The multidimensional space of the integral characteristics of biocenotic assemblages: The self-similarity or scale invariance of its structure

In a virtual multidimensional space whose coordinate axes are integral characteristics, such as logarithms of the abundance and size of individuals, as well as the components of species diversity, the points that correspond to samples from various biocenotic assemblages form multilayered geometric figures of a similar shape. As was shown based on examples of pelagic macrofauna in the Bering Sea, Sea of Okhotsk, Sea of Japan, and adjacent waters of the Pacific Ocean, as well as phytoplankton, zooplankton, and zoobenthos in Lake Ladoga, Neva Bay, and the Gulf of Finland in the Baltic Sea, these figures possess some properties of fractals. This phenomenon results from the multidimensional domain of the integral characteristics, in which a multitude of points is aggregated along a segment, whose length and orientation relative to the coordinate axes reflects universal power laws at the biocenotic level of the organization of matter; power laws, such as y = a · x ^b , are known to be an unlimited source of self-similarity and scale invariance.     

Interpreting plots of a multidimensional dose-response surface in a parallel coordinate system

The dose-response surface for a combination of drugs is a multidimensional figure. Consequently, it is not possible to view such a surface using orthogonal axes when the number of dimensions exceeds 3. Parallel axes have been used to represent hyperdimensional figures. This paper reports on the use of parallel coordinate axes to plot the dose-response surface and its contours of constant response (isobols) for a combination of drugs. It is shown that patterns formed by intersecting line segments in the parallel system can aid in the interpretation of the fitted dose-response surface. More generally, analytic results are developed that permit the ready visualization and characterization of interaction effects of a polynomial model.     

Consideration of digitization precision when building local coordinate axes for a foot model

This study investigated whether points digitized for the purpose of embedding coordinate systems into the foot accurately represented the orientation of the bone described. Eight complete data sets were collected from 9 adult cadaver specimens. Palpable landmarks defined 5 segments to include the calcaneus, navicular, medial cuneiform, first metatarsal, and hallux. With use of the Flock of Birds electromagnetic motion tracking device, a single examiner digitized a minimum of 3 points for each segment. Coordinate definitions followed the right-hand rule, with left-sided data converted to right-sided equivalency. Local axes were created where X projected approximately forward, Y upward, and Z laterally. Matrix transformation computations calculated the angular precision in degrees between coordinates built from points digitized pre- and post-dissection of surface tissues covering bone. The condition of post-dissection was considered the criterion standard for comparison. Change about the X-axis represented the angular precision of the coordinate in the frontal anatomical plane; Y-axis in the transverse plane; Z-axis in the sagittal plane. The calcaneus and navicular coordinate axes changed by an average of <3° across conditions. Mean coordinate angulation of the cuneiform X, Y, Z axes changed by 6.0°, 4.6°, 11.9°, respectively. Change in coordinate angulation was largest for the X-axis at the first metatarsal (48.6°) and hallux (36.5°). A two-way repeated measures ANOVA found a significant interaction between the axis and segment (F=8.87, P=0.00). Tukey post-hoc comparisons indicated the change in coordinate angulation at the X-axis for the cuneiform, metatarsal, and hallux to be significantly different (P <0.05) from the calcaneus and navicular. The X-axis of the first metatarsal and hallux was different from all other axis-segment combinations except for the Z-axis of the cuneiform. Differences in locating landmarks reduced angular precision of the coordinate axes most in the smallest foot segments where points digitized were located close together. We can recommend the proposed landmarks for the calcaneus and navicular segments, but kinematics determined about the coordinate axes for the small sized medial cuneiform, and the long (X) axis for the first metatarsal and hallux have excessive error.     

