Maximum Path Length Research Articles

Approximate sequential optimization for informative path planning

We consider the problem of finding an informative path through a graph, given initial and terminal nodes and a given maximum path length. We assume that a linear noise corrupted measurement is taken at each node of an underlying unknown vector that we wish to estimate. The informativeness is measured by the reduction in uncertainty in our estimate, evaluated using several Gaussian process-based metrics. We present a convex relaxation for this informative path planning problem, which we can readily solve to obtain a bound on the possible performance. We develop an approximate sequential method where the path is constructed segment by segment through dynamic programming. This involves solving an orienteering problem, with the node reward acting as a surrogate for informativeness, taking the first step, and then repeating the process. The method scales to very large problem instances and achieves performance close to the bound produced by the convex relaxation. We also demonstrate our method’s ability to handle adaptive objectives, multimodal sensing, and multi-agent variations of the informative path planning problem.

Disjoint paths construction algorithm in the data center network DPCell

Abstract With the development of the fourth industrial revolution, the importance of data centers has significantly increased. Data centers are widely used in many fields due to their ability to provide efficient, secure, and reliable data storage and processing services. However, with the increasing amount of data, traditional data center networks (DCNs) are currently facing various challenges, prompting academia and industry to propose new DCN architectures. As a dual-port server-based DCN, DPCell has excellent scalability and bisection width, enabling it to meet the demands of large-scale data storage, processing, and computation in the digital revolution. In order to ensure the secure and reliable data communication in the DPCell, this paper designs a disjoint paths communication scheme based on the actual DCN routing requirements. This scheme constructs the optimal number of disjoint paths in DPCell, with a maximum path length of $2^{k}+3$, where $k$ represents the dimension of the DPCell. Furthermore, experiments have verified that the time complexity of this scheme is sublinear, making it more efficient than the current optimal maximum flow algorithm. To a certain extent, this scheme provides DPCell with the required high bandwidth, fault tolerance, and security for data communication.

Neuronal branching is increasingly asymmetric near synapses, potentially enabling plasticity while minimizing energy dissipation and conduction time.

Neurons' primary function is to encode and transmit information in the brain and body. The branching architecture of axons and dendrites must compute, respond and make decisions while obeying the rules of the substrate in which they are enmeshed. Thus, it is important to delineate and understand the principles that govern these branching patterns. Here, we present evidence that asymmetric branching is a key factor in understanding the functional properties of neurons. First, we derive novel predictions for asymmetric scaling exponents that encapsulate branching architecture associated with crucial principles such as conduction time, power minimization and material costs. We compare our predictions with extensive data extracted from images to associate specific principles with specific biophysical functions and cell types. Notably, we find that asymmetric branching models lead to predictions and empirical findings that correspond to different weightings of the importance of maximum, minimum or total path lengths from the soma to the synapses. These different path lengths quantitatively and qualitatively affect energy, time and materials. Moreover, we generally observe that higher degrees of asymmetric branching-potentially arising from extrinsic environmental cues and synaptic plasticity in response to activity-occur closer to the tips than the soma (cell body).

Clothoid-Based Path Planning for a Formation of Fixed-Wing UAVs

Unmanned aerial vehicles (UAVs) are playing an increasingly crucial role in many applications such as search and rescue, delivery services, and military operations. However, one of the significant challenges in this area is to plan efficient and safe trajectories for UAV formations. This paper presents an optimization procedure for trajectory planning for fixed-wing UAV formations using graph theory and clothoid curves. The proposed planning strategy consists of two main steps. Firstly, the geometric optimization of paths is carried out using graphs for each UAV, providing piece-wise linear paths whose smooth connections are made with clothoids. Secondly, the geometric paths are transformed into time-dependent trajectories, optimizing the assigned aircraft speeds to avoid collisions by solving a mixed-integer optimal control problem for each UAV of the flight formation. The proposed method is effective in achieving suboptimal paths while ensuring collision avoidance between aircraft. A sensitivity analysis of the main parameters of the algorithm was conducted in ideal conditions, highlighting the possibility of decreasing the length of the optimal path by about 4.19%, increasing the number of points used in the discretization and showing a maximum path length reduction of about 10% compared with the average solution obtained with a similar algorithm using a graph based on random directions. Furthermore, the use of clothoids, whose parameters depend on the UAV performance constraints, provides smoother connections, giving a significant improvement over traditional straight-line or circular trajectories in terms of flight dynamics compliance and trajectory tracking capabilities. The method can be applied to various UAV formation scenarios, making it a versatile and practical tool for mission planning.

