This computer program calculates the orientational variants, the operators and the composition table of a groupoid.
A computer program called GenOVa, written in Python, calculates the orientational variants, the operators (special types of misorientations between variants) and the composition table associated with a groupoid structure. The variants can be represented by three-dimensional shapes or by pole figures.
variants; orientation; groupoids; pole figures; simulations; computer programs; GenOVa
The quasivariety of groupoids (N,∗) satisfying the implication a∗b=c∗d⇒a∗d=c∗b=a∗b generalises rectangular semigroups and central groupoids. We call them rectangular groupoids and find three combinatorial structures based upon arrays, matrices and graphs that are closely related.
These generalise several groupoids of independent interest. The quasivariety generates the variety of all groupoids; they satisfy no nontrivial equations. We see some strong connections with isotopy, this being one of the classes of algebras (along with quasigroups) closed under isotopy. We investigate some constructions and show that a regular automorphism exists iff the groupoid is derived from a group via a Cayley graph construction.
Path property; Transversals; Matrix identities; General algebra; Dualities; Quasivarieties; Subvarieties; Isotopy; Groupoids
In this paper we provide a review of selected mathematical ideas that can help us better understand the boundary between living and non-living systems. We focus on group theory and abstract algebra applied to molecular systems biology. Throughout this paper we briefly describe possible open problems. In connection with the genetic code we propose that it may be possible to use perturbation theory to explore the adjacent possibilities in the 64-dimensional space-time manifold of the evolving genome.
With regards to algebraic graph theory, there are several minor open problems we discuss. In relation to network dynamics and groupoid formalism we suggest that the network graph might not be the main focus for understanding the phenotype but rather the phase space of the network dynamics. We show a simple case of a C6 network and its phase space network. We envision that the molecular network of a cell is actually a complex network of hypercycles and feedback circuits that could be better represented in a higher-dimensional space. We conjecture that targeting nodes in the molecular network that have key roles in the phase space, as revealed by analysis of the automorphism decomposition, might be a better way to drug discovery and treatment of cancer.
• Background and Aims Fractal analysis allows calculation of fractal dimension, fractal abundance and lacunarity. Fractal analysis of plant roots has revealed correlations of fractal dimension with age, topology or genotypic variation, while fractal abundance has been associated with root length. Lacunarity is associated with heterogeneity of distribution, and has yet to be utilized in analysis of roots. In this study, fractal analysis was applied to the study of root architecture and acquisition of diffusion‐limited nutrients. The hypothesis that soil depletion and root competition are more closely correlated with a combination of fractal parameters than by any one alone was tested.
• Model The geometric simulation model SimRoot was used to dynamically model roots of various architectures growing for up to 16 d in three soil types with contrasting nutrient mobility. Fractal parameters were calculated for whole roots, projections of roots and vertical slices of roots taken at 0, 2·5 and 5 cm from the root origin. Nutrient depletion volumes, competition volumes, and relative competition were regressed against fractal parameters and root length.
• Key Results Root length was correlated with depletion volume, competition volume and relative competition at all times. In analysis of three‐dimensional, projected roots and 0 cm slices, log(fractal abundance) was highly correlated with log(depletion volume) when times were pooled. Other than this, multiple regression yielded better correlations than regression with single fractal parameters. Correlations decreased with age of roots and distance of vertical slices from the root origin. Field data were also examined to see if fractal dimension, fractal abundance and lacunarity can be used to distinguish common bean genotypes in field situations. There were significant differences in fractal dimension and fractal abundance, but not in lacunarity.
• Conclusions These results suggest that applying fractal analysis to research of soil exploration by root systems should include fractal abundance, and possibly lacunarity, along with fractal dimension.
Fractal dimension; fractal abundance; lacunarity; phosphorus; depletion; competition; Phaseolus vulgaris; SimRoot; simulation modelling
A computer program has been written to reconstruct the parent grains from EBSD data of phase transition materials.
