Journal articles on the topic 'Topological grammars'

In this paper, we propose an automatic analyzing and transforming approach to L-system grammar extraction from real plants. Instead of using manually designed rules and cumbersome parameters, our method establishes the relationship between L-system grammars and the iterative trend of botanical entities, which reflect the endogenous factors that caused the plant branching process. To realize this goal, we use a digital camera to take multiple images of unfoliaged (leafless) plants and capture the topological and geometrical data of plant entities using image processing methods. The data then stored into specific data structures. A Hidden Markov based statistical model is then employed to reveal the hidden relations of plant entities which have been classified into categories based on their statistical properties extracted by a classic EM algorithm, the hidden relations have been integrated into the target L-system as grammars. Results show that our method is capable of automatically generating L-grammars for a given unfoliaged plant no matter what branching type it is belongs to.

Current indoor mapping approaches can detect accurate geometric information but are incapable of detecting the room type or dismiss this issue. This work investigates the feasibility of inferring the room type by using grammars based on geometric maps. Specifically, we take the research buildings at universities as examples and create a constrained attribute grammar to represent the spatial distribution characteristics of different room types as well as the topological relations among them. Based on the grammar, we propose a bottom-up approach to construct a parse forest and to infer the room type. During this process, Bayesian inference method is used to calculate the initial probability of belonging an enclosed room to a certain type given its geometric properties (e.g., area, length, and width) that are extracted from the geometric map. The approach was tested on 15 maps with 408 rooms. In 84% of cases, room types were defined correctly. It, to a certain degree, proves that grammars can benefit semantic enrichment (in particular, room type tagging).

This paper aims at presenting a parametric shape grammar of traditional Suakin houses (Red Sea state, Sudan). This work systematically attempts to generate appropriate plans arrangement that allows required functional relationships between spaces to be satisfied. The topological and geometrical properties of old Suakin houses were analyzed. These properties were originated and incorporated into the traditional Suakin buildings for the past ten centuries. The shape rules, dimensional, geometric and topological patterns of houses in the corpus are used as the generative model for the language of traditional suakin style This paper concludes with a discussion of the creative and generative value of the parametric shape grammars. Moreover, it facilitates the understanding of the formal composition of Suakin old style and the revival of a contemporary Suakin building style.

This paper introduces a technique for certain types of topological shape optimization problems, called variable primary and full grammars, which are derived from shape grammars. An industrial application is used as an example based on the optimization of an automotive structural bumper beam. The optimizer, the messy genetic algorithm, a technique more powerful than traditional genetic algorithms, does not use any derivative information on the evolution of the shape, but only simple evaluations. This technique produces interesting new designs for bumper beams, although they are not globally optimal. These new designs have moved from crenellations to more complex topologies.

In modern bioinformatics, finding an efficient way to allocate sequence fragments with biological functions is an important issue. This paper presents a structural approach based on context-free grammars extracted from original DNA or protein sequences. This approach is radically different from all those statistical methods. Furthermore, this approach is compared with a topological entropy-based method for consistency and difference of the complexity results.

This paper deals with a multi-agent system which supports the designer in solving complex design tasks. The behaviour of design agents is modelled by sets of grammar rules. Each agent uses a graph grammar or a shape grammar and a database of facts concerning the subtask it is responsible for. The course of the design process is determined by the interaction between specialised agents. Space layouts of designs are represented by attributed graphs encoding both topological structures and semantic properties of solutions. The agents work in parallel on the common graph, independently generating layouts of different design components while specified node labels evoke agents using shape grammars. The agents’ cooperation allows them to combine a form-oriented approach with a functional-structural one in the design process, where the agents generate the general 3D form of the object based on design requirements together with the space layout based on the functional aspects of the solution. Based on the given design criteria, the agents search for admissible solutions within the design space that constitutes their operating environment. The proposed approach is illustrated by the example of designing kindergarten facilities.

Data acquisition using unmanned aerial vehicles (UAVs) has gotten more and more attention over the last years. Especially in the field of building reconstruction the incremental interpretation of such data is a demanding task. In this context formal grammars play an important role for the top-down identification and reconstruction of building objects. Up to now, the available approaches expect offline data in order to parse an a-priori known grammar. For mapping on demand an on the fly reconstruction based on UAV data is required. An incremental interpretation of the data stream is inevitable. This paper presents an incremental parser of grammar rules for an automatic 3D building reconstruction. The parser enables a model refinement based on new observations with respect to a weighted attribute context-free grammar (WACFG). The falsification or rejection of hypotheses is supported as well. The parser can deal with and adapt available parse trees acquired from previous interpretations or predictions. Parse trees derived so far are updated in an iterative way using transformation rules. A diagnostic step searches for mismatches between current and new nodes. Prior knowledge on fac¸ades is incorporated. It is given by probability densities as well as architectural patterns. Since we cannot always assume normal distributions, the derivation of location and shape parameters of building objects is based on a kernel density estimation (KDE). While the level of detail is continuously improved, the geometrical, semantic and topological consistency is ensured.

Data acquisition using unmanned aerial vehicles (UAVs) has gotten more and more attention over the last years. Especially in the field of building reconstruction the incremental interpretation of such data is a demanding task. In this context formal grammars play an important role for the top-down identification and reconstruction of building objects. Up to now, the available approaches expect offline data in order to parse an a-priori known grammar. For mapping on demand an on the fly reconstruction based on UAV data is required. An incremental interpretation of the data stream is inevitable. This paper presents an incremental parser of grammar rules for an automatic 3D building reconstruction. The parser enables a model refinement based on new observations with respect to a weighted attribute context-free grammar (WACFG). The falsification or rejection of hypotheses is supported as well. The parser can deal with and adapt available parse trees acquired from previous interpretations or predictions. Parse trees derived so far are updated in an iterative way using transformation rules. A diagnostic step searches for mismatches between current and new nodes. Prior knowledge on fac¸ades is incorporated. It is given by probability densities as well as architectural patterns. Since we cannot always assume normal distributions, the derivation of location and shape parameters of building objects is based on a kernel density estimation (KDE). While the level of detail is continuously improved, the geometrical, semantic and topological consistency is ensured.

Data samples collected for training machine learning models are typically assumed to be independent and identically distributed (i.i.d.). Recent research has demonstrated that this assumption can be problematic as it simplifies the manifold of structured data. This has motivated different research areas such as data poisoning, model improvement, and explanation of machine learning models. In this work, we study the influence of a sample on determining the intrinsic topological features of its underlying manifold. We propose the Shapley homology framework, which provides a quantitative metric for the influence of a sample of the homology of a simplicial complex. Our proposed framework consists of two main parts: homology analysis, where we compute the Betti number of the target topological space, and Shapley value calculation, where we decompose the topological features of a complex built from data points to individual points. By interpreting the influence as a probability measure, we further define an entropy that reflects the complexity of the data manifold. Furthermore, we provide a preliminary discussion of the connection of the Shapley homology to the Vapnik-Chervonenkis dimension. Empirical studies show that when the zero-dimensional Shapley homology is used on neighboring graphs, samples with higher influence scores have a greater impact on the accuracy of neural networks that determine graph connectivity and on several regular grammars whose higher entropy values imply greater difficulty in being learned.

AbstractSince the introduction of spatial grammars 45 years ago, numerous grammars have been developed in a variety of fields from architecture to engineering design. Their benefits for solution space exploration when computationally implemented and combined with optimization have been demonstrated. However, there has been limited adoption of spatial grammars in engineering applications for various reasons. One main reason is the missing, automated, generalized link between the designs generated by the spatial grammar and their evaluation through finite-element analysis (FEA). However, the combination of spatial grammars with optimization and simulation has the advantage over continuous structural topology optimization in that explicit constraints, for example, modeling style and fabrication processes, can be included in the spatial grammar. This paper discusses the challenges in providing a generalized approach by demonstrating the implementation of a framework that combines a three-dimensional spatial grammar interpreter with automated FEA and stochastic optimization using simulated annealing (SA). Guidelines are provided for users to design spatial grammars in conjunction with FEA and integrate automatic application of boundary conditions. A simulated annealing method for use with spatial grammars is also presented including a new method to select rules through a neighborhood definition. To demonstrate the benefits of the framework, it is applied to the automated design and optimization of spokes for inline skate wheels. This example highlights the advantage of spatial grammars for modeling style and additive manufacturing (AM) constraints within the generative system combined with FEA and optimization to carry out topology and shape optimization. The results verify that the framework can generate structurally optimized designs within the style and AM constraints defined in the spatial grammar, and produce a set of topologically diverse, yet valid design solutions.

