Traversal Time Research Articles

DARTS: Diffusion Approximated Residual Time Sampling for Time-of-flight Rendering in Homogeneous Scattering Media

Time-of-flight (ToF) devices have greatly propelled the advancement of various multi-modal perception applications. However, achieving accurate rendering of time-resolved information remains a challenge, particularly in scenes involving complex geometries, diverse materials and participating media. Existing ToF rendering works have demonstrated notable results, yet they struggle with scenes involving scattering media and camera-warped settings. Other steady-state volumetric rendering methods exhibit significant bias or variance when directly applied to ToF rendering tasks. To address these challenges, we integrate transient diffusion theory into path construction and propose novel sampling methods for free-path distance and scattering direction, via resampled importance sampling and offline tabulation. An elliptical sampling method is further adapted to provide controllable vertex connection satisfying any required photon traversal time. In contrast to the existing temporal uniform sampling strategy, our method is the first to consider the contribution of transient radiance to importance-sample the full path, and thus enables improved temporal path construction under multiple scattering settings. The proposed method can be integrated into both path tracing and photon-based frameworks, delivering significant improvements in quality and efficiency with at least a 5x MSE reduction versus SOTA methods in equal rendering time.

Neuroprotective Role of Transchalcone in Parkinson's Disease through AMP-activated Protein Kinase-mediated Signaling Pathway.

Parkinson's disease (PD) is a gradually worsening neurodegenerative condition marked by the deterioration of dopaminergic neurons, motor dysfunction, and mitochondrial dysfunction. Trans-chalcone, a natural flavonoid, has shown promise in various disease models because of its antioxidant and anti-inflammatory features. This study investigates the neuroprotective effects of transchalcone in a rat model of PD, focusing on its impact on the activation levels of AMP-activated protein kinase (AMPK) signaling pathway, sirtuin1 (SIRT1) and peroxisome proliferator-activated receptor gamma coactivator 1-alpha (PGC1α) proteins, and mitochondrial-inflammatory responses. Male Sprague Dawley rats were allocated into five groups Control, Control plus transchalcone, PD, PD plus transchalcone, PD plus compound-C, and PD plus Compound-C and trans-chalcone. PD was induced using intranigral 6-hydroxydopamine injection. Trans-chalcone (100 μg/kg) and compound-C (20 mg/kg) were intraperitoneally administered daily for 4 weeks in PD rats. Motor function was assessed using rota-rod and grid tests. Striatal dopamine and cytokines (interleukin 1-beta [IL-1 β], IL-10) and p65-nuclear factor kappa-B (NF-κB) levels were measured with enzyme-linked immunosorbent assay. Mitochondrial function was evaluated by fluorometric techniques. The expression of phosphorylated AMPK, PGC-1α, and SIRT1 was analyzed by Western blotting. Trans-chalcone treatment significantly improved motor function, evidenced by increased latency to fall in the rota-rod test and recovered traversal time in the grid test. It also restored dopamine levels, enhanced mitochondrial function (reduced reactive oxygen species levels, increased membrane potential, and adenosine triphosphate production), normalized cytokines (IL-1 β, IL-10) and p65-NF-κB, and upregulated the proteins expression in rats with PD. Inhibition of AMPK activity with compound-C suppressed the neuroprotective impacts of trans-chalcone, highlighting the contribution of AMPK signaling pathway in its mechanism of action. Neuroprotective and mitoprotective impacts of trans-chalcone were mostly mediated through the activation of AMPK-SIRT1-PGC1α pathway. These results indicate that trans-chalcone could be a promising therapeutic agent for PD, warranting further investigation to assess its efficacy and safety in human patients.

Reconstruction of Surface Electron Spectrum and Cyclotron Motion in the Charge Density Wave Phase of Weyl Semimetals.

Charge density wave (CDW) instability drastically affects the surface electron spectrum of a Weyl semimetal. We show that in the CDW phase, the Fermi arcs reconnect into either closed Fermi loops or Frieze patterns traversing the reconstructed surface mini Brillouin zone. For the closed reconnection topology, application of an out of plane magnetic field leads to a cyclotron motion of the surface electrons. We determine the cyclotron frequency as a function of the electron energy and the magnitude of the CDW gap Δ for various orientations of the Fermi arcs. For weak coupling, the period of cyclotron motion is dominated by the time of traversal of the arc reconnection regions and is inversely proportional to Δ.