A computer program called ARPGE written in Python uses the theoretical results generated by the computer program GenOVa to automatically reconstruct the parent grains from electron backscatter diffraction data obtained on phase transition materials with or without residual parent phase. The misorientations between daughter grains are identified with operators, the daughter grains are identified with indexed variants, the orientations of the parent grains are determined, and some statistics on the variants and operators are established. Some examples with martensitic transformations in iron and titanium alloys were treated. Variant selection phenomena were revealed.
electron backscatter diffraction (EBSD); reconstruction; phase transformation; titanium; steel; groupoids; computer programs; ARPGE; GenOVa
In this paper we discuss a symbolic-numeric algorithm for Boolean operations, closed in the algebra of curved polyhedra whose boundary is triangulated with algebraic patches (A-patches). This approach uses a linear polyhedron as a first approximation of both the arguments and the result. On each triangle of a boundary representation of such linear approximation, a piecewise cubic algebraic interpolant is built, using a C1-continuous prism algebraic patch (prism A-patch) that interpolates the three triangle vertices, with given normal vectors. The boundary representation only stores the vertices of the initial triangulation and their external vertex normals. In order to represent also flat and/or sharp local features, the corresponding normal-per-face and/or normal-per-edge may be also given, respectively. The topology is described by storing, for each curved triangle, the two triples of pointers to incident vertices and to adjacent triangles. For each triangle, a scaffolding prism is built, produced by its extreme vertices and normals, which provides a containment volume for the curved interpolating A-patch. When looking for the result of a regularized Boolean operation, the 0-set of a tri-variate polynomial within each such prism is generated, and intersected with the analogous 0-sets of the other curved polyhedron, when two prisms have non-empty intersection. The intersection curves of the boundaries are traced and used to decompose each boundary into the 3 standard classes of subpatches, denoted in, out and on. While tracing the intersection curves, the locally refined triangulation of intersecting patches is produced, and added to the boundary representation.
The effects of crystal-plasticity on the U-Th-Pb system in zircon is studied by quantitative microstructural and microchemical analysis of a large zircon grain collected from pyroxenite of the Lewisian Complex, Scotland. Electron backscatter diffraction (EBSD) mapping reveals a c.18° variation in crystallographic orientation that comprises both a gradual change in orientation and a series of discrete low-angle (<4°) boundaries. These microstructural data are consistent with crystal-plastic deformation of zircon associated with the formation and migration of dislocations. A heterogeneous pattern of dark cathodoluminescence, with the darkest domains coinciding with low-angle boundaries, mimics the deformation microstructure identified by EBSD. Geochemical data collected using the Sensitive High Resolution Ion MicroProbe (SHRIMP) shows a positive correlation between concentrations of the elements U, Th and Pb (ranging from 20–60 ppm, 30–110 ppm, and 14–36 ppm, respectively) and Th/U ratio (1.13 – 1.8) with the deformation microstructure. The highest measured concentrations and Th/U coincide with low-angle boundaries. This enrichment is interpreted to reflect enhanced bulk diffusion of U and Th due to the formation and migration of high-diffusivity dislocations. 207Pb/206Pb ages for individual analyses show no significant variation across the grain, and define a concordant, combined mean age of 2451 ± 14 Ma. This indicates that the grain was deformed shortly after initial crystallization, most probably during retrograde Inverian metamorphism at amphibolite facies conditions. The elevated Th over U and consistent 207Pb/206Pb ages indicates that deformation most likely occurred in the presence of a late-stage magmatic fluid that drove an increase in the Th/U during deformation. The relative enrichment of Th over U implies that Th/U ratio may not always be a robust indicator of crystallization environment. This study provides the first evidence of deformation-related modification of the U-Th system in zircon and has fundamental implications for the application and interpretation of zircon trace element data.
Shift radix systems form a collection of dynamical systems depending on a parameter r which varies in the d-dimensional real vector space. They generalize well-known numeration systems such as beta-expansions, expansions with respect to rational bases, and canonical number systems. Beta-numeration and canonical number systems are known to be intimately related to fractal shapes, such as the classical Rauzy fractal and the twin dragon. These fractals turned out to be important for studying properties of expansions in several settings.
In the present paper we associate a collection of fractal tiles with shift radix systems. We show that for certain classes of parameters r these tiles coincide with affine copies of the well-known tiles associated with beta-expansions and canonical number systems. On the other hand, these tiles provide natural families of tiles for beta-expansions with (non-unit) Pisot numbers as well as canonical number systems with (non-monic) expanding polynomials.
