Pathwidth Research Articles

Magnitude and Speed of Consecutive Market Crashes in a Diffusion Model

In this paper, in a time-homogeneous diffusion setting, we study a sequence of last passage times of generalized drawdown processes before the first passage time of another monitoring generalized drawdown process. These quantities are closely related to consecutive small market downward movements before a final big market crash modeled by the first passage time of the monitoring generalized drawdown process. Our theoretical framework simultaneously incorporates the first passage time, the absolute and relative drawdown times, and generalizes the scope of (Zhang and Hadjiliadis Methodol Comput Appl Probab 14(8):739–752 2012). We explicitly determine the path decompositions bridging these random times, the stochastic differential equations (SDE) governing each of the path fragments, and derive the Laplace transform of durations between any two of these random times. Applications include designing various risk measures summarizing several market information (e.g. historical maximum/minimum, absolute drawdown, relative drawdown) altogether. They allow us to study, in a microscopic way, a sequence of smaller drawdowns (signals) before a big drawdown (market crash) actually realizes. They can have applications to the detection of a potential market crash from signals of market drawdowns. We illustrate our results using a drifted Brownian motion.

A Pore-Scale Model for Quantifying Airflow Paths through Grain Bulks

Abstract. A commercial discrete element software package (PFC3D) was used to develop a model to simulate pore structures of grain beds. Based on the simulated structure of a grain bed, an algorithm reported in the literature was adopted and modified to determine airflow paths in the grain bed by treating the grain bed as a series of four-particle tetrahedrons. Critical characteristic parameters of the airflow path were predicted, including path length (tortuosities), width, and local turning angle (change in airflow direction at a location in the grain bed). The predicted tortuosities were in good agreement with the range of tortuosity values reported in the literature for porous beds consisting of spherical particles. The average path width was in the range of 0.83 to 5.93 mm. The local turning angles were mostly in the 0° to 10° range. Keywords: Airflow, Discrete element method, Grain bed, Pore structure, Tortuosity.

Enumerating minimum path decompositions to support route choice set generation

Abstract: This paper concerns the structure of movements as were recorded by GPS traces and converted to routes by map matching. Each route in a transportation network corresponds to a collection of directed paths or cycles in a digraph. When considering only directed paths, corresponding to utilitarian trips, the path is not necessarily a shortest path between its origin and destination, and can be split up into a small number of segments, each of which is a shortest or least cost path. Two consecutive segments are separated by split vertices . Split vertices act as intermediate destinations in the mind of travellers who try to hop between them using minimum cost paths. Hence they provide useful information to build route choice models. In this paper we identify and enumerate all possible decompositions of a path into a minimum number of shortest segments. This gives us an indication of the importance of split vertices occurring in particular sets of revealed routes that belong either to a single traveller or to a specific group. The proposed technique allows for automatic extraction of frequently used intermediate destinations (way-points) from revealed preference data.

Splitting and time reversal for Markov additive processes

We consider a Markov additive process with a finite phase space and study its path decompositions at the times of extrema, first passage and last exit. For these three families of times we establish splitting conditional on the phase, and provide various relations between the laws of post- and pre-splitting processes using time reversal. These results offer valuable insight into the behaviour of the process, and while being structurally similar to the Lévy process case, they demonstrate various new features. As an application we formulate the Wiener–Hopf factorization, where time is counted in each phase separately and killing of the process is phase dependent. Restricting to the case of no positive jumps, we find concise formulas for these factors, and also characterize the time of last exit from the negative half-line. The latter result is obtained using three quite different approaches based on the established path decomposition theory, which further demonstrates its applicability.

The degree of misjudgment between perceived and actual gait ability in older adults

Successful execution of motor tasks requires an integration of the perception of one's physical abilities and the perception of the task itself. Physical and cognitive decline associated with ageing may lead to misjudgments of these perceived and actual abilities and possibly to errors that may lead to balance loss. We aimed to directly quantify the degree to which older adults misjudge their actual gait ability. Twenty-seven older adults participated and were instructed to walk on a narrow path projected on a treadmill. We tested two paradigms to estimate the participants’ perceived gait ability: a path width manipulation, in which participants had to indicate the smallest path width that they could walk on without stepping outside or losing balance (at given speed), and a treadmill speed manipulation, in which they had to indicate the maximum speed that they could use at a given path width. We determined their actual ability as the probability of stepping inside the path over a range of path widths and speeds. The path width paradigm seemed suitable for evaluating self-perception of actual gait ability and revealed that participants appeared to show a range of misjudgment towards either over- or underestimating their actual abilities. Better abilities appeared not associated with better judgment. Direct quantification of the degree of misjudgment provides insight in the interplay between cognition and physical abilities and can be of added value towards prevention of falls and promotion of healthy ageing.

