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...     

Response Characteristics of Soil Fractal Features to Different Land Uses in Typical Purple Soil Watershed

As a fundamental characteristic of soil physical properties, the soil Particle Size Distribution (PSD) is important in the research on soil moisture migration, solution transformation, and soil erosion. In this research, the PSD characteristics with distinct methods in different land uses are analyzed. The results show that the upper bound of the volume domain of the clay domain ranges from 5.743μm to 5.749μm for all land-use types. For the silt domain of purple soil, the value ranges among 286.852~286.966 μm. For all purple soil land-use types, the order of the volume domain fractal dimensions is D_clay<D_silt<D_sand. However, the values of D_silt and D_sand in the Pinus massoniana Lamb, Robinia pseudoacacia L and Ipomoea batatas are all higher than the corresponding values in the Citrus reticulate Blanco and Setaria viridis. Moreover, in all the land-use types, all of the parameters in volume domain fractal dimension (D_vi) are higher than the corresponding parameter values from the United States Department of Agriculture (D_vi(U)). The correlation study between the volume domain fractal dimension and the soil properties shows that the intensity of correlation to the soil texture and soil organic matter has the order as: D_silt>D_silt(U)>D_sand (U)>D_sand and D_silt>D_silt(U)>D_sand>D_sand(U), respectively. As it is compared with all D_vi, the D_silt has the most significant correlativity to the soil texture and organic matter in different land uses of the typical purple soil watersheds. Therefore, D_silt will be a potential indictor for evaluating the proportion of fine particles in the PSD, as well as a key measurement in soil quality and productivity studies.     

Fractal parameters and vascular networks: facts & artifacts

Background

Several fractal and non-fractal parameters have been considered for the quantitative assessment of the vascular architecture, using a variety of test specimens and of computational tools. The fractal parameters have the advantage of being scale invariant, i.e. to be independent of the magnification and resolution of the images to be investigated, making easier the comparison among different setups and experiments.

Results

The success of several commercial and/or free codes in computing the fractal parameters has been tested on well known exact models. Based on such a preliminary study, we selected the code Frac-lac in order to analyze images obtained by visualizing the angiogenetic process occurring in chick Chorio Allontoic Membranes (CAM), assumed to be paradigmatic of a realistic 2D vascular network. Among the parameters investigated, the fractal dimension D_f proved to be the most robust estimator for CAM vascular networks. Moreover, only D_f was able to discriminate between effective and elusive increases in vascularization after drug-induced angiogenic stimulations on CAMs.

Conclusion

The fractal dimension D_f is likely to be the most promising tool for monitoring the effectiveness of anti-angiogenic therapies in various clinical contexts.     

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.     

Detection of Glucose and Related Analytes by Biosensors: A Fractal Analysis

A fractal analysis is used to model the binding and dissociation kinetics of connective tissue interstitial glucose, adipose tissue interstitial glucose, insulin, and other related analytes on biosensor surfaces. The analysis provides insights into diffusion-limited analyte-receptor reactions occurring on heterogeneous biosensor surfaces. Numerical values obtained for the binding and the dissociation rate coefficients are linked to the degree of heterogeneity or roughness [fractal dimension (D_f)] present on the biosensor chip surface. The binding and dissociation rate coefficients are sensitive to the degree of heterogeneity on the surface. For example, for the binding of plasma insulin, as the fractal dimension value increases by a factor of 2.47 from D_f1 = 0.6827 to D_f2 = 1.6852, the binding rate coefficient increases by a factor of 4.92 from k₁ = 1.0232 to k₂ = 5.0388. An increase in the degree of heterogeneity on the probe surface leads to an increase in the binding rate coefficient. A dual-fractal analysis is required to fit the binding kinetics in most of the cases presented. A single fractal analysis is adequate to describe the dissociation kinetics. Affinity (ratio of the binding to the dissociation rate coefficient) values are also presented. Interferents for glucose, such as uric acid and ascorbic acid, were also detected by using glucose biosensors based on carbon nanotube (CNT) nanoelectrode ensembles (NEEs) (Lin Y, Lu F, Tu Y, Ren Z. Nano Lett 2004, 4, 191–195).     

