We study the zero-visibility cops and robbers game, where the robber is invisible to the cops until they are caught. This differs from the classic game where full information about the robber’s location is known at any time. A previously known solution for capturing a robber in the zero-visibility case is based on the path decomposition. We provide an alternative solution based on a separation hierarchy, improving capture time and space complexity without asymptotically increasing the zero-visibility cop number in most cases. In addition, the alternative approach leads to a better bound on the approximate zero-visibility cop number for various classes of graphs, where approximate refers to the restriction to polynomial time computable strategies.

ABSTRACT The first tornado dataset for Canada covered the years 1950–1979 and allowed a 30-year tornado climatology to be attempted. This was followed by a second 30-year national climatology covering the years 1980–2009. Guided by World Meteorological Organization recommendations, the current study is a 10-year update of the Canadian tornado climatology covering the years 1991–2020. Data conventions and quality control procedures developed by the Northern Tornadoes Project are used to ensure a high-quality, nationally consistent dataset, and are also applied back to 1980 for completeness. The updated 30-year dataset comprises 1948 tornadoes with the vast majority (88%) of these rated F/EF0-1, while 11% had a rating of F/EF2 and only 1% had a rating of F/EF3 or higher. Tornadoes were recorded in nearly every province and territory with the highest annual mean frequency in Ontario (18.5 tornadoes per year). Gridded tornado incidence values were highest in the southern Prairies and southern Ontario with a notable regional maximum in the area west of Toronto, even when only F/EF2 + tornadoes are considered. Tornadoes occurred most frequently from June to August and from 1600 to 1859 LT, inclusive. The median lengths and widths of tornado damage paths are 5615 and 260 m, respectively. F/EF2 + tornadoes were found to peak later in the year and later in the day, with more than double the median path length and path width. A total of 20 tornado outbreaks were identified.

This study introduces a novel virtual robotic approach for automated characterization of pedestrian network accessibility from semantically segmented 3D LiDAR point clouds. With approximately 8 million Canadians living with disabilities, scalable accessibility assessment methods are critical. The proposed methodology integrates a Tangent Bug navigation algorithm-extended from 2D to 3D point cloud environments-with a triangular virtual robot grounded in ADA and IBC accessibility standards. The robot navigates classified point cloud data to simultaneously extract related parameters per step including those related to the accessibility assessment, including running slope, cross-slope, path width, surface type, and step height, aligned with the Measure of Environmental Accessibility (MEA) framework. Unlike existing approaches, the method characterizes not only formal sidewalk segments but also the critical transitional linkages between building entrances and the pedestrian network. Rather than evaluating features against fixed binary thresholds, it records continuous raw measurements enabling personalized accessibility assessment tailored to individual user profiles. Quantitative validation demonstrates high accuracy for path width (NRMSE = 2.71%) and reliable slope tracking. The proposed approach is faster, more cost-effective, and more comprehensive than traditional manual methods, and its segment-independent architecture makes it well-suited for future city-scale deployment.

The paper addresses the problem of maneuverability assessment of unmanned ground robotic complexes equipped with steerable platforms, which are characterized by complex kinematic motion schemes and the ability to perform various maneuvering modes. It is shown that the use of conventional maneuverability indicators, such as the minimum turning radius and the swept path width, does not provide an unambiguous quantitative assessment for such complexes, since identical values of these indicators may correspond to different geometric motion modes and different levels of spatial compactness of maneuvering.Based on a kinematic–geometric analysis of symmetric steering of the platforms, the regularities of trajectory formation of characteristic points of the unmanned ground robotic complexes body are established, and the dependences of the inner and outer turning radii on the steering angle of the platforms are obtained. The variation of the swept path width with respect to the steering angle is analyzed, and the existence of a region of ambiguity is demonstrated, in which this indicator cannot be used for correct comparison of different maneuvering modes. To eliminate this ambiguity, an integral indicator – the maneuvering area – is proposed and analytically substantiated. This indicator accounts for the actual spatial region occupied by the robotic complex during turning and turning-in-place maneuvers. The dependence of the maneuvering area on the steering angle of the platforms is investigated, and rational ranges of steering angles are determined, within which the most intensive reduction of the occupied space is achieved. The proposed approach improves the maneuverability assessment method for unmanned ground robotic complexes with steerable platforms and can be applied for comparative evaluation of different geometric layouts and for substantiation of rational motion control parameters.