Energy Constrained Depth First Search

Depth first search is a natural algorithmic technique for constructing a closed route that visits all vertices of a graph. The length of such a route equals, in an edge-weighted tree, twice the total weight of all edges of the tree and this is asymptotically optimal over all exploration strategies. This paper considers a variant of such search strategies where the length of each route is bounded by a positive integer B (e.g. due to limited energy resources of the searcher). The objective is to cover all the edges of a tree T using the minimum number of routes, each starting and ending at the root and each being of length at most B. To this end, we analyze the following natural greedy tree traversal process that is based on decomposing a depth first search traversal into a sequence of limited length routes. Given any arbitrary depth first search traversal R of the tree T, we cover R with routes R1,…,Rl\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R_1,\\ldots ,R_l$$\\end{document}, each of length at most B such that: Ri\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R_i$$\\end{document} starts at the root, reaches directly the farthest point of R visited by Ri-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R_{i-1}$$\\end{document}, then Ri\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R_i$$\\end{document} continues along the path R as far as possible, and finally Ri\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R_i$$\\end{document} returns to the root. We call the above algorithm piecemeal-DFS and we prove that it achieves the asymptotically minimal number of routes l, regardless of the choice of R. Our analysis also shows that the total length of the traversal (and thus the traversal time) of piecemeal-DFS is asymptotically minimum over all energy-constrained exploration strategies. The fact that R can be chosen arbitrarily means that the exploration strategy can be constructed in an online fashion when the input tree T is not known in advance. Each route Ri\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R_i$$\\end{document} can be constructed without any knowledge of the yet unvisited part of T. Surprisingly, our results show that depth first search is efficient for energy constrained exploration of trees, even though it is known that the same does not hold for energy constrained exploration of arbitrary graphs.

Reducing treatment time for robotic radiosurgery by considering path efficiency during node selection.

Robotic radiosurgery treatments allow for precise non-coplanar beam delivery by utilizing a robot equipped with a linac that traverses through a set of predetermined nodes. High quality treatment plans can be produced but treatment times can grow large, with one substantial component being the robot traversal time. The aim of this study is to reduce the treatment time for robotic radiosurgery treatments by introducing algorithms for reducing the robot traversal time. The algorithms are integrated into a commercial treatment planning system. First, an optimization framework for robotic radiosurgery planning is detailed, including a heuristic optimization method for node selection. Second, two methods aimed at reducing the traversal time are introduced. One utilizes a centrality measure focusing on the structure of the node network, while the other is based on the direct computation of traversal times during optimization. A comparison between plans with and without the time-reducing algorithms is made for three brain cases and one liver case with basis in treatment time, plan quality, monitor units, and network structure of the selectednodes. Large decreases in traversal times are obtained by the traversal time reducing algorithms, with reductions of up to 49 % in the brain cases and 31 % in the liver case. The resulting reductions in treatment times are up to 30 % and 13 %, respectively. Small differences in plan quality are observed, with similar dose-volume histograms, dose distributions, and conformity/gradientindices. The total treatment time of the robotic radiosurgery treatments can be reduced by selecting nodes with more efficient robot traversal paths, while maintaining planquality.

Antiaris africana aqueous extract inhibits chronic demyelination and seizures in mice

Demyelinating diseases are commonly associated with epileptic seizures and have limited management options. Hence, the need to investigate potential options for management of such seizures. Antiaris Africana extract (AE) was investigated for effect in chronic demyelinating seizures. Cuprizone treatment induced short but frequent spike discharges in mice. Antiaris Africana extract (300 mg/kg) treatment abolished epileptiform discharges. Cuprizone administration caused severe demyelination in the corpus callosum. After the demyelination phase, myelin content decreased to 22.86 ± 1.92 % in the cuprizone-only group. However, there was an increase to 52.14 ± 3.91 % in cuprizone-only group and 62.00 ± 2.78 % in the Antiaris africana extract group respectively, after a 4-week cuprizone cessation period. Treatment with AE and LEV visibly altered myelin growth. Antiaris africana extract treatment produced significant (P < 0.001, F (3, 16) = 698.4) increase in locomotor activity similar to LEV (P < 0.001,F (2, 12) = 678.7) and DZP (P < 0.001, F (2, 12) = 620.4) and improved beam traversal time (18.71 ± 2.244 s; 95 % CI: 13.22–24.20) while causing significantly (P < 0.05, F (2, 15) = 6.667) fewer stepping errors. Antiaris africana extract inhibits seizures induced by chronic demyelination and has beneficial effects on motor coordination.

