatividad

This article describes the phenomenon of creativity through an approach that focuses on linguistic aspects, beyond the narrative level of linguistic-literary description, based on the main theories of Linguistics. The concept of linguistic creativity, a phenomenon that only manifests itself in human language, is little explored and known in Languages and Literature, although it is extremely productive for writing practices, inside and outside the classroom. In the first part of the article, the concepts of writing, creative writing, creativity and linguistic creativity are discussed; in the second one, the relations between linguistic theories and creativity are discussed based on the concepts of phrase, paradigm, recursion, change, variation and grammaticalization; in the third part, we bring some points from the works of Guimarães Rosa. In the final considerations, we emphasize the expansion of the sense of “creativity”, in order to encompass all textual productions, as a means of making these productions more expressive. This work adopted a bibliographic review as a research methodology.

Sustainable energy policies from a complexity perspective.

The energy policies of the countries have become a key aspect of development. They must be formulated to guarantee economic and social development, state security and compliance with the objectives of sustainable development. In this framework, generation technologies must be considered not only in terms of available natural resources but also in terms of possible contingency scenarios. The purpose of this article is to prioritize technologies by applying a fuzzy inference model and uncertainty model and to address the principles of complex thinking to a case study. The methodology considers the integral vision of the dimensions under the systemic, feedback, autonomy/dependence, holographic and recursive principles, the assignment of weights for the dimension of sustainable development and, finally, the formulation of contingent scenarios. These scenarios consider: exhaustion of a primary source and change of technology with negative or positive impact. As a result, priority is given to the development of wind technology among renewable sources, followed by hydropower and geothermal. In the field of conventional energy, natural gas remains in the first place, since it also reinforces the security and fairness of the system. It is concluded that the process of formulating energy policies based on economic variables and the incorporation of sustainability, in terms of restrictions and linearity in the study models. This must be complemented with the adaptation of the legal and institutional framework that allows the fulfillment of the objectives that are expected to be achieved. Finally, it is necessary to keep constantly updated on changes and improvements in technology, which can modify the variables under study, in order to adapt strategies to new conditions.

The Value of Unity

The Value of Unity

Recursive Identification of Time-Varying Hammerstein Systems With Matrix Forgetting

The real-time estimation of the time-varying Hammerstein system by using a noniterative learning schema is considered and extended to incorporate a matrix forgetting factor. The estimation is cast in a Variational-Bayes framework to best emulate the original posterior distribution of the parameters within the set of distributions with feasible moments. The recursive concept we propose approximates the exact posterior comprising undistorted information about the estimated parameters. In many practical settings, the incomplete model of parameter variations is compensated by forgetting of obsolete information. As a rule, the forgetting operation is initiated by the inclusion of an appropriate prediction alternative into the time update. It is shown that the careful formulation of the prediction alternative, which relies on Bayesian conditioning, results in partial forgetting. The paper inspects two options with respect to the order of the conditioning in the posterior, which proves vital in the successful localization of the source of inconsistency in the data-generating process. The geometric mean of the discussed alternatives then modifies recursive learning through the matrix forgetting factor. We adopt the decision-making approach to revisit the posterior uncertainty by dynamically allocating the probability to each of the prediction alternatives to be combined.

Classical consequences of constructive systems.

This is a survey of formal axiomatic systems for the three main varieties of constructive analysis, in a common language and with intuitionistic logic, which are as nearly as possible compatible with classical analysis and with one another. Classically sound consequences of principles of intuitionistic mathematics are emphasized. Compatibility with classical analysis is of two kinds. On the one hand, Bishop's constructive mathematics and a very substantial part of intuitionistic analysis are classically correct, sharing with constructive recursive mathematics a neutral subsystem adequate for recursive function theory and elementary real analysis. On the otherhand, each constructive system considered here is separately consistent with the negative interpretation of each of its classically sound subsystems, establishing internal compatibility with the classical context it is intended to refine. A possibly new criterion for the transposability of unique existential quantifiers and a recent theorem of Vafeiadou on the internal compatibility of classical and intuitionistic analysis are included. This article is part of the theme issue 'Modern perspectives in Proof Theory'.

Calibration of Inverted Asphalt Pavement Rut Prediction Model, Based on Full-Scale Accelerated Pavement Testing.