Dynamic perception of dynamic affordances: walking on a ship at sea.

Motion of the surface of the sea (waves, and swell) causes oscillatory motion of ships at sea. Generally, ships are longer than they are wide. One consequence of this structural difference is that oscillatory ship motion typically will be greater in roll (i.e., the ship rolling from side to side) than in pitch (i.e., the bow and stern rising and falling). For persons on ships at sea, affordances for walking on the open deck should be differentially influenced by ship motion in roll and pitch. Specifically, the minimum width of a walkable path should be greater when walking along the ship's short, or athwart axis than when walking along its long, or fore-aft axis. On a ship at sea, we evaluated the effects of walking in different directions (fore-aft vs. athwart) on actual walking performance. We did this by laying out narrow paths on the deck and asking participants (experienced maritime crewmembers) to walk as far as they could while remaining within the lateral path boundaries. As predicted, participants walked farther along the athwart path than along the fore-aft path. Before actual walking, we evaluated participants' judgments of their walking ability in the fore-aft and athwart directions. These judgments mirrored the observed differences in walking performance, and the accuracy of judgments did not differ between the two directions. We conclude that experienced maritime crewmembers were sensitive to affordances for walking in which the relevant properties of the environment were exclusively dynamic.

EVACUATION SIMULATION IN KALAYAAN RESIDENCE HALL, UP DILIMAN USING GAMA SIMULATION SOFTWARE

Abstract. Agent-Based Modeling (ABM) has recently been adopted in some studies for the modelling of events as a dynamic system given a set of events and parameters. In principle, ABM employs individual agents with assigned attributes and behaviors and simulates their behavior around their environment and interaction with other agents. This can be a useful tool in both micro and macroscale-applications. In this study, a model initially created and applied to an academic building was implemented in a dormitory. In particular, this research integrates three-dimensional Geographic Information System (GIS) with GAMA as the multi-agent based evacuation simulation and is implemented in Kalayaan Residence Hall. A three-dimensional GIS model is created based on the floor plans and demographic data of the dorm, including respective pathways as networks, rooms, floors, exits and appropriate attributes. This model is then re-implemented in GAMA. Different states of the agents and their effect on their evacuation time were then observed. GAMA simulation with varying path width was also implemented. It has been found out that compared to their original states, panic, eating and studying will hasten evacuation, and on the other hand, sleeping and being on the bathrooms will be impedances. It is also concluded that evacuation time will be halved when path widths are doubled, however it is recommended for further studies for pathways to be modeled as spaces instead of lines. A more scientific basis for predicting agent behavior in these states is also recommended for more realistic results.

Tool path generation via the multi-criteria optimisation for flat-end milling of sculptured surfaces

A method of generating optimal tool paths for sculptured surface machining with flat-end cutters is presented in this paper. The inclination and tilt angles, as well as the feed directions of the cutter at each cutter contact point on a machining path are optimised as a whole so that the machining width of the tool path can be as large as possible, and concerns such as smooth cutter motion, gouging avoidance, scallop height and machining widths overlap are also considered when calculating a path. A multi-criteria tool path optimisation model is introduced, and it is converted into a single objective optimisation with the weighted sum method. The Differential Evolution (DE) algorithm is suitable for solving this highly non-linear problem. However, the searching process of the DE algorithm may be trapped in local minima due to large number of design variables. Therefore, an algorithm combining the DE algorithm and the sequence linear programming algorithm is developed to solve this optimisation model. The proposed method is applied to two freeform surfaces to illustrate its effectiveness.

Effects of Flow Path Geometrical Parameters on Flow Characteristics and Hydraulic Performance of Drip Irrigation Emitters

AbstractIn this paper, 13 fractal flow paths were designed and the effects of flow path geometric parameters on the internal flow characteristics and hydraulic performance explored. The results showed as the flow path width increased from 0.9 to 1.3 mm, the flow velocity followed from 1.83 to 2.43 m s−1. There was significant difference in the turbulence intensity. The flow velocity (about 2.14 m s−1) and turbulence intensity distribution (5.6–48.1%) in flow paths with different depths were approximately the same. Different flow path lengths would obviously affect the values of the flow characteristics, while the distributions were similar. The length increased from 128 to 256 mm, the flow velocity decreased from 2.52 to 1.84 m s−1 and the maximum turbulence intensity dropped from 55.6 to 40.1%. As for hydraulic performance, the flow regime indexes were all about 0.49. The flow coefficient was obviously positively related to flow path width and depth, but very negatively correlated with flow path length and a prediction model of flow coefficient was constructed (R2 = 0.94). After comprehensive consideration, the optimized flow path width was about 1.0 mm, the length should be less than 224 mm, and a series of emitters with different flow rates could be developed by changing the depth. Copyright © 2016 John Wiley & Sons, Ltd.

