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Background Daily walking paths exhibit varying environment features and require continuous adjustments to locomotor trajectories. Humans maintain lateral balance while navigating paths by modifying stepping in accordance with changing side-to-side path limitations (e.g. path width, lateral location). These processes are influenced by one’s actual physical ability to maintain balance, as well as their self-perceived balance ability. Older adults experience decreases in each of these abilities, which may alter their capacity to execute appropriate lateral stepping adaptations. Research Question How do age, physical and self-perceived balance abilities interact to influence lateral stepping adaptations of older adults walking in complex environments with dynamic lateral path features? Methods Twenty young (age mean ± SD: 21.7 ± 2.6) and 18 older adults (age mean ± SD: 71.6 ± 6.0) walked on an instrumented treadmill in a virtual-reality system. Participants adjusted lateral stepping during two competing lateral balance sub-tasks that manipulated either path width or location. Participants began walking on a gradually-narrowing path (sub-task A), then decided when/ how to laterally maneuver to an adjacent path (sub-task B). Recorded path characteristics were used to quantify spatial thresholds for stepping error onset and sub-task exchange. Results Older adults made sub-task A stepping errors on wider paths and exchanged sub-tasks earlier. These differences were not directly attributed to age. Statistical path analyses revealed that physical balance ability mediated age effects on stepping error onset, while self-perceived balance ability mediated age effects on sub-task exchange. Both age groups exchanged sub-tasks when stepping accuracy likelihoods were similar and high, ∼90 %. Significance This work demonstrates important mechanisms for how age, via degradation of physical and self-perceived balance abilities, indirectly and differentially influences navigation of competing lateral balance tasks. Mediating physical and perceptual factors are potential targets for improving older adults’ navigation of complex environments.

Walking stability is an important factor that is related to working accidents at height. The understanding of the relationship between walking stability and walking conditions remains an unmet need. Therefore, this study aimed to investigate the effect of path height, width, and asymmetric conditions on the pressure and time information of the foot-ground interaction during walking. 12 subjects were required to walk at two height, three width, and asymmetric conditions. Plantar pressures during walking were measured with the F-scan insole sensors. The total pressures were normalized with body weight, and the temporal parameters were normalized with stance time. When the walking height increased, the plantar pressure at the “heel strike” phase did not change significantly, while that at “heel rise” and “toe off” phases significantly increased, and the “heel rise” occurred earlier, indicating a greater foot-ground interaction at the forefoot part of the sole. As the path width increased from 0.6 m to 1.2 m, the foot-ground interaction as well as the asymmetric effect approached to that of overground walking. The findings could help improve the risk assessment and footwear design.

Many of the tools developed for the theory of tree-decompositions of graphs do not work for directed graphs. In this paper we show that some of the most basic tools do work in the case where the model digraph is a directed path. Using these tools we define a notion of a directed blockage in a digraph and prove a min-max theorem for directed path-width analogous to the result of Bienstock, Roberston, Seymour and Thomas for blockages in graphs. Furthermore, we show that every digraph with directed path width $\geq k$ contains each arboresence of order $\leq k + 1$ as a butterfly minor. Finally we also show that every digraph admits a linked directed path-decomposition of minimum width, extending a result of Kim and Seymour on semi-complete digraphs., 13 pages

Rock avalanches involve extremely rapid, flow-like movement of fragmented rock with extreme destructive potential. With increasing development pressures in mountainous regions, there is a need for simple, stochastic estimates of runout distances to aid in hazard assessments and prioritize sites for more detailed investigation. To support the development of an empirical predictive tool, a systematic method was used to describe 49 rock avalanches in the Canadian Cordillera, which had been documented in the literature but not previously compiled into a regional inventory. These cases were described using measured or estimated numerical values for volume, fall height, runout length, total impacted area and the ratio of total impacted area over runout length (referred to as mean path width), and qualitative descriptions of the topographic confinement, substrate material and source geology. Linear regressions were fit to the data, with qualitative attributes treated as indicator variables. A strong relationship was found for runout distance predicted from volume, fall height and lateral confinement. A second relationship was found for mean path width over runout length predicted from volume. These relationships were converted to survival functions to estimate the runout exceedance probability and the mean path width exceedance probability. These survival functions were implemented in a computer tool, called the Probabilistic Runout Estimator—Rock Avalanche (PRE-RA), which can be used to estimate spatial impact probability ranges for rock avalanche runout. An application of this tool was demonstrated using two recent Canadian rock avalanches, which were not used in the dataset to estimate the statistical relationships.