“Reinforcement learning particle swarm optimization based trajectory planning of autonomous ground vehicle using 2D LiDAR point cloud”

The advent of autonomous mobile robots has spurred research into efficient trajectory planning methods, particularly in dynamic environments with varied obstacles. This study focuses on optimizing trajectory planning for an Autonomous Ground Vehicle (AGV) using a novel Reinforcement Learning Particle Swarm Optimization (RLPSO) algorithm. Real-time mobile robot localization and map generation are introduced through the utilization of the Hector-SLAM algorithm within the Robot Operating System (ROS) platform, resulting in the creation of a binary occupancy grid. The present research thoroughly investigates the performance of the RLPSO algorithm, juxtaposed against five established Particle Swarm Optimization (PSO) variants, within the context of four distinct physical environments. The experimental design is tailored to emulate real-world scenarios, encompassing a spectrum of challenges posed by static and dynamic obstacles. The AGV, equipped with LiDAR sensors, navigates through diverse environments characterized by obstacles of different geometries. The RLPSO algorithm dynamically adapts its strategies based on feedback, enabling adaptable trajectory planning while effectively avoiding obstacles. Numerical results obtained from extensive experimentation highlight the algorithm's efficacy. The navigational model's validation is achieved within a MATLAB 2D virtual environment, employing 2D Lidar mapping point data. Transitioning to physical experiments with an AGV, RLPSO continues to demonstrate superior performance, showcasing its potential for real-world applications in autonomous navigation. On average, RLPSO achieves a 10–15 % reduction in path distances and traversal time compared to the following best-performing PSO variant across diverse scenarios. The adaptive nature of RLPSO, informed by feedback from the environment, distinguishes it as a promising solution for autonomous navigation in dynamic settings, with implications for practical implementation in real-world scenarios.

Tunnel Effect for Ultrasonic Waves in Tapered Waveguides

Traversal time in the tunneling effect for ultrasonic waves in tapered waveguides is derived considering its analogy with quantum and electromagnetic wave tunneling. If, as traversal time, the so-called phase time is considered, the ultrasonic wave packet shows the equivalent in acoustics of superluminality, i.e., the derived velocity, crosses the limit of bulk transverse ultrasonic waves in the medium of the waveguide that is the equivalent of c in the quantum and electromagnetic cases. The graphs clearly illustrating this so-called Hartman effect are obtained confirming the experimental results in the three different fields.

Optimizing the traversal time for gantry trajectories for proton arc therapy treatment plans

Background. Proton arc therapy (PAT) is an emerging radiation therapy technique where either the gantry or the patient continuously rotates during the irradiation treatment. One of the perceived advantages of PAT is the reduced treatment time, but it is still unclear exactly how long these treatment times will be, given that no machine capable of its delivery is available on the market at the time of writing. Objective. We introduce the algorithm arc trajectory optimization method (ATOM), which aims to determine an efficient velocity profile for the gantry for rapid delivery of a given proton arc treatment plan. This algorithm could be used to minimize the delivery time of a proton arc plan without changing the plan or updating the machine. Approach. ATOM computes the trajectory with the shortest delivery time while ensuring there is enough time to deliver all spots in each energy layer and switch energy between layers. The feasibility of the dynamic gantry movement was assured by enforcing maximum and minimum limits for velocity, acceleration, and jerk. This was achieved by discretizing the gantry velocity and combining the A* algorithm with the open-source motion generation library Ruckig. The algorithm was tested on a synthetic data set as well as a liver case, a prostate case and a head and neck case. Main results. Arc trajectories for plans with 360 energy layers were calculated in under a second using 256 discrete velocities. The delivery time of the liver case, the prostate case and the head and neck case were 284 s, 288 s and 309 s respectively, for 180 energy layers. Significance. ATOM is an open-source C++ library with a Python interface that rapidly generates velocity profiles, making it a highly efficient tool for determining proton arc delivery times, which could be integrated into the treatment planning process.

