Framework Of Graph Theory Research Articles

Multi-AUV heterogeneous bipartite consensus formation obstacle avoidance algorithm based on event triggering-RMPC under measurement-communication union framework

This paper investigates a robust model predictive control-based event triggering (ET-RMPC) for heterogeneous autonomous underwater vehicle (AUV) bipartite consensus formation in obstacle avoidance. Firstly, a scheme of heterogeneous AUV bipartite formation control base on signed graph theory and implicit interactive measure-communication union framework is proposed. Next, a RMPC based on the proposed framework for heterogeneous AUV bipartite consensus formation is designed. Additionally, to alleviate the computational burden, a novel event-triggering mechanism is devised based on the error between the estimated state and actual state of the AUV formation trajectory. Then, the stability of the system and the upper and lower bounds of the trigger interval are analyzed based on innovation and Lyapunov theory. Finally, the effectiveness of the proposed method is validated through bipartite consensus formation tracking and obstacle avoidance scenarios.

Incorporating network diffusion and peak location information for better single-cell ATAC-seq data analysis.

Single-cell assay for transposase-accessible chromatin using sequencing (scATAC-seq) data provided new insights into the understanding of epigenetic heterogeneity and transcriptional regulation. With the increasing abundance of dataset resources, there is an urgent need to extract more useful information through high-quality data analysis methods specifically designed for scATAC-seq. However, analyzing scATAC-seq data poses challenges due to its near binarization, high sparsity and ultra-high dimensionality properties. Here, we proposed a novel network diffusion-based computational method to comprehensively analyze scATAC-seq data, named Single-Cell ATAC-seq Analysis via Network Refinement with Peaks Location Information (SCARP). SCARP formulates the Network Refinement diffusion method under the graph theory framework to aggregate information from different network orders, effectively compensating for missing signals in the scATAC-seq data. By incorporating distance information between adjacent peaks on the genome, SCARP also contributes to depicting the co-accessibility of peaks. These two innovations empower SCARP to obtain lower-dimensional representations for both cells and peaks more effectively. We have demonstrated through sufficient experiments that SCARP facilitated superior analyses of scATAC-seq data. Specifically, SCARP exhibited outstanding cell clustering performance, enabling better elucidation of cell heterogeneity and the discovery of new biologically significant cell subpopulations. Additionally, SCARP was also instrumental in portraying co-accessibility relationships of accessible regions and providing new insight into transcriptional regulation. Consequently, SCARP identified genes that were involved in key Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways related to diseases and predicted reliable cis-regulatory interactions. To sum up, our studies suggested that SCARP is a promising tool to comprehensively analyze the scATAC-seq data.

Grain boundary network plasticity: Reduced-order modeling of deformation-driven shear-coupled microstructure evolution

Microstructural evolution in structural materials is known to occur in response to mechanical loading and can often accommodate substantial plastic deformation through the coupled motion of grain boundaries (GBs). This can produce desirable behavior, such as increased ductility, or undesirable behavior such as mechanically-induced coarsening. In this work a novel, multiscale model is developed for capturing the combined effect of plasticity mediated by multiple GBs simultaneously. This model is referred to as “grain boundary network plasticity”. The mathematical framework of graph theory is used to describe the microstructure connectedness, and the evolution of microstructure is represented as volume flow along the graph. By using the principle of minimum dissipation potential, which has previously been applied to grain boundary migration, a set of evolution equations are developed that transfer volume and eigendeformation along the graph edges in a physically consistent way. It is shown that higher-order geometric effects, such as the pinning effect of triple points, may be accounted for through the incorporation of a geometric hardening that causes geometry-induced GB stagnation. The result is a computationally efficient reduced order model that can be used to simulate the initial motion of grain boundaries in a polycrystal with parameters informed by atomistic simulations. The effectiveness of the model is demonstrated through comparison to multiple bicrystal atomistic simulations, as well as a select number of GB engineered and non-GB engineered data obtained from the literature. The effect of the network of shear-coupling grain boundaries is demonstrated through mechanical response tests and by examining the yield surfaces.