We also prove basic properties for tiles associated with shift radix systems. Indeed, we prove that under some algebraic conditions on the parameter r of the shift radix system, these tiles provide multiple tilings and even tilings of the d-dimensional real vector space. These tilings turn out to have a more complicated structure than the tilings arising from the known number systems mentioned above. Such a tiling may consist of tiles having infinitely many different shapes. Moreover, the tiles need not be self-affine (or graph directed self-affine).
Beta expansion; Canonical number system; Shift radix system; Tiling
Corresponding two-dimensional grain maps from the diffraction contrast tomography and electron backscatter diffraction characterization methods were aligned and compared, focusing on the spatial resolution at the internal interfaces. The compared grain boundary networks show a remarkably good agreement both morphologically and in crystallographic orientation.
Microstructure reconstructions resulting from diffraction contrast tomography data of polycrystalline bulk strontium titanate were reinvestigated by means of electron backscatter diffraction (EBSD) characterization. Corresponding two-dimensional grain maps from the two characterization methods were aligned and compared, focusing on the spatial resolution at the internal interfaces. The compared grain boundary networks show a remarkably good agreement both morphologically and in crystallographic orientation. Deviations are critically assessed and discussed in the context of diffraction data reconstruction and EBSD data collection techniques.
microstructure characterization; diffraction contrast tomography; electron backscatter diffraction
A general approach to the analysis of structural continuity in twins is presented and applied to the known twins in melilite.
The reticular theory of twinning gives the necessary conditions on the lattice level for the formation of twins. The latter are based on the continuation, more or less approximate, of a substructure through the composition surface. The analysis of this structural continuity can be performed in terms of the eigensymmetry of the crystallographic orbits corresponding to occupied Wyckoff positions in the structure. If is the space group of the individual and a space group which fixes the twin lattice obtained as an intersection of the space groups of the individuals in their respective orientations, then a structural continuity is obtained if (1) the eigensymmetry of an orbit under contains the twin operation; (2) the eigensymmetry of a union of orbits under contains the twin operation; (3) the eigensymmetry of a split orbit under contains the twin operation; or (4) the eigensymmetry of a union of split orbits under contains the twin operation. The case of the twins in melilite is analysed: the (approximate) restoration of some of the orbits explains the formation of these twins.
melilite; structural continuity; twinned crystals
The ability to assemble nano- and micro- sized colloidal components into highly ordered configurations is often cited as the basis for developing advanced materials. However, the dynamics of stochastic grain boundary formation and motion have not been quantified, which limits the ability to control and anneal polycrystallinity in colloidal based materials. Here we use optical microscopy, Brownian Dynamic simulations, and a new dynamic analysis to study grain boundary motion in quasi-2D colloidal bicrystals formed within inhomogeneous AC electric fields. We introduce “low-dimensional” models using reaction coordinates for condensation and global order that capture first passage times between critical configurations at each applied voltage. The resulting models reveal that equal sized domains at a maximum misorientation angle show relaxation dominated by friction limited grain boundary diffusion; and in contrast, asymmetrically sized domains with less misorientation display much faster grain boundary migration due to significant thermodynamic driving forces. By quantifying such dynamics vs. compression (voltage), kinetic bottlenecks associated with slow grain boundary relaxation are understood, which can be used to guide the temporal assembly of defect-free single domain colloidal crystals.
Several domains of neuroscience offer map-like models that link location on the cortical surface to properties of sensory representation. Within cortical visual areas V1, V2, and V3, algebraic transformations can relate position in the visual field to the retinotopic representation on the flattened cortical sheet. A limit to the practical application of this structure-function model is that the cortex, while topologically a two-dimensional surface, is curved. Flattening of the curved surface to a plane unavoidably introduces local geometric distortions that are not accounted for in idealized models. Here, we show that this limitation is overcome by correcting the geometric distortion induced by cortical flattening. We use a mass-spring-damper simulation to create a registration between functional MRI retinotopic mapping data of visual areas V1, V2, and V3 and an algebraic model of retinotopy. This registration is then applied to the flattened cortical surface anatomy to create an anatomical template that is linked to the algebraic retinotopic model. This registered cortical template can be used to accurately predict the location and retinotopic organization of these early visual areas from cortical anatomy alone. Moreover, we show that prediction accuracy remains when extrapolating beyond the range of data used to inform the model, indicating that the registration reflects the retinotopic organization of visual cortex. We provide code for the mass-spring-damper technique, which has general utility for the registration of cortical structure and function beyond the visual cortex.
