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We address the following questions in this paper: (1) Which set or number existence axioms are needed to prove the theorems of 'ordinary' mathematics? (2) How should Frege's theory of numbers be adapted so that it works in a modal setting, so that the fact that equivalence classes of equinumerous properties vary from world to world won't give rise to different numbers at different worlds? (3) Can one reconstruct Frege's theory of numbers in a non-modal setting without mathematical primitives such as "the number of Fs" ( # F ) or mathematical axioms such as Hume's Principle? Our answer to question (1) is 'None'. Our answer to question (2) begins by defining 'x numbers G' as: x encodes all and only the properties F such that being-actually-F is equinumerous to G with respect to discernible objects. We answer (3) by showing that the mere existence of discernible objects allows one to reconstruct Frege's derivation of the Dedekind-Peano axioms in a non-modal setting. [ABSTRACT FROM AUTHOR]

Psychotherapy is a relational process that emerges from the meeting of two people. There is an ontological difference between the individual psychopathology of the patient and relational therapy; the present work aims to overcome the patient-centric conception of psychotherapy, restoring the dyadic nature of the therapy through the interpretation of the psychological interview as a fractal process. Recursion, namely the application of the same logical operator to the result of the operation itself, is presented here as the basic procedural element of psychotherapy. The paper is divided into two parts: The first has epistemological nature and focuses on complexity theory and cybernetics: Edgar Morin and recursion as a process of existence, Heinz von Foerster and epistemology as second-order praxis. From the thought of Gregory Bateson, it is here postulated the self-similarity of the content and structure of the mind, to the point of conceptualizing the dyadic relationship as a Mind of a different logical type compared to the individual mind. The second part of the present work introduces two intellectual tools designed to conceptualize psychotherapy as a fractal process: the psychopathological hologram, useful for clinical work although of a non-clinical nature, that consists in a fraction of the patient's experiential flow, while the psychotherapeutic string is presented here as the basic recursive element of psychotherapeutic process. [ABSTRACT FROM AUTHOR]

Languages with applicative morphology vary in whether their applied arguments can stack, or "recurse." Focusing primarily on Bantu languages, I argue that the availability of applicative recursion in a given language depends on abstract nominal licensing—in particular, on whether the applicative heads responsible for introducing applied arguments are nominal licensers. Applicative recursion therefore provides a novel diagnostic for the presence of abstract nominal licensing, which is argued to be driven not by Case but by ϕ-feature checking. The proposed approach to applicative recursion provides evidence for the role of abstract licensing in Bantu languages and has implications for approaches to double object symmetry as well as for recursion in causatives. [ABSTRACT FROM AUTHOR]

One apparent feature of mental time travel is the ability to recursively embed temporal perspectives across different times: humans can remember how we anticipated the future and anticipate how we will remember the past. This recursive structure of mental time travel might be formalized in terms of a 'grammar' that is reflective of but more general than linguistic notions of absolute and relative tense. Here, I provide a foundation for this grammatical framework, emphasizing a bounded (rather than unbounded) recursive function that supports mental time travel to a limited temporal depth and to actual and possible scenarios. Anticipated counterfactual thinking, for instance, entails three levels of mental time travel to a possible scenario ('in the future, I will reflect on how my past self could have taken a different future action') and is centrally implicated in complex human decision-making. This perspective calls for further research into the mechanisms, ontogeny, functions and phylogeny of recursive mental time travel, and revives the question of links with other recursive forms of thinking such as theory of mind. This article is part of the theme issue 'Elements of episodic memory: lessons from 40 years of research'. [ABSTRACT FROM AUTHOR]

