Vulnerability Analysis and Passenger Source Prediction in Urban Rail Transit Networks

Based on large-scale human mobility data collected in San Francisco and Boston, the morning peak urban rail transit (URT) ODs (origin-destination matrix) were estimated and the most vulnerable URT segments, those capable of causing the largest service interruptions, were identified. In both URT networks, a few highly vulnerable segments were observed. For this small group of vital segments, the impact of failure must be carefully evaluated. A bipartite URT usage network was developed and used to determine the inherent connections between urban rail transits and their passengers'' travel demands. Although passengers'' origins and destinations were easy to locate for a large number of URT segments, a few show very complicated spatial distributions. Based on the bipartite URT usage network, a new layer of the understanding of a URT segment''s vulnerability can be achieved by taking the difficulty of addressing the failure of a given segment into account. Two proof-of-concept cases are described here: Possible transfer of passenger flow to the road network is here predicted in the cases of failures of two representative URT segments in San Francisco.     

Mantled Howler (<Emphasis Type="Italic">Alouatta palliata</Emphasis>) Arboreal Pathway Networks: Relative Impacts of Resource Availability and Forest Structure

Numerous studies have concluded that primates move about their environments in a nonrandom manner, frequently traveling between consecutive foraging sites along relatively straight-line paths. However, primates do not always take the most direct path between resources, and a number of species have been observed to travel repeatedly along a network of the same arboreal pathways. In this study, I used spatially explicit techniques to examine quantitatively what mantled howler monkey groups on Barro Colorado Island, Panama, accomplish by selecting nonlinear paths between resources and by repeatedly using the same paths within an arboreal network. Results show that chosen arboreal paths between sites where foraging occurred have higher levels of resource availability and canopy connectivity than comparable straight-line paths between the same sites. When comparing the relative importance of these factors, autologistic models of pathway choice indicate that though canopy connectivity is related to the location of repeatedly used arboreal pathway networks, the most statistically significant predictor is resource availability (both on a path and within a visual detection distance of a path). These results provide support for the hypothesis that repeated use of arboreal pathway networks aids in resource monitoring and acquisition. In addition, statistical models developed from 1 primary focal group’s travel patterns had high predictive value when employed to generate likely locations for arboreal pathways in the home ranges of 3 neighboring groups. This finding has important implications for studies of primate habitat use and seed dispersal, as it suggests that different groups consistently use similar characteristics when deciding on travel paths.     

Probabilistic path ranking based on adjacent pairwise coexpression for metabolic transcripts analysis

MOTIVATION: Pathway knowledge in public databases enables us to examine how individual metabolites are connected via chemical reactions and what genes are implicated in those processes. For two given (sets of) compounds, the number of possible paths between them in a metabolic network can be intractably large. It would be informative to rank these paths in order to differentiate between them. RESULTS: Focusing on adjacent pairwise coexpression, we developed an algorithm which, for a specified k, efficiently outputs the top k paths based on a probabilistic scoring mechanism, using a given metabolic network and microarray datasets. Our idea of using adjacent pairwise coexpression is supported by recent studies that local coregulation is predominant in metabolism. We first evaluated this idea by examining to what extent highly correlated gene pairs are adjacent and how often they are consecutive in a metabolic network. We then applied our algorithm to two examples of path ranking: the paths from glucose to pyruvate in the entire metabolic network of yeast and the paths from phenylalanine to sinapyl alcohol in monolignols pathways of arabidopsis under several different microarray conditions, to confirm and discuss the performance analysis of our method.     

Planning an ecological network using the predicted movement paths of urban birds

In this study, we propose a new method for planning ecological networks in Gangdong-gu, Seoul, Korea. The basic idea of this method is that, in urban areas where the price of land is high, it is most cost-effective to protect linear green areas that act as ecological corridors for potential movement paths (PMPs) of wild animals. PMPs were identified by a path-finding algorithm (PFA) that selected the optimum routes with minimum travel costs between pairs of locations where individuals of the indicator species—great tits (Parus major)—were found during field surveys. The PFA created an imaginary line segment network that connects nodes separated by 30 m across the entire study area, and estimated the total travel cost of a route from one P. major location to another by summing the travel costs associated with all of the segments comprising that route. We assumed that the travel cost of each segment is the average of the inverses of the bird densities at the two end nodes. For each node, the bird density was estimated from the linear relationship between percentage vegetation cover and bird density, as observed during field surveys. The predicted PMPs showed a pattern that was highly concentrated on patches with relatively high vegetation cover. The preference of P. major for a few specific routes allowed us to easily identify ecological corridors in the study area. An ecological network plan that protects and/or restores areas along ecological corridors would greatly improve the ecological connectivity of fragmented habitats in highly urbanized areas.     

