Nonlinear fractal dynamics of human colonic pressure activity based upon the box-counting method

The computational fractal dimension of human colonic pressure activity acquired by a telemetric capsule robot under normal physiological conditions was studied using the box-counting method. The fractal dimension is a numeric value that quantifies to measure how rough the signal is from nonlinear dynamics, rather than its amplitude or other linear statistical features. The colonic pressure activities from the healthy subject during three typical periods were analysed. The results showed that the activity might be fractal with a non-integer fractal dimension after it being integrated over time using the cumsum method, which was never revealed before. Moreover, the activity (after it being integrated) acquired soon after wakening up was the roughest (also the most complex one) with the largest fractal dimension, closely followed by that acquired during sleep with that acquired long time after awakening up (in the daytime) ranking third with the smallest fractal dimension. Fractal estimation might provide a new method to learn the nonlinear dynamics of human gastrointestinal pressure recordings.     

A single- and a dual-fractal analysis of antigen-antibody binding kinetics for different biosensor applications.

The diffusion-limited binding kinetics of antigen (or antibody) in solution to antibody (or antigen) immobilized on a biosensor surface is analyzed within a fractal framework. The data is adequately described by a single- or a dual-fractal analysis. Initially, the data was modelled by a single-fractal analysis. If an inadequate fit was obtained then a dual-fractal analysis was utilized. The regression analysis provided by Sigmaplot, 1993 (Scientific Graphing Software: User's Manual. Jandel Scientific, San Rafael, CA) was utilized to determine if a single-fractal analysis is sufficient, or a dual-fractal analysis is required. In general, it is of interest to note that the binding rate coefficient and the fractal dimension exhibit changes in the same direction (except for a single example) for the antigen-antibody systems analyzed. Binding rate coefficient expressions as a function of the fractal dimension developed for the antigen-antibody binding systems indicate a high sensitivity of the binding rate coefficient on the fractal dimension when both a single -as well as a dual-fractal analysis is used. For example, for a single-fractal analysis and for the binding of human endothelin-1 (ET-1) antibody in solution to ET-1(15-21) x BSA (bovine serum albumin) immobilised on a surface plasmon resonance surface, the order of dependence of the binding rate coefficient, k on the fractal dimension, Df is 7.0945. Similarly, for a dual-fractal analysis and for the binding of parasite L. donovani diluted pooled sera in solution to fluorescein isothiocyanate-labeled anti-human immunoglobulin IgG immobilized on an optical fibre, the order of dependence of k1 and k2 on Df1 and Df2 were 6.8018 and -4.393, respectively. Binding rate coefficient expressions are also developed as a function of the analyte (antigen or antibody) concentration in solution. The binding rate coefficient expressions developed as a function of the fractal dimension(s) are of particular value since they provide a means to better control biosensor performance by linking it to the heterogeneity on the surface, and emphasize in a quantitative sense the importance of the nature of the surface in biosensor performance.     

Use of the fractal dimension for the analysis of electroencephalographic time series

 Electroencephalogram (EEG) traces corresponding to different physiopathological conditions can be characterized by their fractal dimension, which is a measure of the signal complexity. Generally this dimension is evaluated in the phase space by means of the attractor dimension or other correlated parameters. Nevertheless, to obtain reliable values, long duration intervals are needed and consequently only long-term events can be analysed; also much calculation time is required. To analyse events of brief duration in real-time mode and to apply the results obtained directly in the time domain, thus providing an easier interpretation of fractal dimension behaviour, in this work we optimize and propose a new method for evaluating the fractal dimension. Moreover, we study the robustness of this evaluation in the presence of white or line noises and compare the results with those obtained with conventional spectral methods. The non-linear analysis carried out allows us to investigate relevant EEG events shorter than those detectable by means of other linear and non-linear techniques, thus achieving a better temporal resolution. An interesting link between the spectral distribution and the fractal dimension value is also pointed out. Received: 21 November 1996 / Accepted in revised form: 1 July 1997     

