Improving Accuracy and Precision in Estimating Fractal Dimension of Animal movement paths

It is difficult to watch wild animals while they move, so often biologists analyse characteristics of animal movement paths. One common path characteristic used is tortuousity, measured using the fractal dimension (D). The typical method for estimating fractal D, the divider method, is biased and imprecise. The bias occurs because the path length is truncated. I present a method for minimising the truncation error. The imprecision occurs because sometimes the divider steps land inside the bends of curves, and sometimes they miss the curves. I present three methods for minimising this variation and test the methods with simulated correlated random walks. The traditional divider method significantly overestimates fractal D when paths are short and the range of spatial scales is narrow. The best method to overcome these problems consists of walking the dividers forwards and backwards along the path, and then estimating the path length remaining at the end of the last divider step.     

青藏高原不同草地利用方式对土壤粒径分形特征的影响

研究青藏高原草地土壤粒径结构分形特征,为该地区土壤质量评价和生态恢复提供科学依据。以青藏高原4种高寒草地(放牧、围栏禁牧、围栏禁牧+补植、未干扰)为对象,采用分形理论,研究不同利用方式对高寒草地土壤颗粒组成及分形特征的影响,明确土壤粒径分形特征的影响因素。结果表明：与放牧和围栏禁牧+补植相比,围栏禁牧草地中黏粒和粉粒体积分数分别增加了60%—91.1%、43.5%—80.1%,禁牧能够促进土壤砂粒向黏粒和粉粒转变。不同草地利用方式对分形维数有显著影响,单重分形维数D值依次为放牧草地<围栏禁牧+补植草地<未干扰草地=围栏禁牧草地,多重分形维数,包括信息维数D₁、信息维数/容量维数比值D₁/D₀和关联维数D₂依次为放牧草地<围栏禁牧+补植草地<围栏禁牧草地<未干扰草地。单重分形维数D与土壤黏粒、粉粒呈极显著正相关(P<0.01);砂粒、黏粒、粉粒、有机碳和全氮是多重分形维数的限制因素。信息维数D₁、信息维数/容量维数比值D₁...     

Length–weight relationship and condition factor of wild,grow‐out and ‘loose‐shell affected’ giant tiger shrimp,Penaeus monodon (Fabricius, 1798) (Decapoda: Penaeidae)

Length–weight relationships and condition factors of wild, cultured, and cultured loose‐shell affected Penaeus monodon (2,609 specimens total) were studied from March to August 2007. The regression equation for healthy cultured shrimps was log W = ?1.811 + 2.721 log L (r² = 0.71); log W = ?1.444 + 2.485 log L (r² = 0.91) for wild shrimps; and log W = ?1.112 + 2.237 log L (r² = 0.92) for loose‐shell affected shrimps. All shrimps showed negative allometric growth, although ancova indicated significant differences (P < 0.05) among them. This study presents the first known reference dealing with LWRs and condition factors of cultured, wild and loose‐shell affected P. monodon.     

Planning tendon paths using an interactive graphic workstation

This study provides a technique to be used for planning tendon paths in thumb reconstruction surgery. All mathematical modeling computations are performed on a VAX 11/750 host computer and the graphic manipulation is carried out by the Evans & Sutherland PS390 color display system. The results of the simulation are stored in a log file, including the rotation angles of the joints and the location of the pulley and the insertion points as a record of the tendon transfer design for a specific hand. The methods are based on the modeling of two separate types of tendon paths that consist of straight line segments and curved segments that follow bone contours. The method further assumes that the path of the tendon will always evolve to a planar curve. By integrating this technique with an existing kinematic model of the hand derived from CT-scans, a clinically relevant method has been developed.     

Scaling distributional patterns of butterflies across multiple scales: Impact of range history and habitat type

Aim

Assessing the threat status of declining but yet widespread species poses a challenge to applied ecologists. Previous studies using a common metric to describe the spatial aggregation of occurrences across multiple scales, the fractal dimension D_ij, have suggested that species’ distributional trends may be deduced from readily understandable spatial patterns: Expanding species are expected to show more aggregated spatial distributions (higher value of D_ij) than declining species (lower value of D_ij). Here, we revisited these predictions using a large‐scale empirical dataset on Finnish butterflies.