Fractal analysis of extra‐embryonic vascularization in Japanese quail embryos exposed to extremely low frequency magnetic fields

Magnetic fields (MF) can alter the dynamic behavior of vascular tissue and may have a stimulatory or inhibitory effect on blood vessel growth. Fractal geometry has been used in several studies as a tool to describe the development of blood vascular networks. Due to its self‐similarity, irregularity, fractional dimension, and dependence on the scale of vessel dimensions, vascular networks can be taken as fractal objects. In this work, we calculated the fractal dimension by the methods of box counting (D_bc) and information dimension (D_inf) to evaluate the development of blood vessels of the yolk sac membrane (YSM) from quail embryos exposed to MF with a magnetic flux density of 1 mT and a frequency of 60 Hz. The obtained results showed that when the MF was applied to embryos aged between 48 and 72 h, in sessions of 2 h (6 h/day) and 3 h (9 h/day) with exposure intervals between 6 and 5 h, respectively, blood vascular formation was inhibited. Exposure sessions shorter than 2 h or longer than 3 h had no observable change on the vascular process. In contrast, the magnetic field had no observable change on the YSM vascular network for embryos aged between 72 and 96 h, irrespective of the exposure time. In conclusion, these results show a “window effect” regarding exposure time. Bioelectromagnetics 34:114–121, 2013. © 2012 Wiley Periodicals, Inc.     

The duality of fractals: roughness and self-similarity

The fractal dimension (D _HB) is an interesting metrics because it is supposed to quantify by a single value, scale independence and roughness of ecological objects. However, we show here that those two properties may be quantified by a single dimension only in some specific cases. In general, a non-integer D _HB quantifies only the roughness, and self-similarity needs to be evidenced or postulated by other means. Second, we revisit some aspects of the practical estimation of D _HB. We recommend the use of madogram instead of variogram for estimations based on geostatistics. We propose a simplification of its estimation for 2D fields and discuss its possible relationship with self-similarity. We finally underline the problem of scale and resolution. Field data recorded during a scientific acoustic survey on the North Sea herring are used for illustrations. The paper concludes on a synthesis of practical recommendations to ecologists when using fractal dimension.     

Estimating quantity and equity of carbon emission from roads based on an improved LCA approach: the case of China

Purpose

Carbon emission from roads is an important contributor of a nation’s greenhouse gas emission that causes climate change. However, the existing life cycle assessment (LCA) analysis of road carbon emissions focus on project-level, ignoring regional differences. Significant challenges remain in developing regional road’s carbon emission mitigation strategies. This study estimates the quantity of carbon emissions from roads in China and calculated the regional equity of road carbon emissions.

Methods

An improved LCA approach, which considered the regional difference of raw materials’ carbon emissions, carbon emissions caused by traffic jam and road category, was applied to calculate the quantity of carbon emissions of roads. Sensitive analysis was conducted to find the key influential factors. Gini coefficient was used to calculate the equity degree of carbon emissions by roads based on the LCA results. The decomposition model of Gini coefficient is applied to analyze the causes of carbon emission differences.

Results

The total national carbon emissions by roads in 2019 increased by 2.2 times compared to 2009. Carbon emission from roads in the operation phase increased from 62% in 2009 to 83% in 2019. The functional unit for expressway in this study ranging from 1646 to 1794 t CO₂e/km in 31 provinces. An estimated uncertainty of plus or minus 4% of the traffic flow allocation between expressway and other roads makes an increase of 38% or a decrease of 15% of the life cycle emission. The overall Gini coefficient of carbon emissions from roads in China is under the warning line of 0.4. Outer inequity between regions contributes 88.83% of the whole inequity and the most developed three regions contribute 66.23%.

Conclusions

Large quantity of road construction in the past in China makes the burden of carbon emission transfer from the construction phase to the operation phase. Regional differences of raw materials’ carbon emissions, traffic jam, and road hierarchy are important factors influencing the LCA-based estimation of road carbon emission. To improve the national equity degree of road carbon emission, quota allocation of road carbon emission rights between regions and cross-regional carbon emission reduction policies would help.

