Function Of Segment Length Research Articles

On the number of tiles visited by a line segment on a rectangular grid

AbstractConsider a line segment placed on a two‐dimensional grid of rectangular tiles. This paper addresses the relationship between the length of the segment and the number of tiles it visits (i.e., has intersection with). The square grid is also considered explicitly, as some of the specific problems studied are more tractable in that particular case. The segment position and orientation can be modeled as either deterministic or random. In the deterministic setting, the maximum possible number of visited tiles is characterized for a given length, and conversely, the infimum segment length needed to visit a desired number of tiles is analyzed. In the random setting, the average number of visited tiles and the probability of visiting the maximum number of tiles on a square grid are studied as a function of segment length. These questions are related to Buffon's needle problem and its extension by Laplace.

Effect of segment length, sampling frequency, and imaging modality on the estimation of measures of brain meta-state activation: an MEG/EEG study.

The main objective of this study was to examine the influence that recording length, sampling frequency, and imaging modality have on the estimation and characterization of spontaneous brain meta-states during rest. To this end, a recently developed method of meta-state extraction and characterization was applied to a subset of 16 healthy elderly subjects from two independent electroencephalographic and magnetoencephalographic (EEG/MEG) databases. The recordings were segmented into the first 5, 10, 15, 20, 25, 30, 60 and 90-s of artifact-free activity and meta-states were extracted. Temporal activation sequence (TAS) complexity, which characterizes the complexity of the metastateactivation sequences during rest, was calculated. Then, its stability as a function of segment length, sampling frequency, and imaging modality was assessed. The results showed that, in general, the minimum segment length needed to fully characterize resting-state meta-state activation complexity ranged from 15 to 25 seconds. Moreover, it was found that the sampling frequency has a slight influence on the complexity measure, and that results were similar across EEG and MEG. The findings indicate that the proposed methodology can be applied to both EEG and MEG recordings and displays stable behavior with relatively short segments. However, methodological choices, such as sampling frequency, should be carefully considered.

Robust calculation of slopes in detrended fluctuation analysis and its application to envelopes of human alpha rhythms

Detrended fluctuation analysis (DFA) is a popular method to analyze long-range temporal correlations in time series of many different research areas but in particular also for electrophysiological recordings. Using the classical DFA method, the cumulative sum of data are divided into segments, and the variance of these sums is studied as a function of segment length after linearly detrending them in each segment. The starting point of the proposed new method is the observation that the classical method is inherently non-stationary without justification by a corresponding non-stationarity of the data. This leads to unstable estimates of fluctuations to the extent that it is impossible to estimate slopes of the fluctuations other than by fitting a line over a wide range of temporal scales. We here use a modification of the classical method by formulating the detrending as a strictly stationary operation. With this modification the detrended fluctuations can be expressed as a weighted average across the power spectrum of a signal. Most importantly, we can also express the slopes, calculated as analytic derivatives of the fluctuations with respect to the scales, as statistically robust weighted averages across the power spectra. The method is applied to amplitudes of brain oscillations measured with magnetoencephalography in resting state condition. We found for envelopes of the the alpha rhythm that fluctuations as a function of time scales in a double-logarithmic plot differ substantially from a linear relation for time scales below 10 seconds. In particular we will show that model selections fail to determine accurate scaling laws, and that standard parameter settings are likely to yield results depending on signal to noise ratios than on true long range temporal correlations.