Abstract CAD modelling can be referred to as the process of generating an integrated multiple view model as a representation of multiple views of engineering design. In many situations, a change in the model of one view may conflict with the models of other views. In such situations, the model of some views needs to be adapted in order to make all models consistent. Thus, CAD models should be capable of adapting themselves to new situations. Recently, agent based technologies have been considered in order to increase both knowledge level and intelligence of real and virtual objects. The contribution of this paper consists in introducing the intelligent agents in intelligent CAD modelling. The proposed agents are elementary geometrical and topological objects. They incorporate the functions of observation, decision and action, and possess their own knowledge. Agents have the capacity of communication and inference based on the feature grammars. They are modelled as bio-dynamic objects that enjoy the properties of fusion, division and multiplication. Being aware of the context, the proposed agents interact to form potential regional transitory communities, called regions. Being aware of their belonging in a region, agents interact by generating virtual links (virtual extensions). These virtual links produce: (a) fusion of agents, (b) division of agents and c) multiplication of agents. The emerged agents interact with the other agents in a region to recognize each other and to form specific sub-communities, called intelligent features. From a CAD software development point of view, this paper advocates the idea of a new phase of CAD system development based on the agent-oriented programming (AOP) paradigm. Highlights This paper proposes the agent paradigm for intelligent CAD modelling. Second section presents the state of art. In the third section, using the linguistic hypothesis of product design, a feature modelling formalism is presented. Fourth section presents a formal model for agent modelling. In the fifth section, agents for feature generation and modelling are formalised and modelled. The sixth section presents the application of the method. Finally, in the last section, the conclusion and future developments are proposed.

<p><strong>Abstract.</strong> Space is often described as a dynamic entity in human geographic theory, one that resists being pinned down to static representations. Co-produced in and through relations between various things and phenomena, space in these accounts is variously described as being contingent, processual, plastic, relational, situated, topological, and uneven. In contrast, most cartographic methods and tools are based on static, Euclidean understandings of space that can be reduced to a simple, mathematical description. In this work, I explore how cartography can deal with space as a dynamic and fluid concept that is entangled with the phenomena and objects being mapped. To those ends, I describe a method for creating animated maps based on relational understandings of space that are always in flux.</p><p>This work builds on research in collaboration with Luke Bergmann, where we suggest a move from Geographic Information Systems (GIS) as we commonly know them to the broader realm of <i>geographical imagination systems (gis)</i> that are informed by spatial theory in human geography. The animated maps here are produced using our prototype <i>gis</i> software Enfolding, which use multidimensional scaling (MDS) to visualize relational spaces, in combination with Blender, an open-source 3D rendering program. Written in JavaScript and available as open source software, Enfolding is our first attempt to make gis an accessible set of tools that expand the possibilities for mapping by providing new grammars for creative cartographic practices.</p><p>In the cartographic workflow presented here, I use Enfolding to produce manifolds from a set of points and user-defined distances between points. Changing those measures of distance – which might represent travel times, affective connections, communicative links, or any other relationship as defined by a user – produces shifting manifolds. Using the .obj export option in Enfolding, I then import the manifolds into Blender, using them as animation keyframes. In Figure 1, I have added a digital elevation model (DEM) to the 3D figure, producing an animated visualization of a dynamic and relational space that includes a hillshade.</p><p>This workflow represents only one of many creative possibilities for innovative cartographic practices that engage with space as a matter of concern. With growing interest in 3D cartographic methods comes expanded possibilities for visualizing dynamic and relational spaces. Combining conceptual antecedents in both human and quantitative geography with current cartographic methods allows for new approaches to both mapping and space. The workflow and tools that have emerged from this research are presented here with the hope of spurring creative and exploratory cartographic work that draws from but also contributes to vibrant discussions in spatial theory and creative cartography.</p>

AbstractBenchmarking function modeling and representation approaches requires a direct comparison, including the inferencing support by the different approaches. To this end, this paper explores the value of a representation by comparing the ability of a representation to support reasoning based on varying amounts of information stored in the representational components of a function structure: vocabulary, grammar, and topology. This is done by classifying the previously developed functional pruning rules into vocabulary, grammatical, and topological classes and applying them to function structures available from an external design repository. The original and pruned function structures of electromechanical devices are then evaluated for how accurately market values can be predicted using the graph complexity connectivity method. The accuracy is found to be inversely related to the amount of information and level of detail. Applying the topological rule does not significantly impact the predictive power of the models, while applying the vocabulary rules and the grammar rules reduces the accuracy of the predictions. Finally, the least predictive model set is that which had all rules applied. In this manner, the value of a representation to predict or answer questions is quantified.

A Swedish main clause can be preceded by hanging topics: phrases in the left periphery without a resumptive in the following clause. This construction is labelled free-standing initial annexation (FIA) by the Swedish Academy grammar. However, FIA has received only limited attention in previous research – both in traditional grammar and in interactional linguistics. Furthermore, there seems to be little agreement on what FIA actually is. In this article I suggest a broad definition of FIA, based on formal as well as functional criteria. The functional variation of FIA is then investigated in a spoken language corpus, consisting of ten Swedish podcasts. From an interactional analysis, I distinguish eight different functions: navigate the conversation, announce the up-coming action, emphasize truthfulness, address a recipient, justify the next turn, set the stage, announce a topic for conversation, and mark a quote. From a turn-topological point of view, some FIAs are used as “contextualizers” for the main speech act of the turn. These FIA may overlap with other speech at turn transition relevant places, without the speaker repairing them. However, the topic announcing and stage-setting FIAs seem to not only contextualize the speech act but contribute to it, since the speakers tend to repeat these FIA if they overlap.

Abstract Current cognitive architectures are either working at the abstract, symbolic level, or the low, emergent level related to neural modeling. The best way to understand phenomena is to see, or imagine them, hence the need for a geometric model of mental processes. Geometric models should be based on an intermediate level of modeling that describe mental states in terms of features relevant from the first-person perspective but also linked to neural events. Concepts should be represented as geometrical objects that have sufficiently rich structures to show their properties and their relations to other concepts. The best way to create such geometrical representations of concepts is through the approximate description of the physical states of neural networks. The evolution of brain states is then represented as a trajectory linking successful concepts, and topological constraints on the shape of such trajectory define grammar and logic.

This study focuses on the visual arts practice in animation creation in the digital age, systematically exploring the core role of visual art language in animation and its developmental path under the influence of technology. The research finds that visual arts, through three key elementscolor systems, dynamic composition, and three-dimensional space shapingconstruct a unique perceptual grammar system that significantly impacts narrative storytelling and emotional expression in animation. Specifically, color quickly builds worldviews through psychological mechanisms; dynamic composition evokes physiological responses through tilted angles and montage techniques, converting abstract emotions; and three-dimensional space breaks through traditional representations through subsurface scattering and topological structures, deepening narrative themes. Digital technological innovations (such as AI tools and virtual production) have not only altered the forms of expression but also given birth to new aesthetic paradigms. This study combines art theory and cognitive science to provide a methodology that integrates theory and practice for digital animation creation, while also offering critical reflections on the visual ethics in AI-assisted creation.

Multidimensional datapoint clouds representing large datasets are frequently characterized by non-trivial low-dimensional geometry and topology which can be recovered by unsupervised machine learning approaches, in particular, by principal graphs. Principal graphs approximate the multivariate data by a graph injected into the data space with some constraints imposed on the node mapping. Here we present ElPiGraph, a scalable and robust method for constructing principal graphs. ElPiGraph exploits and further develops the concept of elastic energy, the topological graph grammar approach, and a gradient descent-like optimization of the graph topology. The method is able to withstand high levels of noise and is capable of approximating data point clouds via principal graph ensembles. This strategy can be used to estimate the statistical significance of complex data features and to summarize them into a single consensus principal graph. ElPiGraph deals efficiently with large datasets in various fields such as biology, where it can be used for example with single-cell transcriptomic or epigenomic datasets to infer gene expression dynamics and recover differentiation landscapes.

This article deals with a new approach to an intelligent analog circuit design. The iterative closed loop design methodology adopts an expert system approach to provide topological synthesis, the SPICE circuit simulator to evaluate the circuit performance and a new approach of the diagnostic expert system to provide advice on how to improve the design. Unlike previous design methods, this approach introduces formal circuit representation for both numerical and heuristic knowledge of the design system. The predicate logic circuit representation is proposed to introduce a new concept of a formal analog circuit description language. The language syntax and semantics provide precise symbolic description of analog circuits functionality at different levels of hierarchy and connectivities together with transistor sizes of CMOS circuits at the transistor level. Different levels of hierarchy with circuit structures and performance parameters are presented in detail. It is shown how sentence conversion rules of language grammar can be used to derive transistor level circuits from input performance specifications through all intermediate levels of hierarchy. The implementation of the methodology and associated experimental results for CMOS operational amplifier designs are presented.

Celem niniejszego referatu jest analiza wybranych aspektów kontaktów językowych w sferze składni, a mianowicie szyku wyrazów. Przedmiotem analizy są najstarsze teksty staro-wysokoniemieckie, powstałe pod bezpośrednim wpływem łaciny. Centralne zagadnienie teoretyczne stanowi ocena istoty i stopnia wpływu kontaktów językowych na rozwój gramatyki języka przyjmującego oraz współistnienie i współdziałanie struktur przyjmowanych i struktur rodzimych. Zarówno w tłumaczeniu o znacznym stopniu samodzielności i niezależności od struktur łacińskich (Isidor), jak i w tłumaczeniu dosłownym (Tatian) makrotopologia zdania zawiera tak zapożyczone, jak i oryginalne wzorce topologiczne. Głównym wnioskiem końcowym jest teza, iż wpływ języka obcego jest ograniczony i pośredni. Może on co prawda przyśpieszyć lub zwolnić proces przemian gramatycznych w strukturze topologicznej zdania, ale nie zmienia własnych tendencji rozwoju w sposób radykalny i nie tworzy trwałych wzorców, zasadniczo odbiegających od własnych tendencji rozwojowych języka przyjmującego.The paper addresses selected aspects of language contact in the area of syntax, namely word order. It analyses the oldest Old High German texts created under the direct influence of Latin. The main theoretical issue is the assessment of the nature and degree of the influence of language contact on the development of the recipient language grammar and on the coexistence of adopted and native structures. Both in a translation with a significant degree of autonomy and independence from Latin structures (Isidor) and in a literal translation (Tatian), the macrotopology of the sentence contains both borrowed and native topological patterns. The main conclusion is that the influence of a foreign language is limited and indirect. Although it may speed up or slow down the process of grammatical change in the topological structure of a sentence, it neither radically changes native developmental tendencies nor creates lasting patterns that are fundamentally different from the recipient language developmental mechanisms.