Partial- and full-tunneling processes across potential barriers

We introduce the concept of partial-tunneling and full-tunneling processes to explain the seemingly contradictory non-zero and vanishing tunneling times often reported in the literature. Our analysis starts by considering the traversal time of a quantum particle through a potential barrier, including both above- and below-barrier traversals, using the theory of time-of-arrival operators. We then show that there are three traversal processes corresponding to non-tunneling, full tunneling, and partial tunneling. The distinction among the three depends on the support of the incident wave packet's energy distribution in relation to the shape of the barrier. Non-tunneling happens when the energy distribution of the quantum particle lies above the maximum of the potential barrier. Otherwise, full-tunneling process occurs when the energy distribution of the particle is below the minimum of the potential barrier. For this process, the obtained traversal time is interpreted as the tunneling time. Finally, the partial-tunneling process occurs when the energy distribution lies between the minimum and maximum of the potential barrier. This signifies that the quantum particle tunneled only through some portions of the potential barrier. We argue that the duration for a partial-tunneling process should not be interpreted as the tunneling time but instead as a partial traversal time to differentiate it from the full-tunneling process. We then show that a full-tunneling process is always instantaneous, while a partial-tunneling process takes a non-zero amount of time. We are then led to the hypothesis that experimentally measured non-zero and vanishing tunneling times correspond to partial- and full-tunneling processes, respectively.

Towards Autonomous Firefighting UAVs: Online Planners for Obstacle Avoidance and Payload Delivery

Drone technology is advancing rapidly and represents significant benefits during firefighting operations. This paper presents a novel approach for autonomous firefighting missions for Unmanned Aerial Vehicles (UAVs). The proposed UAV framework consists of a local planner module that finds an obstacle-free path to guide the vehicle toward a target zone. After detecting the target point, the UAV plans an optimal trajectory to perform a precision ballistic launch of an extinguishing ball, exploiting its kinematics. The generated trajectory minimises the overall traversal time and the final state error while respecting UAV dynamic limits. The performance of the proposed system is evaluated both in simulations and real tests with randomly positioned obstacles and target locations. The proposed framework has been employed in the 2022 UAV Competition of the International Conference on Unmanned Aircraft Systems (ICUAS), where it successfully completed the mission in several runs of increasing difficulty, both in simulation and in real scenarios, achieving third place overall. A video attachment to this paper is available on the website https://www.youtube.com/watch?v=_hdxX2xXkVQ.

Data-driven reference trajectory optimization for precision motion systems

We propose a data-driven optimization-based pre-compensation method to improve the contour tracking performance of precision motion stages by modifying the reference trajectory and without modifying any built-in low-level controllers. The position of the precision motion stage is predicted with data-driven models, a linear low-fidelity model is used to optimize traversal time, by changing the path velocity and acceleration profiles then a non-linear high-fidelity model is used to refine the previously found time-optimal solution. We experimentally demonstrate that the proposed method is capable of simultaneously improving the productivity and accuracy of a high precision motion stage. Given the data-based nature of the models, the proposed method can easily be adapted to a wide family of precision motion systems.

Key Transmission Section Search Based on Graph Theory and PMU Data for Vulnerable Line Identification in Power System

Failure of vulnerable lines in the power system often results in tidal shifts, and triggering chain failures and their corresponding transmission sections are concentrated manifestations of the weak links in the power system. It is very important to identify the vulnerable lines and search the transmission section to prevent the chain faults as well as to analyze the stability of the power system. Aiming at the problems of inaccurate search of vulnerable lines, difficulties adapting to the complex and changing power system as well as wrong selection and omission of transmission section search in the existing references, this paper proposes an algorithm for searching vulnerable lines and their key transmission sections based on the graph theory and PMU (phasor measurement unit) data. First, the method combines with the graph theory and PMU data to construct the grid topology map. Second, the comprehensive indicators for screening vulnerable lines are proposed by fully considering the network topology and line capacity, which combines with power exchange efficiency and energy fluctuation probability. Third, the distance matrix in the Floyd algorithm is transformed into a unit group that can store more elements, which reduces the traversal times of the algorithm and improves computational efficiency. The fast localization of transmission cross sections associated with vulnerable lines is realized. Finally, the critical transmission cross sections are screened according to the line outage distribution factor and line safety margin. The IEEE 39-bus system is selected for simulation experiments, and the simulation results show that the key transmission section search method proposed in this paper can better adapt to the variable power grid and is faster and more accurate than the other common method.