Validity and reliability of the assessment of hand flexors stiffness using a new electromechanical oscillatory device in people with stroke.

Hyper-resistance after a central nervous system injury has been largely referred to as spasticity, which is but one of its neural components. Assessment largely relies on clinical scales (Modified Ashworth scale - MAS and Modified Tardieu scale, MTS) which are unable to distinguish between the non-neural (tissue-related) and the neural (central nervous system-related) components. This study assessed criterion validity and reliability (reproducibility) of muscle stiffness measures, namely, maximum elastic stiffness (ELmax), viscous stiffness (VI), and path length (L-path) in the hand flexor muscles among people with stroke. Measurements were obtained with a wrist-electromechanical oscillatory device (w-EOD). Twenty-four people with arm impairment after stroke were evaluated with the w-EOD and clinical assessment (MAS and MTS), twice on the same day (short-term reliability) and once 10 days later (long-term reliability). For criterion validity, a Spearman coefficient ( r ) was calculated between stiffness values and the clinical scales. For reliability, intraclass correlation coefficients (ICCs), SEM, and MDC95 were calculated. Moderate correlations were observed between EL max and MAS ( r = 0.49) and MTS (V2, r = 0.43; V3, r = 0.49) of the wrist flexors, and finger flexors (MAS, r = 0.60; MTS V2, r = 0.56; MTS V3, r = 0.55). There was a poor correlation between the clinical scales and VI and L-path. Reliability was excellent for all stiffness measurements at short term (EL max : 0.95, VI: 0.94, L-path: 0.92) and good at long term (EL max : 0.87, VI: 0.76, L-path: 0.82). In conclusion, stiffness measurements are valid and reliable to evaluate hyper-resistance in people with stroke.

A Novel Clock Tree Aware Placement Methodology for Single Flux Quantum Logic Circuits With Maximum Path Length Consideration

In a single-flux-quantum (SFQ) circuit, almost all cells need to receive the clock signal that incurs a high clock routing overhead. Besides, the clock tree of an SFQ circuit requires the insertion of a clock splitter cell at every tree branching point that renders the conventional design flow of placement followed by clock tree synthesis (CTS) ineffective to obtain a high quality clock tree with low clock skew. Moreover, very few works in the literature attempted to minimize the maximum path length during SFQ circuit placement. The maximum path length, which is the length of the longest source-to-sink path of any data signal, should be minimized to achieve a higher final performance and to reduce the overhead for length matching in subsequent routing. To address these issues, we propose a two-stage global placement methodology and a placement refinement algorithm after placement legalization. Our two-stage global placement methodology first applies a conventional global placement algorithm to place the cells in the given SFQ circuit evenly, which is followed by CTS and clock splitter insertion, and then, performs a second stage of global placement to replace both the original cells and clock splitters at the same time. In the second global placement stage, the look-ahead legalization technique is used to spread out the original cells and the clock splitters, and the clock tree is resynthesized several times to obtain an optimized clock tree topology such that there are little overlaps of the clock splitters with the original circuit cells. We propose a novel net model in global placement that facilitates the concurrent optimization of the total wirelength and the maximum path length. After legalizing the placement of all cells, a specialized placement refinement method is run to further reduce the clock skew and the maximum path length. Compared with the previous state-of-the-art work, on average, we reduced the total half-perimeter wirelength by 9%, reduced the maximum path length by 58%, and reduced the clock skew by 32%.

Research on optimal parking trajectory based on parking planning model

This paper mainly deals with the planning problem of unmanned vehicle parking path in parking lot. For each different parking problem and different parking constraints, a suitable parking model is established in this paper. First of all, the Akman turned to the geometric model, and the original four -wheel car model was equivalent to a two -wheeled bicycle model, so that the two different corners of the front wheels were equivalent to a corner 6.462m. In the solution to the shortest distance, this article first establishes the shortest distance model of accelerating to the same maximum speed under any condition. The shortest distance required to solve the maximum limit of 20km/h is 5.561m. Lately, the vehicle motion equation model was established, and the change rate of the maximum curvature relative path length was 1.140m-2. Aiming at problem 2: First, the turning process in parking is analyzed, and the minimum turning radius when the control point is located at the axisymmetric center of the rear wheel is recalculated to be 4.974m, which is used in the subsequent parking path planning. Finally, using the above analysis of the motion situation of the unmanned vehicle and the planning of the parking trajectory, the parking trajectory in each case and the relationship between the changes of each physical quantity over time are given.