     

Structural complexity in mussel beds: the fractal geometry of surface topography

Seafloor topographic complexity is ecologically important because it provides habitat structure and alters boundary-layer flow over the bottom. Despite its importance, there is little agreement on how to define and measure surface complexity. The purpose of this investigation was to utilize fractal geometry of vertical cross-section profiles to characterize the surface topography of the soft-bottom mussel bed (Mytilus edulis L.) at Bob's Cove, ME, USA. Mussels there have been shown previously to have spatially ordered fractal characteristics in the horizontal plane. Two hypotheses were tested. The first was that the bed surface is fractal over the spatial scale of 1.44-200 mm, with fractal dimension less than or equal to 1.26, the value for the Koch curve, our model for bed profiles. The second was that bed surface topography (i.e., in vertical profile) is less complex than the mussel bed spatial pattern (i.e., aerial view in the horizontal plane). Both hypotheses were supported. Cross-sections of plaster casts of the bed produced 88 surface profiles, all of which were fractal over the entire spatial scale of more two orders of magnitude employed in the analysis. Fractal dimension values (D) for individual profiles ranged from 1.031 to 1.310. Fractal dimensions of entire casts ranged up to mean (1.242+/-0.046) and median (1.251) values similar to 1.26, the theoretical value of the Koch curve. The bed surface was less complex than the bed spatial pattern because every profile had D<1.36, the smallest value previously obtained from aerial views of the bed. The investigation demonstrated for the first time that surface topography of a soft-bottom mussel bed was fractal at a spatial scale relevant to hydrodynamic processes and habitat structure important for benthic organisms. The technique of using cross-section profiles from casts of the bed surface avoided possible underestimates of fractal dimension that can result from other profiling methods reported in the literature. The results demonstrate that fractal dimension can be useful in the analysis of habitat space and water flow over any irregular seafloor surface because it incorporates the size, shape, and scale of roughness elements into a simple, numerical metric.     

Influence analysis for the behavior of dewaterability of excess sludge in a two-stage vermifilter

To improve excess sludge dewaterability, a two-stage vermifilter was developed to qualitatively and quantitatively analyze sludge physico-chemical properties (fractal dimension, zeta potential, extracellular polymeric substances (EPS), particle size distribution, etc.) and to correlate them with sludge dewatering characteristics (specific resistance to filtration (SRF) and capillary suction time (CST)). Results demonstrated that sludge dewatering performance was significantly improved after the primary vermifilter VF₁ and the second-stage vermifilter VF₂. In addition, the further VF₂ treatment exhibited higher effects on sludge dewatering performance. The particle boundary of sludge after VF₂ treatment was clearer and smoother than VF₁ sludge (VF₁S), apart from the fact that sludge morphological structure got denser and more compact. Comparing with VF₁S, the fractal dimension D₁ calculated within 1D topological space was closer to 1 after VF₂ treatment, and the fractal dimension D₂ within 2D topological space closer to 2, indicating a better dewatering performance after VF₂ treatment. Additionally, the changes of sludge floc surface properties (such as zeta potential and EPS) resulted in small particles agglomerating into larger ones and then the increase of particle diameter. In summary, the two-stage vermifilter got a better sludge dewatering performance, and thus beneficial for subsequent processing of sludge.

     

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.

     

The relative importance of habitat complexity and surface area in assessing biodiversity: Fractal application on rocky shores

Theoretical work predicts that complex habitats allow more species to co-exist in a given area. However, more field studies are still needed to clarify this relationship, especially in intertidal habitats. Furthermore, the potential separate effects of surface complexity and area on species richness and abundance have rarely been addressed. We tested the hypotheses that a more complex substratum or larger surface area will support a greater number of individuals and species of mobile macrofauna on three rocky shores in Hong Kong. Surface complexity, assessed by using fractals, was an important factor in species–area relationships. The number of species increased proportionally to habitat complexity and this relationship was homogeneous among different shores. Total abundance of animals, however, was more dependent on the available surface area. The slope of the size–frequency distribution of animals in samples taken on surfaces with different fractal dimensions (D) was significantly steeper with an increase in fractal dimension, showing that the relative abundance of small animals increased with surface complexity. Thus, surface complexity and area may be important in determining different aspects of the macrofaunal community structure on rocky shores. The resulting increase in surface area on more rough surfaces may introduce bias in density and species number assessments when two-dimensional sampling units (i.e., quadrats) are employed. It is necessary, therefore, to account for the surface complexity in the design and interpretation of the results of benthic studies. Using D as an index of surface complexity is very useful, but also involves some practical problems, e.g., surfaces may be anisotropic and different methods may give different estimates of D. Therefore, these different methods need to be calibrated before comparisons of D values between them are meaningful.     

