The singularities of the visual mapping

In this article we treat purely metrical properties of the visual image, e.g. the time changes of the relative positions and orientations of image details. Self-induced movements of an observer relative to rigid bodies in his environment generate charactertistic motion parallax fields. The observer may regard those fields as proprioceptive and interprete the geometrical invariants of the fields as indicators of solid shape. In this way his perceptions become object-oriented, which is the normal case as the many constancy-phenomena show. Similar arguments apply to the disparity field of binocular vision. In this paper we treat the qualitative nature of such fields. [In this case the qualitative nature is basic. Compare the case of an equation with a single unknown. Often one is interested primarily in the qualitative solution (are there roots? How many?), and only slightly in the quantitative information (the numerical value of a root).] The qualitative nature of the fields is fixed if their singularities are known. It is shown that the singularities are of two types: isolated points (so-called specular points) and line-singularities (so-called folds, cusps and T-junctions). It is shown that for most vantage points that an observer can occupy, the topological structure of the set of singularities does not change if the observer performs small exploratory movements. That is most vantage points are stable. At an unstable vantage point the set of singularities changes and the observer experiences an event. Because certain properties of the set of singularities are shown to be preserved, only a few simple types of event are possible. A complete list is presented. The occurrence of an event is shown to be simply related to the solid shape of the objects of vision. Our geometrical theory enables us to understand the structure of the observer's internal models of external bodies.     

Geometric and potential driving formation and evolution of biomolecular surfaces

This paper presents new geometrical flow equations for the theoretical modeling of biomolecular surfaces in the context of multiscale implicit solvent models. To account for the local variations near the biomolecular surfaces due to interactions between solvent molecules, and between solvent and solute molecules, we propose potential driven geometric flows, which balance the intrinsic geometric forces that would occur for a surface separating two homogeneous materials with the potential forces induced by the atomic interactions. Stochastic geometric flows are introduced to account for the random fluctuation and dissipation in density and pressure near the solvent–solute interface. Physical properties, such as free energy minimization (area decreasing) and incompressibility (volume preserving), are realized by some of our geometric flow equations. The proposed approach for geometric and potential forces driving the formation and evolution of biological surfaces is illustrated by extensive numerical experiments and compared with established minimal molecular surfaces and molecular surfaces. Local modification of biomolecular surfaces is demonstrated with potential driven geometric flows. High order geometric flows are also considered and tested in the present work for surface generation. Biomolecular surfaces generated by these approaches are typically free of geometric singularities. As the speed of surface generation is crucial to implicit solvent model based molecular dynamics, four numerical algorithms, a semi-implicit scheme, a Crank–Nicolson scheme, and two alternating direction implicit (ADI) schemes, are constructed and tested. Being either stable or conditionally stable but admitting a large critical time step size, these schemes overcome the stability constraint of the earlier forward Euler scheme. Aided with the Thomas algorithm, one of the ADI schemes is found to be very efficient as it balances the speed and accuracy.      

The geometric theory of adaptive evolution: trade-off and invasion plots

The purpose of this paper is to take an entirely geometrical path to determine the evolutionary properties of ecological systems subject to trade-offs. In particular we classify evolutionary singularities in a geometrical fashion. To achieve this, we study trade-off and invasion plots (TIPs) which show graphically the outcome of evolution from the relationship between three curves. The first invasion boundary (curve) has one strain as resident and the other strain as putative invader and the second has the roles of the strains reversed. The parameter values for one strain are used as the origin with those of the second strain varying. The third curve represents the trade-off. All three curves pass through the origin or tip of the TIP. We show that at this point the invasion boundaries are tangential. At a singular TIP, in which the origin is an evolutionary singularity, the invasion boundaries and trade-off curve are all tangential. The curvature of the trade-off curve determines the region in which it enters the singular TIP. Each of these regions has particular evolutionary properties (EUS, CS, SPR and MI). Thus we determine by direct geometric argument conditions for each of these properties in terms of the relative curvatures of the trade-off curve and invasion boundaries. We show that these conditions are equivalent to the standard partial derivative conditions of adaptive dynamics. The significance of our results is that we can determine whether the singular strategy is an attractor, branching point, repellor, etc. simply by observing in which region the trade-off curve enters the singular TIP. In particular we find that, if and only if the TIP has a region of mutual invadability, is it possible for the singular strategy to be a branching point. We illustrate the theory with an example and point the way forward.     