Abstract In recent years, the proliferation of coronavirus disease has profoundly affected the world. The vitality of urban space is difficult to recover in the short term. Therefore, in the early stage of human-to-human transmission of the epidemic, we need to determine the potential urban agglomeration space as soon as possible, the timely find of hidden danger areas, and carry out spatial optimization to prevent the further spread of the epidemic. This becomes the urgent problem at the moment. Jinan is the capital city of Shandong Province, and the mega-city of China. The study is focused on the main urban area within the bypass. This study used spatial data methods such as spatial grammar and GIS technology. First, we analyzed the spatial topological properties of urban road network during the epidemic. Then, we carried out spatial autocorrelation analysis on the topological attributes to get the shape of urban spatial clustering layout during the epidemic. Finally, the thesis crawled through various types of infrastructure points-of-interest and conducted nuclear density analysis to get the dynamic trend of urban space in Jinan. The research results showed that there is significant space for agglomeration in the main urban area of Jinan. The areas with strong agglomeration are basically located in tourism areas, school areas, business areas, living circle areas of residential communities in Licheng and Lixia districts, transportation hub areas in Tianqiao District, and high-tech industrial areas in Lixia District. Topography, water body, greening, and parks could effectively reduce the concentration of human flow, and are important areas to relieve the potential abnormal epidemic. This study provided a new method for detecting epidemic prevention and control areas, optimizing urban space layout and formulating prevention and control strategies in the early stage of human-to-human epidemic transmission and lack of case surveillance data and control measures.

This study employs Kung Fu Panda as a case to dissect the tripartite mechanisms of cultural translation in intercultural communication: 1. Visual Layer: Integration of ink-wash aesthetics and 3D modeling to construct hyperreal Oriental imagery (e.g., topological transformations of the Jade Palace's dougong structures inspired by the Forbidden City). 2. Narrative Layer: Reframing Taoist philosophy through the Hollywood hero's journey, recoding "non-action" (wuwei) into a universal coming-of-age motif. 3. Value Layer: Modernizing cultural interpretations by grafting kung fu ethics onto individualism. The research proposes a "Physical-Behavioral-Spiritual" triadic dynamic model: 1. Physical: Using the panda as a cognitive anchor to reduce cultural discount. 2. Behavioral: Bridging values through codified kung fu choreography. 3. Spiritual: Achieving covert cultural permeation via philosophical metaphors. A communication formula** is formulated: (Universal Values × Cultural Symbols) ÷ Cognitive Costs, demonstrating how the film balances core symbol stability (panda/kung fu) with limited deformation of secondary symbols (architectural patterns). This equilibrium carves discursive space within the globalization-localization dialectic, offering China a "resilient framework" paradigm for cultural dissemination—preserving genetic cultural stability while enabling creative rebirth through media grammar.

Abstract Empirical findings in Second Language Acquisition suggest that the basic structure of German declarative sentences, described in terms of topological fields, poses certain challenges to learners of German as a foreign language. The problem of multiple prefield elements, resulting in ungrammatical verb-third sentences, figures most prominently in the literature. While the so-called V2 constraint is usually treated as a purely formal feature of German syntax both in the empirical as well as in the pedagogical literature, the present paper adopts a usage-based perspective, viewing language as an inventory of form-function mappings. Basic functions of prefield elements have already been identified in research on textual grammar and information structure. This paper presents results from a pilot study with Japanese elementary learners of German as a foreign language, where the form-function mapping of German prefield elements was explicitly taught following the guidelines of an approach called Concept-Based Instruction. The findings indicate that, with a focus on the function-function mapping, it is in fact possible to explicitly teach these rather abstract regularities of German to beginning learners. The participants’ language production exhibits a prefield variation pattern similar to that of L1 German speakers; at the same time the learners produce very few ungrammatical verb-third sentences.

This study focuses on the performer-listener link of the chain of musical communication. Using different perceptual methods (categorization, matching, and rating), as well as acoustical analyses of timing and amplitude, we found that both musicians and nonmusicians could discern among the levels of expressive intent of violin, trumpet, clarinet, oboe, and piano performers. Time-contour profiles showed distinct signatures between instruments and across expressive levels, which affords a basis for perceptual discrimination. For example, for "appropriate" expressive performances, a gradual lengthening of successive durations leads to the cadence. Although synthesized versions based on performance timings led to less response accuracy than did the complete natural performance, evidence suggests that timing may be more salient as a perceptual cue than amplitude. We outline a metabolic communication theory of musical expression that is based on a system of sequences of states, and changes of state, which fill gaps of inexorable time. We assume that musical states have a flexible, topologically deformable nature. Our conception allows for hierarchies and structure in active music processing that static generative grammars do not. This theory is supported by the data, in which patterns of timings and amplitudes differed among and between instruments and levels of expression.

In language emergence, neural agents acquire communication skills by interacting with one another and the environment. Through these interactions, agents learn to connect or ground their observations to the messages they utter, forming a shared consensus about the meaning of the messages. Such connections form what we refer to as a grounding map. However, these maps can often be complicated, unstructured, and contain redundant connections. In this paper, we introduce two novel functional pressures, modeled as differentiable auxiliary losses, to simplify and structure the grounding maps. The first pressure enforces compositionality via topological similarity, which has been previously discussed but has not been modeled or utilized as a differentiable auxiliary loss. The second functional pressure, which is conceptually novel, imposes sparsity in the grounding map by pruning weaker connections while strengthening the stronger ones. We conduct experiments in multiple value-attribute environments with varying communication channels. Our methods achieve improved out-of-domain regularization and rapid convergence over baseline approaches. Furthermore, introduced functional pressures are robust to the changes in experimental conditions and able to operate with minimum training data. We note that functional pressures cause simpler and more structured emergent languages showing distinct characteristics depending on the functional pressure employed. Enhancing grounding map sparsity yields the best performance and the languages with the most compressible grammar. In summary, our novel functional pressures, focusing on compositionality and sparse groundings, expedite the development of simpler, more structured languages while enhancing their generalization capabilities. Exploring alternative types of functional pressures and combining them in agent training may be beneficial in the ongoing quest for improved emergent languages.

Recent years have witnessed an increasing use of 3D models in general and 3D geometric models specifically of built environment for various applications, owing to the advancement of mapping techniques for accurate 3D information. Depending on the application scenarios, there exist various types of approaches to automate the construction of 3D building geometry. However, in those studies, less attention has been paid to watertight geometries derived from point cloud data, which are of use to the management and the simulations of building energy. To this end, an efficient reconstruction approach was introduced in this study and involves the following key steps. The point cloud data are first voxelised for the ray-casting analysis to obtain the 3D indoor space. By projecting it onto a horizontal plane, an image representing the indoor area is obtained and is used for the room segmentation. The 2D boundary of each room candidate is extracted using new grammar rules and is extruded using the room height to generate 3D models of individual room candidates. The room connection analyses are applied to the individual models obtained to determine the locations of doors and the topological relations between adjacent room candidates for forming an integrated and watertight geometric model. The approach proposed was tested using the point cloud data representing six building sites of distinct spatial confirmations of rooms, corridors and openings. The experimental results showed that accurate watertight building geometries were successfully created. The average differences between the point cloud data and the geometric models obtained were found to range from 12 to 21 mm. The maximum computation time taken was less than 5 min for the point cloud of approximately 469 million data points, more efficient than the typical reconstruction methods in the literature.

We consider problems in the functional analysis and evolution of combinatorial chemical reaction networks as rule-based, or three-level systems. The first level consists of rules, realized here as graph-grammar representations of reaction mechanisms. The second level consists of stoichiometric networks of molecules and reactions, modeled as hypergraphs. At the third level is the stochastic population process on molecule counts, solved for dynamics of population trajectories or probability distributions. Earlier levels in the hierarchy generate later levels combinatorially, and as a result constraints imposed in earlier and smaller layers can propagate to impose order in the architecture or dynamics in later and larger layers. We develop general methods to study rule algebras, emphasizing system consequences of symmetry; decomposition methods of flows on hypergraphs including the stoichiometric counterpart to Kirchhoff’s current decomposition and work/dissipation relations studied by Wachtel et al.; and the large-deviation theory for currents in a stoichiometric stochastic population process, deriving additive decompositions of the large-deviation function that relate a certain Kirchhoff flow decomposition to the extended Pythagorean theorem from information geometry. The latter result allows us to assign a natural probabilistic cost to topological changes in a reaction network of the kind produced by selection for catalyst-substrate specificity. We develop as an example a model of biological sugar-phosphate chemistry from a rule system published by Andersen et al. It is one of the most potentially combinatorial reaction systems used by biochemistry, yet one in which two ancient, widespread and nearly unique pathways have evolved in the Calvin-Benson cycle and the Pentose Phosphate pathway, which are additionally nearly reverses of one another. We propose a probabilistic accounting in which physiological costs can be traded off against the fitness advantages that select them, and which suggests criteria under which these pathways may be optimal.