Optimal design of the transversely vibrating Euler–Bernoulli beams segmented in the longitudinal direction

In this study, optimal design of the transversely vibrating Euler–Bernoulli beams segmented in the longitudinal direction is explored. Mathematical formulation of the beams in bending vibration is obtained using transfer matrix method, which is later coupled with an eigenvalue routine using the “fmincon solver” provided in Matlab Optimization Toolbox. Characteristic equations, namely frequency equations, for determining natural frequencies of the segmented beams for all end conditions are obtained and for each case, square of this equation is selected as a fitness function together with constraints. Due to the explicitly unavailable objective functions for the natural frequencies as a function of segment length and volume fraction of the materials, especially for the beams made of a large number of segments, initially, prescribed value is assumed for the natural frequency and then the variables minimizing objective function and satisfying the constraints are searched. Clamped–free, clamped–clamped, clamped–pinned and pinned–pinned boundary conditions are considered. Among the end conditions, maximum increment in the fundamental natural frequency is more pronounced for the case of clamped–clamped end condition and for this case, maximum increment up to 17.3274% is attained. Finally, the beam configurations maximizing fundamental natural frequencies will be presented.

Critical buckling load optimization of the axially graded layered uniform columns

This study presents critical buckling load optimization of the axially graded layered uniform columns. In the first place, characteristic equations for the critical buckling loads for all boundary conditions are obtained using the transfer matrix method. Then, for each case, square of this equation is taken as a fitness function together with constraints. Due to explicitly unavailable objective function for the critical buckling loads as a function of segment length and volume fraction of the materials, especially for the column structures with higher segment numbers, initially, prescribed value is assumed for it and then the design variables satisfying constraints are searched using Differential Evolution (DE) optimization method coupled with eigen-value routine. For constraint handling, Exterior Penalty Function formulation is adapted to the optimization cycle. Different boundary conditions are considered. The results reveal that maximum increments in the critical buckling loads are attained about 20% for cantilevered and pinned-pinned end conditions and 18% for clamped-clamped case. Finally, the strongest column structure configurations will be determined. The scientific and statistical results confirmed efficiency, reliability and robustness of the Differential Evolution optimization method and it can be used in the similar problems which especially include transcendental functions.

Methodology to Compute Travel Time of a Roundabout Corridor

Urban and suburban arterials with roundabouts in series are becoming more prevalent in North America. While the Highway Capacity Manual (HCM) provides a methodology for computing segment travel time of urban streets with various forms of intersection control, the manual does not provide a similar procedure for corridors with interdependent roundabouts. Such a methodology is necessary to evaluate performance of roundabout corridors and will allow the practitioner to compare both roundabout and signalized treatments for the same series of intersections. This paper presents a series of models intended to predict arterial travel time for a corridor with roundabouts, including a model for free-flow speed (FFS), a model to predict the length of the roundabout influence area (RIA, the area where geometric delay has incurred), a model for geometric delay, and models for impeded delay and average travel speed. These models were calibrated with data from seven roundabout corridors. The resulting models suggest that while FFS is a function of segment length, posted speed limit, and central island diameter, RIA length and geometric delay are functions of the FFS itself, as well as other geometric elements. The impeded delay and average travel speed are functions of traffic congestion and FFS. After validating the models with travel time data from two additional roundabout corridors not used in model development, the authors present a framework for incorporating the procedure for travel time prediction into the HCM analysis of urban streets.

Shape recognition: convexities, concavities and things in between

Previous studies on shape recognition have drawn different conclusions regarding the importance of specific object features, such as convexities, concavities and intermediate points. Some studies found evidence for a predominant role of convexities, whereas others favored concavities or intermediate parts. However, most studies have employed familiar objects or simple geometric shapes not necessarily containing curves (polygons) as their stimuli. Here we present a novel set of shapes with well-defined convexities, concavities and points between convexities and concavities. The shapes were composed of the sum of three different radial frequency (RF) components with random phases, segmented to remove all but variable lengths of contour centred on the feature of interest. Observers were required to match the segmented test shape to one of two subsequently presented whole-contour re-scaled test shapes. Observers were never presented with the same shape twice. Results show that for short (dot-sized) segment lengths, performance was significantly higher for convexities than for either concavities or intermediate points. For the convexities, performance remained constant as a function of segment length, and although performance improved with segment length for concavities and intermediate points, it only reached convexity performance at the largest lengths tested. No significant differences between concavities and intermediates were found. We present a model by which positions of convexities are extracted and connected to form shape primitives (polygons) that are matched to the test shapes. These results indicate that these closed shapes are encoded from the positions of convexities, rather than from the positions of either concavities or intermediates. Meeting abstract presented at VSS 2015