{ We use computer simulations to demonstrate and assess the validity of the theoretical results and algorithms developed in this paper. } We develop exact simulation algorithms for the joint distribution of the maximum and its location for several constrained Brownian motion processes: Brownian excursion, Brownian meander, and restricted Brownian meander. Our approach leverages path decompositions, particularly Williams's decomposition for excursion and meander processes, and analytic expressions for joint densities involving Bessel process exit times. The resulting joint laws admit factorized forms, allowing for efficient simulation via rejection sampling. We derive sharp piecewise bounds for these densities, enabling rejection sampling with explicitly computable constants and high acceptance rates. These methods are exact, involve no discretization error, and are suitable for high-throughput applications. The algorithms provide a practical and rigorous foundation for exact sampling of path extrema and are directly applicable to simulation-based inference, rare event analysis, and stochastic modelling involving constrained diffusions.

The path decomposition of a graph G is the process of decomposing it into edge-disjoint paths. An induced signed graph is a signed graph formed from an ordinary unsigned graph by assigning signs to its edges according to some protocol. In this paper, we introduce the notion of a path-induced signed graph as an induced signed graph whose edges receive a sign according to whether its end vertices are the end vertices of a path in a path decomposition of G. We also discuss some characteristics of this type of signed graph.

We prove that isomorphism of tournaments of twin width at most $k$ can be decided in time $k^{O(\log k)}n^{O(1)}$. This implies that the isomorphism problem for classes of tournaments of bounded or moderately growing twin width is in polynomial time. By comparison, there are classes of undirected graphs of bounded twin width that are isomorphism complete, that is, the isomorphism problem for the classes is as hard as the general graph isomorphism problem. Twin width is a graph parameter that has been introduced only recently (Bonnet et al., J. ACM 2022), but has received a lot of attention in structural graph theory since then. On directed graphs, it is functionally smaller than clique width. We prove that on tournaments (but not on general directed graphs) it is also functionally smaller than directed tree width (and thus, the same also holds for cut width and directed path width). Hence, our result implies that tournament isomorphism testing is also fixed-parameter tractable when parameterized by any of these parameters. Our isomorphism algorithm heavily employs group-theoretic techniques. This seems to be necessary: as a second main result, we show that the combinatorial Weisfeiler-Leman algorithm does not decide isomorphism of tournaments of twin width at most 35 if its dimension is $o(n)$. (Throughout this abstract, $n$ is the order of the input graphs.) 37 pages. This is the TheoretiCS journal version

We introduce PSM path decomposition labeling of graphs for graph labeling using the sequence of centered triangular numbers. This labeling is assigned on the families of generalized friendship graphs and cycle cactus graphs . For particular values of ` ' some suitable examples are presented for each of graphs.

Automized segmentation of animal paths in UAS Imagery using deep learning - a case study from the Kruger National Park

Path decompositions of Eulerian graphs

The first written mention of computing based on mapping of topological structures and mathematical algorithms onto graphs to be built into hardware, for graph-based computing, dates back to January 1984, when one of the authors of this text, as a Purdue University faculty member, submitted a related proposal to the Defense Department of RCA, Camden, New Jersey, USA. A preliminary study concluded that the optimal structure for mapping algorithms onto hardware is not square, but of the hexagonal shape referred to as “honeycomb”. That is how the term honeycomb was created in the context of mapping structures and algorithms onto hardware. According to the open literature the first structures ever mapped onto the honeycomb architecture are interconnection networks and the first algorithms ever mapped onto the honeycomb architecture are neural networks. If a structure or an algorithm is mapped onto a graph to be built into the hardware, conditions are met for data to flow from inputs to outputs, driven by the voltage difference between inputs and outputs. If that goal is accomplished, potentials are generated for data to move faster, which means that the algorithms get executed with a speed-up. If the data movement is accomplished with a slower clock, less energy is consumed during data propagation through structures and the execution of an algorithm. Consequently, since no control mechanisms have to be implemented, the volume of the engine becomes smaller. And finally, since the structure of the data path is formed at the time of mapping the graph into hardware, the width of the data path could be made as wide as needed, and no wider than needed, which leads to a lot better precision, at no cost in the domain of execution time. Of course, the described paradigm shift became utilizable in practice only after the reconfigurable hardware was invented. That is why the first data flow machines, based on the same or similar concept, appeared only after the FPGA circuits became widespread. However, the full utilization of this paradigm will be possible only after the Analog See of Gates circuits become feasible, which enables a lot lower operational frequency (a lot lower power consumption) and a lot higher speed (due to fewer obstacles on the data propagation paths). This article sheds light on the complexity and speed related to the mapping of structures and algorithms.