Fractal analysis of the Orce skull sutures

Methods of fractal geometry (Mandelbrot, 1983) are used here to analyse the relative complexity of the sagittal and lambdoid sutures visible in the skull fragment formed by parts of an occipital squame and parietals found in a sealed deposit at the early Lower Pleistocene site of Venta Micena (Orce, Granada, Spain), generally regarded as human bone but occasionally suggested as belonging to an equid. For comparison with the fossil, corresponding sutures of various primates (hominids, pongids and cercopithecids) and two other groups of mammals (equids and ruminants) were analysed using the computer program FRACTAL-D (Slice, 1989) in order to determine their fractal dimensions as a measure of differential sutural design complexity. The results show that the fractal dimension of the Venta Micena skull sutures lies within the range of variation for infant specimens of both modern and Plio-Pleistocene hominids. Sutural complexity in young pongids and cercopithecids overlaps the range of fractal dimensions found in hominids, whereas values obtained from equids and ruminants are significantly greater than those for all the primates analysed here. Therefore, in terms of fractal dimension measures of relative complexity, the sutures preserved in the Venta Micena fossil could not have belonged to an equid (pace Agusti & Moyà-Sola, 1987); rather, its fractal dimension is consistent with the attribution of the fossil to an infant of Homo sp.     

Progressive Indosinian N-S Deformation of the Jiaochang Structure in the Songpan-Ganzi Fold-Belt,Western China

Integrated field data, microstructural and three-dimensional strain analyses are used to document coaxial N-S shortening and southward increase in deformation intensity and metamorphism at the Jiaochang structure. Two episodes of deformation (D₁,D₂) with localized post-D₂ deformation have been identified in the area. The first deformation (D₁) episode is defined by a main axial-plane of parallel folds observable on a micro- to kilometer-scale, while the second episode of deformation (D₂) is defined by micro-scale metamorphic folds, associated with E–W oriented stretching lineation. These processes are the result of Indosinian tectonism (Late Triassic to Early Jurassic) characterized by nearly coaxial N-S compression and deformation. This is indicated by E–W trending, sub-parallel to parallel foliation (S₁, e.g. axial-plane of folds, and S₂, i.e. axial-plane of metamorphic folds, crenulation cleavage) and lineation (L₁, e.g. axis of folds, and L₂, i.e. stretching lineation, axis of metamorphic folds and B-axis of echelon lens). Most of the porphyroblasts and minerals (e.g. pyrite, biotite) show two growth phases with localized growth in the third phase (muscovite). The progressive D₁–D₂ structure is widespread in the south of the Jiaochang area, but only D₁ structure crops out at the north. The strain intensity (γ), compression ratios (c%) and octahedral strain intensity (ε_s) are similar across the Jiaochang structure (i.e., γ ≈ 1.8, c ≈ 27%, ε_s = 0.9), showing a broad range of Flinn values (K = 0.77 to 7.57). The long-axis orientations are roughly symmetric between two limbs of the structure. Therefore, we suggest that the architecture of the Jiaochang structure has been controlled by coaxial N-S shortening and deformation (D₁–D₂) during the Indosinian tectonic epoch, with insignificant post-D₂ deformation.     

