Complex Description Research Articles

Once-Marking and Always-Marking 1-Limited Automata

Single-tape nondeterministic Turing machines that are allowed to replace the symbol in each tape cell only when it is scanned for the first time are also known as [Formula: see text]-limited automata. These devices characterize, exactly as finite automata, the class of regular languages. However, they can be extremely more succinct. Indeed, in the worst case, the size gap from [Formula: see text]-limited automata to one-way deterministic finite automata is double exponential. Here we introduce two restricted versions of [Formula: see text]-limited automata, once-marking[Formula: see text]-limited automata and always-marking[Formula: see text]-limited automata, and study their descriptional complexity. We prove that once-marking [Formula: see text]-limited automata still exhibit a double exponential size gap to one-way deterministic finite automata. However, their deterministic restriction is polynomially related in size to two-way deterministic finite automata, in contrast to deterministic [Formula: see text]-limited automata, whose equivalent two-way deterministic finite automata in the worst case are exponentially larger. For always-marking [Formula: see text]-limited automata, we prove that the size gap to one-way deterministic finite automata is only a single exponential. The gap remains exponential even in the case the given machine is deterministic. We obtain other size relationships between different variants of these machines and finite automata and we present some problems that deserve investigation.

On the computational completeness of several descriptional complexity restrictions of semi-conditional grammars

A semi-conditional grammar, introduced by Gheorghe Păun, is a form of regulated rewriting system where each rule consists of a context-free core rule A → w along with two strings w + , w − . The rule is applicable if w + (the positive condition) occurs as a substring of the current sentential form, but w − (the negative condition) does not. The maximum lengths i, j of the positive or negative conditional strings, respectively, give a natural measure of descriptional complexity, known as the degree of such grammars. Employing several normal form results on phrase-structure grammars as derived in particular by Viliam Geffert, we improve on previously obtained results by reducing the number of nonterminals of semi-conditional grammars of a given degree ( i , j ) while maintaining computational completeness of the said mechanisms.

HPC software for modelling field electron emission

The aim of this work is modeling processes of field electron emission in strong electromagnetic fields. This problem is relevant for many technical and medical applications. At present time, electrical devices that combine a large value of field, a powerful relativistic effect and an ultra-short time interval of action are in demand. They find their application in the treatment of the surfaces with inorganic, organic and mixed structures. Modeling of such devices encounters certain difficulties due to the complexity of the mathematical description of the emission processes. In this paper, an approach using the method of large smoothed particles in combination with grid calculation of fields based on Maxwell's equations is proposed. The study was carried out within the framework of the problem of calculating the field emission of electrons from the surface of axisymmetric metal cathodes on Cartesian and unstructured curved meshes. To implement the approach, a complex mathematical model, a parallel numerical algorithm and its software realization have been developed. The elaborated software is focused on the use of multiprocessor computing systems with a central architecture. Test calculations confirmed the correctness of the proposed approach and the high efficiency of its software implementation.

Planning sentences and sentence intonation in Estonian

The notion of advance planning of sentence intonation is grounded in the positive correlation between the sentence-initial intonation peaks and sentence duration. This study examined real-time sentence planning and intonation using visual world speech production. In two eye-tracking experiments, native Estonian speakers described transitive events involving multiple actors. Conceptual complexity of the resulting picture descriptions was manipulated through a pictorial design, while sentence length was controlled for by manipulating specific task characteristics. In Experiment I, conceptual complexity of the picture descriptions varied together with linguistic complexity, while linguistic complexity was held constant in Experiment II. As the conceptual complexity of utterances increased, the duration of naming gazes also increased, indicating less incremental conceptual planning. Notably, while utterance-initial intonation peaks did not correlate with the relative duration of naming gazes, they were influenced by utterance length. These findings highlight advance planning of intonation in Estonian. Furthermore, they suggest that intonation planning depends on linguistic information that is rapidly activated after establishing a comprehensive conceptual framework during earliest stages of preverbal planning.

