PocketGraph : graph representation of binding site volumes

The representation of small molecules as molecular graphs is a common technique in various fields of cheminformatics. This approach employs abstract descriptions of topology and properties for rapid analyses and comparison. Receptor-based methods in contrast mostly depend on more complex representations impeding simplified analysis and limiting the possibilities of property assignment. In this study we demonstrate that ligand-based methods can be applied to receptor-derived binding site analysis. We introduce the new method PocketGraph that translates representations of binding site volumes into linear graphs and enables the application of graph-based methods to the world of protein pockets. The method uses the PocketPicker algorithm for characterization of binding site volumes and employs a Growing Neural Gas procedure to derive graph representations of pocket topologies. Self-organizing map (SOM) projections revealed a limited number of pocket topologies. We argue that there is only a small set of pocket shapes realized in the known ligand-receptor complexes

DAIRY GRAZING FINANCES IN MICHIGAN AND WISCONSIN, 1999

The purpose of this paper is to demonstrate possible outcomes and problems of merging farm data sets from multiple states in order to build a statistically sound body of financial information that will help individual farmers analyze their own situations. This paper is in support of a grant titled "Regional/Multi-State Interpretation of Small Farm Financial Data" recently funded by USDA - IFAFS - Farm Efficiency and Profitability. Financial data sets came from dairy farms using management intensive grazing (MIG) strategies during 1999. There were 12 farms from Michigan and 19 farms from Wisconsin. Finpack and Finansum were used to process the data from all farms. Definitions and formulas are not given in this paper as they can be found in Finpack users' guides and manuals. The averages for all 31 farms are given in Tables 1 through 10 plus Figures 1 and 2. The averages for farms with less than 70 milk cows are given in Tables 11 through 20. Averages for farms with over 70 cows are in Tables 21 through 30. Towards the end of the paper is a discussion of the strengths and weaknesses of the data set and what should be considered as more states' data are merged into the grant project. The last page, Table 32, gives some income and expense categories on a per cow basis which may be useful in doing an individual farm comparative analysis.Agricultural Finance, Livestock Production/Industries,

Sobolev Metrics on Diffeomorphism Groups and the Derived Geometry of Spaces of Submanifolds

Given a finite dimensional manifold $N$, the group $\operatorname{Diff}_{\mathcal S}(N)$ of diffeomorphism of $N$ which fall suitably rapidly to the identity, acts on the manifold $B(M,N)$ of submanifolds on $N$ of diffeomorphism type $M$ where $M$ is a compact manifold with $\dim M<\dim N$. For a right invariant weak Riemannian metric on $\operatorname{Diff}_{\mathcal S}(N)$ induced by a quite general operator $L:\frak X_{\mathcal S}(N)\to \Gamma(T^*N\otimes\operatorname{vol}(N))$, we consider the induced weak Riemannian metric on $B(M,N)$ and we compute its geodesics and sectional curvature. For that we derive a covariant formula for curvature in finite and infinite dimensions, we show how it makes O'Neill's formula very transparent, and we use it finally to compute sectional curvature on $B(M,N)$.Comment: 28 pages. In this version some misprints correcte

Lectures on mathematical aspects of (twisted) supersymmetric gauge theories

Supersymmetric gauge theories have played a central role in applications of quantum field theory to mathematics. Topologically twisted supersymmetric gauge theories often admit a rigorous mathematical description: for example, the Donaldson invariants of a 4-manifold can be interpreted as the correlation functions of a topologically twisted N=2 gauge theory. The aim of these lectures is to describe a mathematical formulation of partially-twisted supersymmetric gauge theories (in perturbation theory). These partially twisted theories are intermediate in complexity between the physical theory and the topologically twisted theories. Moreover, we will sketch how the operators of such a theory form a two complex dimensional analog of a vertex algebra. Finally, we will consider a deformation of the N=1 theory and discuss its relation to the Yangian, as explained in arXiv:1308.0370 and arXiv:1303.2632.Comment: Notes from a lecture series by the first author at the Les Houches Winter School on Mathematical Physics in 2012. To appear in the proceedings of this conference. Related to papers arXiv:1308.0370, arXiv:1303.2632, and arXiv:1111.423