Quantum Black Holes in Conformal Dilaton–Higgs Gravity on Warped Spacetimes

A promising method for understanding the geometric properties of a spacetime in the vicinity of the horizon of a Kerr-like black hole can be developed by applying the antipodal boundary condition on the two opposite regions in the extended Penrose diagram. By considering a conformally invariant Lagrangian on a Randall–Sundrum warped five-dimensional spacetime, an exact vacuum solution is found, which can be interpreted as an instanton solution on the Riemannian counterpart spacetime, R+2×R1×S1, where R+2 is conformally flat. The antipodal identification, which comes with a CPT inversion, is par excellence, suitable when quantum mechanical effects, such as the evaporation of a black hole by Hawking radiation, are studied. Moreover, the black hole paradoxes could be solved. By applying the non-orientable Klein surface, embedded in R4, there is no need for instantaneous transport of information. Further, the gravitons become “hard” in the bulk, which means that the gravitational backreaction on the brane can be treated without the need for a firewall. By splitting the metric in a product ω2g˜μν, where ω represents a dilaton field and g˜μν the conformally flat “un-physical” spacetime, one can better construct an effective Lagrangian in a quantum mechanical setting when one approaches the small-scale area. When a scalar field is included in the Lagrangian, a numerical solution is presented, where the interaction between ω and Φ is manifest. An estimate of the extra dimension could be obtained by measuring the elapsed traversal time of the Hawking particles on the Klein surface in the extra dimension. Close to the Planck scale, both ω and Φ can be treated as ordinary quantum fields. From the dilaton field equation, we obtain a mass term for the potential term in the Lagrangian, dependent on the size of the extra dimension.

Inhibiting cholinergic signalling in the cerebellar interpositus nucleus impairs motor behaviour.

The role of neuromodulators in the cerebellum is not well understood. In particular, the behavioural significance of the cholinergic system in the cerebellum is unknown. To investigate the importance of cerebellar cholinergic signalling in behaviour, we infused acetylcholine receptor antagonists, scopolamine and mecamylamine, bilaterally into the rat cerebellum (centred on interpositus nucleus) and observed the motor effects through a battery of behavioural tests. These tests included unrewarded behaviour during open field exploration and a horizontal ladder walking task and reward-based beam walking and pellet reaching tasks. Infusion of a mix of the antagonists did not impair motor learning in the horizontal ladder walking or the reaching task but reduced spontaneous movement during open field exploration, impaired coordination during beam walking and ladder walking, led to fewer reaches in the pellet reaching task, slowed goal-directed reaching behaviour and reduced reward pellet consumption in a free access to food task. Infusion of the muscarinic antagonist scopolamine on its own resulted in deficits in motor performance and a reduction in the number of reward pellets consumed in the free access to food task. By contrast, infusion of the nicotinic antagonist mecamylamine on its own had no significant effect on any task, except beam walking traversal time, which was reduced. Together, these data suggest that acetylcholine in the cerebellar interpositus nucleus is important for the execution and coordination of voluntary movements mainly via muscarinic receptor signalling, especially in relation to reward-related behaviour.

Injected coherence and phase control in the tunneling of ultra slow three-level atoms

Our research aims to investigate the impact of injecting atomic coherence on the phase tunneling time of ultra slow cascade three-level atoms traversing through high-quality cavities. Prior to interacting with the cavity in the Fock state, the atoms are initially prepared in a superposition of the two upper levels. Our study has demonstrated that the coherence of the injected atoms can be tuned to control the phase time. Specifically, we have observed that the injected coherence can regulate the peak values and sub-superclassical nature of the traversal time. Moreover, we have investigated how the number of superclassical peaks and resonances in the tunneling time curve can be influenced by the cavity length and de Broglie waves of the atom. Additionally, we have discovered that the phase time behavior is not only affected by the center-of-mass (CM) motion but also by the atom–field detuning and the final internal state of the transmitted atoms. These findings have potential implications for developing and controlling ultracold atom-based technologies, such as quantum sensors, quantum information processing, and quantum simulation.

Lexicographic maximum dynamic evacuation modeling with partial lane reversal based on hesitant fuzzy TOPSIS