Evaluating the impact of filler size and filler content on the stiffness, strength, and toughness of polymer nanocomposites using coarse-grained molecular dynamics

Their great versatility makes polymer nanocomposites an important class of engineering materials. In order to gain detailed insights into the nanoscale mechanisms underlying their macroscopic mechanical properties, molecular dynamics (MD) simulations are a valuable tool to complement experimental studies. In this work, we modify the analytical potential functions of an efficient bead–spring model representing a generic polymer nanocomposite to account for the breaking of covalent bonds. We perform uniaxial tensile simulations of double-notched specimens and validate the model using experimental trends for overall stiffness, strength, and toughness. First, we study the effects of sample size, notch geometry, strain rate, temperature, and molar mass for the pure thermoplastic matrix material. Second, we analyze the influence of filler size and filler content on the mechanical behavior of the polymer nanocomposite. With this study, we show that in both the development of new materials and the optimization of established materials, it is possible to gain important preliminary insights into the effects of pertinent material characteristics with a simple MD setup, which can then be further refined by increasing the complexity of the material description and the boundary conditions.

How many inflectional forms does a Somali verb have?

Abstract The Somali verb is traditionally presented as having a quite large number of inflectional paradigms with, e.g., special negative forms and several kinds of subordinate clause forms. The complexity of traditional descriptions tends to overshadow important generalisations that would otherwise reflect a relative simplicity of the Somali verb system. The most important reasons for the abundance of paradigms are that forms, periphrastic constructions and their functions are not systematically differentiated, but also that the tonal accent and case marking are treated as parts of the inflection, instead of phrasal marking of syntactic or pragmatic functions. The aim of this article is therefore to suggest a simplified analysis and to define the minimal set of synthetic forms and analytical constructions that are necessary for the description of Somali verb inflection as well as the basic syntactic functions of these forms and constructions.

Pebble-depth

In this paper we introduce a new feasible notion of Bennett's logical depth based on pebble transducers. This notion is defined based on the difference between the minimal length descriptional complexity of prefixes of infinite sequences from the perspective of finite-state transducers and pebble transducers. Our notion of pebble-depth satisfies the four fundamental properties of depth: i.e. deep sequences exist, trivial sequences are not deep, random sequences are not deep, and the existence of a slow growth law type result. We also compare pebble-depth to other depth notions based on finite-state transducers, pushdown compressors, and the Lempel-Ziv 78 compression algorithm. We first demonstrate how there exists a normal pebble-deep sequence even though there is no normal finite-state-deep sequence. We next build a sequence that has a pebble-depth level of roughly 1, a pushdown-depth level of roughly 1/2 and a finite-state-depth level of roughly 0. We then build a sequence that has a pebble-depth level of roughly 1/2 and a Lempel-Ziv-depth level of roughly 0.

Universal enzymatic numerical P systems with small number of enzymatic rules

Enzymatic Numerical P Systems (ENPSs) are a model of membrane computing that is well-suited for the simulation of physical processes and that has been used for the design and the implementation of motion controllers for wheeled robots and flying drones. The ENPSs model has been proven to be Turing universal and the theoretical effort was focused on minimizing various descriptional complexity parameters. In this paper, we explore the minimum number of enzymatic rules needed to achieve universality in ENPSs, specifically focusing on the all-parallel derivation mode where all applicable rules are applied at the same time. We show that in the case of a linear restriction for production functions, the universality can be obtained using 21 enzymatic rules, substantially improving previously known results. If production functions are allowed to be polynomials of degree 2, we show that a single enzymatic rule is sufficient to achieve universality. To obtain these results, a new proof method is introduced based on the translation of ENPSs to systems of conditional recurrences.

The descriptive complexity of the set of Poisson generic numbers

Let [Formula: see text] be an integer. We show that the set of real numbers that are Poisson generic in base [Formula: see text] is [Formula: see text]-complete in the Borel hierarchy of subsets of the real line. Furthermore, the set of real numbers that are Borel normal in base [Formula: see text] and not Poisson generic in base [Formula: see text] is complete for the class given by the differences between [Formula: see text] sets. We also show that the effective versions of these results hold in the effective Borel hierarchy.

