Graph Formalism Research Articles

Heuristic-based recommendation system for dealing with abnormal situations in industrial applications

Abstract The effective management of process deviations and abnormal events depends on operational actions in providing the appropriate responses to each situation. Applications with requirements focused on the provision of resources tend to be handled by a Human-Machine Interface (HMI) along with Supervisory Control and Data Acquisition (SCADA). Process reliability is achieved if the operation ensures that actions will be performed according to the required response and priority levels. This paper presents a novel architecture entitled the Heuristic-Based Recommendation System (HB-RS). The main goal is to provide resources capable of streamlining the process of actively handling abnormal situations. For recommendation purposes, the use of probabilistic networks is proposed, which are well suited to represent uncertainty elements present in engineering applications. To create the inference mechanism for these systems, a Multi-Entity Bayesian Network (MEBN) is proposed, highlighting the importance of semantic characterization via knowledge-based, probabilistic graphical model formalism, which is closely linked to the modeling paradigm in which we can predict situations. The developed capabilities have been applied to a real case study in the operation of a metro train system, and the results obtained indicate the value of the proposed method.

МЕТОДИКА СОЗДАНИЯ КОМПЬЮТЕРНОЙ МОДЕЛИ КОНСТРУКТИВА СКУЛЬПТУРЫ

Abstract. The levels of internal dynamics of the sculpture are proposed in the article, taking into account the position of the four main axes of the sculpture frame. This gives us the opportunity to model the frame of a sculpture using the Poser computer program, taking into account the historical experience of creating a sculpture. Subject of research: To study the dynamics of form on the example of sculptural compositions that convey the dynamics of living objects, based on the formalization of the dynamic properties of sculpture. Materials and methods: The analysis of geometric aspects of artistic shaping was carried out on the basis of determining the leading principles of the organization of an integral composition (the principle of subordination of elements), characteristics of methodological techniques for graphic formalization of art objects and substantiation of computer modeling of compositional formations. Results: The dynamic properties of a circular sculpture are realized in its external manifestations as a result of the displacement of the center of gravity of a free-standing figure relative to the compositional axis and are characterized by the position of the center of gravity (outside the support or within the support). Conclusions: The development of an algorithm for creating a computer model of the sculpture frame, taking into account its internal dynamics, seems necessary for the activities of sculptors and designers performing architectural and landscape projects using computer technology.

String diagrams for Strictification and Coherence

Whereas string diagrams for strict monoidal categories are well understood, and have found application in several fields of Computer Science, graphical formalisms for non-strict monoidal categories are far less studied. In this paper, we provide a presentation by generators and relations of string diagrams for non-strict monoidal categories, and show how this construction can handle applications in domains such as digital circuits and programming languages. We prove the correctness of our construction, which yields a novel proof of Mac Lane's strictness theorem. This in turn leads to an elementary graphical proof of Mac Lane's coherence theorem, and in particular allows for the inductive construction of the canonical isomorphisms in a monoidal category.

Topology-aware reinforcement learning for tertiary voltage control

Topology-aware reinforcement learning for tertiary voltage control

ITS4Tsunamis: An Intelligent Transportation System for tsunami emergencies

ITS4Tsunamis: An Intelligent Transportation System for tsunami emergencies

An extended phase graph-based framework for DANTE-SPACE simulations including physiological, temporal, and spatial variations.