INTRODUCTION: Tandem gait abnormalities have been reported to increase with advancing age, play a role in fall-prediction in Parkinson’s disease, and distinguish it from atypical parkinsonism. Tandem gait has been scored based on the number of side steps off a straight line in these studies. Objective measurement of spatiotemporal tandem gait parameters in Parkinson’s disease has not been previously reported. METHODS: Subjects (74 Parkinson’s disease and 28 controls) were enrolled after IRB approval. Those with more than 1 fall/day or a Montreal Cognitive Assessment score

Laboratory experiments were used to estimate the hydraulic performance of emitters, i.e., the emitter flow variation (qvar) and manufacturer’s coefficient of variation (CVm), by measuring the discharge of different labyrinth-channel emitters at different operating pressures (P) and water temperatures (T). Considering the importance of the structural parameters of the labyrinth-channel emitters in drip irrigation design, which has been experimentally confirmed, artificial neural network (ANN) and gene expression programming (GEP) models were developed to predict qvar and CVm. The ANN and GEP models were trained and tested using structural parameters (including the number, height (H), and spacing of trapezoidal units and the flow path width and length) of different labyrinth-channel emitters, P and T as the input variables, and qvar and CVm as the outputs. Statistical criteria, including the coefficients of correlation (r), relative root-mean-square error (RRMSE), and mean absolute error (MAE), were used to examine the accuracy of the developed models. The ANN models exhibited good correlation with experimental values, with high r values 0.995 and 0.969 for qvar and 0.997 and 0.947 for CVm in the training and testing processes, respectively. The ANN models had lower RRMSE and MAE values than the GEP models. Furthermore, H was the dominant variable for obtaining the most accurate prediction model. The results confirm that the ANN models are superior to the GEP models for the prediction of the hydraulic performance of emitters.

The solar eclipse will take place if the moon is between the Earth and sun as well as its shadow touches the Earth. Some hadiths narrated that the phenomena had occurred in the era of Prophet saw. then He commanded Muslims to perform prayer, remembrance, and donation. Hence, the solar eclipse in Islam is crucial as it is respected to worship to God. The objective of this paper is to calculate the solar eclipse using Meeus Algorithm. After preparing the Bessel elements and arranging the Meeus Algorithm, it can be determined accurately both the eclipse type, time, place, path width of the eclipse and the sun position as it lasts. Sun eclipse calculation using Meeus algorithm on June, 21th 2020 results 1.380 N and 18.060 E for the coordinate, 0.28 for altitude, azimuth of 66.56, 84.9 km width, as well as total duration of 1 minutes 22.3 and seconds. Those all are accurate due to the similarity with NASA calculation using ELP and VSOP87 algorithm.

In this study, we examined the effects of changes in path width on distance perception and gaze position. The subjects experienced the straight path constructed in the virtual environment through the pseudo walking by foot stepping. Distance perception was quantified by comparing the memorized distances with the replay results. The gaze position was analyzed by measuring the gaze point of the subjects walking on the path. As a result, when the path width was widened, the path was perceived short, and when the path width was narrowed, the path was perceived to the same extent. And it was suggested that the gaze position of the subject who perceived the distance as short moved to the back of the path.

Although the multi-agent pickup and delivery (MAPD) problem, wherein multiple agents iteratively carry materials from some storage areas to the respective destinations without colliding, has received considerable attention, conventional MAPD algorithms use simplified, uniform models without considering constraints, by assuming specially designed environments. Thus, such conventional algorithms are not applicable to some realistic applications wherein agents have to move in a more complicated and restricted environment; for example, in a rescue or a construction site, their paths and orientations are strictly restricted owing to the path width, and the sizes of agents and materials they carry. Therefore, we first formulate an N-MAPD problem, which is an extension of the MAPD problem for a non-uniform environment. We then propose an N-MAPD algorithm, the path and action planning with orientation (PAPO), to effectively generate collision-free paths meeting the environmental constraints. The PAPO is an algorithm that considers not only the direction of movement but also the orientation of agents as well as the cost and timing of rotations in our N-MAPD formulation by considering the agent and material sizes, node sizes, and path widths. We experimentally evaluated the performance of the PAPO using our simulated environments and demonstrated that it could efficiently generate not optimal but acceptable paths for non-uniform environments.

We report the realization of ultrathin metallic metasurface pathways that can guide strongly confined spoof surface plasmon polaritons (SSPP's) at terahertz frequencies. The subwavelength metasurface path width enables a tight in-plane confinement of the SSPPs, which allows to route them along arbitrary signal paths without the loss of their field confinement perpendicular to the surface. By the use of a near-field imaging terahertz spectroscope, we were able to investigate propagating SSPP's on fabricated samples, which delivers new insights into the spatio-temporal and spectral properties of these guiding structures.

Examination of users&rsquo, preferences and needs can provide an additional and strong basis for decision making, which is applicable in the case of urban street renewal. In this study, a choice experiment on street renewal plans in Shanghai was conducted using an online survey (N = 546), and people&rsquo, s willingness to pay (WTP) for a set of street attributes was estimated, including bicycle lane separation, pedestrian path width, green looking ratio and recreational and commercial amenities. By comparing WTPs, the results show that people had greater preferences for adding resting facilities than any other attributes in this scene, and they also give some examples of prices of street attributes in a street renewal scene. The gender, age and occupation of participants had a significant effect on WTPs. Females showed greater WTP for setting separate bicycle lanes and improving greening and amenities, and the age of street users had a positive effect on WTP through the payment for street renewal. The reasoning section of the survey indicated the concern on the cost&ndash, benefit ratio, the need to renew and overall impression when choosing, and only a few participants were unwilling to pay anything for street improvement. This kind of economic valuation can estimate the values that people place on street attributes that are otherwise not measurable in design and planning practice, it can help us understand public preferences for street renewal and support decision making.