Context • According to Humberto Maturana and Francisco Varela, faced with perturbations from the environment, a living system reacts by reproducing its components under the condition of preserving the organization, that is, the set of relationships between all its components. This activity is recursive, as it operates to preserve its own ability to operate. It not only defines the living but also the way in which the living system understands its environment. This makes the concept of recursion a key interpretative framework for phenomena of life and cognition. > Problem • Since experience emerges from biological recursion, we address the question of how experiences of the continuum and the discrete can result from it. > Method • Even if we draw on set and number theories in our arguments, the topic is not primarily addressed as a mathematical problem, but rather as a cognitive one. The arguments are developed using tools of analytic philosophy. > Results • We argue that, as with all recursive processes, the operator of a biological process remains unchanged, while its results vary in an inductive (and therefore historical) manner. We conclude that the phenomenon of the continuum originates from the invariance of this operator, while that of the discrete originates from the operator's results. > Implications • This work is part of the authors' research aimed at proposing a metamathematics based on the concept of number as a biological process rather than as a "thing." This is done using the concepts of "objectivity in parentheses" and "without parentheses" introduced by Maturana. Furthermore, the article may contribute to studies on the relationship between digital systems and human intelligence. In contrast to the latter, the former are discrete not only concerning inputs and outputs but also in terms of operators, which are constituted by discrete sets of algorithms, themselves composed of discrete sets of instructions. > Constructivist content • This work employs the ideas of Humberto Maturana and Francisco Varela. [ABSTRACT FROM AUTHOR]

The weighted Tower of Hanoi problem is a new generalization of the classical Tower of Hanoi problem, where a move of a disc between two pegs i and j is weighted by a positive real w i j . This new problem generalizes the concept of finding the minimum number of moves to solve the Tower of Hanoi, to find a sequence of moves with the minimum total weight. We present an optimal dynamic algorithm to solve the weighted Tower of Hanoi problem, as well as some of its properties. We also show the link of this generalization to the Tower of Hanoi variants with restricted disc moves, and how this new problem can generalize the concept of restricting a disc move. [ABSTRACT FROM AUTHOR]

In this paper, we present a comprehensive investigation into the construction of electromagnetic timelike particles within the frame of Minkowski space, employing the Bishop model. Our study involves deriving the fractional derivatives of key Lorentz forces namely Ω (t) , Ω (v 1) , and Ω (v 2) . Furthermore, we delve into the computation of essential normalizing and recursion operators tailored to magnetic vector fields, drawing from the principles outlined in the Bishop model. Additionally, we extend our analysis to determine the Fermi–Walker (FW) fractional derivatives, which play a crucial role in understanding the behavior and dynamics of the normalizing and recursion operators. Through this thorough exploration, we aim to provide valuable insights into the electromagnetic properties of timelike particles within the context of Minkowski space. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach for identifying distributed dynamic loads in the time domain. Using polynomial andmodal analysis, the load is transformed intomodal space for coefficient identification. This allows the distributed dynamic load with a two-dimensional form in terms of time and space to be simultaneously identified in the form of modal force, thereby achieving dimensionality reduction. The Impulse-based Force Estimation Algorithm is proposed to identify dynamic loads in the time domain. Firstly, the algorithm establishes a recursion scheme based on convolution integral, enabling it to identify loads with a long history and rapidly changing forms over time. Secondly, the algorithm introduces moving mean and polynomial fitting to detrend, enhancing its applicability in load estimation. The aforementioned methodology successfully accomplishes the reconstruction of distributed, instead of centralized, dynamic loads on the continuum in the time domain by utilizing acceleration response. To validate the effectiveness of the method, computational and experimental verification were conducted. [ABSTRACT FROM AUTHOR]

Individual survival and evolutionary selection require biological organisms to maximize reward. Economic choice theories define the necessary and sufficient conditions, and neuronal signals of decision variables provide mechanistic explanations. Reinforcement learning (RL) formalisms use predictions, actions, and policies to maximize reward. Midbrain dopamine neurons code reward prediction errors (RPE) of subjective reward value suitable for RL. Electrical and optogenetic self-stimulation experiments demonstrate that monkeys and rodents repeat behaviors that result in dopamine excitation. Dopamine excitations reflect positive RPEs that increase reward predictions via RL; against increasing predictions, obtaining similar dopamine RPE signals again requires better rewards than before. The positive RPEs drive predictions higher again and thus advance a recursive reward-RPE-prediction iteration toward better and better rewards. Agents also avoid dopamine inhibitions that lower reward prediction via RL, which allows smaller rewards than before to elicit positive dopamine RPE signals and resume the iteration toward better rewards. In this way, dopamine RPE signals serve a causal mechanism that attracts agents via RL to the best rewards. The mechanism improves daily life and benefits evolutionary selection but may also induce restlessness and greed. [ABSTRACT FROM AUTHOR]