Resistance-Geodesic Distance and Its Use in Image Segmentation

Measuring the distance is an important task in many clustering and image-segmentation algorithms. The value of the distance decides whether two image points belong to a single or, respectively, to two different image segments. The Euclidean distance is used quite often. In more complicated cases, measuring the distances along the surface that is defined by the image function may be more appropriate. The geodesic distance, i.e. the shortest path in the corresponding graph, has become popular in this context. The problem is that it is determined on the basis of only one path that can be viewed as infinitely thin and that can arise accidentally as a result of imperfections in the image. Considering the k shortest paths can be regarded as an effort towards the measurement of the distance that is more reliable. The drawback remains that measuring the distance along several paths is burdened with the same problems as the original geodesic distance. Therefore, it does not guarantee significantly better results. In addition to this, the approach is computationally demanding. This paper introduces the resistance-geodesic distance with the goal to reduce the possibility of using a false accidental path for measurement. The approach can be briefly characterised in such a way that the path of a certain chosen width is sought for, which is in contrast to the geodesic distance. Firstly, the effective conductance is computed for each pair of the neighbouring nodes to determine the local width of the path that could possibly run through the arc connecting them. The width computed in this way is then used for determining the costs of arcs; the arcs whose use would lead to a small width of the final path are penalised. The usual methods for computing the shortest path in a graph are then used to compute the final distances. The corresponding theory and the experimental results are presented in this paper.

Valuing resettable convertible bonds: Based on path decomposing

We price resettable convertible bonds (RCBs) whose embedded options contain conversion, call and put provisions and reset clause using complete path decomposition. The reset clause stipulates that the conversion price is adjusted downwards if the underlying stock price is lower than the conversion price by some pre-specified percentage. By assuming or identifying optimal strategies of RCBs’ issuers and investors, we completely decompose the value of RCBs into three parts: A sum of values of several path-dependent exotic options, the value of coupon payments, and the par value. Our method provides comprehensible insight of different provisions contained in RCBs.

Strong inference from transect sign surveys: combining spatial autocorrelation and misclassification occupancy models to quantify the detectability of a recovering carnivore

Monitoring of species using surveys of ambiguous signs and assuming 100% detectability produces potentially biased occupancy estimates. Novel analytical tools have been developed that correct for bias arising from imperfect detectability, species misidentification and spatial autocorrelation between detection survey replicates that can affect transect surveys. To date they have been applied individually, but their combined value is unclear.The recovery of carnivores such as the European pine marten Martes martes potentially has far reaching, but largely unknown, implications for ecosystem restoration. Analysis of the species' distribution has as yet been crude and hence unsuited for informing management. We aimed to assess the validity of standard scat surveys to provide recommendations to increase inference from future surveys.We employed spatially replicated scat surveys along forest paths in NE Scotland, genetic verification of scat provenance and occupancy modelling techniques to quantify pine marten detectability and variation therein. Detectability for 1 km and 1.5 km transects, comparable to standard protocols, was estimated to be 0.35 and 0.58 respectively, highlighting the importance of accounting for imperfect detectability. Detection probabilities decreased with vegetation cover and increased with path width. Models accounting for spatial autocorrelation between adjacent transect segments suggested that segments of ≥ 400 m could be analysed as spatial replicates with negligible bias. As is the norm, not all scats yielded DNA to genetically verify they were produced by pine marten. This was accounted for through the use of ‘miss‐classification occupancy models’ which allowed the use of unverified scats, increasing detection probabilities while accounting for the probability of unverified scats being false positive detections.This study exemplifies that robust inference on species occupancy is achievable through careful consideration of sampling design and the application of readily available analytical techniques. Adopting best‐practice need not increase monitoring costs and can even increase cost‐efficiency.

Conditioning subordinators embedded in Markov processes

The running infimum of a Lévy process relative to its point of issue is known to have the same range that of the negative of a certain subordinator. Conditioning a Lévy process issued from a strictly positive value to stay positive may therefore be seen as implicitly conditioning its descending ladder height subordinator to remain in a strip. Motivated by this observation, we consider the general problem of conditioning a subordinator to remain in a strip. Thereafter we consider more general contexts in which subordinators embedded in the path decompositions of Markov processes are conditioned to remain in a strip.