Changes in the surface roughness of snow from millimetre to metre scales

The roughness of snow influences the movement of air across the snow surface and resulting transfers of energy. Here we focus on the roughness of the snowpack surface to determine its range of variability for different snow conditions (e.g., time since last snowfall), across spatial scales that ranged from 0.01 cm (card) to more than 1000 cm (transect) or more than 5-orders of magnitude, and due to the deposition of aeolian constituents. Digital photogrammetry of snow surfaces was used to compute two roughness metrics at two mountain sites in north-central Colorado. These metrics are the random roughness (RR) that disregards the spatial structure and the fractal dimension (D) computed from variogram analysis.At the crystal scale, D is between 1.67 (card) and 1.60 (board), which increases to 1.77 between 0.1 and 1.0 cm. At longer scales, D is 1.53 (board) to 1.56 (transect). There was no significant change in surface roughness during the accumulation season, with RR values at about 0.002. During the melt season the surface roughness doubled, with the RR values increasing from about 0.002 to 0.004. Snow was more rough parallel to the wind when dunes were present, and roughness varied spatially. The average RR value computed for the white snow surface of 0.014 is substantially greater than the value computed for the red dust surface of 0.0032. Due to undulations of smaller amplitude and as a result of the dust itself, the red dust surface is more random (D is 2.62 versus 2.23 for the white snow). Our results show that there is consistency in roughness over different scales, yet large scale processes (e.g., wind and radiation activity) influence the magnitude of roughness metrics much more than small scale processes (e.g., crystal form and metamorphism).     

A critical appraisal of a combined stomatal-photosynthesis model for C3 plants

Gas-exchange measurements on Eucalyptus grandis leaves and data extracted from the literature were used to test a semi-empirical model of stomatal conductance for CO₂ g_Sc=g_o+a₁A/(c_s-I) (1+D_s/D_o)] where A is the assimilation rate; D_s and c_s are the humidity deficit and the CO₂ concentration at the leaf surface, respectively; g₀ is the conductance as A → 0 when leaf irradiance → 0; and D₀ and a₁ are empirical coefficients. This model is a modified version of g_sc=a₁A h_s/c_s first proposed by Ball, Woodrow & Berry (1987, in Progress in Photosynthesis Research, Martinus Mijhoff, Publ., pp. 221–224), in which h_s is relative humidity. Inclusion of the CO₂ compensation point, τ, improved the behaviour of the model at low values of c_s, while a hyperbolic function of D_s for humidity response correctly accounted for the observed hyperbolic and linear variation of g_sc and c_i/c_s as a function of D_s, where C_i is the intercellular CO₂ concentration. In contrast, use of relative humidity as the humidity variable led to predictions of a linear decrease in g_sc and a hyperbolic variation in c_i/c_s as a function of D_s, contrary to data from E. grandis leaves. The revised model also successfully described the response of stomata to variations in A, D_s and c_s for published responses of the leaves of several other species. Coupling of the revised stomatal model with a biochemical model for photosynthesis of C₃ plants synthesizes many of the observed responses of leaves to light, humidity deficit, leaf temperature and CO₂ concentration. Best results are obtained for well-watered plants.     

Influence of benthic organisms on solute transport in lake sediments

Increased inputs of nutrients into the waters of Lake Okeechobee has raised concern that the lake is becoming hypereutrophic. One aspect in understanding the overall cycling and dynamics of the nutrients in the system is the effect of benthic organisms on solute transport. Various diffusional models have been used to approximate the effect of benthic organisms on solute transport within sediments using diffusion coefficient values which represent the pooled contributions of molecular diffusion (D _s ) and enhanced solute mixing due to macrobenthos activity (D _i ). The objective of this study was to investigate the impact of benthic activity on solute transport by measuringD _s (i.e., no benthic activity) and an apparent-dispersion or mixing coefficientD _m (i.e., with benthic activity) for the four major sediment types of Lake Okeechobee, Florida using a reservoir technique. This method involved monitoring the depletion of a conservative tracer (tritiated water) from the overlying water (reservoir) resulting from transport into sediments using disturbed sediments repacked in cores (3.2 cm diam.) and undisturbed cores (3.2 to 12 cm diam.) obtained from the lake. Additional estimates ofD _m andD _s were also obtained by measuring tracer concentration profiles in the sediment cores at the end of a specified diffusion period. Molecular diffusion coefficients (D _s ) measured forrepacked cores of sand, littoral, mud and peat sediments ranged from 0.90 to 1.29 cm² d⁻¹, and estimates ofD _s were slightly higher in undisturbed cores without benthic organisms.D _m values for undisturbed cores of mud, sand and littoral sediments having macrobenthic populations ranged from 2.09 to 24.78 cm² d⁻¹; values that were 1.6 to 15 times higher than those in sediments without benthic activity. Undisturbed cores of varying diameter from mud sediments had similar estimates ofD _m for tritium; however, the undisturbed cores with larger diameters from littoral sediments yielded larger estimates ofD _m , reflecting the heterogeneity of benthic population densities and activity. Therefore,D _s estimates may not adequately represent transport processes for mud, sand and littoral sediments of Lake Okeechobee; hence careful consideration should be given to the role of benthic organisms in the overall transport of solutes across the sediment-water interface. A contribution of the Florida Agricultural Experiment Station Journal Series No. R-01150. A contribution of the Florida Agricultural Experiment Station Journal Series No. R-01150.     