This article considers a way to test the hypothesis that two collections of objects are from the same uniform distribution of such objects. The exact p-value is calculated based on the distribution for the observed overlaps. In addition, an interval estimate of the number of distinct objects, when all objects are equally likely, is indicated. [ABSTRACT FROM AUTHOR]

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Abstract The damage caused by the rain streak attached to the rainy image to the background seriously affects the analysis of image information and subsequent research. Aiming at the problem that the current single image rain removal methods cannot extract the deep rain streak features, a single image deraining algorithm based on multi‐stage recurrent network is proposed, which is committed to separating the rain streak layer and the background layer. The network consists of three stages, each stage is mainly composed of upper and lower scale dilation blocks, the upper scale dilation block includes multi‐scale dilated convolution and scale fusion, the lower scale dilation block is set the same, and the stages are connected using improved gated recurrent units to facilitate parameter sharing between them. The experimental results show that the proposed algorithm outperforms the comparative algorithm in both quantitative indicators and qualitative analysis on synthetic and real datasets, and the restored image retains more detailed information.

The gap between the limited human sense of how living entities change over time and the ways in which living systems change is one of the most potent uncertainties in ecological knowledge. This gap remains a significant source of problems and errors for those working with the transformations of living systems. This article foregrounds Mary Catherine Bateson's cybernetic practice of working with narratives in order to cultivate better understanding and responses to change, at the level of both societies and individuals. To do so, I investigate some significant moments, encounters and projects that connect her practice to the ecological ideas of her father, Gregory Bateson and situate their ideas on abduction, metaphor, recursion and narrative within broader discussions of ecological change. The Batesons did not seek a particular attitudinal change towards the transformation of selves, cities and worlds but rather sought to change the very understanding of what an attitude towards change should be, a distinction that is worth pondering given the challenges of attending to change within the present ecological crisis. [ABSTRACT FROM AUTHOR]

The aim of this paper is to discuss the emergence of recursive thinking through the famous problem posed by Fibonacci regarding the growth of the rabbit population. This paper qualitatively analyzes and discusses the semiotic aspects raised by the students working with this historical source in the form of a story. From this perspective, the value of the historical problems as socio-cultural references (voices) and of the narrations as mediating factors to enhance students' learning of new mathematical concepts, such as recursion, is explored in depth. The focus lies on the pivotal role played by the students' construction of personal senses during in-group mathematical activities, in dialectics with the normative and mathematical meanings. It is highlighted that fostering environments conducive to dialogue among peers, as well as linking various shapes and contexts of knowledge, is necessary. Here, storytelling and history are regarded as fruitful resources aiding students in the gradual construction of a personal sense of mathematical concepts, including recursion. [ABSTRACT FROM AUTHOR]

> Context • In the conventional sciences, artistic work and aesthetic experience are explained from different theoretical perspectives through heterogeneous mechanisms at different system levels. > Problem • Due to the methodological constraints of Science I, it is hardly possible to develop an integrative theory that coordinates the complex relational interplay of multi-layered systemic processes in the field of art. Various descriptions and explanations at different levels of artistic work and aesthetic experience will be integrated into an approach to a systems theory of art within the framework of Science II. > Method • First-person observations and coordination of doings in the performing arts and various theoretical explanations of their artistic work and aesthetic practice at different system levels are re-entered, coordinated, and consistently explained in terms of Science II. > Results • The first-person observations of the performance Soul Chain and the theoretical views of structural determinism, second-order cybernetics, the interpenetration of psychic and social systems, deconstructive différance, and the autopoietic feedback loop are re-framed in Science II. As reflections of specific generative mechanisms, they are integrated into a systems-theoretical approach that explains the performing arts and aesthetic practice through the mechanism of self-reflexive recursive coordination of structural relations. > Implications • The general generative mechanism of recursive coordination of structural relations explains the self-constitution of human existence at all domains and levels, including the process of explaining. Science II allows for a higher-order integration and generality of theories than the conventional science under the subject-object-epistemology paradigm. > Constructivist content • The possibility of consistently coordinating and explaining the first-person and theoretical observations of art and aesthetic practice at the different levels of systemic self-constitution in Science II confirms its claim to central theoretical relevance. [ABSTRACT FROM AUTHOR]