Location

Finland.

Methods

For each butterfly species (n = 97) and across three spatial scales (grid squares of 10 km, 50 km and 100 km), we calculated the area of occupancy (AOO_i) as the sum of occupied grid squares. We employed values of AOO_i to derive the D_ij for each butterfly species. We then used these metrics to compare the changes in spatial patterns of distribution (?AOO_i and ?D_ij) between two time periods, 2000–2002 and 2009–2011.

Results

Majority of the studied butterfly species showed declining areas of occupancy (at the scale of 10 km, ?AOO₁₀) and fractal dimensions (across the scales from 10 km to 100 km, ?D_10–100) between the two study periods. In contrast to predictions, AOO₁₀ and D_10–100 showed negative impacts on the ?AOO₁₀, an observation that may be explained by the high proportion of declining species in our data. Butterfly species with the greatest fractal dimensions at regional scales (D_10–100) in the years 2000–2002 showed both positive long‐term distributional trends and most notable northern recent range limit shifts.

Main conclusions

Our results were in most cases congruent with the prediction of higher fractal dimension values in expanding compared to declining species. As a novel observation, many butterflies expanded northwards in spite of their occurrences getting simultaneously more scattered, particularly in southern Finland.

     

Strangers in the dark: behavioral and biochemical evidence for trail pheromones in Hawaiian tree snails

The importance of pheromones in insect and mammal social systems is well documented, but few studies have addressed the role of pheromones in land snail behavior. In this investigation, we used a series of behavioral trials and direct analysis in real time mass spectrometry (MS) to test the hypothesis that land snails use mucous trails in orientation and chemical communication. We worked with six endemic Hawaiian land snail species in four genera, three subfamilies, and two families. We tested conspecific trail following in five of these species, and trail following occurred at a statistically significant frequency for each of the species tested (n=181, p‐values ranged <0.0001–0.0494). Percentage of conspecific trials that showed trail following ranged 66.7–94.1%. None of the interspecific tests revealed evidence of trail following among species (n=105, with p‐values of 0.0577–0.5000). Juvenile achatinelline snails did not follow trails of conspecific juveniles (n=30, p=0.5722) or adults (n=30, p=0.4278), nor did adults follow juvenile trails (n=30, p=0.5722). Comparative MS analysis of adult and juvenile trails showed distinct chemical signatures in the two groups. Signals corresponding to medium‐ and long‐chain fatty acids and other unidentified small molecules were present in adult but not in juvenile trails. Considered together, these results support the hypotheses that trail following could serve an important social and reproductive function. This discovery provides evidence for the presence of an ephemeral tree snail pheromone, which could have important implications for the conservation of these increasingly rare and threatened species.     

Molecular configuration of amylose and its complexes in aqueous solutions. Part III. Investigation of the DP distribution of helical segments in amylose–iodine complexes

The equilibrium normality [I_f] of free iodine in amylose-iodine complex formation is a function of the length of the polyiodine chains. This length depends on the DP of helical segments of amylose (sDP _n). Values of [I_f] and of the concentration of the bound iodine [I_b] were determined by the continuous photometric titration with automatic recording. Plots of [I_b] versus [I_f] give an integral distribution curve. Since the relation between [I_f] and sDP _n is known, the graphic differentiation of the [I_b] versus [l_f] curve furnishes the differential distribution curve, representing the mass distribution of the helical segments according to their DP . The peak of this curve is characteristic of the percentage and DP of those helical segments, which occur in the largest amount. On the basis of the differential distribution curve the polymolecularity of the investigated sample may be judged. The titration of amylose samples degraded by various methods gives different distribution curves. Titrating mixtures of samples with widely differing average DP values results in differential curves having more than one maximum.     