This study investigates the establishment and calibration method of the rut depth (RD) prediction model of inverted asphalt pavements (IAPs), based on full-scale accelerated pavement testing (APT), which facilitates the accurate and reliable design or maintenance of IAPs. A power function is adopted for the prediction model construction of the rut progression before the failure stage, based on the typical permanent deformation progression curve of flexible pavements. The APT loading history is divided into units, according to the difference in physical conditions, providing the basis for a cumulative RD analysis and model calibration. The nonlinear incremental recursive (IR) principle is applied in the RD analysis to consider the influence of the nonlinear material property, performance deterioration, and loading history on the RD development. Further, the rut shift function relating prediction models obtained from laboratory tests and full-scale APT is established to introduce the APT data in the calibration process. Accordingly, the mechanistic-empirical RD prediction model calibration method, based on APT and the IR principle, is proposed and applied in a case study of a IAP RD prediction model calibration. Four 3.5 m × 4 m IAP test sections S1-S4 are constructed and instrumented and 700,000- and 900,000-wheel loads are applied on test sections S1-S2 and S3-S4, respectively, using the heavy vehicle simulator. The test data from the different APT load units are utilized for the model calibration, and the resultant prediction errors range from -2.16 mm to 1.18 mm. The calibrated model can also be used for the RD prediction of IAPs with other design schemes, by updating the corresponding material-related coefficients and the finite element model, which is essential for the design and maintenance of IAPs. The proposed calibration method could be a useful reference for the establishment of flexible pavement performance prediction models.

ABOUT SCIENTIFIC AND PHILOSOPHICAL PROBLEMS OF FOLK POET RY OF AZERBAIJAN: SYNERGIC APPROACH

The article examines some aspects of the scientific and philosophical problems of folk poetry of Azerbaijan from the standpoint of synergetic principles. The isomorphism between the Universe, the brain and the topological structures of Azerbaijani (Turkic) folk poetry is substantiated. It has been determined that the structures of Azerbaijani folk poetry are formed according to the principle of recursion and convergence. The genesis of Azerbaijani folk poetry is based on the principle from simple to complex, thanks to heredity and processuality, it gradually approaches its optimal form, which corresponds to Kolmogorov’s epistemological principle. All poetic forms of folk poetry have a common structure, i.e. the lines converge into rhymes, which are semantic centers that ensure the integrity of the poetic work. Azerbaijani folk poetry, as a non-linear multi-level system, has its own specific processes of convergence, divergence and parallelism. The integrity of folk poetry is dynamic in nature and this is important for reflecting the dynamics of the surrounding world. In organisms, convergent similarity is never deep. But in poetry, the situation is different. Unlike living organisms, convergent similarity in poetry has a deep basis, since points of convergence constitute rhymes, and thereby the integrity of the poem. Purpose: to study of ontognoseological problems of Azerbaijani folk poetry using synergetic paradigms. Methodology: To study the systemic-structural problems of folk poetry, evolutionary epistemology, categories of optimality, nonlinear synthesis, the principle of dominance of A. A. Ukhtomsky and the theory of functional systems of P. K. Anokhin were used, and the principles of parallelism and convergence were involved in the study of the problem of adequate reflection of reality. Scientific novelty: An isomorphism has been established between Azerbaijani folk poetry, the Universe and the structures of the brain. The role of the principles of parallelism and convergence in the evolution and development of living organisms and folk poetry has been studied, and similar and different aspects have been identified using the comparative method.

Household Items with Inscriptions of the Late 19th – the First Half of the 20th Century as Creolized Works of Folklore: A Need to Create Systematized Databases

The article deals with the necessity to create systematized databases (or to make interactive indices) for samples which are known as written folklore or, using linguistic terminology, creolized (verbal-iconic) texts. In particular, these folklore works include household items with inscriptions of the late XIXth to the first half of the XXth century. The authoress shortly describes the operating principle of the Interactive Index of Folklore Formulae developed by her on the materials of epigraphic embroidery. This index was created taking into account the fact that each item (a sample of epigraphic embroidery) consists of its structural elements. The latter are verbal and visual (iconic) folkloric formulae. Folkloric formulae can be both very short (for example, only one word) and long (for instance, an entire work can be only one folkloric formula). Folklore formulae can be both short (from one word) and long (for example, the whole work can be only one folklore formula). In the case of epigraphic embroidery, works mostly consist of one visual (iconic) and one verbal formula. However, there are also combinations of several verbal and/ or several visual formulae, which are embroidered on one towel and perceived as a single work. Having applied the recursion principle, the authoress managed to create the Index of folkloric formulae of epigraphic embroidery, where all the elements successfully interact. It is accentuated that such indexes (systematized databases) provide an opportunity for scientific research of concrete folkloric works.