A two-dimensional projection of the visual world, termed a retinotopic map, is spread across the striate and extra-striate areas of the human brain. The organization of retinotopic maps has been described with algebraic functions that map position in the visual field to points on the cortical surface. These functions represent the cortical surface as a flat sheet. In fact, the surface of the brain is intrinsically curved. Flattening the cortical surface thus introduces geometric distortions of the cortical sheet that limit the fitting of algebraic functions to actual brain imaging data. We present a technique to fix the problem of geometric distortions. We collected retinotopic mapping data using functional MRI from a group of people. We treated the cortical surface as a mass-spring-damper system and corrected the topology of the cortical surface to register the functional imaging data to an algebraic model of retinotopic organization. From this registration we construct a template that is able to predict the retinotopic organization of cortical visual areas V1, V2, and V3 using only the brain anatomy of a subject. The accuracy of this prediction is comparable to that of functional measurement itself.
We present a derivation of relativistic spacetime largely untethered from specific physical considerations, in constrast to the many physically-based derivations that have appeared in the last few decades. The argument proceeds from the inherent magma (groupoid) existing on the union of spacetime frame components and Euclidean which is consistent with an “inversion symmetry” constraint from which the Minkowski norm results. In this context, the latter is also characterized as one member of a class of “inverse norms” which play major roles with respect to various unital -algebras more generally.
Grain rotation is a well-known phenomenon during high (homologous) temperature deformation and recrystallization of polycrystalline materials. In recent years, grain rotation has also been proposed as a plasticity mechanism at low temperatures (for example, room temperature for metals), especially for nanocrystalline grains with diameter d less than ~15 nm. Here, in tensile-loaded Pt thin films under a high-resolution transmission electron microscope, we show that the plasticity mechanism transitions from cross-grain dislocation glide in larger grains (d>6 nm) to a mode of coordinated rotation of multiple grains for grains with d<6 nm. The mechanism underlying the grain rotation is dislocation climb at the grain boundary, rather than grain boundary sliding or diffusional creep. Our atomic-scale images demonstrate directly that the evolution of the misorientation angle between neighbouring grains can be quantitatively accounted for by the change of the Frank–Bilby dislocation content in the grain boundary.
Grain rotation is proposed as an active deformation mechanism in nanocrystalline metals at room temperature. Here, during in-situ atomic scale experimentation, the authors observe that grains with a size <6 nm deform by coordinated rotation of multiple grains, associated with dislocation climb at grain boundaries.
A series of studies aimed at developing methods and systems of analyzing epigenetic information in cells and in cell networks, as well as that of genetic information, was examined to expand our understanding of how living systems are determined. Because cells are minimum units reflecting epigenetic information, which is considered to map the history of a parallel-processing recurrent network of biochemical reactions, their behaviors cannot be explained by considering only conventional DNA information-processing events. The role of epigenetic information on cells, which complements their genetic information, was inferred by comparing predictions from genetic information with cell behaviour observed under conditions chosen to reveal adaptation processes, population effects and community effects. A system of analyzing epigenetic information was developed starting from the twin complementary viewpoints of cell regulation as an “algebraic” system (emphasis on temporal aspects) and as a “geometric” system (emphasis on spatial aspects). Exploiting the combination of latest microfabrication technology and measurement technologies, which we call on-chip cellomics assay, we can control and re-construct the environments and interaction of cells from “algebraic” and “geometric” viewpoints. In this review, temporal viewpoint of epigenetic information, a part of the series of single-cell-based “algebraic” and “geometric” studies of celluler systems in our research groups, are summerized and reported. The knowlege acquired from this study may lead to the use of cells that fully control practical applications like cell-based drug screening and the regeneration of organs.