Improving virtual heat transfer description of developed and undeveloped annular gap flows at high Taylor numbers

Increased power densities of electric machines are, amongst other factors, related also to the increase of the rotors’ rotating velocities. These can be combined with axial flow to improve the heat transfer in the annular gap. The resulting high rotating and axial velocities are characterized with high Taylor (Ta) and Reynolds (Re) numbers. Such flow regimes are currently not yet thoroughly described. The reasons are in the complex interactions between the operating conditions, annular gap geometry and the conditions at the gap inlet, which affect the flow development in the gap. Each of these impacts varies between different electric machines, adding to the complexity of description. To address this, a numerical study based on 3D CFD simulations is performed. The study accounts for the impacts of the flow conditioning at the entrance to the annular gap and the possibility that the small scale turbulent structures might not be well resolved at high Ta numbers. Thus, different inflow configurations are applied using both RANS and LES models. The results are compared with available experimental and numerical data and provide a valuable insight into the requirements for reliable heat transfer description in the increasingly interesting flow conditions.

On the computational completeness of generalized forbidding matrix grammars

Matrix grammars are one of the first approaches ever proposed in regulated rewriting, prescribing that rules have to be applied in a certain order. In traditional regulated rewriting, the most interesting case shows up when all rules are context-free. Typical descriptional complexity measures incorporate the number of nonterminals or the length, i.e., the number of rules per matrix. When viewing matrices as program fragments, it becomes natural to consider additional applicability conditions for such matrices. Here, we focus on forbidding sets, i.e., a matrix is applicable to a sentential form w only if none of the words in its forbidding set occurs as a subword in w. This gives rise to further natural descriptional complexity measures: How long could words in forbidding sets be? How many words could be in any forbidding set? How many matrices contain non-empty forbidding contexts? As context-free grammars with forbidding sets are known as generalized forbidding grammars, we call this variant of matrix grammars also generalized forbidding. In this paper, we attempt to answer the four questions above while studying the computational completeness of generalized forbidding matrix grammars. In the course of our studies, we also define several new normal forms for type-0 grammars that might be of independent interest.

Fractal networks: Topology, dimension, and complexity.

Over the past two decades, the study of self-similarity and fractality in discrete structures, particularly complex networks, has gained momentum. This surge of interest is fueled by the theoretical developments within the theory of complex networks and the practical demands of real-world applications. Nonetheless, translating the principles of fractal geometry from the domain of general topology, dealing with continuous or infinite objects, to finite structures in a mathematically rigorous way poses a formidable challenge. In this paper, we overview such a theory that allows to identify and analyze fractal networks through the innate methodologies of graph theory and combinatorics. It establishes the direct graph-theoretical analogs of topological (Lebesgue) and fractal (Hausdorff) dimensions in a way that naturally links them to combinatorial parameters that have been studied within the realm of graph theory for decades. This allows to demonstrate that the self-similarity in networks is defined by the patterns of intersection among densely connected network communities. Moreover, the theory bridges discrete and continuous definitions by demonstrating how the combinatorial characterization of Lebesgue dimension via graph representation by its subsets (subgraphs/communities) extends to general topological spaces. Using this framework, we rigorously define fractal networks and connect their properties with established combinatorial concepts, such as graph colorings and descriptive complexity. The theoretical framework surveyed here sets a foundation for applications to real-life networks and future studies of fractal characteristics of complex networks using combinatorial methods and algorithms.

Complexity Column

Descriptive complexity theory initiated by celebrated Fagin's theorem aims to characterize complexity classes by the kind of logic necessary to express problems in the class. For many complexity classes such a characterization has been found; this includes the class NP that, according to Fagin's theorem, can be characterized by the monadic second order logic. Some classes, however, eludes such a characterization, and this famously includes the class P. Due to the importance of the class P, finding a logic for P is one of the central open problems in descriptive complexity.

A Logic for P: Are we Nearly There Yet?

Whether or not there is a logic for P is the classic problem of descriptive complexity theory. It has been an open problem for over four decades (since its first formulation by Chandra and Harel [1980]) now and much has been written about it, including surveys and textbook presentations (see, for instance [Ebbinghaus and Flum 1999, Chapter 11]. The problem remains a focus of active research and there have been significant recent developments related to it. These may not be well known outside a specialist group of researchers and one aim of the present article is to bring these to a wider audience. To place the new results in their context, we begin with a wider perspective on the question.