Testing the hypothesis of tolerance strategies in Hiatella arctica L. (Mollusca: Bivalvia)

The physiological and biocenotic optima of Hiatella arctica L. inhabiting shallow water fouling communities of the White Sea were compared. The biomass and proportion of H. arctica in communities were used for the estimation of biocenotic optima or community success. The physiological state of populations was assessed by means of the fluctuating asymmetry. The fluctuating asymmetry of H. arctica was calculated using the valve weights. It was determined that the shell of H. arctica possesses a slight directional asymmetry, the right valve usually being larger (and heavier) than the left one. The relationship between fluctuating and directional asymmetries is discussed. High biomass and proportion of H. arctica in the community generally correspond with high levels of fluctuating asymmetry. Thus, a discrepancy between physiological and ecological optima is observed, which is recognised as being characteristic of a tolerance strategy. However, in the absence of pressure from major filter-feeding competitors such as the mussel Mytilus edulis L. and the solitary ascidian Styela rustica L., populations of H. arctica possess a high biomass and low levels of fluctuating asymmetry. It appears that H. arctica prefers to inhabit shelters or depressions, or to be covered by other organisms. Populations of H. arctica existing in the absence of shelter had extremely high levels of fluctuating asymmetry despite the absence of filter-feeding competitors. Thus, the strategy adopted by H arctica L. in the investigated upper 5 m layer of water in the White Sea can be described as a stress- and competitor-tolerant strategy.     

Application of Empirical Wave Run-Up Formulas to the Polish Baltic Sea Coast

Advanced, multidimensional models are typically applied when researching processes occurring in the nearshore. Relatively simple, empirical equations are commonly used in coastal engineering practice in order to estimate extreme wave run-up on beaches and coastal structures. However, they were mostly calibrated to the characteristics of oceanic coasts, which have different wave regime than a semi-enclosed basin like the Baltic Sea. In this paper we apply the formulas to the Polish Baltic Sea coast. The equations were adjusted to match local conditions in two test sites in Międzyzdroje and Dziwnówek, where beaches are under continuous video surveillance. Data from WAM wave model and coastal gauge stations were used, as well as precise measurements of the beaches'' cross-sections. More than 600 run-up events spanning from June to December 2013 were analysed, including surges causing dune erosion. Extreme wave run-up R_2% was calculated and presented as a percentage value indicating what part of the beach was inundated. The method had a root-mean-square error of 6.1 and 6.5 percentage points depending on the test site. We consider it is a fast and computationally undemanding alternative to morphodynamic models. It will constitute a part of the SatBałtyk Operating System-Shores, delivering forecasts of wave run-up on the beaches for the entire Polish coastline.     

Correction formulae for the misalignment of axes in the measurement of the orthotropic elastic constants

In the experimental determination of the orthotropic elastic constants, one often encounters the situation in which the symmetry axes of the material are not coincident with specimen axes along which the material testing is accomplished. The problem of calculating the compliance coefficients in the symmetry coordinate system from measurements of the compliance coefficients made in an arbitrary, specimen fixed, coordinate system is considered here.     

Crustaceans in the splash and upper sublittoral zones of the Opukskii Nature Reserve (Crimea,Black Sea)

Work at local biodiversity checklists in nature reserves is essential for the preservation of this diversity, which is the principal aim of establishing nature reserves. Such work is also important for understanding biocenotic connections in marine systems. Crustaceans are among the most numerous and functionally important groups of organisms dwelling in the zones along the coastline. We studied this group in the splash zone and on algal thalli and stems of marine plants in the littoral zone of the Black Sea in and around the Opukskii Nature Reserve, the fauna of which is not sufficiently known. Nineteen crustacean species were found, most of these being members of the order Isopoda. Some of the recorded species have not been observed recently in other areas of the Black Sea. The species composition of crustaceans is peculiar to the reserve and its environs.     