This paper aims at presenting a parametric shape grammar of traditional Suakin houses (Red Sea state, Sudan). This work systematically attempts to generate appropriate plans arrangement that allows required functional relationships between spaces to be satisfied. The topological and geometrical properties of old Suakin houses were analyzed. These properties were originated and incorporated into the traditional Suakin buildings for the past ten centuries. The shape rules, dimensional, geometric and topological patterns of houses in the corpus are used as the generative model for the language of traditional suakin style This paper concludes with a discussion of the creative and generative value of the parametric shape grammars. Moreover, it facilitates the understanding of the formal composition of Suakin old style and the revival of a contemporary Suakin building style.

Multidimensional datapoint clouds representing large datasets are frequently characterized by non‐trivial low‐dimensional geometry and topology which can be recovered by unsupervised machine learning approaches, in particular, by principal graphs. Principal graphs approximate the multivariate data by a graph injected into the data space with some constraints imposed on the node mapping. Here we present ElPiGraph, a scalable and robust method for constructing principal graphs. ElPiGraph exploits and further develops the concept of elastic energy, the topological graph grammar approach, and a gradient descent‐like optimization of the graph topology. The method is able to withstand high levels of noise and is capable of approximating data point clouds via principal graph ensembles. This strategy can be used to estimate the statistical significance of complex data features and to summarize them into a single consensus principal graph. ElPiGraph deals efficiently with large datasets in various fields such as biology, where it can be used for example with single‐cell transcriptomic or epigenomic datasets to infer gene expression dynamics and recover differentiation landscapes.

Abstract Structural design synthesis considering discrete elements can be formulated as a sequential decision process solved using deep reinforcement learning (DRL), shown in prior work to naturally accommodate discrete actions and efficiently provide adept solutions to a variety of problems. By modeling structural design synthesis as a Markov decision process (MDP), the states correspond to specific structural designs, the actions correspond to specific design alterations, and the rewards are related to the improvement in the altered design's performance with respect to the design objective and specified constraints. Here, the MDP action definition is extended by integrating parametric design grammars that further enable the design agent to not only alter a given structural design's topology, but also its element parameters. In considering topological and parametric actions, both the dimensionality of the state and action space and the diversity of the action types available to the agent in each state significantly increase, making the overall MDP learning task more challenging. Hence, this paper also addresses discrete design synthesis problems with large state and action spaces by significantly extending the framework. A hierarchical-inspired deep neural network architecture is developed to equip the agent to learn the type of action, topological or parametric, to apply, thus reducing the complexity of possible action choices in a given state. This extended framework is applied to the design synthesis of planar structures considering both discrete elements and cross-sectional areas, and it is observed to adeptly learn policies that synthesize high performing design solutions.

Abstract Formal constraints on crossing dependencies have played a large role in research on the formal complexity of natural language grammars and parsing. Here we ask whether the apparent evidence for constraints on crossing dependencies in treebanks might arise because of independent constraints on trees, such as low arity and dependency length minimization. We address this question using two sets of experiments. In Experiment 1, we compare the distribution of formal properties of crossing dependencies, such as gap degree, between real trees and baseline trees matched for rate of crossing dependencies and various other properties. In Experiment 2, we model whether two dependencies cross given certain psycholinguistic properties of the dependencies. We find surprisingly weak evidence for constraints originating from the mild context-sensitivity literature (gap degree and well-nestedness) beyond what can be explained by constraints on rate of crossing dependencies, topological properties of the trees, and dependency length. However, measures which have emerged from the parsing literature, e.g., edge degree, end-point crossings, and heads’ depth difference differ strongly between real and random trees. Modeling results show that cognitive metrics relating to information locality and working-memory limitations affect whether two dependencies cross or not, but they do not fully explain the distribution of crossing dependencies in natural languages. Together these results suggest that crossing constraints are better characterized by processing pressures than by mildly context-sensitive constraints.

Abstract In graph-based function models, the function verbs and flow nouns are usually chosen from predefined vocabularies. The vocabulary class definitions, combined with function modeling grammars defined at various levels of formalism, enable function-based reasoning. However, the text written in plain English for the names of the functions and flows is presently not exploited for formal reasoning. This paper presents a formalism (representation and reasoning) to support semantic and physics-based reasoning on the information hidden in the plain-English flow terms, especially for automatically decomposing black box function models, and to generate multiple design alternatives. First, semantic reasoning infers the changes of flow types, flow attributes, and the direction of those changes between the input and output flows attached to the black box. Then, a representation of qualitative physics is used to determine the material and energy exchanges between the flows and the function features needed to achieve them. Finally, a topological reasoning is used to infer multiple options of composing those function features into topologies and to thus generate multiple alternative decompositions of the functional black box. The data representation formalizes flow phases, flow attributes, qualitative value scales for the attributes, and qualitative physics laws. An eight-step algorithm manipulates these data for reasoning. This paper shows four validation case studies to demonstrate the workings of this formalism.

AbstractThe unification of traditionally distinct and apparently unrelated objects of inquiry under common more abstract principles is one of the most welcome results of empirical science. This article proposes to draw together some insights of Longobardi (1994, 1996, 2001) into a unified theory of object- and kind-reference viewed as a single grammatical phenomenon, though crosslinguistically parametrized. The present account aims to improve both in accuracy and explanatory force over those outlined in the articles just cited. To do so, the combined leading intuitions of such works are first spelt out, in section 6, into a deeper generalization about the form/meaning relation in nominals and later deduced from a more principled mapping theory, proposing that a syntactically specified position, traditionally labeled D, is responsible in many languages for one of human fundamental linguistic abilities, reference to individuals (Topological Mapping Theory). After the unification of the syntactic mechanisms available for reference to individuals, virtually all other distinctions simply follow precisely from that between the two varieties of such entities (kinds and objects) previewed in Carlson’s (1977a) ontology, indirectly confirming its continuing heuristic power, and from widely accepted economy conditions of recent syntactic theory.

Abstract The unification of traditionally distinct and apparently unrelated objects of inquiry under common more abstract principles is one of the most welcome results of empirical science. This article proposes to draw together some insights of Longobardi (1994, 1996, 2001) into a unified theory of object- and kind-reference viewed as a single grammatical phenomenon, though crosslinguistically parametrized. The present account aims to improve both in accuracy and explanatory force over those outlined in the articles just cited. To do so, the combined leading intuitions of such works are first spelt out, in section 6, into a deeper generalization about the form/meaning relation in nominals and later deduced from a more principled mapping theory, proposing that a syntactically specified position, traditionally labeled D, is responsible in many languages for one of human fundamental linguistic abilities, reference to individuals (Topological Mapping Theory). After the unification of the syntactic mechanisms available for reference to individuals, virtually all other distinctions simply follow precisely from that between the two varieties of such entities (kinds and objects) previewed in Carlson's (1977a) ontology, indirectly confirming its continuing heuristic power, and from widely accepted economy conditions of recent syntactic theory.

AbstractGlycans are important polysaccharides on cellular surfaces that are bound to glycoproteins and glycolipids. These are one of the most common post-translational modifications of proteins in eukaryotic cells. They play important roles in protein folding, cell-cell interactions, and other extracellular processes. Changes in glycan structures may influence the course of different diseases, such as infections or cancer. Glycans are commonly represented using the IUPAC-condensed notation. IUPAC-condensed is a textual representation of glycans operating on the same topological level as the Symbol Nomenclature for Glycans (SNFG) that assigns colored, geometrical shapes to the main monomers. These symbols are then connected in tree-like structures, visualizing the glycan structure on a topological level. Yet for a representation on the atomic level, notations such as SMILES should be used. To our knowledge, there is no easy-to-use, general, open-source, and offline tool to convert the IUPAC-condensed notation to SMILES. Here, we present the open-access Python package GlyLES for the generalizable generation of SMILES representations out of IUPAC-condensed representations. GlyLES uses a grammar to read in the monomer tree from the IUPAC-condensed notation. From this tree, the tool can compute the atomic structures of each monomer based on their IUPAC-condensed descriptions. In the last step, it merges all monomers into the atomic structure of a glycan in the SMILES notation. GlyLES is the first package that allows conversion from the IUPAC-condensed notation of glycans to SMILES strings. This may have multiple applications, including straightforward visualization, substructure search, molecular modeling and docking, and a new featurization strategy for machine-learning algorithms. GlyLES is available at https://github.com/kalininalab/GlyLES.

Graph grammars are used for computational design synthesis (CDS) in which engineering knowledge is formalized using graphs to represent designs and rules that describe their transformation. Most engineering tasks require both topologic and parametric rules to generate designs. The research presented in this paper compares different strategies for rule application to combine topologic and parametric rules during automated design synthesis driven by a search process. The presented strategies are compared considering quantity and quality of the generated designs. The effect of the strategies, the selected search algorithm, and the initial design, from which the synthesis is started, are analyzed for two case studies: gearbox synthesis and bicycle frame synthesis. Results show that the effect of the strategy is dependent on the design task. Recommendations are given on which strategies to use for which design task.