on-chip cellomics; genetic information; epigenetic information; algebraic viewpoint; geometric viewpoint; microchamber array; optical tweezers; agarose microchamber array; multi-electrode array (MEA); photo-thermal etching; Escheirchia coli (E. coli); inheritance; population effect; community effect; adaptation; variability; individuality
The notion of a fuzzy upper bound over a groupoid is introduced and some properties of it are investigated. We also define the notions of an either-or subset of a groupoid and a strong either-or subset of a groupoid and study some of their related properties. In particular, we consider fuzzy upper bounds in Bin(X), where Bin(X) is the collection of all groupoids. Finally, we define a fuzzy-d-subset of a groupoid and investigate some of its properties.
1. The kinetics of the reversible combination of one enzyme center with one molecule of a substrate or inhibitor is treated as a true bimolecular instead of a pseudomonomolecular reaction. The general equations describing such a reaction are presented and analyzed algebraically and graphically. 2. A new term, "specific concentration," is introduced to denote the concentration of reactants in units equal to the dissociation constant. Its use makes the kinetic equations universally applicable to all reversible systems of the given type. 3. It is shown that such a system exhibits three "zones" of behavior. Each zone is characterized and shown to exhibit significant differences in the function relating the concentrations of the components of the system at equilibrium. The zone boundaries are rigorously defined in terms of the specific enzyme concentration, for the mathematical error tolerable with a given experimental accuracy; and approximate boundaries for practical use are proposed. 4. The classical treatment of enzyme kinetics is shown to be a limiting case valid only for low specific enzyme concentrations (zone A) and to be inapplicable in a number of systems whose dissociation constants are very small or whose molar enzyme concentrations are very great, and in which, therefore, the specific enzyme concentrations are large. See Table I for a summary of zone differences. 5. In an enzyme system containing substrate or inhibitor, dilution before determination of reaction velocities is shown to be a crucial operation, entailing large changes in the fraction of enzyme in the form of a complex. The changes in fractional activity or inhibition with dilution are shown to be a function of specific enzyme concentration, the dilution factor, and the fraction of enzyme initially in the form of complex. Equations are given permitting the calculation of the state of the system at any concentration. The errors introduced into physiological work by failure to take the dilution effect into account are pointed out. 6. Experimental data are presented showing that the system composed of serum cholinesterase and physostigmine behaves as predicted by the dilution effect equations. 7. Two other conclusions of practical pharmacological importance are drawn from the theory of zone behavior: (a) The finding that a biological response is a linear function of the dose of a drug does not necessarily mean that the reaction is irreversible, but only that if reversible, the reactant with which the drug combines has a high specific concentration. (b) If a tissue enzyme has a high specific concentration, all reversible inhibitors will be equally potent in combining with it, regardless of their relative potency in dilute systems; provided only that their dissociation constants are within certain broad limits. 8. It is shown how the type of analysis here applied to bimolecular reactions can be applied in toto to systems of the type E + nX ⇋ EXn, where n molecules of substrate or inhibitor unite with one enzyme center. The zone boundaries and the magnitude of the dilution effect change with n, but the general characteristics of the zones are the same for all values of n. 9. Since the analysis is based only on mass law assumptions, it is applicable to any system that is formally analogous to the one here treated.