This paper deals with the current-carrying capacity of silver cermet thick-film conductors. Ten different patterns of thick-film conductors were created on the alumina substrate (96 % Al$_{2}O_{3}$). The electrical current load concerning the width of the conductive path was determined from the performed measurements. During the measuring process, the electrical current was rising by 0.1A per 10s increasing voltage and temperature. Conductive path widths from 0.20 - 0.65 in 0.05mm steps were tested. The terminals on the samples were connected by two methods, mechanical and solder joints. Results showed that the thick-film path was working up to 550°C, with the current load up to approximately 8.6A for mechanically connected terminals. Soldered terminals were loaded by up to 7.1A and its temperature increased to 350° C. Both results were measured for 0.65mm path width.

The 1984 Ivanovo tornado outbreak is one of the most fatal tornado events in Europe with previously unspecified tornado track characteristics. In this paper, we used Landsat images to discover tornado-induced forest disturbances and restore actual characteristics of tornadoes during the outbreak. We defined boundaries of tornado-induced windthrows by visual comparison of satellite images and specified them with Normalized Difference Infrared Index. We confirmed the occurrence of eight tornadoes during the outbreak and determined their location, path width and length. Other tornadoes occurrence during the outbreak was discussed. Fujita-scale intensity of confirmed tornadoes was estimated based on the related literature corpus including previously omitted sources. In addition, information on tornado path lengths and widths was used to estimate minimal tornado intensity for those tornadoes that passed no settlements. In total, the Ivanovo outbreak includes 8–13 tornadoes with F-scale rating mean ranges from 1.8–2.5 and has adjusted Fujita length around 540 km, which makes the outbreak one the strongest in Europe and places it within the upper quartile of U.S. outbreaks. Characteristics of certain tornadoes within the Ivanovo outbreak are exceptional for Russia. The widest tornado path during the Ivanovo outbreak is 1740 m; the longest is from 81.5–85.9 km. With the example of the Ivanovo outbreak, we showed that existing databases on historical Russian tornadoes tend to overestimate tornado path length (for very long tornadoes) and underestimate maximum tornado path width.

GEP was developed to predict of the emitter hydraulic performance qvar and CVm.The GEPwithout L model was better than GEPwithout S model for qvar.The GEPwithout S model was better than GEPwithout L model for CVm.The predicted non-pressure-compensating emitters qvar and CVm were more accurate.The GEP approach leads to high model predictability. The different hydraulic measures of emitter flow variation (qvar) and manufacturers coefficient of variation (CVm) at different operating pressure (P) and water temperature (T) were determined by measuring the discharge of different labyrinth-channel emitters. Gene expression programming (GEP) was used to model and predict qvar and CVm of the labyrinth emitters. The structural parameters of each labyrinth emitter [namely, trapezoidal unit number (N), height (H), and spacing (S), and path width (W) and length (L)] as well asP and T were considered as independent variables. The accuracy of GEP models was evaluated by their coefficient of determination (R2), root-mean-square error (RMSE), overall index of model performance (OI), and mean absolute error (MAE). Results of GEP applications established that L and S were the least important variables affecting qvar and CVm, respectively, while N and H were the most important variables. For qvar, the GEPwithout L model gave higher R2 and OI and lower RMSE and MAE than those of the GEPwithout S model. Conversely, for CVm, R2 and OI of the GEPwithout L model were lower and its RMSE and MAE were higher than the corresponding parameters of the GEPwithout S model. Overall, our results indicated that the performance of the developed GEP models were better at predicting qvar and CVm for non-pressure-compensating emitters than pressure-compensating ones. The GEP approach can be a good tool to predict the hydraulic performance of labyrinth emitters.

A crossed four-bar steering mechanism has been considered for a novel four-wheel vehicle which has different wheel locations compared to a conventional four-wheel vehicle. The present paper discusses the advantages of this newly proposed steering mechanism and the novel vehicle. The steering error curve of this novel vehicle has been compared with that of a conventional four-wheel vehicle having Ackermann steering. When both vehicles move on a curved road, the required angle of rotation of the vehicle wheels due to steering effort will be different and depend on the radius of curvature of the road from place to place. It has been found that the vehicle wheels of novel vehicle need to be rotated by smaller angle for steering. The steering error of the novel vehicle is far less. The swept path width will be reduced if the novel vehicle is used instead of the conventional vehicle.