Typicality effects in Spanish as a Foreign Language of intermediate and advanced level Greek learners

Abstract Categorization and identification of typical exemplars within semantic categories is a universal skill of human cognition which is involved in language development. However, cultural, and experiential aspects might influence typicality effects. This paper examines the role of native language and culture on that categorization process and on typicality effects. Towards that objective, we had Spanish native speakers and Spanish FL learners whose mother tongue is Greek complete a category generation word association task. Data were analyzed within a network and graph theory framework as the best fitting for this type of data, bearing in mind previous descriptions of semantic memory. Results showed how, indeed, native speakers and learners of varying proficiency levels differ in their availability and production of typical exemplars, especially in slot-filler categories versus taxonomic categories. Lexical access during category generation might be determined by native language and culture. Additionally, natives’ mental lexicon seems to feature denser connections responsible for more efficient access.

An overview on graph products

Graph product is a very basic idea in graph theory. Graph products include a wide range of operations that join two or more existing graphs to produce new graphs with distinctive properties and uses. In this paper, we explore four forms of graph products, their characteristics, and their significance within the broader framework of graph theory.

Vertex-Based Resolvability Parameters for Identification of Certain Chemical Structures.

Chemical graph theory explores chemical phenomena and entities through the conceptual framework of graph theory. In chemical graph theory, molecular structures are represented by chemical graphs, where edges and vertices correspond to bonds and atoms, respectively. Chemical graphs serve as fundamental data types in cheminformatics for illustrating chemical structures. The computable properties of graphs form the basis for quantitative structure-property and structure-activity predictions, which are central to cheminformatics. These graphs capture the physical characteristics of molecules and can be further reduced to graph-theoretical indices or descriptors. One extensively studied distance-based graph descriptor is the resolving set Z, which enables the distinction of every pair of distinct vertices in a connected simple graph. Resolving sets were specifically employed in pharmaceutical research to find patterns shared by several different drugs. Since very early times, medicinal drugs have played a significant part in human civilization. In this article, we investigate minimum resolving sets for certain significant drug molecular structures, namely, suramin (S86) and acemannan (A116).

A Multidimensional Connectomics- and Radiomics-Based Advanced Machine-Learning Framework to Distinguish Radiation Necrosis from True Progression in Brain Metastases.

We introduce tumor connectomics, a novel MRI-based complex graph theory framework that describes the intricate network of relationships within the tumor and surrounding tissue, and combine this with multiparametric radiomics (mpRad) in a machine-learning approach to distinguish radiation necrosis (RN) from true progression (TP). Pathologically confirmed cases of RN vs. TP in brain metastases treated with SRS were included from a single institution. The region of interest was manually segmented as the single largest diameter of the T1 post-contrast (T1C) lesion plus the corresponding area of T2 FLAIR hyperintensity. There were 40 mpRad features and 6 connectomics features extracted, as well as 5 clinical and treatment factors. We developed an Integrated Radiomics Informatics System (IRIS) based on an Isomap support vector machine (IsoSVM) model to distinguish TP from RN using leave-one-out cross-validation. Class imbalance was resolved with differential misclassification weighting during model training using the IRIS. In total, 135 lesions in 110 patients were analyzed, including 43 cases (31.9%) of pathologically proven RN and 92 cases (68.1%) of TP. The top-performing connectomics features were three centrality measures of degree, betweenness, and eigenvector centralities. Combining these with the 10 top-performing mpRad features, an optimized IsoSVM model was able to produce a sensitivity of 0.87, specificity of 0.84, AUC-ROC of 0.89 (95% CI: 0.82-0.94), and AUC-PR of 0.94 (95% CI: 0.87-0.97).

Integrating spatially-and temporally-heterogeneous data on river network dynamics using graph theory

The study of non-perennial streams requires extensive experimental data on the temporal evolution of surface flow presence across different nodes of channel networks. However, the consistency and homogeneity of available datasets is threatened by the empirical burden required to map stream network expansions and contractions. Here, we developed a data-driven, graph-theory framework aimed at representing the hierarchical structuring of channel network dynamics (i.e., the order of node activation/deactivation during network expansion/retraction) through a directed acyclic graph. The method enables the estimation of the configuration of the active portion of the network based on a limited number of observed nodes, and can be utilized to combine datasets with different temporal resolutions and spatial coverage. A proof-of-concept application to a seasonally-dry catchment in central Italy demonstrated the ability of the approach to reduce the empirical effort required for monitoring network dynamics and efficiently extrapolate experimental observations in space and time.