In statistics, probability theory, and computer science, a derangement, !n, is known to be a basic problem that computes total ways of rearranging n ∈ N items such that a result contains no item i that stands in the same position as it did in the input. Formally, the derangement problem has a problem instance of a finite collection C = {(x1,y1), .∙∙., (xn,yn)}, ∣C∣ = n. With this formulation, !n is a total number of qualified collections C' where C' contains n members of (xi,yj) where i ≠ j and every Xi and yj (1 ≤ i,j < n) must show up exactly once in C'. In this article, we present a dynamic programming algorithm that computes !n and its justification. We also provide a discussion about extending the limitation of the problem with an objective to cover a general case where we have a finite set of variables a1, a2∙∙∙∙ak rather than the traditional scenario that has only two variables: x and y. [ABSTRACT FROM AUTHOR]

The damage caused by the rain streak attached to the rainy image to the background seriously affects the analysis of image information and subsequent research. Aiming at the problem that the current single image rain removal methods cannot extract the deep rain streak features, a single image deraining algorithm based on multi‐stage recurrent network is proposed, which is committed to separating the rain streak layer and the background layer. The network consists of three stages, each stage is mainly composed of upper and lower scale dilation blocks, the upper scale dilation block includes multi‐scale dilated convolution and scale fusion, the lower scale dilation block is set the same, and the stages are connected using improved gated recurrent units to facilitate parameter sharing between them. The experimental results show that the proposed algorithm outperforms the comparative algorithm in both quantitative indicators and qualitative analysis on synthetic and real datasets, and the restored image retains more detailed information. [ABSTRACT FROM AUTHOR]

Motivated by queueing applications, we study various reflected autoregressive processes with dependencies. Among others, we study cases where the interarrival and service times are proportionally dependent on additive and/or subtracting delay, as well as cases where interarrival times depend on whether the service duration of the previous arrival exceeds or not a random threshold. Moreover, we study cases where the autoregressive parameter is constant as well as a discrete or a continuous random variable. More general dependence structures are also discussed. Our primary aim is to investigate a broad class of recursions of autoregressive type for which several independence assumptions are lifted and for which a detailed exact analysis is provided. We provide expressions for the Laplace transform of the waiting time distribution of a customer in the system in terms of an infinite sum of products of known Laplace transforms. An integer-valued reflected autoregressive process that can be used to model a novel retrial queueing system with impatient customers and a general dependence structure is also considered. For such a model, we provide expressions for the probability generating function of the stationary orbit queue length distribution in terms of an infinite sum of products of known generating functions. A first attempt towards a multidimensional setting is also considered. [ABSTRACT FROM AUTHOR]

Background. The proposed work is devoted to research to clarify the axiomatization of arithmetic in connection with the presence of special assumptions in it. The conceptual problem of analyzing new properties of numbers is formulated under the assumption of the possibility of losing any initial premise. Materials and methods. A solution to the conceptual problem is given, followed by a logical analysis of the meaningful axiomatic theory of natural numbers, which led to the discovery of logical errors. An analysis of logical errors is given based on the meaningful axiomatic theory of natural numbers. It is shown that the properties of an established set of "finite real numbers", or positive real numbers contained in a given segment e, have the property of being discovered depending not only on the "requested numbers" of the actually infinite region, but also on real (positive) numbers infinite half-interval. Results. Conditions have been identified that allow us to establish new properties of numbers. Conclusions. The natural series N begins only with 1, there is no zero in it. It has been proven that modern arithmetic has an incorrect axiomatization and is subject to revision.