Dual-Polarization Bandwidth-Bridged Bandpass Sampling Fourier Transform Spectrometer from Visible to Near-Infrared on a Silicon Nitride Platform.

On-chip broadband optical spectrometers that cover the entire tissue transparency window (λ = 650–1050 nm) with high resolution are highly demanded for miniaturized biosensing and bioimaging applications. The standard spatial heterodyne Fourier transform spectrometer (SHFTS) requires a large number of Mach–Zehnder interferometer (MZI) arrays to obtain a broad spectral bandwidth while maintaining high resolution. Here, we propose a novel type of SHFTS integrated with a subwavelength grating coupler (SWGC) for the dual-polarization bandpass sampling on the Si3N4 platform to solve the intrinsic trade-off limitation between the bandwidth and resolution of the SHFTS without having an outrageous number of MZI arrays or adding additional active photonic components. By applying the bandpass sampling theorem, the continuous broadband input spectrum is divided into multiple narrow-band channels through tuning the phase-matching condition of the SWGC with different polarization and coupling angles. Thereby, it is able to reconstruct each band separately far beyond the Nyquist criterion without aliasing error or degrading the resolution. We experimentally demonstrated the broadband spectrum retrieval results with the overall bandwidth coverage of 400 nm, bridging the wavelengths from 650 to 1050 nm, with a resolution of 2–5 nm. The bandpass sampling SHFTS is designed to have 32 linearly unbalanced MZIs with the maximum optical path length difference of 93 μm within an overall footprint size of 4.7 mm × 0.65 mm, and the coupling angles of SWGC are varied from 0° to 32° to cover the entire tissue transparency window.

Practical Fixed-Parameter Algorithms for Defending Active Directory Style Attack Graphs

Active Directory is the default security management system for Windows domain networks. We study the shortest path edge interdiction problem for defending Active Directory style attack graphs. The problem is formulated as a Stackelberg game between one defender and one attacker. The attack graph contains one destination node and multiple entry nodes. The attacker's entry node is chosen by nature. The defender chooses to block a set of edges limited by his budget. The attacker then picks the shortest unblocked attack path. The defender aims to maximize the expected shortest path length for the attacker, where the expectation is taken over entry nodes. We observe that practical Active Directory attack graphs have small maximum attack path length and are structurally close to trees. We first show that even if the maximum attack path length is a constant, the problem is still w[1]-hard with respect to the defender's budget. Having a small maximum attack path length and a small budget is not enough to design fixed-parameter algorithms. If we further assume that the number of entry nodes is small, then we derive a fixed-parameter tractable algorithm. We then propose two other fixed-parameter algorithms by exploiting the tree-like features. One is based on tree decomposition and requires a small tree width. The other assumes a small number of splitting nodes (nodes with multiple out-going edges). Finally, the last algorithm is converted into a graph convolutional neural network based heuristic, which scales to larger graphs with more splitting nodes.

Associations between range of motion, strength, tear size, patient-reported outcomes, and glenohumeral kinematics in individuals with symptomatic isolated supraspinatus tears.