A computer model of fractal myocardial perfusion heterogeneity to elucidate mechanisms of changes in critical coronary stenosis and hypotension

Critical coronary stenosis (critical CS) alone does not lead to an alteration of fractal dimension (D) under resting conditions in a pig model, indicating undisturbed local myocardial perfusion. If critical CS is combined with hypovolemic anemia the resulting hypotension leads to a significant decline of D. The mechanisms involved in this phenomenon have not yet been elucidated. A computer program was developed enabling calculation of D for normal vascular trees, for single vessel coronary stenosis (CS), and for CS in combination with reduced coronary perfusion pressure (CPP). The values of D obtained by the computer program were compared to those available from an existing animal study to confirm that changes of D can largely be explained by changes of arterial branching pattern simulated by the computer program. Using our computer model, D was 1.15 ± 0.06 in normal vascular trees. Third branch critical CS did not alter D (1.14±0.06; n.s.), wheras critical CS combined with a reduction of CPP to 40 mmHg reduced D (1.07 ± 0.03; P < 0.05). These data are comparable to those obtained in the animal study, and therefore show that alterations of vessel diameter and regional blood flow can largely explain changes of fractal dimension during critical CS and hypotension while changes of functional myocardial parameters might play a minor role.     

Power scaling of ammonitic suture patterns from Cretaceous Ancyloceratina: constraints on septal/sutural complexity

The spatial scaling of 77 hemisutures from 65 species of Cretaceous heteromorphic ammonites was quantified with the fractal box‐counting method. Fractal dimensions within Baculites compressus did not significantly differ between adult hemisutures; however, the juvenile suture of this species did exhibit a significantly lower fractal dimension. This suggests that variation in sutural complexity between explicitly adult ontogenetic stages may not contribute to significant noise in comparisons between other species/morphotypes. High‐spired, three‐dimensionally coiled heteromorphs with a larger degree of septal asymmetry exhibit higher fractal dimensions in outer whorl hemisutures than inner whorl hemisutures due to their elongation and improved space occupation over a larger whorl surface. Three‐dimensionally coiled ammonites also have higher fractal dimensions on average (mean D_b = 1.45) with respect to their 2‐D coiled counterparts (mean D_b = 1.38). All ammonites in this study exhibit a positive trend between sutural complexity and shell size (proxied by whorl height). These relationships suggest that septal frilling is constrained by shell morphology and whorl section geometry during septal morphogenesis. This, in turn, influences the scaling, space‐filling properties and scaling limits of ammonitic suture patterns. Sutural/septal complexity is also found to positively influence the amount of liquid retained in marginal septal recesses. However, as these septa approach larger scales, less cameral liquid is retained per septal mass. This may further explain the positive relationship between sutural complexity and shell size.     

A New Preparation Method of Coenzyme A with Microorganisms

The structure of aggregates formed by heating dilute BSA solution was analyzed with the fractal concept using light scattering methods. BSA was dissolved in HEPES buffer of pH 7.0 and acetate buffer of pH 5.1 to 0.1% and 0.001% solutions, respectively, and heated at 95°C, varying the heating time t_a. The fractal dimension D_f of the aggregate in the solution was evaluated from static light scattering experiments. The polydispersity exponent τ and the average hydrodynamic radius <R_h> of the aggregates were calculated from dynamic light scattering experiments using master curves obtained by Klein et al. The values of D_f and τ of heat-induced aggregates of BSA at pH 7.0 were about 2.1 and 1.5, respectively, the values of which agreed with those predicted by the reaction-limited cluster–cluster aggregation (RLCCA) model. On the other hand, D_f of heat-induced aggregates at pH 5.1 was about 1.8, which agreed with that predicted by the diffusion-limited cluster–cluster aggregation (DLCCA) model. The dependence of <R_h> for the sample of pH 7.0 on t_a was similar to that of the polystyrene colloids reported previously.     