Metacognition in Sebastian`s Door: mathematics, education and art

The aim is to show metacognition in how mathematics and culture are related in the sculptural work of Master Sebastián; with a deep playful character from which it emerges. Constituting a kind of artistic syncretism of apparently divergent beliefs between the plastic world, pure mathematics, abstract geometry and computational cybernetics. Methodology, study with a qualitative approach, the variables to consider were: Bach's baroque music with the canon and fugue, Gödel's theorem with the incompleteness of the axiomatic system; Eschery lithographs the reiteration of forms; Borje's literary-mathematical paradoxes; recursive programming routines in artificial intelligence systems (expert systems, mathematics) and Sebastián's sculpture. In conclusion, the convergence between Bach's baroque music can be identified, through the generation of the canon and the fugue; Gödel's theorem on the incompleteness of the axiomatic system, the reiteration of forms that invent themselves in Escher's lithographs, the literary-mathematical paradoxes in the stories of Jorge Luis Borges, and the use of recursive routines in the programming of expert systems or artificial intelligence. This game of plastic metamorphosis with which Sebastián surprised us a few years ago, turns out to predate the concept of the transformers, long before Hollywood made them a commercial success. As in the most diverse efforts of syncretism, Sebastián has traveled close to profanation as the staunch conservatives of the elite of scientists and artists can describe it.

The Concept in the Cognitive-Synergetic Aspect

The article considers the concept from a cognitive-synergetic standpoint. The concept is an open, dissipative, non-linear, fractal structure, the development of which is based on the law of spiral fractality and self-similarity. The concept evolves according to the recursive principle, goes in a circle, returning to the starting point on a new round of evolution. The origin of the concept is based on both external necessity and internal need. By the formation of a concept we mean its transition from the mental area, to the language area, and then to the speech area. The concept arises in consciousness in the form of a virtual image as a result of perceptual perception of reality, and is updated, stored in the language and embodied in speech. The concept strives for perfection, but never reaches it, reaching its peak, it starts the process of evolution again in new conditions.

THEORY OF COMPLEXITY IN A SMALL BRAZILIAN MICROENTERPRISE SITUATED IN THE WESTERN AMAZON

This work has as general objective to elaborate a study of the application of the principles of the theory of complexity in face of the practices adopted in Brazilian microenterprise located in the Amazon. Therefore, the following specific objectives were listed: (I) to characterize the principles related to the theory of complexity; (II) to identify relationships between complexity and organizational theory through the characteristics of complex management; (III) to identify factors present in the micro enterprise related to complexity. As for the method, the research is descriptive, using quantitative analysis. The questionnaire used was adapted from the study by Ramalho, Locatelli and Silva (2018). Among the results, it is highlighted that the reductionist principle was identified in the company when the individual attitude affected the organizational collectivity. The principle of retroactivity was observed from the high positive consistency of the responses obtained through mutual feedbacks. The principle of recursion was found from the synergy between people and the ability to establish dynamic relationships. The limitations of the study permeate the performance of a quantitative study. Future studies may involve replicating the in-depth research using a qualitative method in public and private organizations of different sizes.

A Feasibility Study of an Optimization-Based Active Field Uniformity Compensation Method for Superconducting Magnets

In order to enhance the quality of measurement results of various scientific instruments, such as magnetic property measurement systems, magnetic resonance imaging (MRI), nuclear magnetic resonance (NMR) and others, a spatially uniform magnetic field is required at the magnetic center. However, the measured field uniformity is usually worse than that in the design result due to the manufacturing errors of a superconducting magnet system. Therefore, spatial field uniformity compensation is needed to reduce the effects of manufacturing errors on field uniformity. Conventional field compensation methods require recursive routines of field mapping and compensation coil current adjustments, which lead to a less effective time-consuming process. In this study, a recently developed active field compensation algorithm employing pattern search, an optimization theory, will be introduced. A MATLAB code for active compensation coil current calculations with pattern search was developed, and six compensation coil designs and field distribution calculations with and without the proposed method were also carried out to compare the results. The test results demonstrate the feasibility of the proposed field compensation method for superconducting magnets.