Embedded Algorithmic Noise-Tolerance for Signal Processing and Machine Learning Systems via Data Path Decomposition

Low overhead error-resiliency techniques such as algorithmic noise-tolerance (ANT) have been shown to be particularly effective for signal processing and machine learning kernels. However, the overhead of conventional ANT can be as large as 30% due to the use of explicit estimator block. To overcome this overhead, embedded ANT (E-ANT) is proposed [S. Zhang and N. Shanbhag, “Embedded error compensation for energy efficient DSP systems,” in Proc. GlobalSIP, Dec. 2014, pp. 30–34], where the estimator is embedded in the main computation block via data path decomposition (DPD). E-ANT reduces the logic overhead to be below 8% as compared with the 20%–30% associated with conventional reduced precision replica (RPR) ANT system while maintaining the same error compensation functionality. DPD was first proposed in our original paper [Zhang and Shanbhag, 2014] where its benefits were studied in the case of a simple multiply-accumulator (MAC) kernel. This paper builds upon [Zhang and Shanbhag, 2014] by 1) providing conditions for the existence of DPD, 2) demonstrating DPD for a variety of commonly employed kernels in signal processing and machine learning applications, and 3) evaluating the robustness improvement and energy savings of DPD at the system level for an SVM-based EEG seizure classification application. Simulation results in a commercial 45 nm CMOS process show that E-ANT can compensate for error rates up to 0.38 for errors in FE only, and 0.17 for errors in FE and CE, while maintain a true positive rate ${p}_{\rm tp} > 0.9$ and a false positive rate ${p}_{\rm fp}\leq 0.01$ . This represents a greater than 3-orders-of-magnitude improvement in error tolerance over the conventional system. This error tolerance is employed to reduce energy via the use of voltage overscaling (VOS). E-ANT is able to achieve 51% energy savings when errors are in FE only, and up to 43% savings when errors are in both FE and CE.

On the numerical simulation of the thermal behavior during the selective laser melting process

In the selective laser melting (SLM), components are manufactured layer by layer using an additive process. A laser beam is used as a heat source to fuse fine metal powder. The occurring temperatures during the process have a decisive influence on the manufacturing process itself and the consequential mechanical and technological properties. By varying process parameters such as the laser power, it is possible to influence the temperature level as well as the geometrical extent of the melting zone. A big issue of the selective laser melting technology is thermal distortion resulting in residual stresses that can lead to a fracture of the component. In this study the heat balance during the selective laser melting production process in terms of resultant stresses is analyzed using the Finite Element Method. For this purpose, the melting zones of one single layer are investigated numerically for an initial aluminium alloy process. Afterwards, the geometric extend of the zones are validated using microsections of manufactured components in order to optimize the thermal boundary conditions of the simulation model. The main features here are the path width, the layer thickness and the resulting overlapping zones of the individual melt pools. These preliminary identified findings are used to create a model to investigate the occurring residual stresses. With this analysis, on the one hand the qualitative correctness of the representation of the numerical stresses could be shown. On the other hand, the influence of laser‐power and laser‐spot‐velocity on the component accuracy and so the formation of stresses are investigated by applying a parameter study.

Effects of flow path boundary optimizations on particle transport in drip irrigation emitters

AbstractA modified digital particle image velocimetry (DPIV) was used to test particles' moving characteristics in cylindrical fractal M‐geometries flow paths with three optimized boundaries. Taken the vorticity and characteristics of streamlines distribution in the central area and the velocity field near the boundary into consideration, it was found that the fractal M‐type flow path would be optimized with a design such that the radius of an arc in tooth‐root facing‐water zone, tooth‐tip backing‐water zone and facing‐water zone was half width of the flow path. Moreover, the radius of the arc in the tooth‐root backing‐water zone was desired to be the same with the width of the flow path. This optimization was attributed to two reasons. Firstly, with a large radius arc in the tooth‐tip backing‐water zone and facing‐water zone, the velocity in the central domain and near boundary area was improved. And the following performance of particles near the boundary was suppressed. Secondly, adoption of a small arc in the tooth‐root facing‐water zone could improve the velocity, vorticity and self‐cleaning capability near wall. In conclusion, when optimizing the boundary, the distribution characteristics of vortices should be fully considered to enhance vortices development in the flow path. Copyright © 2016 John Wiley & Sons, Ltd.