The delay alternating with nutation for tailored excitation (DANTE)-sampling perfection with application-optimized contrasts (SPACE) sequence facilitates 3D intracranial vessel wall imaging with simultaneous suppression of blood and CSF. However, the achieved image contrast depends closely on the selected sequence parameters, and the clinical use of the sequence is limited in vivo by observed signal variations in the vessel wall, CSF, and blood. This paper introduces a comprehensive DANTE-SPACE simulation framework, with the aim of providing a better understanding of the underlying contrast mechanisms and facilitating improved parameter selection and contrast optimization. An extended phase graph formalism was developed for efficient spin ensemble simulation of the DANTE-SPACE sequence. Physiological processes such as pulsatile flow velocity variation, varying flow directions, intravoxel velocity variation, diffusion, and effects were included in the framework to represent the mechanisms behind the achieved signal levels accurately. Intravoxel velocity variation improved temporal stability and robustness against small velocity changes. Time-varying pulsatile velocity variation affected CSF simulations, introducing periods of near-zero velocity and partial rephasing. Inclusion of diffusion effects was found to substantially reduce the CSF signal. Blood flow trajectory variations had minor effects, but differences along the trajectory reduced DANTE efficiency in low- areas. Introducing low-velocity pulsatility of both CSF and vessel wall helped explain the in vivo observed signal heterogeneity in both tissue types. The presented simulation framework facilitates a more comprehensive optimization of DANTE-SPACE sequence parameters. Furthermore, the simulation framework helps to explain observed contrasts in acquired data.

Taxonomy-Driven Graph-Theoretic Framework for Manufacturing Cybersecurity Risk Modeling and Assessment

Abstract Identifying, analyzing, and evaluating cybersecurity risks are essential to devise effective decision-making strategies to secure critical manufacturing against potential cyberattacks. However, a manufacturing-specific quantitative approach is lacking to effectively model threat events and evaluate the unique cybersecurity risks in discrete manufacturing systems. In response, this paper introduces the first taxonomy-driven graph-theoretic model and framework to formally represent this unique cybersecurity threat landscape and identify vulnerable manufacturing assets requiring prioritized control. First, the proposed framework characterizes threat actors’ techniques, tactics, and procedures using taxonomical classifications of manufacturing-specific threat attributes and integrates these attributes into cybersecurity risk modeling. This facilitates the systematic generation of comprehensive and generalizable cyber-physical attack graphs for discrete manufacturing systems. Second, using the attack graph formalism, the proposed framework enables concurrent modeling and analysis of a wide variety of cybersecurity threats comprising varying attack vectors, locations, vulnerabilities, and consequences. The risk model captures the cascading attack impact of varying attack methods through different cyber and physical entities in manufacturing systems, leading to specific consequences. Then, the constructed cyber-physical attack graphs are analyzed to comprehend threat propagation through the discrete manufacturing value chain and identify potential attack paths. Third, a quantitative risk assessment approach is presented to evaluate the cybersecurity risk associated with potential attack paths. It also identifies the attack path with the maximum likelihood of success, pointing out critical manufacturing assets requiring prioritized control. Finally, the proposed risk modeling and assessment framework is demonstrated using an illustrative example.

Bond graph model of a PEM fuel cell stack

The fuel cell is a complex system, in which several disciplinary fields are concerned: hydraulics, chemical, thermal and electric. In this paper, we present the hydraulic part of the model of a PEM fuel cell stack via the Bond Graph formalism. The developed model enables to simulate the pressure losses inside the fuel cell. Firstly the basis of Bond Graph modelling is recalled. Then, the structure of the model and its elements are described. Secondly, the model is exploited to study the effects of operating conditions on the pressure losses attached to the distribution of gases in the electrodes.

Representation of the solution of a nonlinear molecular beam epitaxy equation

<p>Stochastic partial differential equations (SPDEs) driven by Lévy noise are extensively employed across various domains such as physics, finance, and engineering to simulate systems experiencing random fluctuations. In this paper, we focus on a specific type of such SPDEs, namely the nonlinear beam epitaxy equation driven by Lévy noise. The Feynman graph formalism emerges as a potent tool for analyzing these SPDEs, particularly in computing their correlation functions, which are essential for understanding the moments of the solution. In this context, the solution to the SPDE and its truncated moments can be expressed as a sum over particular Feynman graphs. Each graph is evaluated according to a set of established rules, providing a systematic method to derive the properties of the solution. Moreover, the study delves into the behavior of the truncated moments for large times. Truncated moments, which capture the statistical properties of the system up to a certain order, are crucial for characterizing the long-term behavior and stability of the solution. The paper will conclude with a discussion on potential applications, highlighting the broader implications of this approach in various scientific and engineering contexts.</p>

