Computer-Aided Topological Analysis of the Faujasite Lattice I: Exact Solution for Zeolite-X

Abstract

In order to study the possible configurations of Aluminum and Silicon atoms on a Faujasite lattice, two different methods of analysis are presented. The first method is based on the study of the physical properties of different lattice structures: the energy and the dipolar moment. The second one examines the topological properties of the configurations in order to count the inequivalent lattice structures. An original algorithm selects the configurations to be generated and compared in order to keep the computer time required at an acceptable level. The results from the two methods are compared and found to be in agreement.

In this paper we specialize our study to zeolite-X but the methods are general and can be applied to other types of lattices.     

Temporal patterns analysis of spontaneous unit activity in the neocortex

An analysis has been made of the spontaneous firing of neurons from the posterior motor cortex of the rabbit. Extracellular recordings were made by means of glass capillary micro-electrodes. The recorded neural activity was processed with a general purpose computer and an adapted data processing system. The impulse interval series were analysed by means of a statistical time series analysis. In the first part of the paper, the first order properties of the neutral activity are examined. Using a mathematical model for data reduction, an overall picture of the first order properties of the activity of the set of recorded neurons are obtained. In the second part of the paper, the second order properties of this activity are examined. Using another simple mathematical model completing the first one, the principal aspect of the second order properties are summarized.     

Analyzing the joint effects of two antibodies and the design of molecularly engineered vaccines

A new analytical approach to determine how antibodies relate to each other in producing immunity is presented. One purpose of this analysis is to decide on the antigenic composition of vaccines. Regression analyses and single discrete analyses are shown to be inappropriate to this task. The proposed analyses makes multiple cut points on two pre-exposure antibody levels. At each resulting discrete classification, additive and multiplicative interaction parameters are calculated. Various models of joint antibody action are shown to produce two general patterns of interaction terms with this type of analysis. One pattern characterizes situations where each antibody, or something substituting for the action of each antibody, is always needed to eliminate all infections. This may be because the antigens to which the antibodies are directed are on separate microbes or because microbes can only be neutralized by the joint action of both antibodies. A second pattern characterizes situations where both antibodies act cooperatively but given high enough levels only one may be needed. This may be because the antibodies have the same molecular effect or because they act by separate means against the same organisms in an innoculum.     

Patterns of morphological discrimination in selected human tarsal elements

A suite of measurements was collected from the talus, calcaneus, navicular, and cuboid of humans from Southern China, Victorian Britain, Roman Britain, and Zulu tribes people from the Republic of South Africa. Univariate and multivariate statistical analyses of dimensions of individual foot bones revealed subtle but distinct patterns of morphological discrimination on the basis of sex and size on the one hand, and geographical relationships on the other. These differences are largely expressed in the first three canonical variates of the multivariate analyses: the first axis expresses both sex and size differences, and the second and third, geographical group differences. Confirmation of morphological patterns obtained from individual multivariate analyses was provided by an integrated analysis of the four tarsal elements together. However, the integrated analysis also gave larger separations with discriminations along different axes. Thus the three geographical groups (Zulus, Southern Chinese, and the two British groups together) were separated by first and third variates. The discrimination of sex and size differences was found in the second axis, mirroring what was found in the first axes of the individual studies. This axis reversal implies that in examining all bones together, there is enough redundant information about sex and size in each individual bone that they are relegated to a second axis. It likewise implies that the data referring to geographic discriminations provided by each individual bone are not redundant; they sum in the integrated analysis, and therefore contribute to the overall analysis to a greater extent, with increased clarity.     