Fractal dimensions of metropolitan area road networks and the impacts on the urban built environment

The fractal dimension of road networks emerges as a measure of the complexity of road transport infrastructures. In this study, we measured fractal dimensions of both the geometric form (i.e., the layout of the roads) and structure hierarchy (i.e., the connections among roads) of the major road networks in the largest 95 U.S. metro areas. We explained the causes of the variances in these fractal dimensions, especially the one for structure hierarchy. Further, we hypothesized the impacts of these fractal dimensions on the urban built environment and validated our hypotheses using path analysis. We found that a larger geometric fractal dimension (D_g) shows a more uniform distribution of roads over the metro area, which provides the accessibility to suburban areas and incentives to low-density development. A larger structural fractal dimension (D_s) indicates the highly-connected roads (e.g., highways) tend to join to other highly-connected roads so that most roads can be reached by a small number of neighboring roads (i.e., the small-world phenomenon). As D_s increases and the small-world effect become more significant, daily vehicle miles traveled per capita (DVMT/Cap) decline. However, D_s should be kept low in order to reduce the DVMT/Cap as population size increases. We consider that the low D_s can contribute to more mixed, polycentric and more uniform on an urban area-wide basis. Overall, higher D_g and D_s of the major road network in a metro area leads to higher per capita carbon emissions of transport, and lower quality of life as population increases. In the end, we conclude that fractal dimensions can provide valuable insight into the nature of the transportation land use nexus.     

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : V. FLASH DURATION AND CRITICAL INTENSITY FOR RESPONSE TO FLICKER

The relation between flash duration and mean critical intensity (white light) for threshold recognition of visual flicker, as a function of flash frequency, was investigated by means of measurements at five values of the light-time fraction: 0.10, 0.25, 0.50, 0.75, 0.90, with flash frequencies of the interrupted beam ranging from 2 to 60 per second. A square area, 6.1 x 6.1°, centrally fixated) was viewed monocularly; the discriminometer used provides automatically an artificial pupil 1.8 mm. in diameter. Except for the slight day-to-day fluctuation in the magnitudes of the parameters, the data for the observer used are shown to form an essentially homogeneous group. As for other animals tested, the F - log I_m curve is enlarged and moved toward lower flash intensities as the light-time fraction is decreased. The high intensity segments of the duplex curves are fitted by normal probability integrals for which F _max. and the abscissa of inflection are rectilinear functions of t_L(t_L + t_D), with opposite slopes. The third parameter, (σ''_{log I}, is invariant. The low intensity segments are composites, their shapes determined by the summation of the lower part of the high intensity curve with an overlapping low intensity population of effects. Both the rising and the declining branches of this latter assemblage suffer competitive partial suppression by the effects in the high intensity population. The detailed analysis shows that these results are consistent with the theory of the central, rather than peripheral, location of the dynamically recognizable elements in the determination of flicker.     

A Monte Carlo Simulation Study of Orientational Domain Clusters in the Planar Quadrupole Model

Abstract

We have carried out a series of Monte Carlo simulations of the planar quadrupole model, using the Distributed Array Processor. A very large system size, 16 384 molecules, was employed, and special attention was given to orientational domain clustering near the order—disorder transition. Very slow fluctuations of the orientational order parameter, possibly associated with switching from one orientational domain to another, are observed. Close to the phase transition, domain clusters become extremely ramified, with highly irregular borders. On heating through the transition, the low-temperature dominant domain disappears, essentially by becoming a fractal object. The associated Hausdorff dimension decreases from D = 2 to D = 1.6 as this occurs. Although our results are consistent with a continuous, rather than a first-order, phase transition, effects of finite system size and long time scales prevent us from drawing a definite conclusion on this point.     