Objective Modern Japanese children have decreased masticatory function, which can be explained by the dietary change to soft foods. In earlier studies involving children with mixed dentition, masticatory exercises were shown to improve masticatory function and modify dental arch growth. Grinding type of mastication with a wide path reportedly increases lateral growth of the dental arch. This study aimed to assess the relationship between masticatory movements and dietary preference, and how masticatory exercises affected masticatory movement during Hellman’s dental stages IIA to IIC (period of first molar eruption). Design In 64 Japanese pre-school children, we measured masticatory movements with foods of five different levels of hardness and investigated the dietary preference for hard foods through a questionnaire. Participants were also required to perform masticatory exercises. Masticatory movements and dietary preference for hard foods were assessed at the start (T1), conclusion (T2), and after six months of exercises (T3). Participants were allocated to Wide and Narrow groups at T1 based on their masticatory path width. Results Baguettes and bananas resulted in the widest and narrowest masticatory paths, respectively, at T1. Results of questionnaire indicated that those eating hard foods had a broad grinding type of masticatory path. Masticatory exercises significantly widened the masticatory path in the Narrow group demonstrating that masticatory exercises help children learn to chew with grinding strokes. Moreover, the masticatory path remained stable on assessment at T3 (six-month follow-up). Conclusions Masticatory exercises are effective in children who are unable to grind hard foods, affecting their dietary preferences.

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.

Bicycle usage is encouraged in many cities because of its health and environmental benefits. As a result, bicycle traffic increases which leads to questions on the requirements of bicycle infrastructure. Design guidelines are available but the scientific substantiation is limited. This research contributes to understanding bicycle traffic flow by studying the aggregated movements of cyclists before and after the onset of congestion within the setting of a controlled bottleneck flow experiment. The paper quantitatively describes the relation between capacity and path width, provides a qualitative explanation of this relation by analyzing the cyclist configuration for different path widths, and studies the existence of a capacity drop in bicycle flow. Using slanted cumulative curves and regression analysis, the capacity of a bicycle path is found to increase linearly with increasing path width. A steady drop in flow rate is observed after the onset of congestion, indicating that the capacity drop phenomenon is observed in bicycle traffic. The results presented in this paper can help city planners to create bicycle infrastructure that can handle high cyclist demand.

There have been many attempts to find directed graph classes with bounded directed path-width and bounded directed tree-width. Right now, the only known directed tree-width-/path-width-bounded graphs are cycle-free graphs with directed path-width and directed tree-width 0. In this paper, we introduce directed versions of cactus trees and pseudotrees and -forests and characterize them by at most three forbidden directed graph minors. Furthermore, we show that directed cactus trees and forests have a directed tree-width of at most 1 and directed pseudotrees and -forests even have a directed path-width of at most 1.

Understanding how infrastructures and urban environments shape the highly differentiated cycling experiences calls for further investigation. The current study addressed this challenge by employing Virtual reality (VR) applications. Quantitative methods were combined with a video simulation approach to model demand for cycling under different scenarios. VR environment mirroring the streetscape of a Dutch city was created. Environment greenness (green vs. no green), Bicycle path width (wide vs. narrow), Traffic volume (low vs. high) were manipulated. Participants had to cycle within the environments created, and thus having VR bike experience translating real world bike ride. VR experiences and cycling behaviour in response to the manipulated factors were measured.The results showed that participants enjoyed cycling most within green environment (than no green), and with wide (than narrow) bicycle lane. It was safer to cycle within wide bicycle path, and within low (than high) traffic volume. The environment was perceived as more aesthetic when cycling within green environment.Regression modelling further explored the relationship between the parameters hypothesised to influence the VR experiences. The better the naturalness and presence were perceived, the higher was the engagement. The higher the engagement was, the more the VR experience was liked.Current outcomes are unambiguous in showing that VR technology opens new avenues in addressing real-life problems with huge societal relevance, like improving urban environment infrastructure to unlock cycling and thus active transport.

We determine the relationship between the graph parameters neighbourhood-width and path-width of trees, that turn out equivalent. As our main combinatorial tool, we show that the neighbourhood-width of a tree T = ( V , E ) is at least k + 1 if for some vertex v ? V , forest T V - { v } has at least three non-edgeless components of neighbourhood-width at least k .

The aim of the work detailed in this article was to describe instances of tornadoes being reported in Europe and in Poland in the years 1998-2013. According to the relevant ESSWD reports (as confirmed and fully verified), 1772 tornadoes occurred in Europe, while 102 were reported for Poland. The largest number of reports concerned Germany, while numerous cases were also observed for the south-eastern part of the British Isles. These results are consistent with previous studies. Antonescu (2016) reports that most tornado reports in European relate to the continent’s northern and central parts. In Poland, it is possible to distinguish a characteristic belt of land along which tornadoes arise most commonly. This runs north-south from the western part of Podkarpacie, through the Silesian-Cracow Upland, the Malopolska Upland and the central part of the Central Polish Lowland, to the eastern part of the South Baltic Lake District. Lorenc (2012) takes a different position over this matter, stating that tornadoes in Poland occur most frequently from the Opole area through the Malopolska region, Central Poland, The Kutno Upland and the region extending from Mazowsze through to the Suwalki region. In the analysed period, tornado reports in Europe and Poland arose most frequently in the summer months (from May through to August). This is in line with the conclusions of Taszarek and Brooks (2015). In turn, Przybylak (2007) states that the period with most tornadoes starts in June and lasts through until August. In Europe, tornadoes are seen to form most often in the afternoon, as is the case in the USA. This common trait stems from the fact that convection only starts developing in the afternoon hours, when the ground is warm enough. This warms the near-ground layer of air and upward movements are initiated. There are exceptions to this rule – morning tornadoes, or even ones occurring at night (Przybylak, 2007; Lorenc, 2012). The average number of tornado reports in Europe amounts to 118 per year, a result in line with the assumptions of Wegener from the early 20th century. However, the present figure is well below the average of some 169 per year given by Dotzek (2003). Where force is concerned, it is weak and moderate tornadoes that dominate in Europe and in Poland, i.e. those of strengths F0, F1 and F2 (on the Fujita scale). A similar situation applies to the Torro scale, with the tornadoes observed most frequently being at the beginning of the scale, i.e. T0, T1 and T2. Poland and Europe experience tornadoes of strength T3 (in 11% of cases in Europe as whole, and 10% where Poland is concerned). In Europe there is a prevalence of tornadoes of path width not exceeding 100m, while the situates observed most frequently are ones in which tornadoes make their landfall and then trek south-west or west (in Poland mostly the south-west direction). Lowlands represent the form of topography most favourable to the occurrence of tornadoes.

