This paper presents a comprehensive analysis of interference events in automotive scenarios based on radar systems equipped with communication-assisted chirp sequence (CaCS). First, it examines the impact of interference on radar and communication functionalities in CaCS systems according to the orientation of the investigated nodes. For this purpose, a graph-based approach is employed with MATLAB simulations to illustrate the potential occurrence of interference on the graph for communication functionality compared with their counterparts on radar. Second, the paper delves into the impact of interference on the synchronization between two communicating CaCS nodes. It extends a previous study to match the frequency of current radar sensors, where chirp estimation, an adjusted version of the Schmidl & Cox algorithm, and correlation are adopted to synchronize the transmitter and receiver of two CaCS communicating nodes in the time-frequency plane. The proposed synchronization method is finally verified by measurements at ${79}\,\mathrm{GHz}$ with a system-on-chip, where the resulting correlation metric and mean square error are illustrated as validation factors.

The generation of floor plan layouts has been extensively studied in recent years, driven by the need for efficient and functional architectural designs. Despite significant advancements, existing methods often face limitations when dealing with specific input adjacency graphs or room shapes and boundary layouts. When adjacency graphs contain separating triangles, the floor plan must include rectilinear rooms (non-rectangular rooms with concave corners). From a design perspective, minimizing corners or bends in rooms is crucial for functionality and aesthetics. In this article, we present a Python-based application called G-Drawer for automatically generating floor plans with a minimum number of bends. G-Drawer takes any plane triangulated graph as an input and outputs a floor plan layout with minimum bends. It prioritizes generating a rectangular floor plan (RFP); if an RFP is not feasible, it then generates an orthogonal floor plan or an irregular floor plan. G-Drawer modifies orthogonal drawing techniques based on flow networks and applies them on the dual graph of a given PTG to generate the required floor plans. The results of this article demonstrate the efficacy of G-Drawer in creating efficient floor plans. However, in future, we need to work on generating multiple dimensioned floor plans having non-rectangular rooms as well as non-rectangular boundary. These enhancements will address both mathematical and architectural challenges, advancing the automated generation of floor plans toward more practical and versatile applications.

A simple property of networks is used as the basis for a scaling algorithm that represents nonsymmetric proximities as network distances. The algorithm determines which vertices are directly connected by an arc and estimates the length of each arc. Network distance, defined as the minimum pathlength between vertices, is assumed to be a generalized power function of the data. The derived network structure, however, is invariant across monotonic transformations of the data. A Monte Carlo simulation and applications to eight sets of proximity data support the practical utility of the algorithm.

We show that separable nonlinear least squares (SNLLS) estimation is applicable to all linear structural equation models (SEMs) that can be specified in RAM notation. SNLLS is an estimation technique that has successfully been applied to a wide range of models, for example neural networks and dynamic systems, often leading to improvements in convergence and computation time. It is applicable to models of a special form, where a subset of parameters enters the objective linearly. Recently, Kreiberg et al. (Struct Equ Model Multidiscip J 28(5):725–739, 2021. https://doi.org/10.1080/10705511.2020.1835484) have shown that this is also the case for factor analysis models. We generalize this result to all linear SEMs. To that end, we show that undirected effects (variances and covariances) and mean parameters enter the objective linearly, and therefore, in the least squares estimation of structural equation models, only the directed effects have to be obtained iteratively. For model classes without unknown directed effects, SNLLS can be used to analytically compute least squares estimates. To provide deeper insight into the nature of this result, we employ trek rules that link graphical representations of structural equation models to their covariance parametrization. We further give an efficient expression for the gradient, which is crucial to make a fast implementation possible. Results from our simulation indicate that SNLLS leads to improved convergence rates and a reduced number of iterations.

A common statistical modelling paradigm used in actuarial pricing is (a) assuming that the possible loss model can be chosen from a dictionary of standard models; (b) selecting the model that provides the best trade-off between goodness of fit and complexity. Machine learning provides a rigorous framework for this selection/validation process. An alternative modelling paradigm, common in the sciences, is to prove the adequacy of a statistical model from first principles: for example, Planck’s distribution, which describes the spectral distribution of blackbody radiation empirically, was explained by Einstein by assuming that radiation is made of quantised harmonic oscillators (photons). In this working party we have been exploring the extent to which loss models, too, can be derived from first principles. Traditionally, the Poisson, negative binomial, and binomial distributions are used as loss count models because they are familiar and easy to work with. We show how reasoning from first principles naturally leads to non-stationary Poisson processes, Lévy processes, and multivariate Bernoulli processes depending on the context. For modelling severities, we build on previous research that shows  how graph theory can be used to model property-like losses. We show how the methodology can be extended to deal with business interruption/supply chain risks by considering networks with higher-order dependencies. For liability business, we show the theoretical and practical limitations of traditional models such as the lognormal distribution. We explore the question of where the ubiquitous power-law behaviour comes from, finding a natural explanation in random growth models. We also address the derivation of severity curves in territories where compensation tables are used. This research is foundational in nature, but its results may prove useful to practitioners by guiding model selection and elucidating the relationship between the features of a risk and the model’s parameters.