Conduction and entropy analysis of a mixed memristor-resistor model for neuromorphic networks

To build neuromorphic hardware with self-assembled memristive networks, it is necessary to determine how the functional connectivity between electrodes can be adjusted, under the application of external signals. In this work, we analyse a model of a disordered memristor-resistor network, within the framework of graph theory. Such a model is well suited for the simulation of physical self-assembled neuromorphic materials where impurities are likely to be present. Two primary mechanisms that modulate the collective dynamics are investigated: the strength of interaction, i.e. the ratio of the two limiting conductance states of the memristive components, and the role of disorder in the form of density of Ohmic conductors (OCs) diluting the network. We consider the case where a fraction of the network edges has memristive properties, while the remaining part shows pure Ohmic behaviour. We consider both the case of poor and good OCs. Both the role of the interaction strength and the presence of OCs are investigated in relation to the trace formation between electrodes at the fixed point of the dynamics. The latter is analysed through an ideal observer approach. Thus, network entropy is used to understand the self-reinforcing and cooperative inhibition of other memristive elements resulting in the formation of a winner-take-all path. Both the low interaction strength and the dilution of the memristive fraction in a network provide a reduction of the steep non-linearity in the network conductance under the application of a steady input voltage. Entropy analysis shows enhanced robustness in selective trace formation to the applied voltage for heterogeneous networks of memristors diluted by poor OCs in the vicinity of the percolation threshold. The input voltage controls the diversity in trace formation.

LGTBIDS: Layer-Wise Graph Theory-Based Intrusion Detection System in Beyond 5G

The advancement in wireless communication technologies is becoming more demanding and pervasive. One of the fundamental parameters that limit the efficiency of the network are the security challenges. The communication network is vulnerable to security attacks such as spoofing attacks and signal strength attacks. Intrusion detection signifies a central approach to ensuring the security of the communication network. In this paper, an Intrusion Detection System based on the framework of graph theory is proposed. A Layerwise Graph Theory-Based Intrusion Detection System (LGTBIDS) algorithm is designed to detect the attacked node. The algorithm performs the layer-wise analysis to extract the vulnerable nodes and ultimately the attacked node(s). For each layer, every node is scanned for the possibility of susceptible node(s). The strategy of the IDS is based on the analysis of energy efficiency and secrecy rate. The nodes with the energy efficiency and secrecy rate beyond the range of upper and lower thresholds are detected as the nodes under attack. Further, detected node(s) are transmitted with a random sequence of bits followed by the process of re-authentication. The obtained results validate the better performance, low time computations, and low complexity. Finally, the proposed approach is compared with the conventional solution of intrusion detection.

Аналіз та розроблення концептуальної моделі управління життєвим циклом спеціалізованого програмного забезпечення безпеко-орієнтованого спрямування

A comprehensive examination of the process of developing specialized safety-oriented software is conducted. The incongruity of the presently known development methodologies with the circumstances in which innovative safety-oriented software systems are created is unveiled. For this reason, the purpose of this article is to investigate the existing methods and formulate novel approaches to managing the life cycle of specialized software (safety-oriented services), which are relevant to the specific requirements of the State Emergency Service of Ukraine and align with the principles of a flexible software life cycle management methodology. A thorough exploration is conducted on the current agile methods and approaches employed in the development of critical services, specifically in sectors such as military, railway, aerospace, medical, and other domains of operation. The aim is to establish the merits of flexibility in fostering innovation within specialized safety-oriented software. The fundamental concepts of agile methods for software system life cycle management are synergistically integrated, taking into consideration the unique requirements of rescue service development. Furthermore, the existing empirical data on the feasibility and advantages of implementing agile methods in the security industry are expanded upon. Especially, the agile Scrum method is enhanced through the proposal of employing the mathematical framework of graph theory (network planning method) to automate the planning stage and identify critical functions, including the critical path, the early execution time of events, the late execution times of events, and reserved time for tasks. This method aids in developing a minimum viable product for a safety-oriented system. A conceptual model of the life cycle management process for safety-oriented services has been meticulously developed. This model is predicated on a flexible approach to software development, which aims to automate the tasks performed by project teams and enhance the overall efficacy of specialized software development. On its basis, it is proposed to develop a decision support system for managing the life cycle of safety-oriented software systems development, which is relevant for the State Emergency Service of Ukraine.