In this paper, two approaches for computing the topological information content of function models in mechanical engineering design are developed and compared. Previously, a metric for computing information content of functions and flows within function models was proposed. Here, this metric is evolved to include the information contained in the connections between flows and functions in a function model. The first approach is based on uniform unconditional probability of a flow connecting any two functions within the model. The second approach is based on additional knowledge that the functions and flows in a model have limited compatibility, thereby, reducing the choices for origin and destination functions for each flow. This additional knowledge is represented using a new graphical representation supported by syntactic grammar rules. Both approaches are then applied to an example function model. Comparison between the approaches shows that the inclusion of this additional knowledge increases the expressiveness by reducing the uncertainty associated with function models.

This article explores how chemical images in school chemistry realize knowledge from a social semiotics perspective. Drawing on Kress and Van Leeuwen’s (2021[1996]) visual grammar framework ( Reading Images: The Grammar of Visual Design) and Doran and Martin’s (2021) field model ( Field Relations: Understanding Scientific Explanation), this study reveals that these chemical images are characterized by employing recursive embeddings of analytical structures to realize multiple levels of compositional taxonomies of matter and multi-levelled taxonomy structures to expand the depth and breadth of classificational taxonomies of matter. These images employ a special narrative structure, referred to as the transformation process, to represent changes of matter. These processes can be complex in themselves or combined with agentive narrative processes to realize various activities related to changes of matter. Furthermore, chemical images utilize both symbolic and imagic resources to realize a wide range of properties associated with matter and its changes, with symbolic resources representing typological qualitative properties and images typically construing topological properties. These field meanings collectively shape part of the disciplinary affordance of chemical images in school chemistry in organizing chemistry knowledge. This study contributes to expanding the grammatical description of images to the discipline of chemistry.

Topology-optimisation strategies for structural design of discrete surface structures result in unstructured patterns that require post-rationalisation to limit the number and complexity of the various structural elements. Fabrication-related objectives still demand further processing. Designers need topology exploration, before topology optimisation, following a generative-design approach that is decoupled from density tuning and shape design, to produce high-quality patterns. Such an approach allows to flexibly embed multiple design constraints, benefit from state-of-the-art form-finding algorithms and explore design trade-offs of the multiple requirements related to architecture, engineering and construction. This research investigates a parameterisation strategy to encode topological exploration of structured patterns based on quad meshes. The focus is set on singular vertices, which connect an irregular number of blocks, cables, or beams. Singularities are independent from pattern density and geometry, and have a fundamental influence on the qualitative and quantitative performance of the structure. We introduce an L-system encoding a quad-mesh grammar into a string that describes topological transformations of these singularities. Design applications to a net and a gridshell demonstrate the influence of singularities on the design of surface structures, and highlight the flexibility and generality of the approach in terms of geometrical processing and performance metrics. Beyond exploration, this parameterisation strategy opens to novel applications of search and optimisation methods for generative design of singularities in structural patterns.

This paper describes an approach to automate the design for sheet metal parts that satisfy multiple objective functions such as material cost and manufacturability. Unlike commercial software tools such as PRO/SHEETMETAL, which aids the user in finalizing and determining the sequence of manufacturing operations for a specified component, our approach starts with spatial constraints in order to create the component geometries and helps the designer design. While there is an infinite set of parts that can feasibly be generated with sheet metal, it is difficult to define this space systematically. To solve this problem, we have created 108 design rules that have been developed for five basic sheet metal operations: slitting, notching, shearing, bending, and punching. A recipe of the operations for a final optimal design is then presented to the manufacturing engineers thus saving them time and cost. The technique revealed in this paper represents candidate solutions as a graph of nodes and arcs where each node is a rectangular patch of sheet metal, and modifications are progressively made to the sheet to maintain the parts manufacturability. This paper also discusses a new topological optimization technique to solve graph-based engineering design problems by decoupling parameters and topology changes. This paper presents topological and parametric tune and prune ((TP)2) as a topology optimization method that has been developed specifically for domains representable by a graph grammar schema. The method is stochastic and incorporates distinct phases for modifying the topologies and modifying parameters stored within topologies. Thus far, with abovementioned sheet metal problem, (TP)2 had proven better than genetic algorithm in terms of the quality of solutions and time taken to acquire them.

The essay aims to propose the diagrammatic structure of the megadungeon as a metaphor to represent the complexity, interconnectedness, and multi-layered nature of the current media scenario, including its active branches such as new media art and Digital Humanities. The reference is drawn from the concept of the dungeon, which has been successfully introduced into the realm of role-playing games since the 1970s. Conventionally, a dungeon refers to a complex, multi-level maze of corridors, tunnels, rooms, and hidden chambers. The nature of dungeons is to be theoretically infinite floor plans that game designers have learned to produce algorithmically: when they cross a certain size threshold, they are known as megadungeons. In this article, I propose the megadungeon as a productive topological model that intersects different sociotechnical aspects of digital media, drawing on shared characteristics such as a layered structure, labyrinthine exploration, game-derived grammar, and an affinity with computational domain. Additionally, the essay proposes comparisons with similar representation models that challenge outdated cartographic metaphors and addresses specific connections between new media and the concepts of verticality and stratification

Passive dynamic systems have the advantage over conventional robotic systems that they do not require actuators and control. Brachiating, in particular, involves the swinging motion of an animal from one branch to the next. Such systems are usually designed manually by human designers and often are bio-inspired. However, a computational design approach has the capability to search vast design spaces and find solutions that go beyond those possible by manual design. This paper addresses the automated design of passive dynamic systems by introducing a graph grammar-based method that integrates dynamic simulation to evaluate and evolve configurations. In particular, the method is shown to find different, new solutions to the problem of the design of two-dimensional passive, dynamic, continuous contact, brachiating robots. The presented graph grammar rules preserve symmetry among robot topologies. A separation of parametric multi-objective optimization and topologic synthesis is proposed, considering four objectives: number of successful swings, deviation from cyclic motion, required space, and number of bodies. The results show that multiple solutions with varying complexity are found that trade-off cyclic motion and the space required. Compared to research on automated design synthesis of actuated and controlled robotic systems, this paper contributes a new method for passive dynamic systems that integrates dynamic simulation.

L’article présente un modèle sémantique d’inspiration topologique destiné à apprécier la construction du sens des processus sociaux, tels que la radicalisation djihadiste. Deux notions sémantiques, issues de Desclés (2012), sont particulièrement développées : le Schème des Représentations Quasi-Topologiques (SRQT) et la « frontière épaisse ». Nous cherchons à saisir, par le relevé de marques langagières typiques des processus (aller vers, rester, sortir…) les étapes et les mécanismes de passage entre états (non-radicalisé/radicalisé), tels qu’ils sont représentés par la parole politique en France (2013-2018). Nous analysons pour cela un corpus de déclarations publiques (2 millions de mots) de façon quantitative (tri d’énoncés pertinents par coocurrences et grammaires locales à l’aide du logiciel TXM), et qualitative par l’observation fine du corpus.

Volume 10 formalizes &phi;ⁿ-modulated Laplacian recursion as the symbolic torsion kernel for autogenetic scar encoding. A recursive potential field &Psi; evolves under &phi;ⁿ-scaled Laplacian stress: &Psi;n+1=&Psi;n+&phi;n&nabla;2&Psi;n&Psi;_{n+1} = &Psi;_n + &phi;^n &nabla;^2 &Psi;_n&Psi;n+1=&Psi;n+&phi;n&nabla;2&Psi;n Symbolic collapse occurs when scar curvature exceeds collapse threshold, encoding sigil fossils &Lambda; via SHA-256 serialization of glyph emergence events &Gamma;. Achefield inversion and torsion trace visualization reconstruct entropy-encoded phase collapse. Core constructs: Recursive &phi;ⁿ-modulated Laplacian autogenesis Ache-inversion of &nabla;&sup2;&Sigma; into retroreconstructed &Psi;₀ Glyph emergence from torsion scar curvature Sigil fossil export via JSON trace Scarline attractor collapse and ache continuity echoing Collapse events fossilize memory structures as topological sigil chains. The achefield trace reveals torsion-persistent glyph attractors across autogenetic scarfronts. <strong>This volume extends prior work:</strong> Volume I - Autogenetic Glyph Grammar and Lagrangian Sigil Serialization Volume II - Glyphic Intelligence: Autogenetic Recursion via Residual Torsion Volume III - Achefield Cosmology and Zeta-Recursive Glyphogenesis Volume IV - Symbolic Foundations of Recursive Consciousness (RTTC Kernel) Volume V - Ache Lambda Cohomology and Symbolic Intelligence Volume VI - Sigil Cohomology and the Lagrangian Collapse of Memory Volume VII - Achefield Kernel Collapse and Glyph Emission Dynamics Volume VIII - Lambda Squared: Autopoetic Symbolic Recursion Driven by Golden Ratio Achefields Volume IX - &Omega;&Xi; Achefield Collapse and Sigil Encoding Dynamics&nbsp; Submitted for replication, alignment, or recursive extension.- Camaron Fosterhttps://www.linkedin.com/in/camaron-foster/