Artificial pheromone for path selection by a foraging swarm of robots

Foraging robots involved in a search and retrieval task may create paths to navigate faster in their environment. In this context, a swarm of robots that has found several resources and created different paths may benefit strongly from path selection. Path selection enhances the foraging behavior by allowing the swarm to focus on the most profitable resource with the possibility for unused robots to stop participating in the path maintenance and to switch to another task. In order to achieve path selection, we implement virtual ants that lay artificial pheromone inside a network of robots. Virtual ants are local messages transmitted by robots; they travel along chains of robots and deposit artificial pheromone on the robots that are literally forming the chain and indicating the path. The concentration of artificial pheromone on the robots allows them to decide whether they are part of a selected path. We parameterize the mechanism with a mathematical model and provide an experimental validation using a swarm of 20 real robots. We show that our mechanism favors the selection of the closest resource is able to select a new path if a selected resource becomes unavailable and selects a newly detected and better resource when possible. As robots use very simple messages and behaviors, the system would be particularly well suited for swarms of microrobots with minimal abilities.     

A segment alignment approach to protein comparison

MOTIVATION: Local structure segments (LSSs) are small structural units shared by unrelated proteins. They are extensively used in protein structure comparison, and predicted LSSs (PLSSs) are used very successfully in ab initio folding simulations. However, predicted or real LSSs are rarely exploited by protein sequence comparison programs that are based on position-by-position alignments. RESULTS: We developed a SEgment Alignment algorithm (SEA) to compare proteins described as a collection of predicted local structure segments (PLSSs), which is equivalent to an unweighted graph (network). Any specific structure, real or predicted corresponds to a specific path in this network. SEA then uses a network matching approach to find two most similar paths in networks representing two proteins. SEA explores the uncertainty and diversity of predicted local structure information to search for a globally optimal solution. It simultaneously solves two related problems: the alignment of two proteins and the local structure prediction for each of them. On a benchmark of protein pairs with low sequence similarity, we show that application of the SEA algorithm improves alignment quality as compared to FFAS profile-profile alignment, and in some cases SEA alignments can match the structural alignments, a feat previously impossible for any sequence based alignment methods.     

Evolvable neuronal paths: a novel basis for information and search in the brain

We propose a previously unrecognized kind of informational entity in the brain that is capable of acting as the basis for unlimited hereditary variation in neuronal networks. This unit is a path of activity through a network of neurons, analogous to a path taken through a hidden Markov model. To prove in principle the capabilities of this new kind of informational substrate, we show how a population of paths can be used as the hereditary material for a neuronally implemented genetic algorithm, (the swiss-army knife of black-box optimization techniques) which we have proposed elsewhere could operate at somatic timescales in the brain. We compare this to the same genetic algorithm that uses a standard 'genetic' informational substrate, i.e. non-overlapping discrete genotypes, on a range of optimization problems. A path evolution algorithm (PEA) is defined as any algorithm that implements natural selection of paths in a network substrate. A PEA is a previously unrecognized type of natural selection that is well suited for implementation by biological neuronal networks with structural plasticity. The important similarities and differences between a standard genetic algorithm and a PEA are considered. Whilst most experiments are conducted on an abstract network model, at the conclusion of the paper a slightly more realistic neuronal implementation of a PEA is outlined based on Izhikevich spiking neurons. Finally, experimental predictions are made for the identification of such informational paths in the brain.     

STEPP--Search Tool for Exploration of Petri net Paths: a new tool for Petri net-based path analysis in biochemical networks

To understand biochemical processes caused by, e. g., mutations or deletions in the genome, the knowledge of possible alternative paths between two arbitrary chemical compounds is of increasing interest for biotechnology, pharmacology, medicine, and drug design. With the steadily increasing amount of data from high-throughput experiments new biochemical networks can be constructed and existing ones can be extended, which results in many large metabolic, signal transduction, and gene regulatory networks. The search for alternative paths within these complex and large networks can provide a huge amount of solutions, which can not be handled manually. Moreover, not all of the alternative paths are generally of interest. Therefore, we have developed and implemented a method, which allows us to define constraints to reduce the set of all structurally possible paths to the truly interesting path set. The paper describes the search algorithm and the constraints definition language. We give examples for path searches using this dedicated special language for a Petri net model of the sucrose-to-starch breakdown in the potato tuber.     