NIMG-08. AN INTEGRATED INFORMATICS MODEL COMBINING CLINICAL FACTORS, RADIOMICS AND A NOVEL CONNECTOMICS FRAMEWORK TO DISTINGUISH PATHOLOGICALLY-PROVEN RADIONECROSIS FROM PROGRESSION IN TREATED BRAIN METASTASES

Abstract PURPOSE/OBJECTIVE(S) To distinguish radionecrosis (RN) from true progression (TP) in brain metastases treated with stereotactic radiosurgery (SRS), we apply machine learning to create a multi-domain model that incorporates clinical factors, multiparametric radiomics(mpRads), and tumor connectomics, a novel MRI-based complex graph theory framework that describes the intricate network of relationships within the tumor and surrounding tissue. MATERIALS/METHODS Metastases treated with SRS that had pathologic confirmation of RN vs. TP after imaging progression were included from a single institution. Regions of interest were manually segmented using the single largest diameter of the T1 post-contrast(T1C) lesion plus the corresponding area of T2 FLAIR hyperintensity. We developed an Integrated Radiomics Informatics System (IRIS) based on an isomap support vector machine (IsoSVM) model to classify TP from RN using leave-one-out cross-validation (LOOCV). Class imbalance was resolved using differential misclassification weighting during model training using IRIS. Area under the receiver operating characteristic (AUC-ROC) and AUC-PR (precision recall) analysis were performed. RESULTS We analyzed 135 lesions in 110 patients. There were 43 cases (31.9%) of RN and 92 cases (68.1%) of TP. The top-performing connectomics features were degree centrality (increased with RN) and average path length (decreased with RN), suggesting greater “connectivity” and increased similarity in intralesional features between the T1C and FLAIR signal regions in RN cases. The top-performing radiomics feature was multidimensional entropy (increased in TP), demonstrating greater heterogeneity in TP cases. Finally, the top-performing clinical features were prior RT before SRS, histology, and treated lesion size. The LOOCV IsoSVM model successfully classified TP from RN with an AUC-ROC of 0.84 (95% CI: 0.77-0.90) and AUC-PR of 0.90 (95% CI: 0.82-0.95). The F1 score was 0.89. CONCLUSION Our novel machine-learning framework was able to efficiently combine features from multiple domains (i.e., radiomics, connectomics, and clinical factors) to distinguish pathologically-proven TP from RN with excellent discrimination.

Impact of Network Topology on the Resilience of Vehicle Platoons

This paper presents a comprehensive study on the impact of information flow topologies on the resilience of distributed algorithms that are widely used for estimation and control in vehicle platoons. In the state of the art, the influence of information flow topology on both internal and string stability of vehicle platoons has been well studied. However, understanding the impact of information flow topology on cyber-security tasks, e.g., attack detection, resilient estimation and formation algorithms, is largely open. By means of a general graph theory framework, we study connectivity measures of several platoon topologies and we reveal how these measures affect the ability of distributed algorithms to reject communication disturbances, to detect cyber-attacks, and to be resilient against them. We show that the traditional platoon topologies relying on interaction with the nearest neighbor are very fragile with respect to performance and security criteria. On the other hand, appropriate platoon topologies, namely <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -nearest neighbor topologies, are shown to fulfill desired security and performance levels. The framework we study covers undirected and directed topologies, ungrounded and grounded topologies, or topologies on a line and on a ring. We show that there is a trade-off in the network design between the robustness to disturbances and the resilience to adversarial actions. Theoretical results are validated via simulations.