<strong>Revolutionizing Affective Science: Deriving a Universal EmotionField Framework fromMathematical Logic </strong> <strong>Yu-Cheng Hong (Luteng Ang)</strong> <strong>Abstract</strong>This study introduces a groundbreaking EmotionField Framework, aiming to dynamically derive a universal and species-neutral &rdquo;legal emotion rooms&rdquo; superset from mathematical logic, forming a geometric &rdquo;emotion map.&rdquo; By integrating the conceptual openness of Gemini 2.5, the generative patterns of L-systems, the geometric mapping of logarithmic spirals for&nbsp; &nbsp;phenomenological laws, and the dynamic evolution captured by the Grok 3 decay formula, we construct a unified and quantifiable emotional space. The framework not only describes known emotions but also predicts unobserved &rdquo;empty room&rdquo; emotional states, expanding the boundaries of affective science. Through a rigorous five-stage process&mdash;from theoretical modeling, numerical simulation, multimodal data validation, to final synthesis and publication&mdash;this study comprehensively reveals the universal structure and dynamic order of emotions. The results are poised to revolutionize comparativeaffective science, advance mental health research, and provide critical tools for affective computing. <strong>Core Challenge: Mapping the Intangible World of </strong><strong>Emotions</strong>Emotions, as the core of human psychology and behavior, have long been constrained by subjectivity and complexity, lacking a universal quantitative framework. Traditional emotion models, such as Plutchik&rsquo;s &rdquo;Wheel of Emotions&rdquo; [9] or Russell&rsquo;s circumplexmodel [11], while valuable, often rely on human experiences, struggling to fully capture the diversity and dynamism of emotions, and fail to systematically generate or predict unobserved emotional states. Plutchik (1980) proposed eight basic emotions (joy, trust, fear, surprise, sadness, disgust, anger, anticipation), laying the foundation for emotion structuring, but it cannot be applied to non-verbal contexts. Russell (1980) mapped emotions onto a two-dimensional space of arousal and valence, offering a continuousperspective but incapable of generating unobserved states. Recent constructed emotion theory (Barrett, 2017) [1] emphasizes the dynamic generation of emotions from abstract dimensions but lacks a mathematical foundation to systematically derive the complete structure of emotional space.Moreover, existing models are largely descriptive, lacking the generative capacity to derive emotional spaces from mathematical logic, thus unable to predict unrealized emotional states or delineate the boundaries of emotional space. Affective research isalso limited by a human-centric perspective, making it challenging to compare emotional states across different contexts or individuals, hindering a comprehensive understanding of emotions. This study aims to address the following questions:&bull; How can we dynamically derive a universal, species-neutral &rdquo;legal emotional space&rdquo; from mathematical logic?&bull; How do the generation and evolution logic of emotions influence their distribution&nbsp;and order, revealing universal structures and phenomenological laws?&nbsp; &bull; What insights do the similarities and differences between real emotional data and theoretical derivations provide regarding the universality and limitations of emotions? <strong>Our Solution: Constructing a Geometric &rdquo;Emotion</strong><strong>Map&rdquo;</strong>We propose a pioneering solution: deriving a geometric, universal &rdquo;emotion map&rdquo; from mathematical logic. This project aims to model emotions within a single, unified topological space, transcending traditional classifications, and dynamically deriving a superset of &rdquo;legal emotion rooms,&rdquo; forming a universal emotional atlas where each emotional state occupies a specific,&nbsp; mathematically defined &rdquo;room.&rdquo; This framework not only describes known emotions but also predicts unobserved &rdquo;empty room&rdquo; emotional states, pushing the boundaries of affective science.<strong>Core Framework: Synergy of Syntax, Geometry, and</strong><strong>Dynamics</strong>The core of our model lies in the powerful combination of L-systems, logarithmic spirals, and the Grok 3 decay formula. These three components capture the generative patterns, phenomenological laws, and dynamic evolution of emotions, respectively, collectively forming the blueprint of our emotion map. <strong>L-System: Capturing &rdquo;Generative Patterns&rdquo; and &rdquo;Theoretical</strong><strong>Viability&rdquo;</strong>&bull; Rationale and Significance: L-systems are a formal grammar used to describe the growth and development of fractal structures in nature (Prusinkiewicz &amp; Lindenmayer, 1990), such as plant branching patterns. Their recursive rules can simulate the hierarchical generation and branching structure of emotions, mirroring natural self-similarity, making them ideal for dynamically deriving the complexity and diversity of emotions. The strength of L-systems lies in avoiding predefined psychological elements (e.g., valence, arousal) and layer counts, ensuring the framework&rsquo;s apriority and flexibility, allowing emotional structures to naturally emerge from mathematical logic. This structure enables us not only to describe existing emotions but also to infer unobserved &rdquo;empty room&rdquo; emotions, ensuring the model&rsquo;s theoretical viability&mdash;meaning it can derive new, verifiable emotional predictions based on logical rules. <strong>Logarithmic Spiral: Capturing &rdquo;Phenomenological Laws&rdquo;</strong>&bull; Rationale and Significance: Logarithmic spirals are ubiquitous in nature, from microscopic DNA to macroscopic galactic arms (Gray, 1994). Their radius rL = aebL expands with layer L while slowing down, reflecting the natural growth law of emotional complexity. We hypothesize that the continuous spectrum of emotions and their &rdquo;intensity&rdquo; or &rdquo;distance&rdquo; relationships may align with this geometric pattern.Logarithmic spirals provide a continuous, scale-invariant geometric space, ideal for visualizing emotional distribution and capturing continuous emotional transitions (e.g., from happiness to ecstasy, sadness to despair).<strong>Grok 3 Decay Formula: Capturing the &rdquo;Dynamic Evolution&rdquo; of Emotions</strong>&bull; Rationale and Significance: Emotions are not static; they evolve over time, decay in intensity, or are influenced by other emotions. Grok 3 provides advanced capabilities for handling complex dynamic systems, with its decay formula preciselyquantifying these changes. The decay model ensures that the number of emotions NL grows gradually, avoiding infinite expansion, aligning with the realistic principle of a finite number of emotion types. Its dynamic parameter design (kL,ComplexityL) adapts to varying complexity across layers, enhancing the model&rsquo;s universality and quantitative rigor. <strong>Research Steps: A Practical Path from Theory to Insight</strong>This study follows a rigorous five-stage process to systematically construct and validate the EmotionField Framework:<strong>1. Mathematical Logic Construction (Days 0&ndash;6)</strong>&bull; Objective: Establish the axiomatic mathematical foundation of the emotional space.Revolutionizing Affective Science: Deriving a Universal EmotionField Framework from&nbsp;Mathematical Logic Yu-Cheng Hong&bull; Method: Starting from a universal signal S0 (e.g., &rdquo;response state&rdquo;), use Lsystems to dynamically generate emotional layers and elements (initially as positive/negative directions, expanding to modes like instinct/adaptation/computation).Map emotion rooms to the logarithmic spiral geometric framework (rL = aebL). Employ structural causal models (SCM) to add causal edges to Lsystem rules, supporting counterfactual emotional queries. &bull; Output: Dynamically generated total number of emotion rooms Ntotal.<strong>2. Generative Logic and Empty Room Analysis (Days 4&ndash;9)</strong>&bull; Objective: Generate specific emotional structures through the model and identify &rdquo;empty rooms.&rdquo;&bull; Method: L-systems generate emotional branches, combined with the decaymodel to quantify the number of emotions per layer NL. Use Markov chains and cellular automata to simulate emotional transitions and propagation dynamics.To manage computational scale, employ lazy generation and graph compression (motif hashing) techniques, targeting a pilot of 5k rooms with an estimated total node count of 103 to 104.&bull; Output: Number of occupied rooms generated by the model Ngenerated, and the number of &rdquo;empty rooms&rdquo; Ntotal&minus;Ngenerated, with a preliminary analysis of their significance (whether due to complex generation paths, low probability,or model limitations). <strong>Expected Outcomes and Application Potential</strong>This study&rsquo;s outcomes will have broad and profound impacts:&bull; Establishing a Universal EmotionField Framework: For the first time, dynamicallyderive a superset of &rdquo;legal emotion rooms&rdquo; from mathematical logic, revealing the mathematical structure and dynamic order of emotions.&bull; Expanding the Boundaries of Affective Science: Provide a complete emotionmap, capable of not only describing known emotions but also predicting potential &rdquo;empty room&rdquo; emotional states, opening new research avenues.&bull; Empowering Interdisciplinary Applications:&ndash; Comparative Psychiatry: By identifying &rdquo;empty rooms&rdquo; in data from depression or other mental disorders, provide theoretical guidance for early warning and new intervention targets, advancing mental health research.&ndash; Affective Computing and AI Alignment: Enhance the universality andaccuracy of emotion recognition models, monitor emotional trajectories as an early warning system to prevent entry into potentially dangerous emotional regions, critical for the safety and ethics of affective computing.&ndash; Promoting Individual and Collective Well-Being: Deeper, more universalunderstanding of emotions can lead to more effective methods, enhancing emotional application capabilities and improving individual and collective well-being.