The "end of the world" trope can be rote in popular culture, but its critical deployment is not so and exposes something about rhetoric's relationship to humanness and to humanism, which is that the capacity for rhetoric acts as a limit of humanness. Such tropes are often used to recast "world" as "worlds" to envision humanness anew. Multiplication of the worlds of humans presents a convoluted problem because of rhetoric's investment in humanism, but more so because of the way that rhetoric sits at the limit of variation for humans and their worlds. The essay addresses humanism as an organizing concern whose belief set is disputed and changeable and discusses how rhetoricity brackets the diversification of the human as multiple. The essay argues that a capacity for rhetoric, undefinable even as speech, permeates the (dis)continuum of humanness, such that the conserving and splintering of humanness becomes rhetoric's troubled place. [ABSTRACT FROM AUTHOR]

We study vibrational properties of non-homogeneous materials. We consider idealized materials composed of one dimensional chains of damped harmonic oscillators represented by a sequence of particles, springs and dampers. The system is linear, thus possesses exact explicit solutions, nevertheless the formulas can be very complicated. Homogeneous chains are used as basic building blocks for characterizing global dynamics of the system. In particular, we determine the solutions for a system composed of two distinct homogeneous chains in terms of the original solutions for these two homogeneous chains, and the original parameters, when uncoupled. Two types of coupling are considered, one with a gluing particle, the other with a gluing spring and damper. [ABSTRACT FROM AUTHOR]

This paper explores a formal model of autopoiesis as presented by Maturana, Uribe and Varela, and analyzes this model and its implications through the lens of the notions of eigenforms (fixed points) and the intricacies of Goedelian coding. The paper discusses the connection between autopoiesis and eigenforms and a variety of different perspectives and examples. The paper puts forward original philosophical reflections and generalizations about its various conclusions concerning specific examples, with the aim of contributing to a unified way of understanding (formal models of) living systems within the context of natural sciences, and to see the role of such systems and the formation of information from the point of view of analogs of biological construction. To this end, we pay attention to models for fixed points, self-reference and self-replication in formal systems and in the description of biological systems. [ABSTRACT FROM AUTHOR]

Much debate in prosodic phonology has centered on the question of recursive prosodic layers versus independent constituents. Recently, Downing and Kadenge (Downing, Laura & Maxwell Kadenge. 2015. Prosodic stems in Zezuru Shona. Southern African Linguistics and Applied Language Studies 33(3). 291–305, Downing, Laura & Maxwell Kadenge. 2020. Re-placing the PStem in the prosodic hierarchy. The Linguistic Review 37(3). 433–461) have advocated for a unique prosodic constituent, the PStem, to match stem-level phonology. They argue that the stem level should not be sensitive to canonically word-level phenomena such as minimality and culminativity. Alternatively, Itô and Mester (Itô, Junko & Armin Mester. 2007. Prosodic adjunction in Japanese compounds. MIT Working Papers in Linguistics. 97–111 et seq.) propose that the PStem/PrWd division can be collapsed into recursive PrWd levels, in which any recursive layer can have any given set of properties. In this paper, I hope to add to this debate by showing that Downing and Kadenge's idea of specifically stem-level processes is falsifiable in light of new empirical evidence from a number of unrelated languages. In terms of the recursion question, I show that there are two types of language behavior with respect to stem- versus word-level phonology: one in which stem and word are the loci of the distinct processes, and one in which stem and word show the same behavior ("recursive identity"). I conclude by showing that arguments intending to reduce recursive identity to cyclicity encounter their own suite of problems. [ABSTRACT FROM AUTHOR]

The paper proposes an algorithm for solving the problem of finding the maximum common subgraph. Both the sequential and the parallel version of the algorithm, their software implementation are described, and an experimental study of their effectiveness is carried out. This problem is one of the most famous NP-complete problems. Its solution may be required when solving many practical problems related to the study of complex structures. We solve it in a statement when we need to find all possible isomorphisms of the found common subgraph. Due to the extremely high complexity of the problem, it is natural to want to speed up its solution by parallelizing the algorithm. To organize parallel computing, the author used the RPM_ParLib library. It allows to develop effective applications for parallel computing on a local network under the control of the runtime environment .NET Framework.The library supports a recursive-parallel programming style and provides effective work distribution and dynamic load balancing of computational modules during program execution. It can be used for applications written in any programming language supported by the .NET Framework. The purpose of the numerical experiment was to study the acceleration achieved due to the recursive-parallel organization of calculations. For the experiment, the author developed a special application in the C# language designed to generate various sets of initial data with specified parameters. The paper describes the features of the generated initial pairs of graphs, as well as the results obtained during the experiment.