Topological Data Analysis of Biological Aggregation Models

We apply tools from topological data analysis to two mathematical models inspired by biological aggregations such as bird flocks, fish schools, and insect swarms. Our data consists of numerical simulation output from the models of Vicsek and D''Orsogna. These models are dynamical systems describing the movement of agents who interact via alignment, attraction, and/or repulsion. Each simulation time frame is a point cloud in position-velocity space. We analyze the topological structure of these point clouds, interpreting the persistent homology by calculating the first few Betti numbers. These Betti numbers count connected components, topological circles, and trapped volumes present in the data. To interpret our results, we introduce a visualization that displays Betti numbers over simulation time and topological persistence scale. We compare our topological results to order parameters typically used to quantify the global behavior of aggregations, such as polarization and angular momentum. The topological calculations reveal events and structure not captured by the order parameters.     

Insights into the organization of biochemical regulatory networks using graph theory analyses

Graph theory has been a valuable mathematical modeling tool to gain insights into the topological organization of biochemical networks. There are two types of insights that may be obtained by graph theory analyses. The first provides an overview of the global organization of biochemical networks; the second uses prior knowledge to place results from multivariate experiments, such as microarray data sets, in the context of known pathways and networks to infer regulation. Using graph analyses, biochemical networks are found to be scale-free and small-world, indicating that these networks contain hubs, which are proteins that interact with many other molecules. These hubs may interact with many different types of proteins at the same time and location or at different times and locations, resulting in diverse biological responses. Groups of components in networks are organized in recurring patterns termed network motifs such as feedback and feed-forward loops. Graph analysis revealed that negative feedback loops are less common and are present mostly in proximity to the membrane, whereas positive feedback loops are highly nested in an architecture that promotes dynamical stability. Cell signaling networks have multiple pathways from some input receptors and few from others. Such topology is reminiscent of a classification system. Signaling networks display a bow-tie structure indicative of funneling information from extracellular signals and then dispatching information from a few specific central intracellular signaling nexuses. These insights show that graph theory is a valuable tool for gaining an understanding of global regulatory features of biochemical networks.     

MartiTracks: a geometrical approach for identifying geographical patterns of distribution

Panbiogeography represents an evolutionary approach to biogeography, using rational cost-efficient methods to reduce initial complexity to locality data, and depict general distribution patterns. However, few quantitative, and automated panbiogeographic methods exist. In this study, we propose a new algorithm, within a quantitative, geometrical framework, to perform panbiogeographical analyses as an alternative to more traditional methods. The algorithm first calculates a minimum spanning tree, an individual track for each species in a panbiogeographic context. Then the spatial congruence among segments of the minimum spanning trees is calculated using five congruence parameters, producing a general distribution pattern. In addition, the algorithm removes the ambiguity, and subjectivity often present in a manual panbiogeographic analysis. Results from two empirical examples using 61 species of the genus Bomarea (2340 records), and 1031 genera of both plants and animals (100118 records) distributed across the Northern Andes, demonstrated that a geometrical approach to panbiogeography is a feasible quantitative method to determine general distribution patterns for taxa, reducing complexity, and the time needed for managing large data sets.     

Advances in blind source separation (BSS) and independent component analysis (ICA) for nonlinear mixtures

In this paper, we review recent advances in blind source separation (BSS) and independent component analysis (ICA) for nonlinear mixing models. After a general introduction to BSS and ICA, we discuss in more detail uniqueness and separability issues, presenting some new results. A fundamental difficulty in the nonlinear BSS problem and even more so in the nonlinear ICA problem is that they provide non-unique solutions without extra constraints, which are often implemented by using a suitable regularization. In this paper, we explore two possible approaches. The first one is based on structural constraints. Especially, post-nonlinear mixtures are an important special case, where a nonlinearity is applied to linear mixtures. For such mixtures, the ambiguities are essentially the same as for the linear ICA or BSS problems. The second approach uses Bayesian inference methods for estimating the best statistical parameters, under almost unconstrained models in which priors can be easily added. In the later part of this paper, various separation techniques proposed for post-nonlinear mixtures and general nonlinear mixtures are reviewed.     