Some observations on the ecology and the population dynamics of Merluccius angustimanus in the South Gulf ofCalifornia*

A population of Merluccius angustimanus Garman has been discovered in the south-east Gulf of California, where it is found at 80–120 m in the south of its range (Mazatlan to Altata) and down to 500 m at the northern end of its range (Isla San Pedro Nolasco, north of Guaymas). Studies of the otoliths and catch curves of M. angustimanus show that it lives up to seven years, and may reach 39 cm long (one fish) although it does not usually exceed 32 cm. Using the notation of Beverton & Holt (1959) the following parameters were estimated: L_∞= 32.7 cm, K= 0.35, t_∞= 0.016, t_∞= 7years, L_m= 22.0 cm, M for 3–7 years of age = 0.79, M for 2–3 years of age = 0.79-0.89. The von Bertalanffy equation for M. angustimanus was: and was shown to give a reasonably close fit to the real growth curve.     

Estimating polymorphic growth curve sets with nonchronological data

1. When we collect the growth curves of many individuals, orderly variation in the curves is often observed rather than a completely random mixture of various curves. Small individuals may exhibit similar growth curves, but the curves differ from those of large individuals, whereby the curves gradually vary from small to large individuals. It has been recognized that after standardization with the asymptotes, if all the growth curves are the same (anamorphic growth curve set), the growth curve sets can be estimated using nonchronological data; otherwise, that is, if the growth curves are not identical after standardization with the asymptotes (polymorphic growth curve set), this estimation is not feasible. However, because a given set of growth curves determines the variation in the observed data, it may be possible to estimate polymorphic growth curve sets using nonchronological data.
2. In this study, we developed an estimation method by deriving the likelihood function for polymorphic growth curve sets. The method involves simple maximum likelihood estimation. The weighted nonlinear regression and least‐squares method after the log‐transform of the anamorphic growth curve sets were included as special cases.
3. The growth curve sets of the height of cypress (Chamaecyparis obtusa) and larch (Larix kaempferi) trees were estimated. With the model selection process using the AIC and likelihood ratio test, the growth curve set for cypress was found to be polymorphic, whereas that for larch was found to be anamorphic. Improved fitting using the polymorphic model for cypress is due to resolving underdispersion (less dispersion in real data than model prediction).
4. The likelihood function for model estimation depends not only on the distribution type of asymptotes, but the definition of the growth curve set as well. Consideration of these factors may be necessary, even if environmental explanatory variables and random effects are introduced.

     

Technical note: Estimating original crown height in worn mandibular canines using aspects of dentin morphology

We present a novel method to estimate original crown height (OCH) for worn human mandibular canines using a cubic regression equation based on ratios of worn crown height and exposed dentin. This method may help alleviate issues frequently presented by worn teeth in dental analyses, including those in bioarchaeology. Mandibular canines (n = 28) from modern day New Zealand and English populations were selected. Crown height and dentin thickness were measured on dental thin sections (n = 19) and the resulting (log10) ratios were fitted to a cubic regression curve allowing OCH in worn crowns to be predicted. Variation in the dentin apex position was recorded and effects of angled wear slopes investigated allowing adjusted values to be generated. Our method is trialed for use on intact and sectioned teeth (n = 17). A cubic regression curve best describes the relationship between (log10) ratios and crown height deciles (R² = 0.996, df₁ = 3, df₂ = 336, p < 0.001). No significant differences were detected between OCH estimates using our method and digitally recreated cusp outlines of the same crowns (t = 1.024, df = 16, p > 0.05), with a mean absolute error of 0.171 mm and an adjusted coefficient of determination of 0.923. Our approach offers a quantitative method to estimate the percentage of OCH remaining on worn mandibular canines, and by extension, the OCH. Our estimates are comparable to digitally recreated cusps but less subjective and not limited to crowns with minimal wear.     