Scorpion venom complexity fractal analysis. Its relevance for comparing venoms

We analyzed the venom elution pattern of 15 scorpions species. Data were scanned at 1 Hz and stored digitally. Approximate fractal dimension (D) [Sevcik (1998)] was calculated for minutes 0-60 of the elutions. D was calculated for either the whole time range, or calculated using a window of 500 points, which was displaced by one time increment recursively, and stored [(t_i,D_i) sets]. We avoid the term complexity as much as possible since defining complexity is difficult; instead we propose the term contortedness and represent it by the variable Q=D−1. To compare venom contortednesses of different species, a phase plot with their (t_i,Q_i) sets was constructed and determination coefficient (d_s) were calculated squaring the Spearman rank correlation coefficient. (t_i,Q_i) sets of several elutions of the same specie were averaged and compared with other species finding that some were amazingly similar (Tityus clathratus vs Tityus caripitensis, d_s = 0.813). Tityus discrepans was similar to 6 of 8 species of the same genus (d_s ranging from 0.23 to 0.49), and also similar to Centruroides gracilis and Chactas laevipes (d_s 0.54 and 0.49, respectively). Serendipitously,T. discrepans was chosen many years ago to produce anti-Tityus antivenom in Venezuela; perhaps the clinical success in neutralizing the venom of the other known Venezuelan Tityus, stems from the mimetism of this venom with the remaining species’ venom.     

Fractal dimension analysis and mathematical morphology of structural changes in actin filaments imaged by electron microscopy

In this work, we examined structural changes of actin filaments interacting with myosin visualized by quick freeze deep-etch replica electron microscopy (EM) by using a new method of image processing/analysis based on mathematical morphology.In order to quantify the degree of structural changes, two characteristic patterns were extracted from the EM images. One is the winding pattern of the filament shape (WP) reflecting flexibility of the filament, and the other is the surface pattern of the filament (SP) reflecting intra-molecular domain-mobility of actin monomers constituting the filament. EM images were processed by morphological filtering followed by box-counting to calculate the fractal dimensions for WP (D_WP) and SP (D_SP). The result indicates that D_WP was larger than D_SP irrespective of the state of the filament (myosin-free or bound) and that both parameters for myosin-bound filaments were significantly larger than those for myosin-free filaments. Overall, this work provides the first quantitative insight into how conformational disorder of actin monomers is correlated with the myosin-induced increase in flexibility of actin filaments along their length as suggested by earlier studies with different techniques. Our method is yet to be improved in details, but promising as a powerful tool for studying the structural change of protein molecules and their assemblies, which can potentially be applied to a wide range of biological and biomedical images.     

Transient Phases of the Isometric Tetanus in Frog's Striated Muscle

In an isometric tetanus in frog's sartorius muscle tension approaches the plateau exponentially with rate constant α. α a depends on sarcomere length, s, and temperature, T, according to the Arrhenius equation See PDF for Equation for temperatures between 1 and 20°C and for sarcomere lengths 2.0–2.8 µm. The energy of activation, E, does not vary significantly with s; E = 13.9 ± 2.4 kcal/mole. A(s) decreases monotonically with s; A(2.1 µm) is about three times greater than A(2.8 µm). Late in relaxation active tension approaches zero exponentially with rate constant r. r decreases exponentially with increasing duration of tetanus, D, from r₀ in a twitch to r_∞ for large D. The rate constant for decrease of r with D increases with s and with T. r₀ and r_∞ obey the Arrhenius equation and decrease with increasing s.