A methodology for performing global uncertainty and sensitivity analysis in systems biology

Accuracy of results from mathematical and computer models of biological systems is often complicated by the presence of uncertainties in experimental data that are used to estimate parameter values. Current mathematical modeling approaches typically use either single-parameter or local sensitivity analyses. However, these methods do not accurately assess uncertainty and sensitivity in the system as, by default, they hold all other parameters fixed at baseline values. Using techniques described within we demonstrate how a multi-dimensional parameter space can be studied globally so all uncertainties can be identified. Further, uncertainty and sensitivity analysis techniques can help to identify and ultimately control uncertainties. In this work we develop methods for applying existing analytical tools to perform analyses on a variety of mathematical and computer models. We compare two specific types of global sensitivity analysis indexes that have proven to be among the most robust and efficient. Through familiar and new examples of mathematical and computer models, we provide a complete methodology for performing these analyses, in both deterministic and stochastic settings, and propose novel techniques to handle problems encountered during these types of analyses.     

A method of analysis of the models of neural nets

Taking into account Caianiello's work of 1961 a model of a neuron quite similar to his is proposed and studied. For this model, where a temporal summation and a period of refractoriness are assumed, a mathematical approach and a simulation on computer were realized. Particular types of nets were used, namely: nets with topological structures, and fully random nets. The difference between the two types is that the first type has a two-dimensional square structure and depends on the rules of the formation of connection between the neurons, while the second type is realized by means of the probability distribution function governing the formation of the structure of the net.These types of neural nets are analysed by means of a method which permits to obtain various parameters which characterize their behaviour in time and space in terms of the trajectory of the system. Many experiments are also reported; the statistical analyses, made on them, show the great importance and influence of refractoriness on the behaviour of neural networks.In the last part of the work an interesting case is reported, in which the reaction of the net to a disturbance shows that a kind of adaptation takes place, although the structure of the net stays unchanged.On leave of absence from the Lithuanian Academy of Sciences, Vilnius, Lithuanian S.S.R.     

Basic concepts of computer simulation of plant growth

The experimental study of plant growth and architecture requires two consecutive and complementary approaches. The first one is qualitative and botanical. Through this qualitative analysis, it is possible to divide a tree into botanically homogeneous subunits. The second one is quantitative. Modeling of the functioning of meristems based on stochastic processes has been carried out in the Laboratoire de Modelisation of CIRAD (1980 1990) in combination with extensive experimental work on temperate and tropical plants. Calculations involved in the tree simulations from field data are based on the probabilistic Monte Carlo method for the topological part and on analytical geometry for the morphological part. Data, such as length, angles, elasticities, tropism, are necessary for geometric construction of the plant. The growth model, together with the geometric calculations enables a random plant simulation in 3-D according to geometry for the morphological one. Computer graphics methods are then used to visualize the computed plant (perspective, colours, texture, shadows); they require special programs and graphic computers.     

Chemotaxonomic differentiation of coryneform bacteria isolated from biofilters.

Coryneform bacteria that were isolated from biofilters which are used for waste gas treatment of animal-rendering plant emissions were differentiated and partially identified by using chemotaxonomic methods. On the basis of the results of a numerical analysis of whole-cell fatty acid profiles, 79 isolates were divided into two major groups; the members of the first group contained saturated and monounsaturated fatty acids, whereas the members of the second group were characterized by iso- and anteiso-branched fatty acids. Division into subclusters was based mainly on quantitative differences in fatty acid composition and was confirmed by the results obtained for additional chemical markers (e.g., respiratory quinones, mycolic acids, polar lipids, cell wall amino acids, and whole-cell sugar patterns). By combining the results obtained for chemotaxonomic analyses that were performed for strains containing saturated and monounsaturated fatty acids, we were able to identify the genus Corynebacterium (two Corynebacterium species were differentiated on the basis of the occurrence of tuberculostearic acid), the genus Gordona, and the genus Mycobacterium. Among the strains that produced iso-anteiso fatty acid patterns, one subgroup was affiliated with the "nicotianae" group of the genus Arthrobacter; however, some strains contained a new combination of chemical markers. Peptidoglycan type A4 alpha, L-Lys-Gly-L-Glu was combined with menaquinones MK-7 and MK-8, whereas peptidoglycan type A4 alpha, L-Lys-L-Glu occurred together with MK-8 and MK-9. The second subgroup was characterized by a new type B peptidoglycan and MK-11, as well as small amounts of MK-12. Differentiation that was based first on chemotaxonomy and second on physiology gave reliable results. Thus, coryneform strains with new characteristics were isolated from biofilters.     