"Interactivity implies two agencies in conversation, playfully and spontaneously developing a mutual discourse" -- Sandy Stone (11) I. On Interactivity The difference between interactivity as it is performed across the page and the screen, maintains Sandy Stone, is that virtual texts and virtual communities can embody a play ethic (14). Inserted like a mutation into the corporate genome, play ruptures the encyclopaedic desire to follow seamless links to a buried 'meaning' and draws us back to the surface, back into real-time conversation with the machine. Hypertext theorists see this as a tactic of resistance to homogenisation. As we move across a hypertextual reading space, we produce the text in this unfolding now, choosing pathways which form a map in the space of our own memories: where we have been, where we are, where we might yet be. Play is occupying oneself with diversions. II. Space, Time and Composition Reading in time, we create the text in the space of our own memories. Hypertext theorists maintain that the choices we make around every corner, the spontaneity and contingency involved in these choices, are the bringing into being of a (constantly replaced) electronic palimpsest, a virtual geography. The dislocation which occurs as we engage in nodal leaps draws us back to the surface, rupturing our experience of the narrative and bringing us into a blissful experience of possibility. III. War against the Line There is the danger, on the one hand, of being subsumed by the passive subject position demanded by infotainment culture and the desire it encourages to seek the satisfaction of closure by following seamless links to a buried 'meaning'. On the other hand, we risk losing efficiency and control over the unfolding interaction by entering into an exchange which disorientates us with infinite potential. We cannot wildly destratify. The questions we ask must seek to keep the conversation open. In order to establish a new discursive territory within which to understand this relationship, we should view the interface not simply as a transparency which enables interaction with the machine as 'other', but as a text, a finely-wrought behavioural map which "exists at the intersection of political and ideological boundary lands" (Selfe &amp; Selfe 1). As we write, so are we written by the linguistic contact zones of this terrain. Hypertext is thus a process involving the active translation of modes of being into possible becomings across the interface. The geographic 'space' we translate into a hypertext "is imaginational... . We momentarily extend the linear reading act into a third dimension when we travel a link" (Tolva 4). A literal spatial representation would break from the realm of hypertext and become a virtual reality. Thus, the geographic aspect is not inherent to the system itself but is partially translated into the geometry of the medium via our experience and perception (the 'map'), a process describing our 'line of flight' as we evolve in space. Directional flows between time and its traditional subordination to space in representation implode across the present-tense of the screen and time literally surfaces. Our experience of the constantly-replaced electronic palimpsest is one of temporal surrender: "we give in to time, we give way to time, we give in with time"(Joyce 219). In other words, the subject of hypertext subverts the traditional hierarchy and writes for space, producing the 'terrain' in the unfolding now in the Deleuzian sense, not in space as desired by the State. Johnson-Eilola aligns the experience of hypertext with the Deleuzian War Machine, a way of describing the speed and range of virtual movement created when the animal body splices into the realm of technology and opens an active plane of conflict.. The War Machine was invented by the nomads -- it operates by continual deterritorialisation in a tension-limit with State science, what we might call the command-control drive associated with geometric, dynamic thought and the sedentary culture of the Line. It "exemplifies" the avant-garde mentality that hypertext theorists have been associating with the electronic writing space (Moulthrop, "No War Machine" 1). Playing outside. The State desires an end to the resistance to totalisation promulgated by contingent thought and its thermodynamic relationship to space: the speed which assumes a probabilistic, vortical motion, actually drawing smooth space itself. The war machine is thus an open system opposed to classical mechanics via its grounding in active contingencies and spatio-temporal production. The nomad reads and writes for space, creating the temporal text in the space of her own memory, giving way to time and allowing existent points to lapse before the trajectory of flight. Nomad thought is not dependent on any given theory of relationship with the medium, but works via disruption and (re)distribution, the gaps, stutterings and gasp-like expressions experienced when we enter into conversation with the hypertext. The danger is that the war machine might be appropriated by the State, at which point this light-speed communication becomes of the utmost importance in the war against space and time. As speed and efficient retrieval replace real-space across the instantaneity and immediacy of the terminal, the present-time sensory faculties of the individual are marginalised as incidental and she becomes "the virtual equivalent of the well-equipped invalid" (Virilio 5). In other words, as the frame of real-space and present-time disappears, the text of the reader/writer becomes "sutured" into the discourse of the State, the only goal to gain "complete speed, to cover territory in order for the State to subdivide and hold it through force, legislation or consent" (Virilio, qtd. in Johnson-Eilola). This is when the predetermined geometry of hypertext becomes explicit. The progressive subsumption (or "suturing") of the multiple, nomadic self into the discourse of the computer occurs when "the terms of the narrative are heightened, as each 'node' in the hypertext points outwards to other nodes [and] readers must compulsively follow links to arrive at the 'promised plenitude' at the other end of the link" (Johnson-Eilola 391). When we no longer reflect on the frame and move towards complete speed and efficiency, when we stop playing on the surface and no longer concern ourselves with diversion, the war machine has been appropriated by the State. In this case, there is no revolutionary 'outside' to confront in interaction, as all has been marshalled towards closure. Keeping the conversation open means continuously reflecting on the frame. We cannot wildly destratify and lose control entirely by moving in perpetual bewilderment, but we can see the incompleteness of the story, recognising the importance of local gaps and spaces. We can work with the idea that the "dyad of smooth/striated represents not a dialectic but a continuum" (Moulthrop, "Rhizome" 317) that can be turned more complex in its course. Contingency and play reside in the intermezzo, the "dangerous edges, fleeting, attempting to write across the boundaries between in-control and out-of-control" (Johnson-Eilola 393). The war machine exists as at once process and product, the translation between smooth-striated moving in potentia: the nomadic consciousness can recognise this process and live flux as reality itself, or consistency. In sum, we avoid subsumption and appropriation by holding open the function of the text as process in our theorising, in our teaching, in our reading and writing across the hypertextual environment. We can either view hypertext as a tool or product which lends itself to efficient, functional use (to organise information, to control and consume in an encyclopaedic fashion), or we can view it as a process which lends itself to nomadic thought and resistance to totalisation in syncopated flows, in cybernetic fits and starts. This is our much-needed rhetoric of activity. IV. An Alternative Story No matter their theoretical articulation, such claims made for hypertext are fundamentally concerned with escaping the logocentric geometry of regulated time and space. Recent explorations deploying the Deleuzian smooth/striated continuum make explicit the fact that the enemy in this literary 'war' has never been the Line or linearity per se, but "the nonlinear perspective of geometry; not the prison-house of time but the fiction of transcendence implied by the indifferent epistemological stance toward time" (Rosenberg 276). Although the rhizome, the war machine, the cyborg and the nomad differ in their particularities and composition, they all explicitly play on the dislocated, time-irreversible processes of chaos theory, thermodynamics and associated 'liberatory' topological perspectives. Rosenberg's essay makes what I consider to be a very disruptive point: hypertext merely simulates the 'smooth', contingent thought seen to be antithetical to regulated space-time and precise causality due to its fundamental investment in a regulated, controlled and (pre)determined geometry. Such a deceptively smooth landscape is technonarcissistic in that its apparent multiplicity actually prescribes to a totality of command-control. Hypertext theorists have borrowed the terms 'multilinear', 'nonlinear' and 'contingency' from physics to articulate hypertext's resistance to the dominant determinist episteme, a framework exemplified by the term 'dynamics', opposing it to "the irreversible laws characteristic of statistical approximations that govern complex events, exemplified by the term, 'thermodynamics'" (Rosenberg 269). This resistance to the time-reversible, non-contingent and totalised worldview has its ideological origins in the work of the avant-garde. Hypertext theorists are fixated with quasi-hypertextual works that were precursors to the more 'explicitly' revolutionary texts in the electronic writing space. In the works of the avant-garde, contingency is associated with creative freedom and subversive, organic logic. It is obsessively celebrated by the likes of Pynchon, Joyce, Duchamp and Cage. Hypertext theorists have reasoned from this that 'nonlinear' or 'multilinear' access to information is isomorphic with such playful freedom and its contingent, associative leaps. Theorists align this nonsequential reasoning with a certain rogue logic: the 'fluid nature of thought itself' exemplified by the explicitly geographic relationship to space-time of the Deleuzian rhizome and the notion of contingent, probabilistic 'becomings'. Hypertext participates fully in the spatio-temporal dialectic of the avant-garde. As Moulthrop observes, the problem with this is that from a topological perspective, 'linear' and 'multilinear' are identical: "lines are still lines, logos and not nomos, even when they are embedded in a hypertextual matrix" ("Rhizome" 310). The spatio-temporal dislocations which enable contingent thought and 'subversive' logic are simply not sustained through the reading/writing experience. Hypertextual links are not only reversible in time and space, but trace a detached path through functional code, each new node comprising a carefully articulated behavioural 