A technique for determining the spatially distributed current densities of micro-and nanosystems, which is based on measuring the magnetic fields of currents with the use of a magnetic-force microscope and subsequent calculations of the spatial current-density distribution from inversion of the Biot–Savart–Laplace equation, is presented. The technique is tested using specially prepared structures of different shapes with a current-conducting path width of about 1 µm, namely a ring and a meander. Two-dimensional current flow is demonstrated to have features associated with the shape of the tested structures. In particular, it is found that components and the current amplitude are changed at points where the structure shape undergoes variations.

In this paper we consider the directed path-width and directed tree-width of directed co-graphs. As an important combinatorial tool, we show how the directed path-width and the directed tree-width can be computed for the disjoint union, series composition, and order composition of two directed graphs. These results imply the equality of directed path-width and directed tree-width for directed co-graphs and a linear-time solution for computing the directed path-width and directed tree-width of directed co-graphs, which generalizes the known results for undirected co-graphs of Bodlaender and Mohring.

Computing the directed path-width of a digraph is NP-hard even for digraphs of maximum semi-degree 3. In this paper we consider a family of graph classes called sequence digraphs, such that for each of these classes the directed path-width can be computed in polynomial time. For this purpose we define the graph classes \(S_{k,\ell }\) as the set of all digraphs \(G=(V,A)\) which can be defined by k sequences with at most \(\ell \) entries from V, such that \((u,v) \in A\) if and only if in one of the sequences u occurs before v. We characterize digraphs which can be defined by \(k=1\) sequence by four forbidden subdigraphs and also as a subclass of semicomplete digraphs. Given a decomposition of a digraph G into k sequences, we show an algorithm which computes the directed path-width of G in time Open image in new window , where N denotes the maximum sequence length. This leads to an XP-algorithm w.r.t. k for the directed path-width problem. As most known parameterized algorithms for directed path-width consider the standard parameter, our algorithm improves significantly the known results for a high amount of digraphs of large directed path-width.

Despite the limitations in the use of aerial applications resulting from Directive 2009/128/EC of the European Parliament and of the Council and the Plant Protection Agents Act (OJ L item 455. 2013), scientific progress in engineering enables the development of new, environmentally safe technologies to expand the use of agroaviation. This paper proposes an innovative method of biological protection of corn against Ostrinia nubilalis with the use of an autogyro and presents the results of these operations. An autogyro adaptation for forest applications is proposed, and the preliminary results of a spray uniformity assessment are presented. Based on a two-year study (542.5 ha), the introduction of the Tricholet preparation against Ostrinia nubilalis was found to be highly effective (73.55%), which is a positive indication for the innovative autogyro method for introducing Trichogramma evanescens. Similarly, positive results were obtained for a liquid agent application using an autogyro-mounted installation: an even coverage of the area was achieved across the entire spray path width while maintaining the required dosing of the plant protection agent.

To get a more comprehensive understanding of the amount of branching in computations of a nondeterministic finite automaton (NFA), we introduce and study the string path width and depth path width measures. For a given NFA, the string path width on a string [Formula: see text] counts the number of all complete computations on [Formula: see text], and the depth path width on an integer [Formula: see text] counts the number of complete computations on all strings of length [Formula: see text]. We give an algorithm to decide the finiteness of the depth path width of an NFA. Deciding finiteness of string path width can be reduced to the corresponding question on ambiguity. An NFA is nearly acyclic if any computation can pass through at most one cycle. The class of nearly acyclic NFAs consists of exactly all NFAs with finite depth path width. Using this characterization we show that the finite depth path width of an [Formula: see text]-state NFA over a [Formula: see text]-letter alphabet is at most [Formula: see text] and that this bound is tight. The nearly acyclic NFAs recognize exactly the class of constant density regular languages.

With the improvement of living conditions and booming tourism in Tibet, more and more people choose Tibet as a tourism destination. More emergency events may happen when lots of people swarm into Tibet. This paper focuses on the accessibility of road network near Jokhang Temple in Lhasa at a peak tourist season with different events coupling. Some data about path lane, path width and trips of road has been collected and accessibility of road near Jokhang Temple has been computed with two disparate events. The result shows different emergencies coupling may cause different consequences to road network. So highway management department can set up various strategies to speed up traffic flow based on the degree of events coupling and make relevant measurements.