Harmonic force field for nitro compounds

Molecular simulations leading to sensors for the detection of explosive compounds require force field parameters that can reproduce the mechanical and vibrational properties of energetic materials. We developed precise harmonic force fields for alanine polypeptides and glycine oligopeptides using the FUERZA procedure that uses the Hessian tensor (obtained from ab initio calculations) to calculate precise parameters. In this work, we used the same procedure to calculate generalized force field parameters of several nitro compounds. We found a linear relationship between force constant and bond distance. The average angle in the nitro compounds was 116°, excluding the 90° angle of the carbon atoms in the octanitrocubane. The calculated parameters permitted the accurate molecular modeling of nitro compounds containing many functional groups. Results were acceptable when compared with others obtained using methods that are specific for one type of molecule, and much better than others obtained using methods that are too general (these ignore the chemical effects of surrounding atoms on the bonding and therefore the bond strength, which affects the mechanical and vibrational properties of the whole molecule).     

Numerical analysis of pollen samples from central Canada: A comparison of methods

The compilation of large and complex sets of modern pollen data has stimulated the use of new methods, including the use of multivariate statistical techniques, for summarizing and presenting these data. This paper compares several of these methods by applying them to Lichti-Federovich and Ritchie's (1968) 131 sediment samples of modern pollen from central Canada. Maps of the major pollen types are presented, and the data are analyzed by canonical variates analysis, principal components analysis, principal coordinates analysis, and minimum-variance cluster analysis.The maps show the geographical distribution of the principal pollen types and reveal that steep gradients in the percentages of eight of the nineteen pollen types used in this study separate the samples in the southwest from the remaining samples. Excluding the southwestern samples, the maps show the frequencies of the other pollen types to be aligned north to south with high values of sedge, birch, and heath pollen in the north, high values of pine in the south, and high values of spruce and alder in between. This same general structure is evident in the results of the four multivariate analyses. The samples are distributed in a closely similar manner along the first two axes derived from canonical varietes analysis, principal components analysis, and principal coordinates analysis. The first axis of each analysis separates the samples in the southwest from the rest of the samples, and the second axis shows these latter samples to be spread fairly evenly along a north—south gradient from the tundra samples to the mixed coniferous—deciduous forest samples. Minimum-variance cluster analysis also shows these divisions by clustering the samples into three major groups: the southwestern samples from the prairie, aspen parkland, and deciduous forest; the northern samples from the tundra and forest—tundra; and the intermediate samples from the mixed forest and closed coniferous forest regions. Further division by the clustering technique yields fourteen groups, and these show the pollen samples to cluster slightly differently from their classification based on their location within the vegetational units. For example, the samples of the forest—tundra and the open coniferous forest are grouped together, but the samples of the upland mixed forest are too heterogeneous in pollen composition to be placed in one group.These results indicate the power of these numerical methods that use prescribed mathematical steps to analyze all samples and major pollen types simultaneously and thereby reveal the basic structure in the data based on numerical criteria alone. These summaries aid an investigator in visualizing the important trends and divisions in a data set and in finding those samples needed for a particular comparison.     