Grain shapes are acknowledged to impact nanomaterials' overall properties. Research works on this issue include grain-elongation and grain-strain measurements and their impacts on nanomaterials' mechanical properties. This paper proposes a stochastic model for grain strain undergoing severe plastic deformation. Most models deal with equivalent radii assuming that nanomaterials' grains are spherical. These models neglect true grain shapes. This paper also proposes a theoretical approach of extending existing models by considering grain shape distribution during stochastic design and modelling of nanomaterials' constituent structures and mechanical properties. This is achieved by introducing grain 'form'. Example 'forms' for 2-D and 3-D grains are proposed. From the definitions of form, strain and Hall-Petch-Relationship to Reversed-Hall-Petch-Relationship, data obtained for nanomaterials' grain size and conventional materials' properties are sufficient for analysis. Proposed extended models are solved simultaneously and tested with grain growth data. It is shown that the nature of form evolution depends on form choice and dimensional space. Long-run results reveal that grain boundary migration process causes grains to become spherical, grain rotation coalescence makes them deviate away from becoming spherical and they initially deviate away from becoming spherical before converging into spherical ones due to the TOTAL process. Percentage deviations from spherical grains depend on dimensional space and form: 0% minimum and 100% maximum deviations were observed. It is shown that the plots for grain shape functions lie above the spherical (control) value of 1 in 2-D grains for all considered grain growth mechanisms. Some plots lie above the spherical value, and others approach the spherical value before deviating below it when dealing with 3-D grains. The physical interpretations of these variations are explained from elementary principles about the different grain growth mechanisms. It is observed that materials whose grains deviate further away from the spherical ones have more enhanced properties, while materials with spherical grains have lesser properties. It is observed that there exist critical states beyond which Hall-Petch Relationship changes to Reversed Hall-Petch Relationship. It can be concluded that if grain shapes in nanomaterials are constrained in the way they evolve, then nanomaterials with desired properties can be designed.
grain shape; grain strain; strain rate; grain size; grain form functions; grain growth; nanomaterials' mechanical properties
Grain/interphase boundaries/interfaces of varying misorientations, free volume fractions, curvatures and irregularities are present in materials, both 3D and 2D, regardless of whether these materials are crystalline or amorphous/glassy. Therefore, a question arises about the central idea on which a general description of grain/interphase boundaries/interfaces can and should be based. It is suggested that a generalized model of a structural/basic unit (crystalline, non-crystalline or of any scale), which depends on the interatomic (including electronic) interactions, the spatial distribution of the atoms and electrons, the number of atoms and free volume fraction present in the structural/basic unit and the experimental conditions should serve the purpose. As the development of a quantitative model, which reflects the effects of all these variables is difficult, slightly defective material boundaries are often modeled by treating the entire boundary as planar and by using the concepts of crystallography. For highly disordered boundaries, a description in terms of a representative volume, made up of a non-crystalline basic unit or a combination of such units, which depend on interatomic (including electronic) interactions and forces, is advocated. The size, shape, free volume fraction and number of atoms in the representative volume could differ with material composition and experimental conditions. In the latter approach, it is assumed that all processes connected to a problem on hand is contained within this representative volume. The unresolved issues are identified.
geometrical approach; grain/interphase boundaries; interfaces; representative volume; structural/basic unit model
The composition of Laboratory Ward Manuals is a time-consuming exercise. To keep manually prepared books up-to-date requires constant effort, amounting to several days or weeks of activity every year. As most of this information is found in the various tables of the usual Laboratory Information System (LIS), it should be possible to reformat this data into a form suitable for publishing on paper or on Web Pages. When the three hospitals in Saskatoon became part of a single operating entity, it became a necessity to redo the procedure manuals and ward manuals for all of the laboratories. As part of this exercise, we sought ways to minimize the work required. One method was to automate the ward manuals. Accordingly, an automated way of producing an Intranet ward manual was devised to reduce the work of the laboratory staff in this continuing endeavour.
The query language of the SoftLab LIS (SCC Clinical Information Systems, Palm Harbor, Fla, USA) was used to extract standard test data, including various descriptive terms, specimens required, minimum volumes, reference ranges, &c, &c in a comma-delimited form for input to a database application program. Paradox 8 (Corel Corporation) was used to build the several files necessary to hold the various forms of data from the many databases of the LIS. Paradox Macros were written to combine records from the various files into a single record containing concatenated strings to format the appropriate data in a form, which would display in a single column in the ultimate report. Using the standard Paradox report forms, HTML Web pages could then be generated which became available for publishing on the Hospital Intranet.
This procedure was used with the Saskatoon LIS to produce Intranet Web Pages, and also a print version of the Ward Manual). Once the Paradox Macros have been debugged, preparation of the updated Web Pages takes only a few minutes, and updates can be incorporated almost completely automatically.