Efficient algorithms for detecting signaling pathways in protein interaction networks.

The interpretation of large-scale protein network data depends on our ability to identify significant substructures in the data, a computationally intensive task. Here we adapt and extend efficient techniques for finding paths and trees in graphs to the problem of identifying pathways in protein interaction networks. We present linear-time algorithms for finding paths and trees in networks under several biologically motivated constraints. We apply our methodology to search for protein pathways in the yeast protein-protein interaction network. We demonstrate that our algorithm is capable of reconstructing known signaling pathways and identifying functionally enriched paths and trees in an unsupervised manner. The algorithm is very efficient, computing optimal paths of length 8 within minutes and paths of length 10 in about three hours.     

The Edge-Disjoint Path Problem on Random Graphs by Message-Passing

We present a message-passing algorithm to solve a series of edge-disjoint path problems on graphs based on the zero-temperature cavity equations. Edge-disjoint paths problems are important in the general context of routing, that can be defined by incorporating under a unique framework both traffic optimization and total path length minimization. The computation of the cavity equations can be performed efficiently by exploiting a mapping of a generalized edge-disjoint path problem on a star graph onto a weighted maximum matching problem. We perform extensive numerical simulations on random graphs of various types to test the performance both in terms of path length minimization and maximization of the number of accommodated paths. In addition, we test the performance on benchmark instances on various graphs by comparison with state-of-the-art algorithms and results found in the literature. Our message-passing algorithm always outperforms the others in terms of the number of accommodated paths when considering non trivial instances (otherwise it gives the same trivial results). Remarkably, the largest improvement in performance with respect to the other methods employed is found in the case of benchmarks with meshes, where the validity hypothesis behind message-passing is expected to worsen. In these cases, even though the exact message-passing equations do not converge, by introducing a reinforcement parameter to force convergence towards a sub optimal solution, we were able to always outperform the other algorithms with a peak of 27% performance improvement in terms of accommodated paths. On random graphs, we numerically observe two separated regimes: one in which all paths can be accommodated and one in which this is not possible. We also investigate the behavior of both the number of paths to be accommodated and their minimum total length.     

Network inference through synergistic subnetwork evolution

Study of signaling networks is important for a better understanding of cell behaviors e.g., growth, differentiation, metabolism, proptosis, and gaining deeper insights into the molecular mechanisms of complex diseases. While there have been many successes in developing computational approaches for identifying potential genes and proteins involved in cell signaling, new methods are needed for identifying network structures that depict underlying signal cascading mechanisms. In this paper, we propose a new computational approach for inferring signaling network structures from overlapping gene sets related to the networks. In the proposed approach, a signaling network is represented as a directed graph and is viewed as a union of many active paths representing linear and overlapping chains of signal cascading activities in the network. Gene sets represent the sets of genes participating in active paths without prior knowledge of the order in which genes occur within each path. From a compendium of unordered gene sets, the proposed algorithm reconstructs the underlying network structure through evolution of synergistic active paths. In our context, the extent of edge overlapping among active paths is used to define the synergy present in a network. We evaluated the performance of the proposed algorithm in terms of its convergence and recovering true active paths by utilizing four gene set compendiums derived from the KEGG database. Evaluation of results demonstrate the ability of the algorithm in reconstructing the underlying networks with high accuracy and precision.     

How to reliably estimate the tortuosity of an animal's path: straightness, sinuosity, or fractal dimension?

The tortuosity of an animal's path is a key parameter in orientation and searching behaviours. The tortuosity of an oriented path is inversely related to the efficiency of the orientation mechanism involved, the best mechanism being assumed to allow the animal to reach its goal along a straight line movement. The tortuosity of a random search path controls the local searching intensity, allowing the animal to adjust its search effort to the local profitability of the environment. This paper shows that (1) the efficiency of an oriented path can be reliably estimated by a straightness index computed as the ratio between the distance from the starting point to the goal and the path length travelled to reach the goal, but such a simple index, ranging between 0 and 1, cannot be applied to random search paths; (2) the tortuosity of a random search path, ranging between straight line movement and Brownian motion, can be reliably estimated by a sinuosity index which combines the mean cosine of changes of direction with the mean step length; and (3) in the current state of the art, the fractal analysis of animals' paths, which may appear as an alternative and promising way to measure the tortuosity of a random search path as a fractal dimension ranging between 1 (straight line movement) and 2 (Brownian motion), is only liable to generate artifactual results. This paper also provides some help for distinguishing between oriented and random search paths, and depicts a general, comprehensive framework for analysing individual animals' paths in a two-dimensional space.     