A new non-orthogonal decomposition method to determine effective torques for three-dimensional joint rotation

This paper describes a new non-orthogonal decomposition method to determine effective torques for three-dimensional (3D) joint rotation. A rotation about a joint coordinate axis (e.g. shoulder internal/external rotation) cannot be explained only by the torque about the joint coordinate axis because the joint coordinate axes usually deviate from the principal axes of inertia of the entire kinematic chain distal to the joint. Instead of decomposing torques into three orthogonal joint coordinate axes, our new method decomposes torques into three "non-orthogonal effective axes" that are determined in such a way that a torque about each effective axis produces a joint rotation only about one of the joint coordinate axes. To demonstrate the validity of this new method, a simple internal/external rotation of the upper arm with the elbow flexed at 90 degrees was analyzed by both orthogonal and non-orthogonal decomposition methods. The results showed that only the non-orthogonal decomposition method could explain the cause-effect mechanism whereby three angular accelerations at the shoulder joint are produced by the gravity torque, resultant joint torque, and interaction torque. The proposed method would be helpful for biomechanics and motor control researchers to investigate the manner in which the central nervous system coordinates the gravity torque, resultant joint torque, and interaction torque to control 3D joint rotations.     

A motion-decomposition approach to address gimbal lock in the 3-cylinder open chain mechanism description of a joint coordinate system at the glenohumeral joint

In this study, the standard-sequence properties of a joint coordinate system were implemented for the glenohumeral joint by the use of a set of instantaneous geometrical planes. These are: a plane that is bound by the humeral long axis and an orthogonal axis that is the cross product of the scapular anterior axis and this long axis, and a plane that is bounded by the long axis of the humerus and the cross product of the scapular lateral axis and this long axis. The relevant axes are updated after every decomposition of a motion component of a humeral position. Flexion, abduction and rotation are then implemented upon three of these axes and are applied in a step-wise uncoupling of an acquired humeral motion to extract the joint coordinate system angles. This technique was numerically applied to physiological kinematics data from the literature to convert them to the joint coordinate system and to visually reconstruct the motion on a set of glenohumeral bones for validation.     

A kinematic model of the human ankle

The spatial gross motion of the foot with respect to the shank is modelled as rotations about two fixed ankle axes: the upper ankle rotation axis (plantarflexion/dorsiflexion) and the subtalar rotation axis (inversion/eversion). The positions of the axes are determined by externally visible bony landmarks of the lower leg and are measured for a living subject. The model input data are the plantarflexion/dorsiflexion and inversion/eversion rotation angles; the model output is a 4 × 4 transformation matrix which quantitatively describes the relative position of a foot coordinate system with respect to a shank coordinate system.     

Polysiphonia perforans sp. nova (Ceramiales,Rhodophyta) from the Mediterranean Sea

ABSTRACT

A new species of the genus Polysiphonia from the Mediterranean Sea is described. It is an ecorticate species, with 4 pericentral cells, showing prostrate axes from which erect axes arise. Rhizoids are formed by pericentral cells in a median position remaining in open connection with them. Erect axes are straight, simple throughout or pseudodichotomous at the base then simple or with one (rarely two-three) orders of branching; trichoblasts and scar cells not observed. Only tetrasporangial plants were found. They show ellipsoid tetrasporangia borne in short straight series, often interrupted by sterile segments. The new species is also characterized by a peculiar habit consisting of prostrate axes, adhering to lower faces of Peyssonnelia spp. by means of rhizoids growing upward, from which erect upright axes perforating thalli of the supporting species arise. A comparison with the related species of Polysiphonia was also carried out.     

A method of determination of the angular velocity vector of a limb segment

A method for the determination of the angular velocity vector of a limb segment in three dimensional motion, is described. It is first necessary to obtain the coordinates, with respect to a space fixed system of Cartesia axes, at suitably small time increments for three non-colinear points on the limb segment. The velocity components with respect to space fixed axes, of the points on the limb segments are then obtained by numerical differentiation. A procedure which is given is then used to calculate the components, with respect to body fixed axes, of the angular velocity vector from the velocity components of the three points.     