Spread Sheet (SS) and Database (dB) Handlers have become highly flexible tools for generating many different types of reports, from almost any form of data. With the addition of HTML generation capabilities in the standard dB and SS application programs this becomes an even easier matter. This puts highly sophisticated Web Page generation capabilities into everyone's hands.
Clinical Laboratory Information Systems; Hospital Information Systems; Database Systems
The W-curve was originally developed as a graphical visualization technique for viewing DNA and RNA sequences. Its ability to render features of DNA also makes it suitable for computational studies. Its main advantage in this area is utilizing a single-pass algorithm for comparing the sequences. Avoiding recursion during sequence alignments offers advantages for speed and in-process resources. The graphical technique also allows for multiple models of comparison to be used depending on the nucleotide patterns embedded in similar whole genomic sequences. The W-curve approach allows us to compare large numbers of samples quickly.
We are currently tuning the algorithm to accommodate quirks specific to HIV-1 genomic sequences so that it can be used to aid in diagnostic and vaccine efforts. Tracking the molecular evolution of the virus has been greatly hampered by gap associated problems predominantly embedded within the envelope gene of the virus. Gaps and hypermutation of the virus slow conventional string based alignments of the whole genome. This paper describes the W-curve algorithm itself, and how we have adapted it for comparison of similar HIV-1 genomes. A treebuilding method is developed with the
W-curve that utilizes a novel Cylindrical Coordinate distance method and gap analysis method. HIV-1 C2-V5 env sequence regions from a Mother/Infant cohort study are used in the comparison.
The output distance matrix and neighbor results produced by the W-curve are functionally equivalent to those from Clustal for C2-V5 sequences in the mother/infant pairs infected with CRF01_AE.
Significant potential exists for utilizing this method in place of conventional string based alignment of HIV-1 genomes, such as Clustal X. With W-curve heuristic alignment, it may be possible to obtain clinically useful results in a short time—short enough to affect clinical choices for acute treatment. A description of the W-curve generation process, including a comparison technique of aligning extremes of the curves to effectively phase-shift them past the HIV-1 gap problem, is presented. Besides yielding similar neighbor-joining phenogram topologies, most Mother and Infant C2-V5 sequences in the cohort pairs geometrically map closest to each other, indicating that W-curve heuristics overcame any gap problem.
Representations of chemical datasets in spreadsheet format are important for ready data assimilation and manipulation. In addition to the normal spreadsheet facilities, chemical spreadsheets need to have visualisable chemical structures and data searchable by chemical as well as textual queries. Many such chemical spreadsheet tools are available, some operating in the familiar Microsoft Excel environment. However, within this group, the performance of Excel is often compromised, particularly in terms of the number of compounds which can usefully be stored on a sheet.
LICSS is a lightweight chemical spreadsheet within Microsoft Excel for Windows. LICSS stores structures solely as Smiles strings. Chemical operations are carried out by calling Java code modules which use the CDK, JChemPaint and OPSIN libraries to provide cheminformatics functionality. Compounds in sheets or charts may be visualised (individually or en masse), and sheets may be searched by substructure or similarity. All the molecular descriptors available in CDK may be calculated for compounds (in batch or on-the-fly), and various cheminformatic operations such as fingerprint calculation, Sammon mapping, clustering and R group table creation may be carried out.
We detail here the features of LICSS and how they are implemented. We also explain the design criteria, particularly in terms of potential corporate use, which led to this particular implementation.
LICSS is an Excel-based chemical spreadsheet with a difference:
• It can usefully be used on sheets containing hundreds of thousands of compounds; it doesn't compromise the normal performance of Microsoft Excel
• It is designed to be installed and run in environments in which users do not have admin privileges; installation involves merely file copying, and sharing of LICSS sheets invokes automatic installation
• It is free and extensible
LICSS is open source software and we hope sufficient detail is provided here to enable developers to add their own features and share with the community.