Regression analyses and motile sperm subpopulation structure study as improving tools in boar semen quality analysis

A precise estimation of the fertilizing ability of a boar ejaculate would be very useful to improve pig assisted reproduction results. For this purpose, we tested the mathematical combination of several parameters of the boar semen quality analysis, including the computer-assisted semen motility analysis (CASA), as a predictive fertility tool. The utilized mathematical relations among parameters were logistic and linear regressions. Two mathematical models obtained by logistic regression involving Osmotic Resistance Test (ORT Test), Hyperosmotic Resistance Test (HRT Test) and viability of fresh samples, showed a significant (P<0.05) correlation between semen characteristics and conception rate. However, none of the obtained models produced a significant correlation model between semen characteristics and prolificacy. The CASA analyses show that three separate subpopulations of spermatozoa with different motility characteristics coexist in boar ejaculates. There were significant (P<0.001) differences in the distribution of these subpopulations among boars, but no clear relationship between motile subpopulation structure and fertility was obtained. Our results support the belief that the predictive use of the results obtained in a standard boar semen quality analysis can reasonably be achieved by applying logistic correlation analyses among several function parameters of boar semen quality analysis and in vivo conception rates obtained after artificial insemination (AI).     

Assessing an unknown evolutionary process: effect of increasing site-specific knowledge through taxon addition

Assessment of the evolutionary process is crucial for understanding the effect of protein structure and function on sequence evolution and for many other analyses in molecular evolution. Here, we used simulations to study how taxon sampling affects accuracy of parameter estimation and topological inference in the absence of branch length asymmetry. With maximum-likelihood analysis, we find that adding taxa dramatically improves both support for the evolutionary model and accurate assessment of its parameters when compared with increasing the sequence length. Using a method we call "doppelg?nger trees," we distinguish the contributions of two sources of improved topological inference: greater knowledge about internal nodes and greater knowledge of site-specific rate parameters. Surprisingly, highly significant support for the correct general model does not lead directly to improved topological inference. Instead, substantial improvement occurs only with accurate assessment of the evolutionary process at individual sites. Although these results are based on a simplified model of the evolutionary process, they indicate that in general, assuming processes are not independent and identically distributed among sites, more extensive sampling of taxonomic biodiversity will greatly improve analytical results in many current sequence data sets with moderate sequence lengths.     

Using topological equivalence to discover stable control parameters in biodynamic systems

In order to better understand the mechanisms that contribute to low back pain, researchers have developed mathematical models and simulations. A mathematical model including neuromuscular feedback control is developed for a person balancing on an unstable sitting apparatus, the wobble chair. When the application of a direct method fails to discover appropriate controller gain parameters for the wobble chair, we show how topological equivalence can be used to indirectly identify appropriate parameter values. The solution is found by first transforming the wobble chair into the Acrobot, another member of the same family of topologically equivalent dynamical systems. After finding appropriate gain parameters for the Acrobot, a continuous transformation is performed to convert the Acrobot back to the wobble chair, during which the gain parameters are adjusted to maintain stability. Thus, we demonstrate how topological equivalence can be used to indirectly solve a problem that was difficult to solve directly.     

Quantifying microhabitat availability: stratified random versus constrained focal-fish methods

During a study of microhabitat use by gilt darters (Percina evides), we compared two methods for quantifying microhabitat availability in a southern Appalachian stream (USA). The first method used stratified random sampling throughout the site and the second involved taking constrained random measurements within a 2-m radius of the focal fish. Darters were generally over-represented in microhabitats with higher average velocities, greater amounts of erosional substrata, and lower amounts of depositional and large substrata. The two methods generally yielded similar patterns of microhabitat use. Nonetheless, of the seven microhabitat categories in which differential microhabitat use occurred in summer, four were present in both data sets, but three differed between methods. We observed no differences between methods for autumn data. Finally, the standard deviations of the summer-stratified random data set were significantly greater (sign test, P < 0.05) than those of the constrained data set. Our results suggest that either method for quantifying microhabitat availability can be used to quantify the general habitat use patterns of this species, but constrained analyses yielded a more restricted view of the total habitat available. Nonetheless, if the fishes range over a site, clearly stratified habitat availability analysis is preferred. Handling editor: J. A. Cambray