Within the context of China’s green economy aimed at sustainable development, research on the linkage between water resources and industry has garnered considerable attention in the academic community. However, the impact of total body water (TBW) transfer and allocation embodied in the labor force—the primary economic actors—has not been addressed in the economic sector. On methodology, the “EEIO-SDA-SPD-II” (ISSI) model employed in this study encompasses measurements methods, such as an environmentally extended input–output model (EEIO), structural decomposition analysis (SDA), structural path decomposition (SPD), and the imbalance index (II), to explore the crucial paths, driving factors, and distribution of water transfer in TWB spanning 15 Chinese industries between 2007 and 2022. The findings indicate that the shifts in TBW in the manufacturing sector are more discernible when viewed through the lens of social driving factors. The construction business exhibits the most significant increase in male total body water (MTBW), whereas the education sector reflects the rapid growth in female total body water (FTBW). Pertaining to final demand, domestic consumption constitutes the primary contributor category to the increase in TWB, followed by fixed capital formation and exports. According to the SPD results, the construction sector exerts the greatest influence on the transfer of MTBW, while the education sector is characterized by the highest path coefficient value for FTBW. In contrast, the manufacturing sector shows the most pronounced initial path. Based on the imbalance index analysis, agriculture derives the greatest economic gains from TBW input, whereas the education sector yields the lowest.

Post-Disaster Investigation and WRF Model Reconstruction of April 27th Tornado in Guangzhou Based on Muti-Source Data Fusion

Deep and ultra-deep drilling operations commonly encounter fractured and fracture-vuggy formations, where weak wellbore strength and well-developed fracture networks lead to frequent lost circulation, presenting a key challenge to safe and efficient drilling. Existing diagnostic practices mostly rely on drilling fluid loss dynamic models of single fractures or simplified discrete fractures to invert fracture geometry, which cannot capture the spatiotemporal evolution of loss in complex fracture networks, resulting in limited inversion accuracy and a lack of quantitative, fracture-network-based loss-dynamics support for bridge-plugging design. In this study, a geologically realistic wellbore–fracture-network coupled loss dynamic model is constructed to overcome the limitations of single- or simplified-fracture descriptions. Within a unified computational fluid dynamics (CFD) framework, solid–liquid two-phase flow and Herschel–Bulkley rheology are incorporated to quantitatively characterise fracture connectivity. This approach reveals how instantaneous and steady losses are controlled by key geometrical factors, thereby providing a computable physical basis for loss-zone inversion and bridge-plugging design. Validation against experiments shows a maximum relative error of 7.26% in pressure and loss rate, indicating that the model can reasonably reproduce actual loss behaviour. Different encounter positions and node types lead to systematic variations in loss intensity and flow partitioning. Compared with a single fracture, a fracture network significantly amplifies loss intensity through branch-induced capacity enhancement, superposition of shortest paths, and shortening of loss paths. In a typical network, the shortest path accounts for only about 20% of the total length, but contributes 40%–55% of the total loss, while extending branch length from 300 mm to 1500 mm reduces the steady loss rate by 40%–60%. Correlation analysis shows that the instantaneous loss rate is mainly controlled by the maximum width and height of fractures connected to the wellbore, whereas the steady loss rate has a correlation coefficient of about 0.7 with minimum width and effective path length, and decreases monotonically with the number of connected fractures under a fixed total width, indicating that the shortest path and bottleneck width are the key geometrical factors governing long-term loss in complex fracture networks. This work refines the understanding of fractured-loss dynamics and proposes the concept of coupling hydraulic deviation codes with deep learning to build a mapping model from mud-logging curves to fracture geometrical parameters, thereby providing support for lost-circulation diagnosis and bridge-plugging optimisation in complex fractured formations.

The purpose of this article is to look at a variety of tactics used in different industries to optimize the operating parameters of 3D printing systems. Fused Deposition Modeling (FDM), one of the most well-known methods, has drawn a lot of interest because of its broad range of applications in fields including die-making and prototype development. FDM creates three-dimensional objects by layering materials one after the other. Because of its great versatility, the technique makes it possible to produce complex geometries that would be challenging to accomplish with conventional manufacturing techniques. However, FDM still has drawbacks with regard to printing speed, production time, and the structural soundness of the printed parts.  The quality of the finished product is directly impacted by a number of variables, including the distance between layers, orientation during printing, percentage of internal fill, deposition angle, path width, and layer depth.  Determining and modifying the most important factors in accordance with the particular needs of the item being produced is therefore crucial. To tackle these challenges, numerous researchers have explored advanced optimization tools like experimental design approaches, surface response modeling, evolutionary algorithms, neural network models, and fuzzy logic systems. Many academics have investigated cutting-edge optimization tools such as fuzzy logic systems, evolutionary algorithms, surface response modeling, experimental design approaches, and neural network models in order to address these issues.  Strength, accuracy, and dependability are some of the important product attributes that are improved by using these instruments.  Objective of this work is to present a thorough analysis of the body of research on enhancing FDM results via efficient process parameter adjustment.