Rank one density for a class of M-bases

In 1990s several papers studied a strong tridiagonal M-basis that did not possess rank one density property. We offer a new method for the study of more generic finite-band M-bases, employing a graph theory framework. We determine the necessary and sufficient conditions for rank one density property in this class of M-bases. Also we give some sufficient conditions concerning k point density property.

Low- and high-density forms of liquid water revealed by a new medium-range order descriptor

We present in this paper a computational approach based on molecular dynamics simulations and graph theory to characterize the structure of liquid water considering not only the local structural arrangement within the first (or second) hydration shell, but also the medium- to long-range order. In particular, a new order parameter borrowed from the graph-theory framework, i.e., the node total communicability (NTC), is introduced to analyze the dynamic network of water molecules in the liquid phase. This order parameter is able not only to accurately report on the different high-density-liquid (HDL) and low-density-liquid (LDL) water phases postulated in the liquid–liquid phase transition hypothesis, but also to show that HDL-like forms are not homogeneous but rather composed by regions at different local density. In particular, the presence of patches at very high density with an increased number of interstitial water molecules is unveiled, both under pressure and at ambient conditions.

Connectome of memristive nanowire networks through graph theory

Hardware implementation of neural networks represents a milestone for exploiting the advantages of neuromorphic-type data processing and for making use of the inherent parallelism associated with such structures. In this context, memristive devices with their analogue functionalities are called to be promising building blocks for the hardware realization of artificial neural networks. As an alternative to conventional crossbar architectures where memristive devices are organized with a top-down approach in a grid-like fashion, neuromorphic-type data processing and computing capabilities have been explored in networks realized according to the principle of self-organization similarity found in biological neural networks. Here, we explore structural and functional connectivity of self-organized memristive nanowire (NW) networks within the theoretical framework of graph theory. While graph metrics reveal the link of the graph theoretical approach with geometrical considerations, results show that the interplay between network structure and its capacity to transmit information is related to a phase transition process consistent with percolation theory. Also the concept of memristive distance is introduced to investigate activation patterns and the dynamic evolution of the information flow across the network represented as a memristive graph. In agreement with experimental results, the emergent short-term dynamics reveals the formation of self-selected pathways with enhanced transport characteristics connecting stimulated areas and regulating the trafficking of the information flow. The network capability to process spatio-temporal input signals can be exploited for the implementation of unconventional computing paradigms in memristive graphs that take into advantage the inherent relationship between structure and functionality as in biological systems.

Restoration priorities for Caatinga dry forests: Landscape resilience, connectivity and biodiversity value

Abstract Restoration actions can halt biodiversity loss and rescue its services. However, in order to be effective, priority areas for restoration should be chosen based on objective large‐scale restoration planning. Here, a multicriteria graph theory framework was used to propose restoration priority areas for the Brazilian Caatinga, the largest seasonally dry tropical forest of the New World, based on landscape resilience, landscape connectivity and biodiversity conservation value, focusing on threatened endemic plant species. We applied this graph theory framework to 10,406 Caatinga catchment basins. Vegetation cover and within‐catchment connectivity were used to select catchments of intermediate landscape resilience, which in principle offer more effective opportunities for restoration. Then, such catchments were independently classified into (a) three classes according their contribution for between‐catchment connectivity and (b) three classes according their value for biodiversity conservation, estimated by the richness of threatened, endemic plant species. By the integration of landscape resilience, landscape connectivity and biodiversity conservation values, three priority classes for restoration were generated. The multicriteria framework generated several restoration priority cut‐offs. Prioritization based on landscape resilience selected 36% of the Caatinga catchments as high priority for restoration. By independently adding landscape connectivity and biodiversity conservation value, only 12% and 3% of the catchments, respectively, were considered as high priority. By combining all three criteria, 9% of the catchments were selected as high priority and &lt;1% as top priority for restoration. Synthesis and applications. Restoration of drylands can contribute immensely to the conservation of its threatened biodiversity but large‐scale planning is quintessential. Here, a multicriteria graph theory framework was applied to indicate priority areas for restoration, which maximizes the effectiveness of restoration actions, landscape connectivity for climate change adaptation and conservation of threatened species. The framework was applied to the Caatinga, the largest seasonally dry tropical forest of the new world, but it can be applied world‐wide under different budged limitations and spatial scales, being useful for private, state and federal initiatives.