Evaluation of a 3D object registration method for analysis of humeral kinematics

In 3D image-based studies of joint kinematics, 3D registration methods should be automatic, insensitive to segmentation inconsistencies and use coordinate systems that have clinically relevant orientations and locations because this is important for analyzing rotation angles and translation directions. We developed and evaluated a registration method, which is based on the cylindrical geometry of the humerus shaft and an analysis of the inertia moments of the humerus head, in order to consistently and automatically orient the humerus coordinate system according to its anatomy. Registration techniques must be thoroughly evaluated. In this study we used a well-detectable marker as reference, from which coordinate system determination errors of a 3D object could be measured. This allowed us to quantify by means of unique error analysis the translational and rotational errors in terms of how much and about/along which humeral axis errors occurred. The evaluation experiments were performed using virtual rotations of 3D humeral binary image, a humerus model and a 3D image of a volunteer's shoulder. They indicated that the humeral coordinate system determination errors primarily originated from segmentation inconsistencies, which influenced mostly the humeral transverse axes orientation. The error analysis revealed that the developed registration method reduced the effect of manual segmentation inconsistencies on the orientation of the humeral transverse axes up to 37%, in comparison to the commonly used inertia registration.     

A scapular coordinate frame for clinical and kinematic analyses

The aim of this study was to define a body-fixed coordinate frame for the scapula that minimises axes variability and is closely related to the clinical frame of reference. Medical images of 21 scapulae were used to quantify 14 different axes from identifiable landmarks. The plane of the blade of the scapula was defined. The orientations of the quantified axes were calculated. The angular relationships between axes were quantified and applied to grade the sensitivity of each axis to inter-scapular variations in the others. The volume of data required to define an axis was noted for its dependency on pathology and the three criteria were weighted according to relative importance. The two axes with the highest weighting were applied to define a body-fixed Cartesian coordinate frame for the scapula. A least square medio-lateral line through the centre of the spine root was the most optimal axis. The plane formed by the spine root line and a least square line through the centre of the lateral border ridge was the most optimal scapular plane. This body-fixed Cartesian coordinate frame is closely aligned to the cardinal planes in the anatomical position and thus is a clinically applicable, specimen invariant coordinate frame that can be used in patient-specific kinematics modelling.     

Comparison of the hindfoot axes of a multi-segment foot model to the underlying bony anatomy

Musculoskeletal models used in gait analysis require coordinate systems to be identified for the body segments of interest. It is not obvious how hindfoot (or rearfoot) axes defined by skin-mounted markers relate to the anatomy of the underlying bones. The aim of this study was to compare the marker-based axes of the hindfoot in a multi-segment foot model to the orientations of the talus and calcaneus as characterized by their principal axes of inertia. Twenty adult females with no known foot deformities had radio-opaque markers placed on their feet and ankles at the foot model marker locations. CT images of the feet were acquired as the participants lay supine with their feet in a semi-weight bearing posture. The spatial coordinates of the markers were obtained from the images and used to define the foot model axes. Segmented masks of the tali and calcanei were used to create 3D bone models, from which the principal axes of the bones were obtained. The orientations of the principal axes were either within the range of typical values reported in the imaging literature or differed in ways that could be explained by variations in how the angles were defined. The model hindfoot axis orientations relative to the principal axes of the bones had little bias but were highly variable. Consideration of coronal plane hindfoot alignment as measured clinically and radiographically suggested that the model hindfoot coordinate system represents the posterior calcaneal tuberosity, rather than the calcaneus as a whole.     

Hydrodynamics in the renal tubule

Explicit solutions of the Navier-Stokes equations are presented for axially symmetric slow flow in an infinite cylinder whose walls reabsorb fluid at a rate which varies exponentially with the longitudinal coordinate. Results similar to those of a previous paper which assumed a constant rate of reabsorption are obtained. When the radius of the tube is small the solutions resemble Poiseuille flow; the longitudinal velocity profile is parabolic, and the drop in mean pressure is proportional to the mean axial flow, the length of tube between reference points, and inversely proportional to the fourth power of the radius. By expressing the tubular reabsorption as a Fourier integral, solutions are obtained for the general case where the rate of reabsorption is an arbitrary function of the longitudinal coordinate.     