Decoupling Photocurrent Loss Mechanisms in Photovoltaic Cells Using Complementary Measurements of Exciton Diffusion

Significant work has been directed at measuring the exciton diffusion length (L_D) in organic semiconductors due to its significance in determining the performance of photovoltaic cells. Several techniques have been developed to measure L_D, often probing photoluminescence or charge carrier generation. Interestingly, in this study it is shown that when different techniques are compared, both the diffusive behavior of the exciton and active carrier recombination loss pathways can be decoupled. Here, a planar heterojunction device based on the donor–acceptor pairing of boron subphthalocyanine chloride‐C₆₀ is examined using photoluminescence quenching, photovoltage‐, and photocurrent‐based L_D measurement techniques. Photovoltage yields the device relevant L_D of both active materials as a function of forward bias subject to geminate recombination losses. These values are used to accurately predict the photocurrent as a function of voltage, suggesting geminate recombination is the dominant mechanism responsible for photocurrent loss. By combining these measurements with photocurrent and photoluminescence quenching, the intrinsic L_D, as well as the voltage‐dependent charge transfer state dissociation and charge collection efficiencies are quantitatively determined. The results of this work provide a method to decouple all relevant loss pathways during photoconversion, and establish the factors that can limit the performance of excitonic photovoltaic cells.     

Polarography of polynucleotides. IV. Effect of the molecular weight of poly(U) on its adsorption at a charged surface

Effects of molecular size on the adsorption properties of poly(U) were studied using alternating current polarography as a technique and a dropping mercury electrode (d.m.e.) as a model interface. The measurements were carried out on fractions (by molecular weight) of poly(U) characterized by sedimentation and viscosity measurements. The data indicate that the rate of poly(U) adsorption is controlled by diffusion. The adsorption equilibrium can be established during the drop-life at higher concentrations of poly(U) where the electrode is fully covered, while at low concentrations corresponding to the linearized isotherm, the time τ for the establishment of the adsorption equilibrium is much longer than can be obtained with d.m.e. The time τ increases with increasing chain length, n (in monomeric units). From the concentration dependence of the course of current time, I ～t, curves, or of the current values at the end of the drop life, a constant K was calculated which depends on n. In the range of molecular weights studied (25 × 10³ to 564 × 10³) the data obeys the relationship log n = a + b log K (where a and b are constants). Area, A, occupied by the monomer of an adsorbed poly(U) molecule was calculated from experimental values of K and D (diffusion coefficient). The decrease of A with increasing n was explained in terms of the looping of longer poly(U) chains out from the electrode surface.     

CRITICAL INTENSITY AND FLASH DURATION FOR RESPONSE TO FLICKER: WITH ANAX LARVAE

Determinations of the flicker response curve (F – log I_m) with larvae of Anax junius (dragonfly) for various ratios t_L/t_D of light time to dark time in a flash cycle provide relations between t_L/t_D and the parameters of the probability integral fundamentally describing the F – log I function, including the variability of I. These relations are quantitatively of the same form as those found for this function in the sunfish, and are therefore non-specific. Their meaning for the theory of reaction to visual flicker is discussed. The asymmetry of the Anax curve, resulting from mechanical conditions affecting the reception of light by the arthropod eye, is (as predicted) reduced by relative lengthening of the fractional light time in a cycle.     

Stomatal behaviour in a beech canopy: an analysis of Bowen ratio measurements compared with porometer data

On the basis of measurements or stand transpiration and microclimate, the bulk stomatal or bulk leaf conductance (g_L) of a beech forest in northern Germany was calculated for periods in which leaves were fully expanded and the canopy was dry. This conductance depends strongly on light and humidity conditions above the forest. During periods with photosynthetic photon flux densities Q > 1200 μmol m^?2s^?1, g_L was reduced from 1500mmol m^?2s^?1 at a vapour pressure deficit D= 0.5kPa to 500 mmol m^?2s^?1 at D= 2kPa. Light saturation of g_L was not reached until Q= 1200 μmol m^?2s^?1 at low D, or until even higher Q at higher D. The dependence of g_L, on Q and D was described mathematically by a non-linear equation that requires two empirical parameters. Values for g_L as simulated by this equation provided a satisfactory agreement with independent porometer data collected on single leaves and scaled up to the canopy. A comparison of stomatal and aerodynamic conductances showed a strong coupling between the forest canopy and the atmosphere, indicating that transpiration of the beech forest is controlled mainly by the stomata.