A nonholonomic system subjected to external noise from the environment, or internal noise in its own actuators, will evolve in a stochastic manner described by an ensemble of trajectories. This ensemble of trajectories is equivalent to the solution of a Fokker–Planck equation that typically evolves on a Lie group. If the most likely state of such a system is to be estimated, and plans for subsequent motions from the current state are to be made so as to move the system to a desired state with high probability, then modeling how the probability density of the system evolves is critical. Methods for solving Fokker-Planck equations that evolve on Lie groups then become important. Such equations can be solved using the operational properties of group Fourier transforms in which irreducible unitary representation (IUR) matrices play a critical role. Therefore, we develop a simple approach for the numerical approximation of all the IUR matrices for two of the groups of most interest in robotics: the rotation group in three-dimensional space, SO(3), and the Euclidean motion group of the plane, SE(2). This approach uses the exponential mapping from the Lie algebras of these groups, and takes advantage of the sparse nature of the Lie algebra representation matrices. Other techniques for density estimation on groups are also explored. The computed densities are applied in the context of probabilistic path planning for kinematic cart in the plane and flexible needle steering in three-dimensional space. In these examples the injection of artificial noise into the computational models (rather than noise in the actual physical systems) serves as a tool to search the configuration spaces and plan paths. Finally, we illustrate how density estimation problems arise in the characterization of physical noise in orientational sensors such as gyroscopes.
State estimation; Lie groups; nonholonomic motion planning; exponential map
To test the hypothesis that non-diabetic dizygotic and monozygotic twin siblings of patients with type 1 diabetes have a similar high prevalence of islet cell autoantibodies, thus suggesting that islet cell autoimmunity is mainly environmentally determined.
Prospective twin study.
Two specialist centres for diabetes in the United States.
Non-diabetic monozygotic twin (n=53), dizygotic twin (n=30), and non-twin (n=149) siblings of patients with type 1 diabetes; 101 controls.
Main outcome measures
Analysis of progression to diabetes and expression of anti-islet autoantibodies.
Monozygotic twin siblings had a higher risk of progression to diabetes (12/53) than dizygotic twin siblings (0/30; P<0.005). At the last follow up 22 (41.5%) monozygotic twin siblings expressed autoantibodies compared with 6 (20%) dizygotic twin siblings (P<0.05), 16 (10.7%) non-twin siblings (P<0.0001), and 6 (5.9%) controls (P<0.0001). Monozygotic twin siblings expressed multiple (⩾2) antibodies more often than dizygotic twin siblings (10/38 v 1/23; P<0.05). By life table analysis the probability of developing positive autoantibodies was higher among the monozygotic twin siblings bearing the diabetes associated HLA DQ8/DQ2 genotype than in those without this genotype (64.2% (95% confidence interval 32.5% to 96%) v 23.5% (7% to 40%) at 10 years of discordance; P<0.05).
Monozygotic and dizygotic twins differ in progression to diabetes and expression of islet cell autoantibodies. Dizygotic twin siblings are similar to non-twin siblings. These two observations suggest that genetic factors play an important part in determination of islet cell autoimmunity, thus rejecting the hypothesis. In addition, there is a high penetrance of islet cell autoimmunity in DQ8/DQ2 monozygotic twin siblings.
Key messagesMonozygotic twin siblings of patients with type 1 diabetes have a higher risk of progression to diabetes and of expressing islet cell antibodies than dizygotic twin and non-twin siblingsMonozygotic twins with the HLA genotype DQ8/DQ2 have a high risk of expression of islet cell autoimmunity and progression to diabetesIslet cell autoimmunity seems to be predominantly genetically determined
The pitfalls of experimental phasing are described.
Developments in protein crystal structure determination by experimental phasing are reviewed, emphasizing the theoretical continuum between experimental phasing, density modification, model building and refinement. Traditional notions of the composition of the substructure and the best coefficients for map generation are discussed. Pitfalls such as determining the enantiomorph, identifying centrosymmetry (or pseudo-symmetry) in the substructure and crystal twinning are discussed in detail. An appendix introduces combined real–imaginary log-likelihood gradient map coefficients for SAD phasing and their use for substructure completion as implemented in the software Phaser. Supplementary material includes animated probabilistic Harker diagrams showing how maximum-likelihood-based phasing methods can be used to refine parameters in the case of SIR and MIR; it is hoped that these will be useful for those teaching best practice in experimental phasing methods.
enantiomers; handedness; absolute configuration; chirality; twinning; experimental phasing