Clinical failure associated with nonoperative treatment of rotator cuff tears may be due to inadequate characterization of the individual's functional impairments. Clinically, restricted passive range of motion (ROM) (restrictions imply capsular tightness), limitations in muscle strength, and larger rotator cuff tears are hypothesized to be related to altered glenohumeral kinematics. Understanding these relationships, as well as the relationship between glenohumeral kinematics and patient-reported outcomes (PROs) prior to exercise therapy, may help characterize functional impairments in individuals with rotator cuff tears. The objectives of the study were to describe the baseline presentation of individuals with an isolated supraspinatus tear, including passive ROM, rotator cuff muscle strength, tear size, PROs, and glenohumeral kinematics, and to determine associations among these variables. One hundred one individuals with symptomatic isolated supraspinatus tears were recruited for the study and underwent assessments of passive glenohumeral ROM, isometric muscle strength, and ultrasonography to assess anterior-posterior tear size. Glenohumeral kinematics during scapular-plane abduction were measured using biplane radiography. Furthermore, PROs including the American Shoulder and Elbow Surgeons (ASES) score and the Western Ontario Rotator Cuff Index (WORC) score were collected. Individuals presented with decreased ROM, external rotation weakness compared with the uninvolved side, and pain and disability as measured by the ASES and WORC scores. These findings were not associated with glenohumeral kinematics, with the exception of a weak positive association between glenohumeral contact path lengths and WORC scores (ρ=0.25, P=.03). Tear size was 11.7±5.7 mm, and maximum anterior translation, superior translation, and contact path length were 3.0%±3.8% of glenoid width, 3.5%±3.8% of glenoid height, and 38.2%±20.7% of glenoid size, respectively. Individuals with a symptomatic isolated supraspinatus tear presented with decreased ROM, external rotation weakness, and pain and disability as measured by the ASES and WORC scores. However, no abnormal kinematics associated with these limitations were observed. Thus, given that the tear is isolated to the supraspinatus tendon and no capsular restrictions are present, normal function of the glenohumeral joint may be possible during scapular-plane abduction.

Connectivity and constructive algorithms of disjoint paths in dragonfly networks

Dragonfly networks have been widely used in the current High Performance Computing (HPC) computers due to lower global network diameter and other advantages of communication performance such as modularity and cost-effectiveness. The original definition of the dragonfly network was very loose on account of its uncertain and diversified global link arrangements. In this paper, we study the logical structure of the dragonfly network which can be treated as a compound graph of complete graphs. Firstly, we give the general definition of the dragonfly network, named DF(n,h,g), and the specific definition of the dragonfly network under the relative global link arrangement, named D(n,h). Then, we prove that the connectivity of D(n,h) is n−1+h. In the end, we propose an O(n) algorithm to give the disjoint path between any two distinct vertices in D(n,h) and analyze the maximum length of these disjoint paths which is no more than 7.

FSO Path Loss Model Based on the Visibility

Free-space optics (FSO) is attracting renewed attention in the frame of 5G, which demands wireless backhauling technologies with extremely high data rates over distances up to a few kilometers. Link availability is a FSO well-known issue due to the large path loss expected during poor visibility, such as in case of fog. Several path loss models, based on the visibility, are assessed through an analytical approach. The simple relationship valid in the visible spectrum can be extended to the first optical window, while, at 1.550 μm, the effect of fog microphysics cannot be ignored. Fog is definitively less challenging in the mid-IR (10.6 µm) even at very low visibility values (less than 0.5 km), which was not evident from older studies. Lower and upper bounds for the extinction coefficient are calculated and substituted into the FSO link budget equation. The combined effect of the microphysics and of the accuracy of visibility measurements may result in large uncertainties on the maximum achievable path length. The latter is also influenced by the microclimate, as links are usually deployed in urban areas while visibility data are collected outside. Path lengths in city areas can double, for the same link availability.

A Collision Free Network with Minimal Routing Path for 2<sup>n</sup> Nodes

In the present work, a simple but complex network which has collision free communications is created. With the help of the binary n-cube the network is formed. This n-cube network connection is formed by connecting distinct N number of nodes which are expressed as a power of 2. If each node has an address of m bits then there are N=2^m number of nodes in the n-cube network. To find out the predefined routing path for the case of this n-cube network, we can apply deterministic algorithm providing us a collision /deadlock free concept. In calculating the predefined routing path(s), node addresses involved in the path are calculated by using the exclusive OR operation, firstly, upon the two node addresses of source and destination, and then, on the derived node-addresses according to the algorithm stated in section 2. Here, the Exclusive-OR operation is performed simply by using 2-input XOR gate which may be made up of either (i) classical CMOS based material, or (ii) Multiple input threshold logic gate , or (iii) Single electron tunneling Transistor (SET). We are concentrated in the case of CMOS based XOR circuit. In this work, an E-cube Routing on a 6-dimensional hypercube has been designed and constructed. We have tried to find out the node addresses for predefining the deadlock free routing path for any set of “source and destination”. To develop a “Collision free network with minimal Routing”, a number of Exclusive-OR gates are arranged in a pattern discussed in section 3 and the desired circuit is implemented. The implemented circuit can supply the predefined path nodes through which the signal/packets/data can pass. Regarding the experimental input –output values, some truth tables are depicted in substantial places. At the time of applying the algorithm, we have investigated that for 6-dimentional hypercube, the maximum path length are confined to 6, i.e. whenever the source and destination points are provided, then 6-node points are produced. Among these 6-pionts some of them may have identical values. As a result path length should be less than 6. For the network, the time required to travel a path is measured and shown. The net designed and implemented must a be a collision free one, since when a truth table is written, there would not be any pair of nodes identical in a column.