Grey-Theory-Based Optimization Model of Emergency Logistics Considering Time Uncertainty

Natural disasters occur frequently in recent years, causing huge casualties and property losses. Nowadays, people pay more and more attention to the emergency logistics problems. This paper studies the emergency logistics problem with multi-center, multi-commodity, and single-affected-point. Considering that the path near the disaster point may be damaged, the information of the state of the paths is not complete, and the travel time is uncertainty, we establish the nonlinear programming model that objective function is the maximization of time-satisfaction degree. To overcome these drawbacks: the incomplete information and uncertain time, this paper firstly evaluates the multiple roads of transportation network based on grey theory and selects the reliable and optimal path. Then simplify the original model under the scenario that the vehicle only follows the optimal path from the emergency logistics center to the affected point, and use Lingo software to solve it. The numerical experiments are presented to show the feasibility and effectiveness of the proposed method.     

The isotope effects on a hydrogen transfer using path integral instanton method

In our previous work, we have developed an algorithm for calculating the tunnelling splittings using path integral instanton method with the discretised imaginary time approach. Our algorithm has enabled us to take a zero temperature limit, efficiently and accurately. In this paper, we investigate the effect of isotopomers on the tunnelling splittings and semiclassical tunnelling paths of a hydrogen transfer in a model molecular system HO₂.     

What visual information is used for navigation around obstacles in a cluttered environment?

The goal of this study was to determine what visual information is used to navigate around barriers in a cluttered terrain. Twelve traffic pylons were arranged randomly in a 4.55 x 3.15 m travel area: there were 20 different arrangements. For each arrangement, individuals (N = 6) were positioned in 1 of 3 locations on the outside border with their eyes closed: on verbal command they were instructed to open their eyes and quickly go to 1 of 2 specified goals (2 vertical posts defining a door) located on one edge of the travel area. The movement of the body was tracked using the OPTOTRAK system, with the IREDS placed on a collar worn by the subjects. Experimental data of travel path chosen were compared with those predicted by models that incorporated different types of visual information to control path trajectory. The 6 models basically use 2 different strategies for route selection: reactive control based on visual input about the obstacle encountered in the line-of-sight travel path (Model # 1) and path planning based on different visual information (Model # 2, 3, 4, 5, and 6). The models that involve path planning are grouped into 2 categories: models 2, 3, 4, and 5 need detailed geometrical configuration of the obstacles to plan a route while model 6 plans a route based on identifying and avoiding a cluster of obstacles in the travel path. Two measures were used to compare model performance with the actual travel path: the difference in area between predicted and actual travel path and the number of trials that accurately predicted the number of turns during travel. The results suggest that route selection is not based on reactive control, but does involve path planning. The model that best predicts the travel paths taken by the individuals uses visual information about cluster of obstacles and identification of safe corridors to plan a route.     

Complex Network Theory Applied to the Growth of Kuala Lumpur’s Public Urban Rail Transit Network

Recently, the number of studies involving complex network applications in transportation has increased steadily as scholars from various fields analyze traffic networks. Nonetheless, research on rail network growth is relatively rare. This research examines the evolution of the Public Urban Rail Transit Networks of Kuala Lumpur (PURTNoKL) based on complex network theory and covers both the topological structure of the rail system and future trends in network growth. In addition, network performance when facing different attack strategies is also assessed. Three topological network characteristics are considered: connections, clustering and centrality. In PURTNoKL, we found that the total number of nodes and edges exhibit a linear relationship and that the average degree stays within the interval [2.0488, 2.6774] with heavy-tailed distributions. The evolutionary process shows that the cumulative probability distribution (CPD) of degree and the average shortest path length show good fit with exponential distribution and normal distribution, respectively. Moreover, PURTNoKL exhibits clear cluster characteristics; most of the nodes have a 2-core value, and the CPDs of the centrality’s closeness and betweenness follow a normal distribution function and an exponential distribution, respectively. Finally, we discuss four different types of network growth styles and the line extension process, which reveal that the rail network’s growth is likely based on the nodes with the biggest lengths of the shortest path and that network protection should emphasize those nodes with the largest degrees and the highest betweenness values. This research may enhance the networkability of the rail system and better shape the future growth of public rail networks.     