Eye movement and online bisection task in unilateral patients with neglect: A new look to the ‘gradient effect’

Primary objective: The present study explored the behavioural and eye-movement measures in spatial unilateral neglect in response to a bisection task.Research design: Four right neglect patients were considered and compared with 11 control subjects during an online task (segment bisection).Methods and procedures: Eye-movements (fixation count and duration) and behavioural responses were monitored during an online bisection task, consisting of unfilled segments (two ending points) to be bisected by subjects. Segment length (six levels) and spatial dislocation (five levels) were modulated to explore a possible ‘gradient effect’” (left-to-right) in neglect bias.Main outcomes and results: Consistent spatial biases were found for both bisection position and eye fixations as a function of segment length (from shorter to longer) and segment spatial dislocation (from right to left). However, only the more eccentric left-positions induced a greater rightward bias in patients, with increasing more right-side bisection and visual right-directed fixations. Also segment length produced significant differences between-groups for behavioural responses, with more right-side bisection for longer segment in patients, and eye movement behaviour, with increased fixation count and duration rightward oriented in response to longer segments.Conclusions: Although a left-to-right and longer-to-shorter ‘continuous-gradient effect’ was not supported by the results, an ‘extreme left-gradient effect’ was suggested and discussed.

Nickel segment-length dependent magnetic properties of Au–Ni–Au nanowires at low temperature fabricated by electrochemical deposition

Segmented wires (Au–Ni–Au) were synthesized by electrochemical deposition. Magnetic study was performed at 6kOe field applied parallel to the wire long axis at 300K and 2K. Coercivity (Hc) and saturation magnetization (Ms) as a function of segment length (l) were constant for longer l (5≤l≤10μm) at 300K and 2K. However, a peak in Hc was observed for l=2.4μm at 300K, whereas a decrease in Hc was found for shorter l. Ms followed a decreasing trend with decreasing segment length from 2.4μm to 200nm.

Band structure of segmented semiconductor nanowires

We have calculated the band structures for strained segmented nanowires involving all combinations of AlN, GaN, InN, AlP, GaP, AlAs, GaAs, InP, InAs, AlSb, GaSb, and InSb, as a function of segment length. This was done for two different growth directions of the wires, [100] and [111]. Both the Gamma and the X conduction-band minima were included in the calculations as well as the valence bands. Short segments behave like strained quantum wells and our results thus include strained quantum wells as a subset. We find all material combinations that give metallic segments due to a negative band gap and we find all the band alignments that may occur. We identify those structures which show spontaneous charge separation as well as those which are suitable for the optical generation of polarized exciton gases, with their rich phase diagram, theoretically predicted to include superfluids and supersolids. Some device related ideas are presented. Due to the amount of data (several hundreds of diagrams) most of our results are presented as a webpage. (Less)

Analyzing Different Parameterizations of the Varying Dispersion Parameter as a Function of Segment Length

Until a few years ago, the dispersion parameter of Poisson–gamma models had been assumed to be invariant of the characteristics of the observations under study, but recent research in highway safety has shown that the dispersion parameter can depend on the covariates of the model. To account for this dependence, some researchers have reported that the dispersion parameter should be modeled solely as a function of segment length. The primary objective of this research was to examine empirically whether the dispersion parameter should be characterized using only the length of the segment. If not, the secondary objective consisted of determining alternative parameterizations using other covariates that would offer a better approach for characterizing the variance function of Poisson–gamma models. To accomplish the study objectives, 10 parameterizations describing the varying dispersion parameter were estimated with three different data sets collected in Texas, California, and Washington State. Flow-only models were used for comparing the parameterizations. The Akaike information criterion and other related goodness-of-fit (GOF) measures were used for evaluating and comparing the different models. The results of this study show that no single functional form or parameterization is suitable for all the data sets. Traffic flow was more significantly associated with the structured variation observed in the data than segment length. It is therefore recommended that transportation safety analysts evaluate different parameterizations and select the most appropriate one using a combination of GOF criteria, including the significance of the model's coefficients.