The U.S. tornado record is subject to inhomogeneities that are due to inconsistent practices in counting tornadoes, assessing their damage, and measuring pathlength and path width. Efforts to improve the modern tornado record (1950–2012) have focused on the following: 1) the rationale for removing the years 1950–52, 2) identification of inconsistencies in F0, F1, and F2 counts based on implementation of the Fujita scale (F scale) and Doppler radar, 3) overestimation of backward-extrapolated F-scale intensity, and 4) a change in path-width reporting from mean width (1953–94) to maximum width (1995–2012). Unique adjustments to these inconsistencies are made by analyzing trends in tornado counts, comparing with previous studies, and making an upward adjustment of tornadoes classified by mean width to coincide with those classified by maximum width. Such refinements offer a more homogeneous tornado record and provide the opportunity to better evaluate climatological trends in significant (F/EF2–F/EF5) tornado activity. The median EF-scale (enhanced Fujita scale) wind speeds Vmed have been adopted for all significant tornadoes from 1953 to 2012, including an adjustment for overestimated intensities from 1953 to 1973. These values are used to calculate annual mean kinetic energy, which shows no apparent trend. The annual mean maximum path width from 1953 to 2012 (adjusted upward from 1953 to 1994 to obtain a common lower threshold), however, displays an increasing trend. Also, the EF-scale median wind speeds are highly correlated with . The quantity (Vmed × PWmax)2 is proposed as a tornado destruction index, and, when calculated as an annual cumulative value, the three largest years are 2007, 2008, and 2011.

The paper focuses on the presentation of a single-track dynamic model of articulated bus, a simplified linear model, which is based on reducing the double-track dynamic model with suitable assumptions that the front body lateral accelerations and rotational angles of the articulated bus are small. On the other hand, the phenomena of friction and interstice, such as articulated system (fifth wheel), are neglected. A coordinate system is defined to precisely describe the translational and rotational motions of the vehicle. In details, the author provides the dynamics model, sets up the kinematics and dynamic relations and builds differential equations of kinematic parameters presenting the articulated bus motions. These are objective functions, which are necessary to determine the gravity centre trajectory of the articulated bus, movement of the joint system and bodies of vehicle in addition to the swept path width of articulated bus. Matlab-Simulink is used to solve mathematical problems and simulate responding dynamics of vehicle. The modelling results are the functions of kinematic and dynamic parameters that allow to determine the motional trajectory and the swept path width of articulated bus, joint system and bodies of vehicle. These suitable results represent the fundaments for exact evaluation of the dynamic model and investigation of dynamics of articulated bus at a higher and more complex level.

The original notion of dimension for posets is due to Dushnik and Miller and has been studied extensively in the literature. Quite recently, there has been considerable interest in two variations of dimension known as Boolean dimension and local dimension. For a poset $P$, the Boolean dimension of $P$ and the local dimension of $P$ are both bounded from above by the dimension of $P$ and can be considerably less. Our primary goal will be to study analogies and contrasts among these three parameters. As one example, it is known that the dimension of a poset is bounded as a function of its height and the tree-width of its cover graph. The Boolean dimension of a poset is bounded in terms of the tree-width of its cover graph, independent of its height. We show that the local dimension of a poset cannot be bounded in terms of the tree-width of its cover graph, independent of height. We also prove that the local dimension of a poset is bounded in terms of the path-width of its cover graph. In several of our results, Ramsey theoretic methods will be applied., Comment: 30 pages, 4 figures

Tree-width and path-width are two important graph parameters introduced by Robertson and Seymour in their famous Graph Minors project. For a fixed positive integer $k$, the classes of graphs of tree-width at most $k$, and path-width at most $k$, are both minor-closed. However, their complete characterizations in terms of excluded minors are known only for $k \leqslant 3$ for tree-width, and for $k \leqslant 2$ for path-width. It is known that the number of excluded minors for the class of graphs of path-width $\leqslant k$ is 2 if $k = 1$; $110$ if $k = 2$; and $\geqslant 122$ million if $k = 3$. Barat et. al. [Studia Sci. Math. Hungar., 49 (2012), pp. 211--222] showed that the class of graphs of path-width $\leqslant 2$, restricted to its 2-connected members, can be characterized by only three excluded minors, and asked whether a similar result may be obtained for 3-connected graphs of path-width $\leqslant 3$. We answer this question in the affirmative by characterizing this class by five excluded minors.

Path-width of matroids naturally generalizes the better known parameter of path-width for graphs, and is NP-hard by a reduction from the graph case. While the term matroid path-width was formally introduced by Geelen-Gerards-Whittle [JCTB 2006] in pure matroid theory, it was soon recognized by Kashyap [SIDMA 2008] that it is the same concept as long-studied so called trellis complexity in coding theory, later named trellis-width, and hence it is an interesting notion also from the algorithmic perspective. It follows from a result of Hlineny [JCTB 2006] that the decision problem, whether a given matroid over a finite field has path-width at most t, is fixed-parameter tractable (FPT) in t, but this result does not give any clue about constructing a path-decomposition. The first constructive and rather complicated FPT algorithm for path-width of matroids over a finite field was given by Jeong-Kim-Oum [SODA 2016]. Here we propose a simpler "self-reduction" FPT algorithm for a path-decomposition. Precisely, we design an efficient routine that constructs an optimal path-decomposition of a matroid by calling any subroutine for testing whether the path-width of a matroid is at most t (such as the aforementioned decision algorithm for matroid path-width).