元宝山南方红豆杉克隆种群分布格局的分形特征

南方红豆杉(Taxus chinensis var. mairei)是提取抗癌药物紫杉醇的珍贵资源植物。分布于广西元宝山自然保护区的南方红豆杉,自然状态下以克隆繁殖方式进行种群更新,研究其种群克隆生长的空间分布格局,可揭示种群克隆繁殖特性和生态适应机制,对南方红豆杉这一珍稀濒危物种的保护和管理具有重要意义。利用分形理论中的计盒维数和信息维数,对元宝山的南方红豆杉克隆种群空间分布格局的分形特征进行了分析,结果表明:种群空间分布格局存在分形特征,其计盒维数介于0.993 1~1.353 1之间,信息维数介于1.350 8~1.652 1。南方红豆杉克隆种群格局的计盒维数远离最大理论维数值2,种群总体对空间的占据能力较弱。克隆构型指数与种群计盒维数密切相关。分析结果显示,克隆构型趋于“密集型”的种群具有较强的空间占据能力,而克隆构型趋于“游击型”的种群其空间占据能力较弱。信息维数与种群的集聚强度密切相关,其差异反映了种群格局强度的变化,较大的信息维数反映种群个体的集聚强度较高,而较小的信息维数则反映出种群个体间的集聚强度较弱,其维数值大小与分株种群数量、分株种群斑块的空间配置密切相关。     

When Money Is Not Enough: Awareness,Success, and Variability in Motor Learning

When performing a skill such as throwing a dart, many different combinations of joint motions suffice to hit the target. The motor system adapts rapidly to reduce bias in the desired outcome (i.e., the first-order moment of the error); however, the essence of skill is to produce movements with less variability (i.e., to reduce the second-order moment). It is easy to see how feedback about success or failure could sculpt performance to achieve this aim. However, it is unclear whether the dimensions responsible for success or failure need to be known explicitly by the subjects, or whether learning can proceed without explicit awareness of the movement parameters that need to change. Here, we designed a redundant, two-dimensional reaching task in which we could selectively manipulate task success and the variability of action outcomes, whilst also manipulating awareness of the dimension along which performance could be improved. Variability was manipulated either by amplifying natural errors, leaving the correlation between the executed movement and the visual feedback intact, or by adding extrinsic noise, decorrelating movement and feedback. We found that explicit, binary, feedback about success or failure was only sufficient for learning when participants were aware of the dimension along which motor behavior had to change. Without such awareness, learning was only present when extrinsic noise was added to the feedback, but not when task success or variability was manipulated in isolation; learning was also much slower. Our results highlight the importance of conscious awareness of the relevant dimension during motor learning, and suggest that higher-order moments of outcome signals are likely to play a significant role in skill learning in complex tasks.     

Neural Processes Underlying the“Same”-“Different” Judgment of Two Simultaneously Presented Objects- An EEG Study

The present study investigated the neural processes underlying “same” and -“different” judgments for two simultaneously presented objects, that varied on one or both, of two dimensions: color and shape. Participants judged whether or not the two objects were “same” or “different” on either the color dimension (color task) or the shape dimension (shape task). The unattended irrelevant dimension of the objects was either congruent (same-same; different-different) or incongruent (same-different). ERP data showed a main effect of color congruency in the time window 190–260 ms post-stimulus presentation and a main effect of shape congruency in the time window 220–280 ms post-stimulus presentation in both color and shape tasks. The interaction between color and shape congruency in the ERP data occurred in a later time window than the two main effects, indicating that mismatches in task-relevant and task-irrelevant dimensions were processed automatically and independently before a response was selected. The fact that the interference of the task-irrelevant dimension occurred after mismatch detection, supports a confluence model of processing.     

A holistic approach to determine tree structural complexity based on laser scanning data and fractal analysis

The three‐dimensional forest structure affects many ecosystem functions and services provided by forests. As forests are made of trees it seems reasonable to approach their structure by investigating individual tree structure. Based on three‐dimensional point clouds from laser scanning, a newly developed holistic approach is presented that enables to calculate the box dimension as a measure of structural complexity of individual trees using fractal analysis. It was found that the box dimension of trees was significantly different among the tested species, among trees belonging to the same species but exposed to different growing conditions (at gap vs. forest interior) or to different kinds of competition (intraspecific vs. interspecific). Furthermore, it was shown that the box dimension is positively related to the trees’ growth rate. The box dimension was identified as an easy to calculate measure that integrates the effect of several external drivers of tree structure, such as competition strength and type, while simultaneously providing information on structure‐related properties, like tree growth.     