Bias in the arrival of variation can dominate over natural selection in Richard Dawkins's biomorphs.

Biomorphs, Richard Dawkins's iconic model of morphological evolution, are traditionally used to demonstrate the power of natural selection to generate biological order from random mutations. Here we show that biomorphs can also be used to illustrate how developmental bias shapes adaptive evolutionary outcomes. In particular, we find that biomorphs exhibit phenotype bias, a type of developmental bias where certain phenotypes can be many orders of magnitude more likely than others to appear through random mutations. Moreover, this bias exhibits a strong preference for simpler phenotypes with low descriptional complexity. Such bias towards simplicity is formalised by an information-theoretic principle that can be intuitively understood from a picture of evolution randomly searching in the space of algorithms. By using population genetics simulations, we demonstrate how moderately adaptive phenotypic variation that appears more frequently upon random mutations can fix at the expense of more highly adaptive biomorph phenotypes that are less frequent. This result, as well as many other patterns found in the structure of variation for the biomorphs, such as high mutational robustness and a positive correlation between phenotype evolvability and robustness, closely resemble findings in molecular genotype-phenotype maps. Many of these patterns can be explained with an analytic model based on constrained and unconstrained sections of the genome. We postulate that the phenotype bias towards simplicity and other patterns biomorphs share with molecular genotype-phenotype maps may hold more widely for developmental systems.

Care complexity, perceptions of complexity and preferences for interprofessional collaboration: an analysis of relationships and social networks in paediatrics

BackgroundIn the context of increasingly intricate healthcare systems, professionals are compelled to collaborate within dynamically changing interprofessional teams. Moreover, they must adapt these collaborative processes to effectively and efficiently manage the evolving complexity of care needs. It remains unclear how professionals determine care complexity and relate this complexity to their preferences for interprofessional collaboration (IPC). This study investigated the relationships between care complexity, professionals’ perceived complexity and IPC preferences, and examined the variation in individual and team characteristics of IPC-practices across different levels of complexity in paediatric care.MethodsIn an online questionnaire, 123 healthcare professionals working at an academic tertiary children’s hospital scored their perceptions of complexity and preferences for IPC. They also selected family and various professions as members of the interprofessional (IP-) team based on thirteen patient cases. We employed conjoint analysis to systematically model the complexity of case descriptions across the five domains of the International Classification of Functioning, Disability and Health (ICF). Additionally, we applied social network analysis to identify important professions, crucial connectors and influential professions in the IP-team, and to describe the cohesiveness of IP-teams.ResultsModelled case complexity, professionals’ perceived complexity and IPC preferences were positively associated. We found large inter-individual variations in the degree of these associations. Social network analysis revealed that the importance and influence of professions was more equally distributed when case complexity increased. Depending on the context and complexity of the case, different professions (e.g. medical doctors, social professionals, extramural professionals) were considered to be more crucial connectors within the IP-team. Furthermore, team cohesion was positively associated with modelled and perceived care complexity.ConclusionsIn conclusion, our study contributes to the existing knowledge by integrating task-specific insights and broadening the use of conjoint and social network analysis in the context of IPC. The findings substantiate the contingency theory that relates characteristics of IPC to care complexity, offering quantified insights into how IP-teams adapt to situational needs. This understanding of relationships and variations within IPC holds crucial implications for designing targeted interventions in both clinical and health profession education contexts. Consequently, it contributes to advancements in healthcare systems.