FitEM2EM--tools for low resolution study of macromolecular assembly and dynamics

Studies of the structure and dynamics of macromolecular assemblies often involve comparison of low resolution models obtained using different techniques such as electron microscopy or atomic force microscopy. We present new computational tools for comparing (matching) and docking of low resolution structures, based on shape complementarity. The matched or docked objects are represented by three dimensional grids where the value of each grid point depends on its position with regard to the interior, surface or exterior of the object. The grids are correlated using fast Fourier transformations producing either matches of related objects or docking models depending on the details of the grid representations. The procedures incorporate thickening and smoothing of the surfaces of the objects which effectively compensates for differences in the resolution of the matched/docked objects, circumventing the need for resolution modification. The presented matching tool FitEM2EMin successfully fitted electron microscopy structures obtained at different resolutions, different conformers of the same structure and partial structures, ranking correct matches at the top in every case. The differences between the grid representations of the matched objects can be used to study conformation differences or to characterize the size and shape of substructures. The presented low-to-low docking tool FitEM2EMout ranked the expected models at the top.     

Nuclear magnetic resonance titration curves of histidine ring protons. Conformational transition affecting three of the histidine residues of ribonuclease.

NMR titration curves are reported for the 4 histidine residues of ribonuclease A in sodium acetate and for ribonuclease S in sodium acetate, phosphate, and sulfate solutions. Evidence is presented that the imidazole side chain of histidine residue 48 undergoes a conformational change, probably also involving the carboxyl side chain of aspartic acid residue 14. This group is considered to be responsible for the low pH inflection with pKa 4.2 present in the NMR titration curve of the C-2 proton resonance of histidine 48. The NMR titration curves of the active site histidine residues 12 and 119 also exhibit inflections at low pH values, although there is no carboxyl group within 9 A of the imidazole side chain of histidine residue 12 in the structure of ribonuclease S determined by x-ray crystallography (Wyckoff, H. W., Tsernoglou, D., Hanson, A. W. Knox, J. R., Lee, B., and Richards, F. M. (1970) J. Biol. Chem. 245, 305-328). Curve fitting was carried out on 11 sets of NMR titration data using a model in which the 3 histidine residues 12, 119, and 48 are assumed to be affected by a common carboxyl group. The results obtained indicate that such a model with fewer parameters gives as good a representation of the data as the model in which each histidine residue is assumed to interact separately with a different carboxyl group. Therefore, it is concluded that the ionization of aspartic acid residue 14 is indirectly experienced by the active site histidine residues through the conformational change at histidine 48. A model assuming mutual interaction of the active site histidine residues does not account for the low pH inflections in these curves.     

FEULGEN HYDROLYSIS OF NORMAL CELLS AND MOUSE ASCITES TUMOR CELLS

The effect of HCl hydrolysis on the dye content (Feulgen reaction) of normal cells and mouse ascites tumor cells was examined by means of cytophotometric measurements. After 11 min of hydrolysis, 16-day-old tumor cells showed a hypotetraploid DNA line with doubling peaks. The DNA values were in the ratios of 1:2:4:8 during all the tested hydrolysis times (3 to 21 min). The size of the nucleus and the DNA concentration did not influence the hydrolysis and the dye content. However, the time of the hydrolysis considerably influenced the dye content of normal and tumor cells. The course of the curves obtained by plotting dye absorption against hydrolysis time showed an inflection of the curve at 9 min' hydrolysis time in tumor cells, whereas the inflection occurred at 8 min in mitotic cells. These inflections were statistically significant. The DNA stem-line¹ for tumor cells shifted during different hydrolysis times when compared to normal cells. The possibility is discussed of two types of DNA which differed in their acid sensitivity and which yielded atypical hydrolysis curves.     