Computation of diameter, radius and center of permutation graphs

For a connected graph [Formula: see text], we use the notation [Formula: see text] to represent the distance between two node points [Formula: see text] and [Formula: see text] and it is the minimum of the lengths of all paths between them. The eccentricity [Formula: see text] of a node point [Formula: see text] is considered as the maximum length of all shortest paths starts from [Formula: see text] to the remaining nodes, i.e., [Formula: see text]. The diameter of a graph [Formula: see text], we denote it by [Formula: see text] and it is the length of the longest shortest path in [Formula: see text], i.e., [Formula: see text]. Also, the radius of a graph [Formula: see text], we denote it by the symbol [Formula: see text] and it is the least eccentricity of all node points in [Formula: see text], i.e., [Formula: see text]. The central vertex/node point [Formula: see text] of a graph [Formula: see text] is a node whose eccentricity is same as [Formula: see text]’s radius, i.e., [Formula: see text]. The collection of all central nodes of a graph [Formula: see text] is considered as the center of [Formula: see text] and it is symbolized by [Formula: see text], i.e., [Formula: see text]. A graph may have one or more central vertices. This paper develops an optimal algorithm to compute the diameter, radius and central node (s) of the permutation graph having [Formula: see text] node points in [Formula: see text] time. We have also established a tight relation between radius and diameter of permutation graphs.

Hybrid evolutionary optimization for takeaway order selection and delivery path planning utilizing habit data

The last years have seen a rapid growth of the takeaway delivery market, which has provided a lot of jobs for deliverymen. However, increasing numbers of takeaway orders and the corresponding pickup and service points have made order selection and path planning a key challenging problem to deliverymen. In this paper, we present a problem integrating order selection and delivery path planning for deliverymen, the objective of which is to maximize the revenue per unit time subject to maximum delivery path length, overdue penalty, reward/penalty for large/small number of orders, and high customer scoring reward. Particularly, we consider uncertain order ready time and customer satisfaction level, which are estimated based on historical habit data of stores and customers using a machine-learning approach. To efficiently solve this problem, we propose a hybrid evolutionary algorithm, which adapts the water wave optimization (WWO) metaheuristic to evolve solutions to the main order selection problem and employs tabu search to route the delivery path for each order selection solution. Experimental results on test instances constructed based on real food delivery application data demonstrate the performance advantages of the proposed algorithm compared to a set of popular metaheuristic optimization algorithms.

Topologic characteristics and sustainable growth of worldwide urban rail networks

The urban rail network system plays a significant role in the urban transportation system and urban economic development. Further study of the urban rail network properties can provide additional guidance to related scholars and designers. This study explored urban rail network properties worldwide, including assessments of their static and dynamic network topologic characteristics. Statically, this study analyzed various related network topological indicators for all of these urban rail networks. We found that, with increasing network size, the average degree slightly increases while the complexity and connectivity decrease. Using the Kolmogorov–Smirnov goodness-of-fit, the scale of the degree interval of these cities is [3.5 12.2]. Approximately 90% of these cities have network efficiency values less than 0.12, and 78% of these cities have lower assortativity coefficients. Focusing on the sustainable growth of rail networks, this study tested some specific networks to further deliberate their network expansion ability, network growth, and network robustness properties. The network expansion capability of small networks is relatively poor, while that of large networks is relatively strong. A simulation of network growth suggests that the connection of nodes with the maximum path length will seriously affect the efficiency and characteristics of the network. The robustness of the network indicates that adopting the maximum nodal degree elimination strategy will affect the function of the network. The results provide essential reference information for the rational planning, structural optimization, safe operation and sustainable growth of rail transit networks.