The article deals with an aspect of the phenomenon of controlled illusion — manipulating emotional reactions and behaviour through the space of an artificially created reality. The subject of the article is a relevant feature of the process — recursion within a fictitious space. The methods of mass suggestion become more complicated with each step of evolution, borrowing the techniques of the past and multiplying them by the technologies of the present. Today’s technologies create a process of self-repetition of elements — a process within a process: artificially created illusions are embodied and massively repeated as patterns. Nowadays, controlled illusion generates a problem of imbalance between the accumulated practice of control and an individual’s ability for distancing. The urgency of the problem is due to the obvious dominance of the methods of manipulating public conscience over the development of an individual via industries of culture. The aim of this article is to define the role of sensory suggestion capabilities through control spaces in the 21st century. The objective is to consider the features of the effects of radiance, the influence of flickering light, and the imitation of the world by adomed structure. These effects stem from the Baroque era, are passed on in evolution, and carry a suggestive potential through an emotional factor. While borrowing and accumulating the techniques of the past, new tools such as artificial intelligence, communication networks, electronics, and biotechnologies bring new qualities to manipulations, including a multisensory impact. The author proposes to reconsider the traditional view on the role of algorithms in cultural objects: what until recently was negatively described as “inanimate” and programmed is now able to control and reveal the emotional potential of a person. The outcome depends on what the algorithms are trained for, who trains them and why. The social function of illusionism is either commercial and political benefit or the promotion of an inclusive culture and the development of a person and their abilities. This cannot but affect the role of designer and artist, whose activity today is increasingly moving away from the decorative and turning to interaction through scientific approaches, which determines the property that offers a choice of path and goal in illusionism.

Recursive procedures that allow placing a vocal signal inside another of a similar kind provide a neuro-computational blueprint for syntax and phonology in spoken language and human song. There are, however, no known vocal sequences among nonhuman primates arranged in self-embedded patterns that evince vocal recursion or potential incipient or evolutionary transitional forms thereof, suggesting a neuro-cognitive transformation exclusive to humans. Here, we uncover that wild flanged male orangutan long calls feature rhythmically isochronous call sequences nested within isochronous call sequences, consistent with two hierarchical strata. Remarkably, three temporally and acoustically distinct call rhythms in the lower stratum were not related to the overarching rhythm at the higher stratum by any low multiples, which suggests that these recursive structures were neither the result of parallel non-hierarchical procedures nor anatomical artifacts of bodily constraints or resonances. Findings represent a case of temporally recursive hominid vocal combinatorics in the absence of syntax, semantics, phonology, or music. Second-order combinatorics, ‘sequences within sequences’, involving hierarchically organized and cyclically structured vocal sounds in ancient hominids may have preluded the evolution of recursion in modern language-able humans.

Claims made by linguist Daniel Everett, that the Pirahã language, spoken by a small group of native Amazonians, lacks features thought to be universally present in languages, captured the imaginations of scholars and prompted broader questions on the nature of language, the diversity in languages, and the universals shared by them. Everett claimed that, in Pirahã, he had found a language without numbers, colors, mythology, abstract thinking, or recursive embedding. These claims were challenged by proponents of a universal grammar and by other biological linguists concerned with identifying shared faculties that undergird human cognitive capacities and by linguistic anthropologists concerned with the products of those potentials as they are actualized in the interactivity of speaking. Situating the Pirahã in historical and sociological context, I question the novelty of a faculty of language and many of Everett's claims of Pirahã exceptionality, and I explore the renewed interest in the nature of language. [ABSTRACT FROM AUTHOR]

The article addresses the problem of polyphony in Joyce Carol Oates's novel The Gravedigger's Daughter. Polyphony is considered not only as a procedure related to textual poetics, but a starting point for placing the compositional and stylistic organization of a literary work in the context of the assumptions of pragmatism and posthumanism. The category derived from Bakhtin's theory can be used to conceptualize the phenomenon of „voices", a form of constructing the identity of the novel's protagonist. „Voices" are quotations of thoughts and statements of other characters in the work, penetrating the inner life of the main character. Multi-voice subjectivity, which is suggested by the procedure of „quoting" voices, establishes a version of identity which is highly dialogical, indeterminate, dynamic and unstable. The world presented in the novel is likely to imply contradictory, ambiguous ideas as to whether American social life supports or prevents individual freedom. Polyphonic subjectivity in Oates' novel entails the acceptance of the pluralism and indeterminacy of the presented world and of the dialogical, incomplete identity of the characters. Thus, the literary form develops an epistemology and an aesthetics equivalent to the philosophical stances of pragmatism and posthumanism. Tracing the „voices" scattered throughout the work requires so much cognitive effort from the reader that it makes them a co-participant in the process of meaning-making. [ABSTRACT FROM AUTHOR]