Human implicit memory for irrelevant dimension values is similar to rats' incidental memory in simultaneous discrimination tasks

Participants completed a category-learning task in which they needed to discover which of three stimulus dimensions (shape, color or size) was relevant. After meeting a learning criterion (nine of 10 consecutive correct responses), participants continued making categorization choices and response latencies associated with these trials were examined. In both Experiments 1 and 2, people responded reliably faster when correct responses matched the previous responses with respect to irrelevant dimension values. Thus, they demonstrated a form of incidental short-term memory analogous to that we previously reported in studies of rats. In Experiment 2, participants' explicit memory for irrelevant dimension values was assessed after category learning was complete. The results indicated that people were unaware of the irrelevant dimension values encountered on trials preceding surprise probe trials. This indicates that memory for the irrelevant dimension values was implicit (i.e. unconscious). The findings are discussed with respect to both human and non-human studies of hippocampus-independent memory and implicit memory.     

Effects of macrophyte architecture and leaf shape complexity on structural parameters of the epiphytic algal community in a Pampean stream

Habitat heterogeneity is one of the main factors determining distribution of organisms, and vegetation is of primary importance in shaping the structural environment in aquatic systems. The effect of macrophyte complexity on macroinvertebrates has been well researched; however, much remains to be revealed about the influence of complexity on epiphytic algae. Here, we used fractal dimension to study the effect of complexity at two scales, macrophyte architecture and leaf shape, on several parameters of the epiphytic algal community (number of individuals, biomass, taxon richness and diversity) in a Pampean stream. Four submerged macrophyte species with different complexities and associated algae were sampled in late spring, summer and autumn. Important differences were found in fractal dimension of the whole plant and leaves among macrophyte species. The particulate organic matter and chlorophyll a associated positively to leaf fractal dimension, but not to plant fractal dimension, partially supporting the hypothesis of a positive effect of macrophyte complexity on periphyton biomass. No association was found in fractal dimension with algal abundance, taxon richness or diversity. Complementary, a mesocosm experiment was performed with plastic imitations of different plant fractal dimensions. After four weeks, there were differences in chlorophyll a and autotrophy index between treatments that suggested a positive effect of complexity on autotrophic periphyton biomass. These results indicate that the well-known positive effect of macrophyte complexity on macroinvertebrates might be partially explained by a positive effect of complexity on periphyton biomass.     

Exploring a coarse-grained distributive strategy for finite-difference Poisson–Boltzmann calculations

We have implemented and evaluated a coarse-grained distributive method for finite-difference Poisson–Boltzmann (FDPB) calculations of large biomolecular systems. This method is based on the electrostatic focusing principle of decomposing a large fine-grid FDPB calculation into multiple independent FDPB calculations, each of which focuses on only a small and a specific portion (block) of the large fine grid. We first analyzed the impact of the focusing approximation upon the accuracy of the numerical reaction field energies and found that a reasonable relative accuracy of 10⁻³ can be achieved when the buffering space is set to be 16 grid points and the block dimension is set to be at least (1/6)³ of the fine-grid dimension, as in the one-block focusing method. The impact upon efficiency of the use of buffering space to maintain enough accuracy was also studied. It was found that an “optimal” multi-block dimension exists for a given computer hardware setup, and this dimension is more or less independent of the solute geometries. A parallel version of thedistributive focusing method was also implemented. Given the proper settings, the distributive method was able to achieve respectable parallel efficiency with tested biomolecular systems on a loosely connected computer cluster.     

Fractal dimension in human cerebellum measured by magnetic resonance imaging

Fractal dimension has been used to quantify the structures of a wide range of objects in biology and medicine. We measured fractal dimension of human cerebellum (CB) in magnetic resonance images of 24 healthy young subjects (12 men and 12 women). CB images were resampled to a series of image sets with different 3D resolutions. At each resolution, the skeleton of the CB white matter was obtained and the number of pixels belonging to the skeleton was determined. Fractal dimension of the CB skeleton was calculated using the box-counting method. The results indicated that the CB skeleton is a highly fractal structure, with a fractal dimension of 2.57 +/- 0.01. No significant difference in the CB fractal dimension was observed between men and women.     