A New City Air Terminal Service Mode: Urban Mobile Station for Luggage Check-in Service and Evolutionary Approach

In order to overcome the demerits of traditional city air terminals (CAT), a brand-new service mode based on urban mobile stations (UMS) is introduced in this article for providing the luggage check-in service in urban area. Different from CAT, for each service time period, the UMSs are located based on the real-time passenger distributions. The objectives are to improve the service quality and enhance the competitiveness of air transportation. First, the system components and operation mode of UMS are described. Second, a mathematical model is set up for locating UMSs and assigning passengers to service stations. Three aspects, including the average path length from passengers to UMSs, the maximum acceptable path length for passengers, and the maximum service capacity of a station are considered. Third, to meet the strict time requirement of the UMS system, an effective evolutionary algorithm for optimizing UMS locations in real time is further developed. In the method, the ripple-spreading algorithm is applied for solving the many-to-many path optimization problem and a two-stage adaptive genetic algorithm is utilised for efficiently locating UMSs. Finally, a test case is set up based on the city centre of Tianjin, China, and passenger source locations are obtained by surveying passengers at Tianjin Airport. The reported method is then applied to dynamically locate UMSs in Tianjin urban area and it is compared to some other existing methods to show its effectiveness and efficiency. The service quality of UMS is compared to CAT in both cases with realistic data and randomly generated data to show its advantages.

Implementation of the toroidal absorption cell with multi-layer patterns by a single ring surface.

We developed a type of toroidal multi-pass cell with multi-layer patterns based on the off-axis model. The effective path length of the original toroidal multi-pass cell is extended several roundtrips in comparison with the single-layer pattern, since the inner surface of the toroidal multi-pass cell is more efficiently utilized. The light pattern has been achieved by using the simple ring surface, which is easy to fabricate. The exact analytical equations for the design of the toroidal multi-pass cell were derived based on analytical vector calculations. A series of numerical ray tracing simulations is presented, and the maximum theoretical optical path length that can be reached is 30 m with a setup of 5 cm column radius. Furthermore, two practical spot patterns are demonstrated with a path length of 8.3 m for a two-layer pattern and 10 m for a three-layer pattern, with respective effective volumes of 63 mL and 94 mL. Furthermore, the fringe effect is substantially reduced to less than 0.5% by the usage of our designed mask.

GPU-accelerated logistics optimisation for biomass production with multiple simultaneous harvesters tours, fields and plants

Within the context of biomass production, this paper proposes a method for logistics optimisation. Starting from a headquarter multiple tours are to be executed simultaneously by groups of harvesting units (HUs) and support units (SUs) to first harvest biomass from multiple agricultural fields, before supplying the biomass to multiple biogas plants (BPs) via shuttling SUs. This problem is relevant on a larger scale in particular for contractors. This problem is complex since there are three interconnected optimisation levels: (i) the assignment of BPs to tours and the ordering of BPs assigned to each tour, (ii) the assignment of fields to BPs and the ordering of fields assigned to each BP, and (iii) determining the number of HUs and SUs assigned to each tour, whereby different HUs and SUs may in general have different working rates and loading capacities. Problem modeling and a solution method are discussed. For the latter, a GPU-accelerated heuristic search algorithm is proposed. For the former, an optimisation criterion minimising both total accumulated path length and the maximum completion time over all harvesters tours, an embedded local minimisation for the assignment of SUs to tours, and demand fulfilment constraints for BPs are discussed. In stochastic simulation experiments it is found that permitting unconstrained assignment of any available field that a contractor services to any available BP, independent of their ownerships, is crucial (i) to attain maximum path length savings, and (ii) also to best balance and minimise uniform completion times over all harvesters tours such that weather-dependent harvesting windows can be exploited optimally.

On the Minimum Number of Distinct Eigenvalues in the Problem for a Tree Formed by Stieltjes Strings

We consider spectral problems related to small vibrations of a tree formed by Stieltjes strings. It is shown that the minimum number of distinct eigenvalues of this problem is equal to the maximum length (measured as the number of point masses) of paths in this tree.