The steering law is an excellent performance model for trajectory-based tasks, such as drawing and writing in GUIs. Current studies on steering tasks focus on the effect of system factors (i.e. path width and amplitude) on the movement time and steering law's related applications. We conducted a series of experiments to further explore the effect of different operational biases (bias speed or accuracy) on steering completion time and standard deviation for two steering trajectory shapes, i.e. a straight steering task and a circular steering task, and then establish a new model accommodating system and subjective factor in steering tasks. Empirical results showed that the new model is more predictive and robust than the traditional steering law.

For the method of characteristic (MOC), a system with large-gradient neutron flux caused by a strong absorber or neutron leakage is reported to entail large errors in spatial mesh discretization and require very fine mesh spacing. To apply the MOC to such fine models, the ray-trace path width has to be fine in order to make many paths cross each region. Our new method intends to obtain good accuracy with a coarse path width. With a coarse path width on the MOC, some tiny regions have less ray-tracing paths. The reliability of flux calculation for the regions can be evaluated with the calculation volumes that are estimated in ray tracing. If the discrepancy between the calculation and true volumes becomes large, the accuracy cannot be expected. In this study, the discrepancies were numerically evaluated, and it is found that the discrepancies occur on a very tiny region. To make the flux calculation of such tiny regions more reliable, an approximation, in which the outgoing flux is equal to the incoming ne...

A 3-connected matroid M is sequential or has path width 3 if its ground set E(M) has a sequential ordering, that is, an ordering (e"1,e"2,...,e"n) such that ({e"1,e"2,...,e"k},{e"k"+"1,e"k"+"2,...,e"n}) is a 3-separation for all k in {3,4,...,n-3}. In this paper, we consider the possible sequential orderings that such a matroid can have. In particular, we prove that M essentially has two fixed ends, each of which is a maximal segment, a maximal cosegment, or a maximal fan. We also identify the possible structures in M that account for different sequential orderings of E(M). These results rely on an earlier paper of the authors that describes the structure of equivalent non-sequential 3-separations in a 3-connected matroid. Those results are extended here to describe the structure of equivalent sequential 3-separations.

Let $\mathcal{N}$ be a set of matroids. A matroid $M$ is strictly $\mathcal{N}$-fragile if $M$ has a member of $\mathcal{N}$ as minor and, for all $e \in E(M)$, at least one of $M\backslash e$ and $M/e$ has no minor in $\mathcal{N}$. In this paper we give a structural description of the strictly $\{U_{2,5},U_{3,5}\}$-fragile matroids that have six inequivalent representations over $\mathrm{GF}(5)$. Roughly speaking, these matroids fall into two classes. The matroids without an $\{X_8, Y_8, Y_8^{*}\}$-minor are constructed, up to duality, from one of two matroids by gluing wheels onto specified triangles. On the other hand, those matroids with an $\{X_8, Y_8, Y_8^{*}\}$-minor can be constructed from a matroid in $\{X_8, Y_8, Y_8^{*}\}$ by repeated application of elementary operations, and are shown to have path width 3. The characterization presented here will be crucial in finding the explicit list of excluded minors for two classes of matroids: the Hydra-5-representable matroids and the 2-regular matroids., 33 pages

A novel on-chip transformer architecture using multipath technique is presented. The newly proposed arithmetic-progression step sub-path width method is used to lower the current-crowding effect induced by the difference between the length of inner sub-path and that of outer sub-path. Full-wave electromagnetic simulated and measured results confirm the better performance of the proposed transformers than the conventional ones. These transformers will be useful in designing high-performance CMOS RF integrated circuits for wireless applications.

Directed path-width was defined by Reed, Thomas and Seymour around 1995. The author and P. Hajnal defined a cops-and-robber game on digraphs in 2000. We prove that the two notions are closely related and for any digraph D, the corresponding graph parameters differ by at most one. The result is achieved using the mixed-search technique developed by Bienstock and Seymour. A search is called monotone, in which the robber's territory never increases. We show that there is a mixed-search of D with k cops if and only if there is a monotone mixed-search with k cops. For our cops-and-robber game we get a slightly weaker result: the monotonicity can be guaranteed by using at most one extra cop.

The corrective reaction time (tcr) is an essential motor property when modelling hand control movements. Many studies designed experiments to estimate tcr, but reported only group means with inconsistent definitions. This study proposes an alternative methodology using Drury's (1994) intermittent illumination model. A total of 24 participants performed circular tracking movements under five levels of visual information delay using a modified monitor in a darkened room. Measured movement speeds and the manipulated delays were used with the model to estimate tcr of individuals and test effects of gender and path width. The results showed excellent model fits and demonstrated individual differences of tcr, which was 273 ms on average and ranged from 87 to 441 ms. The wide range of tcr values was due to significant effects of gender and path width. Male participants required shorter tcr compared to female participants, especially for narrow path widths.This study reports the corrective reaction time (tcr) of individuals using a novel methodology. The estimated tcr ranged from 87 to 441 ms, helping model hand control movements, such as aiming and tracking. The methodology can be continuously applied to study tcr under conditions with various performers and movements.