Effects of conditioning history on selective stimulus control by elements of compound discriminative stimuli

Effects of prior discrimination training on stimulus control by color and shape dimensions of compound stimuli were studied with college students. In Phase 1, single-stimulus discrimination training was conducted for two values of color and shape. Phase 2 discrimination training employed two 2-dimensional compound stimuli composed of the color and shape stimuli trained in Phase 1. For conflict-compound stimuli, the stimulus-response-consequence contingency was altered between phases for one stimulus dimension (target dimension), but not for the other, non-target, dimension. Level of congruence (100%, 25%, and 0%) of the contingency for the target dimension between phases was manipulated across groups. When each stimulus value was tested in Phase 3, level of Phase-2-consistent responding to the target dimension varied with level of Phase-1-to-Phase-2 congruence. In Experiment 2, training history for the non-target dimension was altered across three conditions: (a) Correlated with reinforcement, as in Experiment 1, (b) No-Training, or (c) Not-Correlated. Phase-2-consistent responding to the target cue in Phase 3 was lower under the latter conditions than under the Correlated condition, indicating that the non-target dimension modulated control by the target dimension, consistent with stimulus competition. The data suggest elemental, rather than configural processing of the compound stimuli during Phase 2.     

CHARACTERIZATION OF MULTIPLE FORMS OF BRAIN TUBULIN SUBUNITS

Abstract— Microtubular protein was isolated from rat forebrain by biochemical purification (ammonium sulfate precipitation followed by DEAE cellulose chromatography) or by two cycles of aggregation-disaggregation. The protein subunit structure was examined on two-dimensional electrophoretograms: first dimension, urea isoelectric focusing gel; second dimension, sodium dodecyl sulfate exponential acrylamide slab gel. Two forms of α tubulin were separated in the second dimension on the basis of different rates of migration (α and α₂). Each of these species was further separated into at least three forms with different isoelectric points. β Tubulin was separated into a minor species (BI) and a major species β₂). Multiple subunits were observed using protein from either purification method and in a two-dimensional electrophoretogram of total supernatant proteins from rat brain. Separation and visualization of multiple forms of α and β tubulin is consistent with reports that provide evidence for post-translational modification of these proteins.     

Dimensional analysis revisited

The applicability of dimensional analysis (DA) is discussed in relation to the metabolic scaling laws. The evolution of different theories of biological similarity has shown that the calculated reduced exponents (b) of Huxley's allometric equation are closely correlated with the numerical values obtained from the statistical analysis of empirical data. Body mass and body weight are not equivalent as biological reference systems, since in accordance to Newton's second law, the former has a dimension of a mass, while the latter should be dimensionally considered as a force (W = MLT-2). This distinction affects the coefficients of the mass exponent (alpha). This difference is of paramount importance in microgravity conditions (spaceflight) and of buoyancy during the fetal life in mammals. Furthermore, the coefficients (beta) of the length dimension, and (gamma) of the time dimension do not vary when mass or weight are utilized as reference systems. Consequently, the "specific metabolic time," that results from the ratio of basal oxygen consumption and body mass or body weight yields the "biological meaning" of the time dimension, which is of fractal nature.     

Target-size embracing dimension for sensitive detection of viruses with various sizes and influenza virus strains

The focused ion beam (FIB) technique was employed to precisely fabricate hexagon-like Au nano-rods (fibAu_h) arrays as a surface enhanced Raman scattering - active substrate. A "ring diameter" (D(R)) was created by the convergence of three fibAu_h with respect to the dimension of the target viruses (D(T)), such as adenovirus (Adeno), encephalomyocarditis virus (EMCV), influenza virus (H1N1) with different sizes. Three influenza A virus strains were also compared. The results indicate that as that with a D(R)/D(T) ratio of around 1, the discrimination ability for detecting the target viruses and SERS mechanism become obvious. The enhanced lightning rod effect surrounding the seized target virus is anticipated if its size and dimension is suitably embraced within three fibAu_h. Hence the as-designed fibAu_h sample with a target-size embracing dimension provides good discrimination ability for distinguishing virus of various sizes or virus strains.     