Graph rewriting primitives for semantic graph databases sanitization

Due to the rapid proliferation of data online, an important quantity of private or sensitive informations is being stored as linked data in graph databases (e.g., represented as RDF). For such databases to be shared without jeopardizing privacy, they must first undergo a process known as database sanitization. During this process, databases are transformed following graph transformations that are usually described informally or through ad-hoc processes. However, a more thourough formalization of these transformations would aid in analysing the sanitization process, ensuring its correctness, and demonstrating the resulting privacy guarantees. This paper is an effort toward bridging the gap between the rigorous graph rewriting approaches and graph sanitization. We propose a graph transformation language to serve as a basis for constructing various sanitization mechanisms. This language relies on a set of elementary transformation operators formalized using a generic algebraic graph rewriting approach. Our language takes into account semantic and supports the equivalent of WHERE and EXCEPT clauses. As a proof of concept, we use these operators to implement two mechanisms from the literature, one generic (Local Differential Privacy) and one specifically introduced for semantic graph databases (sensitive attribute masking through anatomization). We propose an open-sourced tool implementing the elementary operators and the privacy mechanisms we derive from them relying on the Attributed Graph Grammar System (AGG) and its java API, providing a concrete tool implementing formal graph rewriting mechanisms to sanitize semantic graph databases. We present experimental results on this implementation regarding both proposed schemes and discuss its efficiency and scalability.

Pushing MP2RAGE boundaries: Ultimate time-efficient parameterization combined with exhaustive T1 synthetic contrasts.

MP2RAGE parameter optimization is redefined to allow more time-efficient MR acquisitions, whereas the T1 -based synthetic imaging framework is used to obtain on-demand T1 -weighted contrasts. Our aim was to validate this concept on healthy volunteers and patients with multiple sclerosis, using plug-and-play parallel-transmission brain imaging at 7 T. A "time-efficient" MP2RAGE sequence was designed with optimized parameters including TI and TR set as small as possible. Extended phase graph formalism was used to set flip-angle values to maximize the gray-to-white-matter contrast-to-noise ratio (CNR). Several synthetic contrasts (UNI, EDGE, FGATIR, FLAWSMIN , FLAWSHCO ) were generated online based on the acquired T1 maps. Experimental validation was performed on 4 healthy volunteers at various spatial resolutions. Clinical applicability was evaluated on 6 patients with multiple sclerosis, scanned with both time-efficient and conventional MP2RAGE parameterizations. The proposed time-efficient MP2RAGE protocols reduced acquisition time by 40%, 30%, and 19% for brain imaging at (1 mm)3 , (0.80 mm)3 and (0.65 mm)3 , respectively, when compared with conventional parameterizations. They also provided all synthetic contrasts and comparable contrast-to-noise ratio on UNI images. The flexibility in parameter selection allowed us to obtain a whole-brain (0.45 mm)3 acquisition in 19 min 56 s. On patients with multiple sclerosis, a (0.67 mm)3 time-efficient acquisition enhanced cortical lesion visualization compared with a conventional (0.80 mm)3 protocol, while decreasing the scan time by 15%. The proposed optimization, associated with T1 -based synthetic contrasts, enabled substantial decrease of the acquisition time or higher spatial resolution scans for a given time budget, while generating all typical brain contrasts derived from MP2RAGE.

A Graphical Representation of the Truncated Moment of the Solution of a Nonlinear SPDE

We consider a stochastic partial differential equation driven by a Lévy type noise (SPDE). Particular attention is given to the correlation function which measures the moments of the solution. Using the Feynman graph formalism, the solution of the SPDE as well as its truncated moments are given as a sum over specific graphs that are evaluated according to some rules. A remark on some applications will be given at the end of this work.