Decision-making under evacuation environment is extremely complex due to the variety of aspects to be considered as well as the necessity of high-speed reaction. Therefore, the elaboration of the evacuation pattern, particularly, finding the priority order of shelters for evacuation, requires multiple experts to be involved in the decision-making process. Moreover, decision-makers cannot provide precise assessments of alternatives due to the uncertainty inherent in the network parameters, dynamic nature of transportation, complexity of the task. In this regard, the method of finding the priority order of terminals for the evacuation based on the fuzzy hesitant TOPSIS method is proposed. The method handles a modified ranking index to find the priority order based on assigned weights of separations. In this method, experts’ assessments are presented as linguistic terms, which are further converted to fuzzy triangular numbers. This leads to the hesitant fuzzy TOPSIS decision-making with completely unknown attribute weights.The existing state of the art of evacuation modeling lacks fuzzy statements of evacuation flow problems. Our work aims to contribute to the design of the algorithm for the lexicographic maximum flow finding in the evacuation dynamic network with fuzzy transit arc capacities and transit traversal time parameters with partial contraflow. The approach reverses only necessary arcs by reversing the traffic in vacant segments, which allows using these segments for movement towards the safe areas as well. In addition, the method based on linear combinations of spreads is proposed to handle fuzzy values, which does not lead to the blurring of a fuzzy number. A case study to find the priority order of four destinations d1,d2,d3,d4 along with the maximum dynamic flow determining is provided to illustrate the proposed method. The hesitant fuzzy TOPSIS evaluated the priority order of destinations for evacuation the maximum number of aggrieved as {d4,d3,d1,d2} along with maximum lexicographic flow with partial lane reversal 62˜ flow units. The method for finding the spreads without blurring a fuzzy number was used to determine the final triangular number (50, 62, 75) units.The sensitivity analysis shows that in all ten cases, the alternatives have unique rank: A4 is the best, A2 is the worst. In the pessimistic case, DMs prefers the alternative that is furthest to FNIS. In the optimistic case, DMs prefer the alternative that is closest to FPIS. We proved that the proposed algorithm is reliable because despite the changes in parameters ω, the same priority order of alternatives is chosen. The obtained results are confirmed by efficiency frontier and coincide with the results of original TOPSIS, Doukas et al.’s, method, Kuo’s method, Yoon and Kim’s behavioral TOPSIS.

Shortest Journeys in Directed Temporal Graphs

Consider a directed temporal graph [Formula: see text] with time ranges on the edges. There can be more than one range on an edge, and each range carries a positive traversal time. Let [Formula: see text] and let [Formula: see text] be the total number of time ranges in [Formula: see text]. We assume that [Formula: see text]. We study the problem of computing shortest journeys that start from a fixed source vertex [Formula: see text] within a given time interval [Formula: see text], where the cost of a journey is equal to the sum of traversal times of the edges on it at the times of crossing those edges. We can construct in [Formula: see text] time a data structure of size [Formula: see text] such that for any vertex [Formula: see text] and any time [Formula: see text], we can report in [Formula: see text] time the cost of the shortest journey that starts from [Formula: see text] within [Formula: see text] and arrives at [Formula: see text] no later than [Formula: see text]. The journey achieving the reported cost can be produced in time linear in its complexity.

Quantized relativistic time-of-arrival operators for spin-0 particles and the quantum tunneling time problem

We provide a full account of our recent report (Flores and Galapon in EPL 141:10001, 2023) which constructed a quantized relativistic time-of-arrival operator for spin-0 particles using a modified Weyl-ordering rule to calculate the traversal time across a square barrier. It was shown that the tunneling time of a relativistic spin-0 particle is instantaneous under the condition that the barrier height $$V_o$$ is less than the rest mass energy. This implies that instantaneous tunneling is an inherent quantum effect in the context of arrival times.

Hierarchical data structures for flowchart

Flowcharts have broad applications in the fields of software development, engineering design, and scientific experimentation. Current flowchart data structure is mainly based on the adjacency list, cross-linked list, and adjacency matrix of the graph structure. Such design originated from the fact that any two nodes could have a connection relationship. But flowcharts have clear regularities, and their nodes have a certain inflow or outflow relationship. When graph structures such as an adjacency table or an adjacency matrix are used to store a flowchart, there is a large room for optimization in terms of traversal time and storage complexities, as well as usage convenience. In this paper we propose two hierarchical data structures for flowchart design. In the proposed structures, a flowchart is composed of levels, layers, and numbered nodes. The nodes between layers are connected according to a certain set of systematic design rules. Compared with the traditional graph data structures, the proposed schemes significantly reduce the storage space, improve the traversal efficiency, and resolve the problem of nesting between sub-charts. Experimental data based on flowchart examples used in this paper show that, compared with adjacency list, the hierarchical table data structure reduces the traversal time by 50% while their storage spaces are similar; compared with adjacency matrix, the hierarchical matrix data structure reduces the traversal time by nearly 70% and saves the storage space by about 50%. The proposed structures could have broad applications in flowchart-based software development, such as low-code engineering for smart industrial manufacturing.