Determining structural route components from GPS traces

Analysis of GPS traces shows that people often do not use the least cost path through the transportation network while making trips. This leads to the question which structural path characteristics can be used to construct realistic route choice sets for use in traffic simulation models. In this paper, we investigate the hypothesis that, for utilitarian trips, the route between origin and destination consists of a small number of concatenated least cost paths. The hypothesis is verified by analyzing routes extracted from large sets of recorded GPS traces which constitute revealed preference information. Trips have been extracted from the traces and for each trip the path in the transportation network is determined by map matching. This is followed by a path decomposition phase for which the algorithm constitutes the first contribution of this paper. There are multiple ways to split a given path in a directed graph into a minimal number of subpaths of minimal cost. By calculating two specific path splittings, it is possible to identify subsets of the vertices (splitVertexSuites) that can be used to generate every possible minimum path splitting by taking one vertex from each such subset. As a second contribution, we show how the extracted information is used in microscopic travel simulation. The distribution for the size of the minimum decomposition, extracted from the GPS traces, can be used in constrained enumeration methods for route choice set generation. The sets of vertices that can act as boundary vertices separating consecutive route parts contain way points (landmarks) having a particular meaning to their user. The paper explains the theoretical aspects of route splitting as well as the process to extract splitVertexSuites from big data. It reports statistical distributions extracted from sets of GPS traces for both multimodal person movements and unimodal car trips.

Trailer Steering Control of a Tractor–Trailer Robot

In this paper, we consider active trailer steering control as a means to improve the maneuverability of (long) truck–trailer combinations during cornering. Hereto, we formulate the problem of reducing the so-called swept path width during cornering and that of eliminating unsafe tail swing of the trailer as a tracking control problem. We present a kinematic tractor–trailer model including off-axle hitching, on the basis of which we design nonlinear control strategies solving this tracking problem. The effectiveness of the proposed approach is evidenced experimentally on a robotic tractor–trailer platform.

Navigation of autonomous tractor for orchards and plantations using a laser range finder: Automatic control of trailer position with tractor

The autonomous control of a tractor-trailer system in orchards and plantations has frequently been observed for the transportation, loading and unloading of products between plants and trees. The objective of this research was to develop a control algorithm for a single-sensor tractor-trailer navigation system for navigating within a row plantation and travelling between plots. A control scheme for stopping the tractor-trailer for various in-field tasks, such as product loading/unloading using a laser range finder (LRF), is presented. The LRF was used to navigate a full-size autonomous agricultural tractor equipped with a two-wheeled trailer. For ease of operation in narrow rows, a sliding hitch bar (SHB) was developed to control the trailer by adjusting the position of the hitch-point between the tractor and trailer. Compared to the tractor-trailer system driven by human, the control system could navigate the tractor-trailer with the RMS differences of 0.275 m (SD: 0.009 m), 0.373 m (SD: 0.030 m) and 0.518 m (SD: 0.022 m) for wide curve , tight curve and U-turn experimental paths, respectively. The SHB unit also supported the navigation system with wider turn for the trailer than conventional single hitch point about 0.383 m (7.66% of the 5 m path width, SD: 0.028 m), 0.762 m (15.23% of 5 m path width, SD: 0.010 m) and 1.094 m (21.88% of 5 m path width, SD: 0.037 m) for wide curve , tight curve and U-turn experimental paths, respectively. The control system also stopped the tractor-trailer at the specified landmarks. The results show that the navigation of the tractor-trailer was demonstrated with satisfactory accuracy and that the trailer position was controlled by the SHB with a wider turn in the experimental paths. Therefore, this laser-based landmark navigation system, and the SHB unit, can be adopted for different applications of autonomous tractor-trailer systems with controlled trailer positioning.

Real-time smooth trajectory generation for nonholonomic mobile robots using Bézier curves

This paper focuses on generating smooth trajectories for a wheeled nonholonomic mobile robot using piecewise Bezier curves with properties ideally suited for this purpose. The developed algorithm generates smooth motion trajectories with C2 continuous curvature. We consider a teleoperated wheeled mobile robot in an indoor environment with ceiling cameras for operator visibility. The motion trajectory is constrained by the operator-specified via points and path width. A method to automatically generate a trajectory based on only these two inputs is proposed and demonstrated. To improve the trackability of the mobile robot, we adopted a Bezier subdivision method and inserted a quintic Bezier segment into high-curvature areas. The proposed algorithm can be used for real-time obstacle-avoidance trajectory generation because it allows trajectory subdivision and arbitrarily setting of the second derivative at the start point. Simulation and experimental results demonstrate the effectiveness of the proposed method. HighlightsNew algorithm to generate smooth trajectories for a wheeled mobile robot.Trajectory generation satisfying operator-specified via points and path width.Trackability enhancement to high-curvature trajectory by Bezier subdivision method.Design of a trajectory tracking controller based on the Lyapunov stability theorem.