We prove that the equational theory of the positive calculus of relations with transitive closure (PCoR*) is EXPSPACE-complete. Here, PCoR* terms consist of the following standard operators on binary relations: identity, empty, universality, union, intersection, composition, converse, and reflexive transitive closure (so, PCoR* terms subsume Kleene algebra and allegory terms as fragments). Additionally, we show that the equational theory of PCoR* extended with tests and nominals (in hybrid logic) is still EXPSPACE-complete; moreover, it is PSPACE-complete for its intersection-free fragment. To this end, we design derivatives on graphs by extending derivatives on words for regular expressions. The derivatives give a finite automata construction on path decompositions, like those on words. Because the equational theory has a linearly bounded pathwidth model property, we can decide the equational theory of PCoR* using these automata.

Optimization algorithms-assisted unified path generation and decomposition for 3D needled preforms with excellent interlaminar properties

Cognitive scientists have discovered normative and heuristic principles that capture human subgoal preferences when partitioning problems into smaller ones. However, it remains unclear where such preferences come from and why they tend to be both effective and efficient. In this work, we study the processes through which these preferences may be implicitly encoded over learning as learners improve towards optimal traversals. We build on the graph-based environments from prior work and use neural networks as model learners to test if learning shortest-path traversal can lead to human-like path decomposition. We find that simple transformer models develop a preference for paths containing nodes that occur frequently on the shortest paths, consistent with human subgoal preferences found in prior work. This preference is observed when models solve shortest path traversals for unseen problems in both known graphs and new graphs, demonstrating that human-like subgoal preferences can arise without requiring explicit preference computation or exhaustively searching over all possible paths. The same preference does not emerge when models learn to perform random or Hamiltonian traversals. Our findings are robust across several transformer variants as well as recurrent neural networks, suggesting they depend more on the data distribution than the network architecture.

BackgroundAgainst the backdrop of converging population aging and digitalization trends, the impact of the digital divide on older adults’ mental health represents a paradox characterized by conflicting empirical findings.MethodsTo address this paradox, this study employs a multi-method analytical strategy—comprising propensity score matching, panel fixed-effects models, and generalized structural equation modeling—utilizing nationally representative data from the China Family Panel Studies (CFPS) 2016–2022. This approach systematically decomposes the complex causal pathways connecting the digital divide, social capital, and mental health among older adults.ResultsAfter rigorously controlling for self-selection bias and time-invariant individual heterogeneity, our findings initially demonstrate a robust null total effect of the digital divide on depressive symptoms among older adults [average treatment effect on the treated (ATT) = 0.02, t = 0.10, p > 0.1]. However, subsequent mechanism analysis reveals that this null effect represents a statistical artifact arising from a suppression effect. Specifically, a beneficial direct pathway (direct effect of physical access on depression: β = −0.052, p < 0.1) is offset by a detrimental indirect pathway, wherein higher-order “motivational access” undermines bridging social capital (effect on interpersonal relationships: β = −0.207, p < 0.001), which subsequently serves as a protective factor for mental health (effect on depression: β = −0.032, p < 0.1).ConclusionThis study empirically establishes that the digital divide functions as a double-edged sword for older adults’ mental health, with its net effect contingent upon the complex interplay between direct technological benefits and indirect social costs. These findings indicate that future digital inclusion policies must transcend the narrow focus on bridging physical access gaps to prioritize “empowering trust.” This objective can be realized through targeted digital literacy interventions that enable older adults to navigate technology safely, thereby advancing the broader policy objective of healthy aging.

We present a comprehensive analysis of various dual emitter (DuE) designs for 4H-SiC PIN photodiodes, which incorporate heavily doped p⁺ regions within a shallow p- emitter. The p⁺ regions act as low-resistance pathways, facilitating efficient transport of photogenerated carriers to the ohmic contacts. Moreover, the lateral electric field established at the p⁺/p⁻ junction promotes effective separation of charge carriers generated proximate to the surface. By systematically varying the p⁺ path widths and spacings, we analyze the impact of different design geometries on the photodiode sensitivities and investigate the carrier collection mechanisms. Sensitivity response measurements at 210 and 280 nm demonstrate that DuE designs significantly enhance UV-C sensitivity while maintaining high responsivity in the UV-A and UV-B ranges. The best performing design investigated achieves a median sensitivity of 33.4 mA/W at 210 nm, representing a substantial improvement over reference designs.