Shape complementarity of protein-protein complexes at multiple resolutions

Biological complexes typically exhibit intermolecular interfaces of high shape complementarity. Many computational docking approaches use this surface complementarity as a guide in the search for predicting the structures of protein-protein complexes. Proteins often undergo conformational changes to create a highly complementary interface when associating. These conformational changes are a major cause of failure for automated docking procedures when predicting binding modes between proteins using their unbound conformations. Low resolution surfaces in which high frequency geometric details are omitted have been used to address this problem. These smoothed, or blurred, surfaces are expected to minimize the differences between free and bound structures, especially those that are due to side chain conformations or small backbone deviations. Despite the fact that this approach has been used in many docking protocols, there has yet to be a systematic study of the effects of such surface smoothing on the shape complementarity of the resulting interfaces. Here we investigate this question by computing shape complementarity of a set of 66 protein-protein complexes represented by multiresolution blurred surfaces. Complexed and unbound structures are available for these protein-protein complexes. They are a subset of complexes from a nonredundant docking benchmark selected for rigidity (i.e. the proteins undergo limited conformational changes between their bound and unbound states). In this work, we construct the surfaces by isocontouring a density map obtained by accumulating the densities of Gaussian functions placed at all atom centers of the molecule. The smoothness or resolution is specified by a Gaussian fall-off coefficient, termed "blobbyness." Shape complementarity is quantified using a histogram of the shortest distances between two proteins' surface mesh vertices for both the crystallographic complexes and the complexes built using the protein structures in their unbound conformation. The histograms calculated for the bound complex structures demonstrate that medium resolution smoothing (blobbyness = -0.9) can reproduce about 88% of the shape complementarity of atomic resolution surfaces. Complexes formed from the free component structures show a partial loss of shape complementarity (more overlaps and gaps) with the atomic resolution surfaces. For surfaces smoothed to low resolution (blobbyness = -0.3), we find more consistency of shape complementarity between the complexed and free cases. To further reduce bad contacts without significantly impacting the good contacts we introduce another blurred surface, in which the Gaussian densities of flexible atoms are reduced. From these results we discuss the use of shape complementarity in protein-protein docking.     

Body shape shifting during growth permits tests that distinguish between competing geometric theories of metabolic scaling

Metabolism fuels all of life's activities, from biochemical reactions to ecological interactions. According to two intensely debated theories, body size affects metabolism via geometrical influences on the transport of resources and wastes. However, these theories differ crucially in whether the size dependence of metabolism is derived from material transport across external surfaces, or through internal resource‐transport networks. We show that when body shape changes during growth, these models make opposing predictions. These models are tested using pelagic invertebrates, because these animals exhibit highly variable intraspecific scaling relationships for metabolic rate and body shape. Metabolic scaling slopes of diverse integument‐breathing species were significantly positively correlated with degree of body flattening or elongation during ontogeny, as expected from surface area theory, but contradicting the negative correlations predicted by resource‐transport network models. This finding explains strong deviations from predictions of widely adopted theory, and underpins a new explanation for mass‐invariant metabolic scaling during ontogeny in animals and plants.     

The temperature dependence of State IV respiration, the calcium uptake system, and the activity of the calcium ionophore A23187 in mitochondria from endo- and ectothermic animals.

1. Arrhenius plots of State IV respiratory activity of liver mitochondria from both rainbow trout and rat were linear over the temperature range 5-35 degrees C. 2. Calcium uptake was monitored by stimulation of oxygen consumption and by calcium electrode recording, with quite comparable results. Rainbow trout gave the usual linear Arrhenius plot but this plot for rat mitochondria exhibited two well-defined inflections or discontinuities. 3. The temperature dependence of the activity of the ionophore A23187 was investigated by measuring the increase in oxygen uptake following a sub-maximal dose of this drug. Again a linear relation was found for rainbow trout, but in this case the rat curves showed only a single inflection point. 4. These results are discussed in relation to other work on the effects of lipid phase transitions on mitochondrial membrane-associated systems.     