Extending the graph formalism to higher-order gates

We present an algorithm for efficiently simulating a quantum circuit in the graph formalism. In the graph formalism, we present states as a linear combination of graphs with Clifford operations on their vertices. We show how a $\calC_3$ gate such as the Toffoli gate or $\frac\pi8$ gate acting on a stabilizer state splits it into two stabilizer states. We also describe conditions for merging two stabilizer states into one. We discuss applications of our algorithm to circuit identities and finding low stabilizer rank presentations of magic states.

The Formal Graph of APRDF

A new alternative model for expressing more complex knowledge has been proposed as an attributed predicate RDF (APRDF). By handling attributes that represent any additional triples of the main triple, APRDF serves as a predicate. Therefore, the formal graph model of APRDF must be defined. Lastly, this work recommends that the APRDF's conventional diagram is a digraph-hypergraph mix. The previous formal graph of RDF is a hypergraph even though, visually intuitively, it is a digraph. It also contains inconsistency. The other new serialization needs to describe its formal model. Eventually, this work can provide the formal graph model of APRDF and maintain consistency. There have been a few definitions proposed. The direct impact of this formal model is that APRDF outperformed the other model significantly when retrieving complex queries within its formal graph. In querying, the initial implementation of the proposed formal graph takes an average of 62 milliseconds. Compared to the other graph models, the proposed formal graph can reduce query time by an average of 90,7 milliseconds on the BF-arch graph and 121,05 milliseconds on the naive/default graph. As the formal graph model is preserved, the attributed predicate of APRDF assumed will drive a new model in the retrieving process that more in using a predicate formed as a link in a graph. It will also be impacted in the mining process by more elaborate links/edges (link mining).

Stochastic-offset-enhanced restricted slice excitation and 180° refocusing designs with spatially non-linear ΔB0 shim array fields.

Developing a general framework with a novel stochastic offset strategy for the design of optimized RF pulses and time-varying spatially non-linear ΔB0 shim array fields for restricted slice excitation and refocusing with refined magnetization profiles within the intervals of the fixed voxels. Our framework uses the decomposition property of the Bloch equations to enable joint design of RF-pulses and shim array fields for restricted slice excitation and refocusing with auto-differentiation optimization. Bloch simulations are performed independently on orthogonal basis vectors, Mx, My, and Mz, which enables designs for arbitrary initial magnetizations. Requirements for refocusing pulse designs are derived from the extended phase graph formalism obviating time-consuming sub-voxel isochromatic simulations to model the effects of crusher gradients. To refine resultant slice-profiles because of voxelwise optimization functions, we propose an algorithm that stochastically offsets spatial points at which loss is computed during optimization. We first applied our proposed design framework to standard slice-selective excitation and refocusing pulses in the absence of non-linear ΔB0 shim array fields and compared them against pulses designed with Shinnar-Le Roux algorithm. Next, we demonstrated our technique in a simulated setup of fetal brain imaging in pregnancy for restricted-slice excitation and refocusing of the fetal brain. Our proposed framework for optimizing RF pulse and time-varying spatially non-linear ΔB0 shim array fields achieve high fidelity restricted-slice excitation and refocusing for fetal MRI, which could enable zoomed fast-spin-echo-MRI and other applications.

Introduction to Graph Enumerations

Summary In this article sets of certain subgraphs of a graph are formalized in the Mizar system [7], [1], based on the formalization of graphs in [11] briefly sketched in [12]. The main result is the spanning subgraph theorem.

About Regular Graphs

Abstract In this article regular graphs, both directed and undirected, are formalized in the Mizar system [7], [2], based on the formalization of graphs as described in [10]. The handshaking lemma is also proven.