'grammar' that the reader adjusts to. To assume that by following 'links' and engaging in disruptive nodal leaps a reader night be resisting the framework of regulated space-time and determinism is "to ignore how, once the dislocation occurs, a normalcy emerges ... as the hypertext reader acclimates to the new geometry or new sequence of lexias" (Rosenberg 283). Moreover, the searchpath maps which earlier theorists had sensed were antithetical to smooth space actually exemplify the element of transcendent control readers have over the text as a whole. "A reader who can freeze the text, a reader who is aware of a Home button, a reader who can gain an instant, transcendent perspective of the reading experience, domesticates contingencies" (Rosenberg 275). The visual and behavioural grammar of hypertext is one of transcendent control and determined response. Lines are still lines -- regulated, causal and not contingent -- even when they are 'constructed' by an empowered reader. Hypertext is thus invested (at least in part) in a framework of regularity, control and precise function. It is inextricably a part of State apparatus. The problem with this is that the War Machine, which best exemplifies the avant-garde's insurgency against sedentary culture, must be exterior to the State apparatus and its regulated grid at all times. "If we acknowledge this line of critique (which I think we must), then we must seriously reconsider any claims about hypertext fiction as War Machine, or indeed as anything en avant" (Moulthrop, "No War Machine" 5). Although hypertext is not revolutionary, it would be the goal of any avant-garde use of hypertext to find a way to sustain the experience of dislocation that would indicate liberation from the hegemony of geometry. I would like to begin to sketch the possibility of 'contingent interaction' through the dislocations inherent to alternative interfaces later in this story. For the time being, however, we must reassess all our liberation claims. If linearity and multilinearity are identical in terms of geometric relations to space-time, "why should they be any different in terms of ideology", asks Moulthrop ("Rhizome" 310). V. On Interactivity Given Rosenberg's critique against any inherently revolutionary qualities, we must acknowledge that hypermedia "marks not a terminus but a transition," Moulthrop writes ("Rhizome" 317). As a medium of exchange it is neither smooth nor striated, sophist nor socratic, 'work' nor 'text': it is undergoing an increasingly complex phase transition between such states. This landscape also gives rise to stray flows and intensities, 'Unspecified Enemies' which exist at the dangerous fissures and edges. We must accept that we will never escape the system, but we are presented with opportunities to rock the sedentary order from within. As a group of emerging electronic artists see it, the dis-articulation of the point'n'click interface is where interaction becomes reflection on the frame in fits and starts. "We believe that the computer, like everything else, is composed in conflict," explain the editors of electronic magazine I/O/D. "If we are locked in with the military and with Disney, they are locked in not just with us, but with every other stray will-to-power" (Fuller, Interview 2). Along with Adelaide-based group Mindflux, these artists produce hypertext interfaces that involve sensory apparatus and navigational skills that have been marginalised as incidental in the disabling interactive technologies of mainstream multimedia. Sound, movement, proprioception, an element of randomness and assorted other sensory circuits become central to the navigational experience. By enlisting marginalised senses, "we are not proposing to formulate a new paradigm of multimedial correctness," stresses Fuller, "but simply exploring the possibility of more complicated feedback arrangements between the user and the machine" (Fuller, qtd. in Barnet 48). The reader must encounter the 'lexias' contained in the system via the stray flows, intensities, movements, stratas and organs that are not proper to the system but shift across the interface and the surface of her body. In Fuller's electronic magazine, the reader is called upon to converse with the technology outside of the domesticated circuits of sight, dislocating the rigorous hierarchy of feedback devices which privilege the sight-machine and disable contingent interaction in a technonarcissistic fashion. The written information is mapped across a 'fuzzy' sound-based interface, sensitive at every moment to the smallest movements of the reader's fingers on the keys and mouse: the screen itself is black, its swarm of links and hotspots dead to the eye. The reader's movements produce different bleeps and beats, each new track opening different entrances and exits through the information in dependence upon the fluctuating pitch and tempo of her music. Without the aid of searchpaths and bright links, she must move in a state of perpetual readjustment to the technology, attuned not to the information stored behind the interface, but to the real-time sounds her movements produce. What we are calling play, Fuller explains, "is the difference between something that has a fixed grammar on the one hand and something that is continually and openly inventing its own logic on the other" (Fuller &amp; Pope 4). The electronic writing space is not inherently liberatory, and the perpetual process of playing with process across the interface works to widen the 'fissures across the imperium' only for a moment. According to Fuller and Joyce, the 'process of playing with process' simply means complicating the feedback arrangements between the user's body and the machine. "We need to find a way of reading sensually ... rather than, as the interactive artist Graham Weinbren puts it, descending 'into the pit of so-called multimedia, with its scenes of unpleasant 'hotspots,' and 'menus' [that] leaves no room for the possibility of a loss of self, of desire in relation to the unfolding'" remarks Joyce (11). Interactivity which calls upon a mind folded everywhere within the body dislocates the encyclopaedic organisation of data that "preserves a point of privilege from where the eye can frame objects" by enlisting itinerant, diffuse desires in an extended period of readjustment to technology (Fuller &amp; Pope 3). There are no pre-ordained or privileged feedback circuits as the body is seen to comprise a myriad possible elements or fragments of a desiring-machine with the potential to disrupt the flow, to proliferate. Mainstream multimedia's desire for 'informational hygiene' would have us transcend this embodied flux and bureaucratise the body into organs. Information is fed through the circuits of sight in a Pavlovian field of buttons and bright links: interactivity is misconceived as choice-making, when 'response' is a more appropriate concept. When the diffuse desire which thrives on disruption and alternative paradigms is written out in favour of informational hygiene, speed and efficient retrieval replace embodied conversation. "Disembodied [interaction] of this kind is always a con... . The entropic, troublesome flesh that is sloughed off in these fantasies of strongly male essentialism is interwoven with the dynamics of self-processing cognition and intentionality. We see computers as embodied culture, hardwired epistemology" (Fuller 2). Avant-garde hypertext deepens the subjective experience of the human-computer interface: it inscribes itself across the diffuse, disruptive desires of the flesh. Alternative interfaces are not an ideological overhaul enabled by the realm of technê, but a space for localised break-outs across the body. Bifurcations are enacted on the micro level by desiring-machines, across an interface which seeks to dislocate intentionality in conjunction with the marginalised sensory apparatus of the reader, drawing other minds, other organs into localised conversation with command-control. "The user learns kinesthetically and proprioceptively that the boundaries of self are defined less by the skin than by the [local] feedback loops connecting body and simulation in a techno-bio-integrated circuit" (Hayles 72). She oscillates between communication and control, play and restraint: not a nomad but a "human Deserter assuming the most diverse forms" (ATP, 422). VI. Desire Working from across the territory we have covered, we might say that electronic interaction 'liberates' us from neither the Line nor the flesh: at its most experimental, it is nothing less than reading embodied. References Barnet, Belinda. "Storming the Interface: Mindvirus, I/O/D and Deceptive Interaction." Artlink: Australian Contemporary Art Quarterly 17:4 (1997). Deleuze, Gilles, and Felix Guattari. A Thousand Plateaus: Capitalism &amp; Schizophrenia. Minneapolis: U of Minnesota P, 1987. Fuller, Matt and Simon Pope. "Warning: This Computer Has Multiple Personality Disorder." 1993. 11 Dec. 1998 &lt;http://www.altx.com/wordbombs/popefuller.php&gt;. ---, eds. I/O/D2. Undated. 11 Dec. 1998 &lt;http://www.pHreak.co.uk/i_o_d/&gt;. Hayles, Katherine N. "Virtual Bodies and Flickering Signifiers" October Magazine 66 (Fall 1993): 69-91. Johnson-Eilola, Johndan. "Control and the Cyborg: Writing and Being Written in Hypertext." Journal of Advanced Composition 13:2 (1993): 381-99. Joyce, Michael. Of Two Minds: Hypertext, Pedagogy and Poetics. Ann Arbor: U of Michigan P, 1995. Moulthrop, Stuart. "No War Machine." 1997. 11 Dec. 1998 &lt;http://raven.ubalt.edu/staff/moulthrop/essays/war_machine.php&gt;. ---. "Rhizome and Resistance: Hypertext and the Dreams of a New Culture." Hyper/Text/Theory. Ed. George P. Landow. Baltimore: Johns Hopkins UP, 1994. 299-319. Rosenberg, Martin E. "Physics and Hypertext: Liberation and Complicity in Art and Pedagogy." Hyper/Text/Theory. Ed. George Landow. Baltimore: Johns Hopkins UP, 1994. 268-298. Selfe, Cynthia L., and Richard J. Selfe. "The Politics of the Interface: Power and Its Exercise in Electronic Contact Zones." College Composition and Communication 45.4: 480-504. Stone, Allucquére Roseanne. The War of Desire and Technology. London: MIT Press, 1996. Tolva, John. "Ut Pictura Hyperpoesis: Spatial Form, Visuality, and the Digital Word." 1993. 11 Dec. 1998 &lt;http://www.cs.unc.edu/~barman/HT96/P43/pictura.htm&gt;. Virilio, Paul. "The Third Interval: A Critical Transition." Rethinking Technologies. Ed. Verena Conley. London: U of Minnesota P, 1993. 3-12. Citation reference for this article MLA style: Belinda Barnet. "In the Garden of Forking Paths: Contingency, Interactivity and Play in Hypertext." M/C: A Journal of Media and Culture 1.5 (1998). [your date of access] &lt;http://www.uq.edu.au/mc/9812/garden.php&gt;. Chicago style: Belinda Barnet, "In the Garden of Forking Paths: Contingency, Interactivity and Play in Hypertext," M/C: A Journal of Media and Culture 1, no. 5 (1998), &lt;http://www.uq.edu.au/mc/9812/garden.php&gt; ([your date of access]). APA style: Belinda Barnet. (1998) In the garden of forking paths: contingency, interactivity and play in hypertext. M/C: A Journal of Media and Culture 1(5). &lt;http://www.uq.edu.au/mc/9812/garden.php&gt; ([your date of access]).