Unsupervised classification of single particles by cluster tracking in multi-dimensional space

In cryo-electron microscopy (cryo-EM) single-particle reconstruction, the heterogeneity of two-dimensional projection image data resulting from the co-existence of different conformational or ligand binding states of a macromolecular complex remains a major obstacle as it impairs the validity of reconstructed density maps and limits the progress toward higher resolution. Classification of cryo-EM data according to the different conformations is difficult because of the coexistence of multiple orientations in a single dataset. Here, we present an unsupervised classification method, termed cluster tracking, which utilizes the continuity in multi-dimensional space induced by angular adjacency of projections in large datasets. In a proof of concept, the testing of cluster tracking on simulated projection data, which were generated from multiple conformations and orientations of an existing volume, produced clusters that are consistent with the conformational identity of the data. The application of the method to experimental cryo-EM projection data is found to result in a partition similar to the one generated by supervised classification.     

Finite-time Lyapunov exponents and metabolic control coefficients for threshold detection of stimulus–response curves

In biochemical networks transient dynamics plays a fundamental role, since the activation of signalling pathways is determined by thresholds encountered during the transition from an initial state (e.g. an initial concentration of a certain protein) to a steady-state. These thresholds can be defined in terms of the inflection points of the stimulus–response curves associated to the activation processes in the biochemical network. In the present work, we present a rigorous discussion as to the suitability of finite-time Lyapunov exponents and metabolic control coefficients for the detection of inflection points of stimulus–response curves with sigmoidal shape.     

Embodied information processing: vibrissa mechanics and texture features shape micromotions in actively sensing rats

Peripheral sensory organs provide the first transformation of sensory information, and understanding how their physical embodiment shapes transduction is central to understanding perception. We report the characterization of surface transduction during active sensing in the rodent vibrissa sensory system, a widely used model. Employing high-speed videography, we tracked vibrissae while rats sampled rough and smooth textures. Variation in vibrissa length predicted motion mean frequencies, including for the highest velocity events, indicating that biomechanics, such as vibrissa resonance, shape signals most likely to drive neural activity. Rough surface contact generated large amplitude, high-velocity "stick-slip-ring" events, while smooth surfaces generated smaller and more regular stick-slip oscillations. Both surfaces produced velocities exceeding those applied in reduced preparations, indicating active sensation of surfaces generates more robust drive than previously predicted. These findings demonstrate a key role for embodiment in vibrissal sensing and the importance of input transformations in sensory representation.     

Modular optical topometric sensor for 3D acquisition of human body surfaces and long-term monitoring of variations.

Optical topometric 3D sensors such as laser scanners and fringe projection systems allow detailed digital acquisition of human body surfaces. For many medical applications, however, not only the current shape is important, but also its changes, e.g., in the course of surgical treatment. In such cases, time delays of several months between subsequent measurements frequently occur. A modular 3D coordinate measuring system based on the fringe projection technique is presented that allows 3D coordinate acquisition including calibrated color information, as well as the detection and visualization of deviations between subsequent measurements. In addition, parameters describing the symmetry of body structures are determined. The quantitative results of the analysis may be used as a basis for objective documentation of surgical therapy. The system is designed in a modular way, and thus, depending on the object of investigation, two or three cameras with different capabilities in terms of resolution and color reproduction can be utilized to optimize the set-up.     

Combinational Reasoning of Quantitative Fuzzy Topological Relations for Simple Fuzzy Regions

In recent years, formalization and reasoning of topological relations have become a hot topic as a means to generate knowledge about the relations between spatial objects at the conceptual and geometrical levels. These mechanisms have been widely used in spatial data query, spatial data mining, evaluation of equivalence and similarity in a spatial scene, as well as for consistency assessment of the topological relations of multi-resolution spatial databases. The concept of computational fuzzy topological space is applied to simple fuzzy regions to efficiently and more accurately solve fuzzy topological relations. Thus, extending the existing research and improving upon the previous work, this paper presents a new method to describe fuzzy topological relations between simple spatial regions in Geographic Information Sciences (GIS) and Artificial Intelligence (AI). Firstly, we propose a new definition for simple fuzzy line segments and simple fuzzy regions based on the computational fuzzy topology. And then, based on the new definitions, we also propose a new combinational reasoning method to compute the topological relations between simple fuzzy regions, moreover, this study has discovered that there are (1) 23 different topological relations between a simple crisp region and a simple fuzzy region; (2) 152 different topological relations between two simple fuzzy regions. In the end, we have discussed some examples to demonstrate the validity of the new method, through comparisons with existing fuzzy models, we showed that the proposed method can compute more than the existing models, as it is more expressive than the existing fuzzy models.     