Novelty detection in the design of synthesis of garnet-structured solid electrolytes

Recent decades have shown arising growth-on-demand fusion of machine learning into all of the areas of chemistry and materials science. In this study, we examine one aspect of using these technologies to gain an advantage in the search for new knowledge in increased amounts of experimental data. The novelty detection approaches are aimed to identify the data artefacts. The analysis of such artefacts, “outliers”, in details of synthesis of garnet-structured solid electrolytes was chosen as an example of the practical application of this methodology. Particular attention was paid to the choice of the precursors. The thermodynamic data such as the heat of formation from the pure oxides as well as the results of drop solution calorimetry for simple oxides were involved as the descriptors for the studied systems. The overall performance of novelty/outlier detection of “outliers” was characterized using the AUC (area under the curve) value and assessed to be 0.71 – 0.72 varying the complexity of data description. It was found that all “outlier” due to the precursors choice compounds were successfully identified. The regression analysis was performed to analyze the impact of outlier/novelty detection on model predictive performance as well as to elucidate the relationship with the data diversity and the complexity of data description.

Performing Regular Operations with 1-Limited Automata

The descriptional complexity of basic operations on regular languages using 1-limited automata, a restricted version of one-tape Turing machines, is investigated. When simulating operations on deterministic finite automata with deterministic 1-limited automata, the sizes of the resulting devices are polynomial in the sizes of the simulated machines. The situation is different when the operations are applied to deterministic 1-limited automata: while for boolean operations the simulations remain polynomial, for product, star, and reversal they cost exponential in size. The costs for product and star do not reduce if the given machines are sweeping two-way deterministic finite automata. These bounds are tight.

Моделирование особенностей работы дистанционной защиты резервных трансформаторов собственных нужд энергоблоков атомной станции при самозапуске мощных двигательных нагрузок

In the article, using computer modeling, an analysis of the operation of distance protection of backup transformers is carried out, providing alternative power supply for the own needs of a nuclear power plant through a backup busbar when disconnected from the power system. During the transition from the main network to the backup network, there is a short period of power off to the sections. At the same time, the powerful motor loads of the sections that have received power begin to operate in the freewheel braking mode. Then the reserve is automatically switched on, which can occur at a more or less favorable moment. At an unfavorable moment, self-starting may be electrically more severe than a short circuit on the busbar. When combining a new network from a backup auxiliary transformer and an autonomous circuit of running machines, transient processes of electromagnetic interaction between machines switching to generator mode and the new network arise. There are some optimal favorable moments for merging networks when it is advisable to carry out self-starting. Due to the complexity of the mathematical description with a high order system of equations and a large number of interaction objects, it is advisable to study these processes using computer modeling. A practical question, which is answered by the calculations and computer modeling, concerns the value of the distance protection setting for the backup transformer for auxiliary needs. Using the developed structural simulation model in MatLab, a series of experiments was carried out on the run-down and self-starting of auxiliary sections with their given composition and load. The range of self-start time corresponded to the operation of automatic switching on of the reserve sections by distance protection. Calculations and modeling show that the adopted setting can be adjusted, ensuring protection of a larger length of the busbar with possible options for connecting auxiliary sections to it. The model is supplemented with an add-on in the form of an external program for detailed processing and visualization of data obtained from oscilloscopes of the MatLab structural model.

Otoritas Ibn 'Asyur dalam Al-Tahrir Wa Al-Tanwir sebagai Pembentuk Wacana dalam Dunia Tafsir (Studi Pendekatan Michel Foucault)

This study aims to explore aspects of Ibn 'Asyur's authority in the tafsir al-Tahrir wa al-Tanwir as a discourse shaper in the scientific world of Qur'anic interpretation. This type of research is library research with descriptive-analytical method. The approach to be used to achieve the research objectives is the archaeology of knowledge approach initiated by Michel Foucault in the concept of power and knowledge relations. The result of this research is that Ibn 'Asyur's tafsir al-Tahrir wa al-Tanwir has an important authority in the scientific world of tafsir. This is characterized by several things. First, the complexity of Ibn 'Asyur descriptions that contain various opinions of scholars without favoring one opinion with another opinion without rational reasons creates new developments in the science of interpretation. This creates its own authority because it is able to release the tendency of laziness by moving to the aspect of rationality. Second, his expertise in the field of maqashid al-syari'ah makes him able to understand the differences in each of the arguments of the scholars of different schools and sometimes seem contradictory. With such insight, Ibn 'Asyur was able to escape the subjetivity of the madhhab and chose to be objective by containing all opinions.