Recursion, and recursion-like design patterns, are used in the entry schemas of dictionaries to model subsenses and subentries. Recursion occurs when elements of a given type, such as sense, are allowed to contain elements of the same or similar type, such as sense or subsense. This article argues that recursion unnecessarily increases the computational complexity of entries, making dictionaries less easily processable by machines. The article will show how entry schemas can be simplified by re-engineering subsenses and subentries as relations (like in a relational database) such that we only have flat lists of senses and entries, while the is-subsense-of and is-subentry-of relations are encoded using pairs of unique identifiers. This design pattern losslessly records the same information as recursion (including – importantly – the listing order of items inside an entry) but decreases the complexity of the entry structure and makes dictionary entries more easily machine-processable. [ABSTRACT FROM AUTHOR]

Recent developments in archeological research extend diverse technological methods for the geometric deciphering and cultural understanding of various historical building components. One of the emerging methods in this field is the development of generative algorithms to develop computational models for the comparative study of variation among different structures belonging to a common era, style, or region. In this study, we present a novel approach for the computational analysis and parametric modeling of muqarnas found among Anatolian Seljuk architecture in Kayseri and Sivas built in the 13th century. Using four different octagonal muqarnas structures, we outline common generative rules showing recursive stacking of geometric layers, fractal patterns and hierarchical branching of the axis of symmetry. A recursive algorithm is developed that can offer a generative study of muqarnas structures using proportions based on the 'silver ratio.' The development of the algorithm is presented through rules and variations that can offer a novel perspective for the geometric understanding and categorization of muqarnas in the region. [ABSTRACT FROM AUTHOR]

Formal mathematical description and analysis of the mathematical model of the problem from the field of medicine about adaptation of dynamic treatment regimes in terms of classification algorithms, and class transition logic, is the main goal of this work. We call these models and procedures classification to the target class, because the global goal of the problem is to assign objects/patients to the normal/healthy class. The usual classification procedure that appears in the first step of the considered procedures is supplemented by the mechanism of bounded transition between classes (boundedness is a property of the considered domain), and this process consisting of (object-action) pairs is repeated recursively, seeking to assign all objects to the same predetermined target class. The correspondences and differences of the obtained model with the main classes and approaches of machine learning—supervised learning, cluster analysis, and reinforcement learning—are analyzed. The class of emergent problems such as model validation and optimization is considered. In particular, a logical analysis of the system of class transitions is given and an augmented graph-theoretic solution for the deterministic case of target class classification problem transitions is obtained. [ABSTRACT FROM AUTHOR]

We address the interaction of various interpretations of lexical items, which leads to a change in the correlation between signifieds and signifiers and the formation of new signs. Addressing the polysemic slogan ‘ОМОН-И-МЫ — АНТОНИМЫ’, we explicate the mechanism of semiotic Perpetuum mobile, that is, the cyclic recursions that allow simultane­ous actualization of various interpretations of this utterance. We demonstrate that the analy­sis of semantic relations in their dynamics requires the introduction of new theoretical con­cepts. The general principle of dynamic semiosis is demonstrated — that is the recursive rela­tions when a signified of one sign through intermediate operations (homonymy and synony­my) becomes a signifier of another and vice versa. In this semantic Perpetuum mobile, no single interpretation reaches the final point. It goes back to the previous state without produc­ing new meanings and signs but repeating the already passed cycle. Each of the co-existing interpretations returns to itself, demonstrating — in a paradoxical and tautological way — Luhman’s concept of paradox and tautology as two only possible states of a self-describing system. The same process, but being considered from the starting point demonstrates the par­adoxicality and tautology of the process of signification.