An algebraic approach to manifold-valued generalized functions

We discuss the nature of structure-preserving maps of varies function algebras. In particular, we identify isomorphisms between special Colombeau algebras on manifolds with invertible manifold-valued generalized functions in the case of smooth parametrization. As a consequence, and to underline the consistency and validity of this approach, we see that this generalized version on algebra isomorphisms in turn implies the classical result on algebras of smooth functions.Comment: 7 page

Shape analysis on homogeneous spaces: a generalised SRVT framework

Shape analysis is ubiquitous in problems of pattern and object recognition and has developed considerably in the last decade. The use of shapes is natural in applications where one wants to compare curves independently of their parametrisation. One computationally efficient approach to shape analysis is based on the Square Root Velocity Transform (SRVT). In this paper we propose a generalised SRVT framework for shapes on homogeneous manifolds. The method opens up for a variety of possibilities based on different choices of Lie group action and giving rise to different Riemannian metrics.Comment: 28 pages; 4 figures, 30 subfigures; notes for proceedings of the Abel Symposium 2016: "Computation and Combinatorics in Dynamics, Stochastics and Control". v3: amended the text to improve readability and clarify some points; updated and added some references; added pseudocode for the dynamic programming algorithm used. The main results remain unchange

Infinitesimals without Logic

We introduce the ring of Fermat reals, an extension of the real field containing nilpotent infinitesimals. The construction takes inspiration from Smooth Infinitesimal Analysis (SIA), but provides a powerful theory of actual infinitesimals without any need of a background in mathematical logic. In particular, on the contrary with respect to SIA, which admits models only in intuitionistic logic, the theory of Fermat reals is consistent with classical logic. We face the problem to decide if the product of powers of nilpotent infinitesimals is zero or not, the identity principle for polynomials, the definition and properties of the total order relation. The construction is highly constructive, and every Fermat real admits a clear and order preserving geometrical representation. Using nilpotent infinitesimals, every smooth functions becomes a polynomial because in Taylor's formulas the rest is now zero. Finally, we present several applications to informal classical calculations used in Physics: now all these calculations become rigorous and, at the same time, formally equal to the informal ones. In particular, an interesting rigorous deduction of the wave equation is given, that clarifies how to formalize the approximations tied with Hook's law using this language of nilpotent infinitesimals.Comment: The first part of the preprint is taken directly form arXiv:0907.1872 The second part is new and contains a list of example

Geometric Integration of Hamiltonian Systems Perturbed by Rayleigh Damping

Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter $\epsilon$, and the schemes under study preserve the symplectic structure in the case $\epsilon=0$. In the case $0<\epsilon\ll 1$ the energy dissipation rate is shown to be asymptotically correct by backward error analysis. Theoretical results on monotone decrease of the modified Hamiltonian function for small enough step sizes are given. Further, an analysis proving near conservation of relative equilibria for small enough step sizes is conducted. Numerical examples, verifying the analyses, are given for a planar pendulum and an elastic 3--D pendulum. The results are superior in comparison with a conventional explicit Runge-Kutta method of the same order

A p38 Mitogen‐Activated Protein Kinase Inhibitor Arrests Active Alveolar Bone Loss in a Rat Periodontitis Model

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141943/1/jper1992.pd

Un-reduction

This paper provides a full geometric development of a new technique called un-reduction, for dealing with dynamics and optimal control problems posed on spaces that are unwieldy for numerical implementation. The technique, which was originally concieved for an application to image dynamics, uses Lagrangian reduction by symmetry in reverse. A deeper understanding of un-reduction leads to new developments in image matching which serve to illustrate the mathematical power of the technique.Comment: 25 pages, revised versio