Ontogenetic changes in the fractal geometry of the bronchial tree in Rattus norvegicus

Respiration and metabolism change dramatically over the course of the development of vertebrates. In mammals these changes may be ascribed to organogenesis and differentiation of structures involved in gas exchange and transport and the increase in size. Since young as well as mature individuals must be well-designed if the species is to survive, the physiological changes during the development should be matched with geometrical or structural adjustments of the respiratory system. The aim of this study was to evaluate changes in the fractal geometry of the bronchial tree during the postnatal development of the rat. The average fractal dimension of the bronchial tree of the rats was 1.587, but that of juveniles was larger than that of the adults. We found a significant negative correlation between age and fractal dimension. This correlation could be considered be misleading because of the difficulty of separating age/body size effects. Nevertheless, because fractal dimensions of the bronchial tree of rabbits and humans are known to be similar, 1.58 and 1.57 respectively, the body size effect may be nil. To our knowledge, this is the first report of ontogenetic changes in the fractal dimension of the bronchial tree in mammals.     

Using fractal dimensions for characterizing tortuosity of animal trails

ABSTRACT. The tortuosity of mite trails was characterized by their fractal dimension, which is the non-Euclidean dimension varying between 1 (completely straight) and 2 (so tortuous that the complete two-dimensional space is used). This index was shown to be a good, discriminative index for mite trails, which is a completely new use of the fractal dimension. The value of this index is compared with other tortuosity indices.     

A simplified 2-D electrophoresis protocol with the aid of an organic disulfide

2-DE is still a relatively cumbersome and labor intensive method. Given the successful cysteinyl protection concept with hydroxyethyl disulfide (specific oxidation) during the first dimension separation, the possibility for a simplified equilibration procedure was investigated. This was achieved by maintaining the S-mercaptoethanol modified cysteinyls throughout the 2-D workflow including second dimension separation, spot handling, protein digestion, and protein identification. The traditional equilibration protocol encompassing thiol reduction and alkylation was compared with a one-step protocol employing continuous exposure to hydroxyethyl disulfide. Both equilibration protocols gave equally well-resolved spot maps with analytical protein loads regardless of IPG strip pH range. Using preparative protein loads, narrow range IPG strips gave comparable results for the two protocols while preparative load on wide range IPG strips was the only condition where classical reduction/alkylation outperformed hydroxyethyl disulfide equilibration. Moreover, with analytical protein loads, the hydroxyethyl disulfide equilibration time could be significantly reduced without apparent loss of spot map quality or quantitative protein transfer from the first- to the second dimension gel. MALDI-TOF mass spectrometric protein identification was successfully performed with either iodoacetamide or hydroxyethyl disulfide as the cysteine modifier, yielding comparable identification results with high confidence in protein assignment, sequence coverage, and detection of cysteine-containing peptides. The results provide a novel and simplified protocol for 2-DE where the concept of hydroxyethyl disulfide as the cysteinyl protecting agent is extended to cover the entire 2-D work flow.     

Dimensional analysis of RR dynamic in 24 hour electrocardiograms

Using dimensional analysis, we demonstrate that it is possible to quantify changes in the topological structure of cardiac dynamics over long periods of time. A method was developed to calculate a dimension-like measure (referred to here as apparent dimension) from a correlation algorithm within a data window of 500 heart beats which is moved in equidistant steps over the time series of the RR intervals over 24 hours. The correspondence between the apparent dimension and the correlation dimension was tested using artificial data sequences. Furthermore 24 hour electrocardiographic recordings of two healthy subjects and of a patient with acute myocardial infarction were examined. The reliability of the analysis could be demonstrated and changes in dimension reflecting physiological as well as pathophysiological changes were observed.     

Analysis of tubulin isoforms by two-dimensional gel electrophoresis using SDS-polyacrylamide gel electrophoresis in the first dimension.

A two-dimensional electrophoretic system using SDS-polyacrylamide gel electrophoresis (SDS-PAGE) in the first dimension and isoelectric focusing (IEF) in the second dimension was devised. In spite of its simplicity, this method could show a markedly high resolution for tubulin isoforms and moreover could classify them into alpha- or beta-tubulin as a two-dimensional profile. With this method, seven alpha- and four beta-tubulin isoforms could be detected within axoneme from Tetrahymena cilia. Moreover this method could also resolve tubulin isoforms from the rabbit brain. These results indicate that the present two-dimensional gel electrophoresis is a useful tool for the electrophoretic analysis of tubulin isoforms from various sources.