The number of excluded minors for the class of graphs with path-width at most two is very large. To give a practical characterization of the obstructions, we introduce some operations which preserve path-width at most two. We give a list of ten graphs such that any graph with path-width more than two can be reduced – by taking minors and applying our operations – to one of the graphs on our list. We think that our operations and excluded substructures give a far more transparent description of the class of graphs with path-width at most two than Kinnersley and Langston's characterization by 110 excluded minors (see [4]).

De novo sequencing is an important computational approach to determining the amino acid sequence of a peptide with tandem mass spectrometry (MS/MS). Most of the existing approaches use a graph model to describe a spectrum and the sequencing is performed by computing the longest antisymmetric path in the graph. The task is often computationally intensive since a given MS/MS spectrum often contains noisy data, missing mass peaks, or post translational modifications/mutations. This paper develops a new parameterized algorithm that can efficiently compute the longest antisymmetric partial path in an extended spectrum graph that is of bounded path width. Our testing results show that this algorithm can efficiently process experimental spectra and provide sequencing results of high accuracy.

Manipulation of features in virtual environments (VE) is known to affect behavior in the real world. We developed a virtual reality augmented cycling system and sought to determine if manipulation VE parameters modified cycling rate. We tested three groups of subjects young adults (n = 4) older adults (n = 6) and individuals post-stroke (n = 5) as they cycled in a virtual park environment while we modified optic flow, path width and path difficulty. There were no between group differences, however, groups differed when making within group comparisons. Manipulation of VE parameters differentially affected cycling behaviors of young, older and people post-stroke.

Although cycling is a widespread form of transportation, little is known about the visual behaviour of bicycle users. This study examined whether the visual behaviour of cyclists can be explained by the two-level model of steering described for car driving, and how it is influenced by cycling speed and lane width. In addition, this study investigated whether travel fixations, described during walking, can also be found during a cycling task. Twelve adult participants were asked to cycle three 15 m long cycling lanes of 10, 25 and 40 cm wide at three different self-selected speeds (i.e., slow, preferred and fast). Participants’ gaze behaviour was recorded at 50 Hz using a head mounted eye tracker and the resulting scene video with overlay gaze cursor was analysed frame by frame. Four types of fixations were distinguished: (1) travel fixations, (2) fixations inside the cycling lane (path), (3) fixations to the final metre of the lane (goal), and (4) fixations outside of the cycling lane (external). Participantswere found to mainly watch the path (41%) and goal (40%) region while very few travel fixations were made (

A pointing device plays an important role in human-computer interaction. The computer mouse is a convenient device for both pointing and steering. The literature related to the effect of mouse gain on steering tasks is scarce. An experiment was conducted with 10 participants and each participant was asked to traverse a constrained path using a computer mouse. There were three levels of gain approximately equal to 2.3, 10, and 15. The experiment had 11 levels of difficulty (D/P) based on path width (P) and path length (D) and three trials for each combination of D and P. Performance was evaluated using movement time taken to traverse the path. The results showed that movement time is minimized, in feedback-controlled steering tasks, at a gain of around nine.

Steering law describes human motor behaviour based on trajectory tasks, such as drawing and writing. Current studies on steering tasks focus on effect of system factors (i.e., path width and amplitude) on the movement time and its related applications. We attempted to conduct a series of experiments to further explore the effect of different operational biases (bias speed or accuracy) on steering completion time and standard deviation for two steering shapes, i.e., a straight steering task and a circular steering task, and then verified that the steering law did not hold when the operational biases were introduced.

Footpath degradation is assessed by comparison of surveys carried out in 1983 and 1992 along the principal cross mountain path - the Brandy Pad. Measurements show that overall path width has generally increased, as have the number of subsidiary tracks and the extent of bare ground. Greatest changes occurred where path width was initially narrow, suggesting that there are maximum widths (wiihin the constraints exercised by local terrain) beyond which walkers will no longer seek detours by establishing new paths.

Let tw( G ), pw( G ), c ( G ), Δ( G ) denote, respectively, the tree-width, path-width, cutwidth and the maximum degree of a graph G on n vertices. It is known that c ( G ≥tw( G ). We prove that c ( G )=O(tw( G )· Δ ( G )·log n ), and if ({ X i : i ∈ I }, T =( I , A )) is a tree decomposition of G with tree-width≤ k then c ( G )≤( k +1)· Δ ( G )· c ( T ). In case that a tree decomposition is given, or that the tree-width is bounded by a constant, efficient algorithms for finding a numbering with cutwidth within the upper bounds are implicit in the proofs. We obtain the above results by showing that pw( G )=O(log n ·tw( G )), and pw( G )≤( k +1)· c ( T ).