Deep Reinforcement Learning Environment Approach Based on Nanocatalyst XAS Diagnostics Graphic Formalization.

The most in-demand instrumental methods for new functional nanomaterial diagnostics employ synchrotron radiation, which is used to determine a material's electronic and local atomic structure. The high time and resource costs of researching at international synchrotron radiation centers and the problems involved in developing an optimal strategy and in planning the control of the experiments are acute. One possible approach to solving these problems involves the use of deep reinforcement learning agents. However, this approach requires the creation of a special environment that provides a reliable level of response to the agent's actions. As the physical experimental environment of nanocatalyst diagnostics is potentially a complex multiscale system, there are no unified comprehensive representations that formalize the structure and states as a single digital model. This study proposes an approach based on the decomposition of the experimental system into the original physically plausible nodes, with subsequent merging and optimization as a metagraphic representation with which to model the complex multiscale physicochemical environments. The advantage of this approach is the possibility to directly use the numerical model to predict the system states and to optimize the experimental conditions and parameters. Additionally, the obtained model can form the basic planning principles and allow for the optimization of the search for the optimal strategy with which to control the experiment when it is used as a training environment to provide different abstraction levels of system state reactions.

A graph approach for fast dense array inter-station phase delay interpretation

SUMMARY We present a phase-delay detection procedure adapted for seismic arrays composed of a large number of stations. We use graph formalism to introduce a direct method to compute station phase delays starting from inter-station phase differences deduced from noise cross-correlation functions. We focus this study on surface wave main arrival as phase-difference evaluation at each station requires high coherence level. Then, we perform numerical experiments with synthetic data computed as a realistic and dense network of 79 stations in a 400 by $400\, \mathrm{km^2}$ square box. For one of the 79 stations, we simulate a phase difference of 15 per cent of the signal period. Further, we evaluate the accuracy and precision of phase-delay estimation at each station with regard to the quality of the cross-correlation functions (i.e. the signal-to-noise ratio). When the inter-station coherence levels are larger than 0.6 (i.e. a high-quality signal), we show good agreement between the phase-delay estimation and its expected value of 15 per cent of the signal period. We introduce a coherence-weighted estimate of phase delay and show that applying this weighting allows us to be less vulnerable to phase-delay underestimation for intermediate-quality signals. Then, the method is applied to experimental data recorded by a high density nodal array with 923 vertical geophones with 19 d of continuous records, centred on the 600 by $600\, \mathrm{m^2}$ damage zone of the Clark branch of the San Jacinto Fault Zone, Southern California (USA). We verify that the San Jacinto network is well synchronized, as most of the estimated phase delays are less than 2 per cent of the central period of the signal, and they are associated with high levels of inter-station coherence. More surprisingly, the spatial features of the estimated phase delays show deterministic geographical patterns that are related to topography and that exhibit similarities with phase velocity maps at $4.5\, \mathrm{Hz}$ from previous 3-D velocity inversions. This suggests that the topographic effect may be accounted for to estimate accurate phase delays. Also, we note that the temporal variability of the estimated phase delays in the case of the San Jacinto data set are related to atmospheric forcing. Our direct method for estimating phase delays is applicable to structure-oriented monitoring studies, and it opens perspectives in the monitoring of seismic velocity variations.

Causal reasoning with causal graphs in educational technology research

Researchers tasked with understanding the effects of educational technology innovations face the challenge of providing evidence of causality. Given the complexities of studying learning in authentic contexts interwoven with technological affordances, conducting tightly-controlled randomized experiments is not always feasible nor desirable. Today, a set of tools is available that can help researchers reason about cause-and-effect, irrespective of the particular research design or approach. This theoretical paper introduces such a tool, a simple graphical formalism that can be used to reason about potential sources of bias. We further explain how causal graphs differ from structural equation models and highlight the value of explicit causal inference. The final section shows how causal graphs can be used in several stages of the research process, whether researchers plan to conduct observational or experimental research.