Atmospheric chemical reactions play an important role in air quality and climate change. While the structure and dynamics of individual chemical reactions are fairly well understood, the emergent properties of the entire atmospheric chemical system, which can involve many different species that participate in many different reactions, are not well described. In this work, we leverage graph-theoretic techniques to characterize patterns of interaction (“motifs”) in three different representations of gas-phase atmospheric chemistry, termed “chemical mechanisms.” These widely used mechanisms, the master chemical mechanism, the GEOS-Chem mechanism, and the Super-Fast mechanism, vary dramatically in scale and application, but they all generally aim to simulate the abundance and variability of chemical species in the atmosphere. This motif analysis quantifies the fundamental patterns of interaction within the mechanisms, which are directly related to their construction. For example, the gas-phase chemistry in the very small Super-Fast mechanism is entirely composed of bimolecular reactions, and its motif distribution matches that of an individual bimolecular reaction well. The larger and more complex mechanisms show emergent motif distributions that differ strongly from any specific reaction type, consistent with their complexity. The proposed motif analysis demonstrates that while these mechanisms all have a similar design goal, their higher-order structure of interactions differs strongly and thus provides a novel set of tools for exploring differences across chemical mechanisms.

The increased complexity of development projects surpass the capabilities of existing methods. While Model Based Systems Engineering pursues technically holistic approaches to realize complex products, aspects of organization as well as risk management, are still considered separately. The identification and management of risks are crucial in order to take suitable measures to minimize adverse effects on the project or the organization. To counter this, a new graph-based method and tool using AI, tailored to the needs of complex development projects and organizations is introduced here.

The research of parallel mechanism (PM) configuration involves many problems. From topology to configuration, dimensional constraint, etc., how to establish the relationship between topology and configuration with effective methods is a long-term challenge for the configuration design. In this paper, the chemical molecular spatial structure (CMSS) is linked with the configuration of symmetrical parallel mechanism (SPM). Starting from the methane molecule (CH4), a spatial structural topological relation is obtained. Based on graph theory and the spatial structural topological relation, a new expression method with topological graph and its kinematic pair adjacency matrix for spatial SPM is proposed. Then, the expression and analysis for the characteristics of spatial SPM are obtained. Finally, by taking the 3-RPS PM and the 3-RRC PM as examples, the effectiveness and corresponding consistency of the proposed expression method are successfully verified. The proposed new expression method paves the way for the subsequent digital and automated design and analysis of the SPM configuration.

We show that for a fixed $q$, the number of $q$-ary $t$-error correcting codes of length $n$ is at most $2^{(1 + o(1)) H_q(n,t)}$ for all $t \leq (1 - q^{-1})n - 2\sqrt{n \log n}$, where $H_q(n, t) = q^n/ V_q(n,t)$ is the Hamming bound and $V_q(n,t)$ is the cardinality of the radius $t$ Hamming ball. This proves a conjecture of Balogh, Treglown, and Wagner, who showed the result for $t = o(n^{1/3} (\log n)^{-2/3})$.

Let $G=(V,E)$ be a countable graph. The Bunkbed graph of $G$ is the product graph $G \times K_2$ , which has vertex set $V\times \{0,1\}$ with “horizontal” edges inherited from $G$ and additional “vertical” edges connecting $(w,0)$ and $(w,1)$ for each $w \in V$ . Kasteleyn’s Bunkbed conjecture states that for each $u,v \in V$ and $p\in [0,1]$ , the vertex $(u,0)$ is at least as likely to be connected to $(v,0)$ as to $(v,1)$ under Bernoulli- $p$ bond percolation on the bunkbed graph. We prove that the conjecture holds in the $p \uparrow 1$ limit in the sense that for each finite graph $G$ there exists $\varepsilon (G)\gt 0$ such that the bunkbed conjecture holds for $p \geqslant 1-\varepsilon (G)$ .