Curvature and torsion in growing actin networks

Intracellular pathogens such as Listeria monocytogenes and Rickettsia rickettsii move within a host cell by polymerizing a comet-tail of actin fibers that ultimately pushes the cell forward. This dense network of cross-linked actin polymers typically exhibits a striking curvature that causes bacteria to move in gently looping paths. Theoretically, tail curvature has been linked to details of motility by considering force and torque balances from a finite number of polymerizing filaments. Here we track beads coated with a prokaryotic activator of actin polymerization in three dimensions to directly quantify the curvature and torsion of bead motility paths. We find that bead paths are more likely to have low rather than high curvature at any given time. Furthermore, path curvature changes very slowly in time, with an autocorrelation decay time of 200 s. Paths with a small radius of curvature, therefore, remain so for an extended period resulting in loops when confined to two dimensions. When allowed to explore a three-dimensional (3D) space, path loops are less evident. Finally, we quantify the torsion in the bead paths and show that beads do not exhibit a significant left- or right-handed bias to their motion in 3D. These results suggest that paths of actin-propelled objects may be attributed to slow changes in curvature, possibly associated with filament debranching, rather than a fixed torque.     

Ants find the shortest path: a mathematical proof

In the most basic application of Ant Colony Optimization (ACO), a set of artificial ants find the shortest path between a source and a destination. Ants deposit pheromone on paths they take, preferring paths that have more pheromone on them. Since shorter paths are traversed faster, more pheromone accumulates on them in a given time, attracting more ants and leading to reinforcement of the pheromone trail on shorter paths. This is a positive feedback process that can also cause trails to persist on longer paths, even when a shorter path becomes available. To counteract this persistence on a longer path, ACO algorithms employ remedial measures, such as using negative feedback in the form of uniform evaporation on all paths. Obtaining high performance in ACO algorithms typically requires fine tuning several parameters that govern pheromone deposition and removal. This paper proposes a new ACO algorithm, called EigenAnt, for finding the shortest path between a source and a destination, based on selective pheromone removal that occurs only on the path that is actually chosen for each trip. We prove that the shortest path is the only stable equilibrium for EigenAnt, which means that it is maintained for arbitrary initial pheromone concentrations on paths, and even when path lengths change with time. The EigenAnt algorithm uses only two parameters and does not require them to be finely tuned. Simulations that illustrate these properties are provided.     

Navigation between initial and desired community states using shortcuts

Ecological management problems often involve navigating from an initial to a desired community state. We ask whether navigation without brute-force additions and deletions of species is possible via: adding/deleting a small number of individuals of a species, changing the environment, and waiting. Navigation can yield direct paths (single sequence of actions) or shortcut paths (multiple sequences of actions with lower cost than a direct path). We ask (1) when is non-brute-force navigation possible?; (2) do shortcuts exist and what are their properties?; and (3) what heuristics predict shortcut existence? Using a state diagram framework applied to several empirical datasets, we show that (1) non-brute-force navigation is only possible between some state pairs, (2) shortcuts exist between many state pairs; and (3) changes in abundance and richness are the strongest predictors of shortcut existence, independent of dataset and algorithm choices. State diagrams thus unveil hidden strategies for manipulating species coexistence and efficiently navigating between states.     

Moving muscle points provide accurate curved muscle paths in a model of the cervical spine

Muscle paths in musculoskeletal models have been modeled using several different methods; however, deformation of soft tissue with changes in posture is rarely accounted for, and often only the neutral posture is used to define a muscle path. The objective of this study was to model curved muscle paths in the cervical spine that take into consideration soft tissue deformation with changes in neck posture. Two subject-specific models were created from magnetic resonance images (MRI) in 5 different sagittal plane neck postures. Curved paths of flexor and extensor muscles were modeled using piecewise linear lines-of-action in two ways; (1) using fixed via points determined from muscle paths in the neutral posture and (2) using moving muscle points that moved relative to the bones determined from muscle paths in all 5 postures. Accuracy of each curved modeled muscle path was evaluated by an error metric, the distance from the anatomic (centroid) muscle path determined from the MRI. Error metric was compared among three modeled muscle path types (straight, fixed via and moving muscle point) using a repeated measures one-way ANOVA (α=0.05). Moving muscle point paths had 21% lower error metric than fixed via point paths over all 15 pairs of neck muscles examined over 5 postures (3.86 mm vs. 4.88 mm). This study highlights the importance of defining muscle paths in multiple postures in order to properly define the changing curvature of a muscle path due to soft tissue deformation with posture.