Non-linear ordination in several dimensions

A method is described for fitting a model in which site characteristics are represented by a set of orthogonal axes, while the probability that a particular species will be present, and its quantity if it is present, are each related to the axes of the system by symmetrical hypersurfaces with an optimum, decreasing asymptotically to zero as conditions depart from the optimum. The method needs initial estimates of the positions of the sample sites within the axis system. Given these starting points, they can be progressively improved by an iterative procedure. Results are reported of an extensive series of tests using artificial data, and of an analysis of field data from brigalow woodland in Queensland.     

Evidence for surface-based processing of binocular disparity

It is convenient to think of an object's location as a point within a Cartesian framework; the x axis corresponds to right and left, the y axis to up and down, and the z axis to forward or backward. When an observer is looking straight ahead, binocular disparities provide information about distance along the z axis from the fixation plane. In this coordinate system, changes in disparity are treated as independent of changes in location along the orthogonal x and y axes. Does the human visual system use this three-dimensional coordinate system, or does it specify feature location in a coordinate frame determined by other nearby visible features? Here we show that the sensitivity of the human stereo system is determined by the distance of points with respect to a local reference plane, rather than by the distance along the z axis with respect to the fixation plane. There is a distinct advantage to using a local frame of reference for specifying location. It obviates the need to construct a complex three-dimensional space in either eye-centered or head-centered coordinates that must be updated with every shift of the eyes and head.     

Bone surface mapping method

Bone shape is an important factor to determine the bone's structural function. For the asymmetrically shaped and anisotropically distributed bone in vivo, a surface mapping method is proposed on the bases of its geometric transformation invariance and its uniqueness of the principal axes of inertia. Using spiral CT scanning, we can make precise measurements to bone in vivo. The coordinate transformations lead to the principal axes of inertia, with which the prime meridian and the contour can be set. Methods such as tomographic reconstruction and boundary development are employed so that the surface of bone in vivo can be mapped. Experimental results show that the surface mapping method can reflect the shape features and help study the surface changes of bone in vivo. This method can be applied to research into the surface characteristics and changes of organ, tissue or cell whenever its digitalized surface is obtained.     

Accurate Inference of Subtle Population Structure (and Other Genetic Discontinuities) Using Principal Coordinates

Background

Accurate inference of genetic discontinuities between populations is an essential component of intraspecific biodiversity and evolution studies, as well as associative genetics. The most widely-used methods to infer population structure are model-based, Bayesian MCMC procedures that minimize Hardy-Weinberg and linkage disequilibrium within subpopulations. These methods are useful, but suffer from large computational requirements and a dependence on modeling assumptions that may not be met in real data sets. Here we describe the development of a new approach, PCO-MC, which couples principal coordinate analysis to a clustering procedure for the inference of population structure from multilocus genotype data.

Methodology/Principal Findings

PCO-MC uses data from all principal coordinate axes simultaneously to calculate a multidimensional “density landscape”, from which the number of subpopulations, and the membership within subpopulations, is determined using a valley-seeking algorithm. Using extensive simulations, we show that this approach outperforms a Bayesian MCMC procedure when many loci (e.g. 100) are sampled, but that the Bayesian procedure is marginally superior with few loci (e.g. 10). When presented with sufficient data, PCO-MC accurately delineated subpopulations with population F_st values as low as 0.03 (G''_st>0.2), whereas the limit of resolution of the Bayesian approach was F_st = 0.05 (G''_st>0.35).

Conclusions/Significance

We draw a distinction between population structure inference for describing biodiversity as opposed to Type I error control in associative genetics. We suggest that discrete assignments, like those produced by PCO-MC, are appropriate for circumscribing units of biodiversity whereas expression of population structure as a continuous variable is more useful for case-control correction in structured association studies.