Model versus model or model versus data? A commentary on Berg and McDowell's "Quantitative, steady-state properties of Catania's computational model of the operant reserve"

Berg and McDowell's (2011) systematic exploration of some parameters of Catania's (2005) operant reserve model generated significant departures from the data predicted by matching models, especially in the form of an inflection point at the low end of the input-output function. The models need to be compared not only with each other but also with data. Much of the data to which both models have been fitted was obtained decades ago using equipment that constrained procedures and created unanalyzed contingencies. For example, in those days scheduled but unobtained reinforcers could not accumulate. To do justice to the sophistication of contemporary models, we need new data sets based on schedules that do not include such artifacts. Without such data, it is impossible to say whether the Berg/McDowell inflections are properties of behavior revealed by the model or are instead deviations of the model from real behavior and from other models.     

目标和干扰子之间的拓扑性质差异可以削弱拥挤效应

"拥挤效应"被认为是外周视觉物体辨认过程中的一个重要瓶颈.它是指当目标被干扰子包围,在外周视野呈现时,观察者辨认目标的能力被大大削弱,尤其是当目标和干扰子之间存在某种相似性时.许多研究分别试图在不同层次上提出解释这一现象的机制.本文通过三个实验,使用了不同的视觉刺激图形的辨认任务(例如,三角形和箭头的朝向判断、数字和字母的辨认以及S形图形的朝向辨认),测量了目标和干扰子之间中心距离的阈值,结果一致地发现,当目标和干扰子之间存在拓扑性质差异(洞的个数差异)时,拥挤效应会显著降低,并且排除了目标和干扰子之间的主观相似性、形状和面积差异等可能的因素.从知觉组织的角度验证了当目标和干扰子之间存在拓扑性质差异时,拥挤效应会显著降低,这是首次发现的一个影响拥挤效应的新的维度.本文结果不仅为拥挤效应的机制提供了一个新的解释,也为大范围首先拓扑知觉在知觉物体形成中的作用提供了支持性证据.     

Differences between non-specific and bio-specific, and between equilibrium and non-equilibrium, interactions in biological systems

The interaction forces between biological molecules and surfaces are much more complex than those between non-biological molecules or surfaces, such as colloidal particle surfaces. This complexity is due to a number of factors: (i) the simultaneous involvement of many different molecules and different non-covalent forces - van der Waals, electrostatic, solvation (hydration, hydrophobic), steric, entropic and 'specific', and (ii) the flexibility of biological macromolecules and fluidity of membranes. Biological interactions are better thought of as 'processes' that evolve in space and time and, under physiological conditions, involve a continuous input of energy. Such systems are, therefore, not at thermodynamic equilibrium, or even tending towards equilibrium. Recent surface forces apparatus (SFA) and atomic force microscopy (AFM) measurements on supported model membrane systems (protein-containing lipid bilayers) illustrate these effects. It is suggested that the major theoretical challenge is to establish manageable theories or models that can describe the spatial and time evolution of systems consisting of different molecules subject to certain starting conditions or energy inputs.     

Analytic examples of force-free toroidal MHD equilibria

Analytically described toroidal (axisymmetric and three-dimensional) equilibrium magnetic field configurations with a “flat” current density, j=λB (λ = const), are proposed. Such configurations are superpositions of several force-free two-dimensional configurations with plane, axial, or helical coordinate symmetry. Each of them is generated by an exact partial solution to the corresponding Grad-Shafranov equation. A variety of toroidal configurations thus obtained allows one to model topological changes of magnetic surfaces, such as magnetic axis splitting (doublets) in axisymmetric equilibrium configurations and the appearance and interaction of magnetic islands and ergodic lines in three-dimensional configurations.