The electronic structure of a Bi/Sb superlattice nanowire

AbstractThe electronic structure of a Bi/Sb superlattice nanowire have been investigated using a theoretical model, in which the nanowire is assumed to possess a circular cross section with a uniform diameter. The variation of the electronic structure as a function of segment length and the total density of states for a Bi/Sb superlattice nanowire with a certain diameter of 5 nm are presented. The minigaps in the total density of states may lead to change in sign of the thermopower for certain energy ranges as the Fermi energy varies, which indicates that the superlattice nanowire can demonstrate n ‐ or p ‐type behavior by using the same dopants. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Sensitivity of the proton and ion transport mechanisms of corn roots to injury

Cutting solution-grown corn ( Zea mays L.) roots into segments causes a rapid reduction in K + ( 86Rb) influx, 36Cl − influx, and net H + efflux. The reduction in K + influx is a function of segment length; other injuries, such as a brief exposure to ice temperatures or low pH, will also reduce K + influx. Washing the segments in dilute, aerated CaCl 2 solutions produces recovery of the fluxes. In contrast, cutting does not reduce phosphate ( 32P) influx, although after a lag period there is a small enhancement of influx of the type previously reported. Estimations of actual H + efflux (net H + efflux plus anion influx) show that H + efflux recovers more rapidly than K + influx. It is proposed that injuries signal a partial collapse of an electrogenic H +/K +-ATPase of the plasmalemma, and washing restores it.

A Preliminary Examination of End Effects in Polyelectrolyte Theory: The Potential of a Line Segment of Charge

The potential, ICT, of a line segment of charge is calculated in the Debye-Huckel approximation. We determine ICT as a function of segment length and the position of the test charge. If the test charge is near the line segment and the length of the line segment of charge is large relative to the screening length, qT is well approximated by the electrostatic potential of an infinite line of charge. When the test charge is far from the line segment, qT reduces to the point charge limit. Recently, considerable attention has been devoted to elucidating the properties of the line of charge model of polyelectrolyte The infinitely long line of charge model has been employed to calculate the colligative properties of dilute polyelectrolyte the diffu- sion constant of a mobile ion in the presence of a polye- lectr~lyte,~,~ and the expansion parameter, 2, of the ex- cluded volume theory.6 We note, however, that real po- lyions are of finite size; as such, it would be quite useful to determine the magnitude of end effects on the elec- trostatic potential arising from a finite line of charge. Hence, a partial motivation of the present work is to de- termine when the replacement of the potential of the line segment of charge by that of an infinite line is justified and when it is not. We also note that the line segment of charge may perhaps be a plausible model for low molecular weight DNA and helical poly(g1utamic acid) at low to moderate ionic strengths. Thus, this paper is a preliminary step toward understanding the dependence of polyelec- trolyte behavior on chain length. If the length of the line segment of charge is large rel- ative to the screening length and if the test charge is near the source, it seems intuitively reasonable that the elec- trostatic potential should be well approximated by the infinite line of charge result. However, when the test charge is far from the line segment of charge, the line segment should appear as a point charge. In the context of the Debye-Huckel approximation, verification of the above conjectures will be presented in what follows. Consider a uniformly charged line segment of length L immersed in bulk solvent. It is assumed that each infin- itesmal piece interacts with the test charge via a screened Coulomb potential. For discussions concerning the ap- plicability of an effective charge density and counterion condensation, we refer to the literat~re.'-~,~ -~ Let the line segment of charge lie on the z axis, in the cylindrical coordinate system (r,O,z), and let one end of the line segment be located at z = 0. Whereupon, the poten- tial, #T, felt at a point r = (r,B,z) by a test charge is given by @ L exp(-K(r2 + (z - z')~)~/~)