How age and L2 proficiency affectthe L2 lexicon

The present paper offers a study of the influence of age co-occurring with school grade and L2 proficiency on vocabulary production. Previous studies in classroom contexts confirmed that learners’ lexical performance changes over time as their knowledge of L2 develops. Specifically, vocabulary becomes wider and more varied with time. In lexical availability studies, in particular, age, school grade, and L2 proficiency have been found to be significant variables. Here, we had 196 EFL learners of two different school grades (with corresponding ages and L2 proficiency levels) complete a lexical availability task: verbal fluency task to look into their vocabulary production and lexicon organization. Responses were analyzed against the framework of graph theory, together with descriptive tests. The results reveal that older learners produce more words, less frequent words, and words belonging to higher proficiency bands; differences between them and younger learners were very small, however. A more interesting result was brought to light by graph metrics, which reveal that learners in both groups used a category-ridden lexicon organization. Older learners display more single connections among peripheral words, giving rise to more disperse semantic networks approaching the structure found in native mental lexicons.

Disruptions in global network segregation and integration in adolescents and young adults with fetal alcohol spectrum disorder.

Fetal alcohol spectrum disorder (FASD) is a significant public health problem that is associated with a broad range of physical, neurocognitive, and behavioral effects resulting from prenatal alcohol exposure (PAE). Magnetic resonance imaging (MRI) has been an important tool for advancing our knowledge of abnormal brain structure and function in individuals with FASD. However, whereas only a small number of studies have applied graph theory-based network analysis to resting-state functional MRI (fMRI) data in individuals with FASD additional research in this area is needed. Resting-state fMRI data were collected from adolescent and young adult participants (ages 12-22) with fetal alcohol syndrome (FAS) or alcohol-related neurodevelopmental disorder (ARND) and neurotypically developing controls (CNTRL) from previous studies. Group independent components analysis (gICA) was applied to fMRI data to extract components representing functional brain networks. Functional network connectivity (FNC), measured by Pearson correlation of the average independent component (IC) time series, was analyzed under a graph theory framework to compare network modularity, the average clustering coefficient, characteristic path length, and global efficiency between groups. Cognitive intelligence, measured by the Wechsler Abbreviated Scale of Intelligence (WASI), was compared and correlated to global network measures. Group comparisons revealed significant differences in the average clustering coefficient, characteristic path length, and global efficiency. Modularity was not significantly different between groups. The FAS and ARND groups scored significantly lower than the CNTRL group on Full Scale IQ (FS-IQ) and the Vocabulary subtest, but not the Matrix Reasoning subtest. No significant associations between intelligence and graph theory measures were detected. Our results partially agree with previous studies examining global graph theory metrics in children and adolescents with FASD and suggest that the exposure to alcohol during prenatal development leads to disruptions in aspects of functional network segregation and integration.

Evolutionary bet-hedging in structured populations

As ecosystems evolve, species can become extinct due to fluctuations in the environment. This leads to the evolutionary adaption known as bet-hedging, where species hedge against these fluctuations to reduce their likelihood of extinction. Environmental variation can be either within or between generations. Previous work has shown that selection for bet-hedging against within-generational variation should not occur in large populations. However, this work has been limited by assumptions of well-mixed populations, whereas real populations usually have some degree of structure. Using the framework of evolutionary graph theory, we show that through adding competition structure to the population, within-generational variation can have a significant impact on the evolutionary process for any population size. This complements research using subdivided populations, which suggests that within-generational variation is important when local population sizes are small. Together, these conclusions provide evidence to support observations by some ecologists that are contrary to the widely held view that only between-generational environmental variation has an impact on natural selection. This provides theoretical justification for further empirical study into this largely unexplored area.