Equipping and Catalyzing Disciple Makers at Front Range Christian Church

The purpose of this doctoral project was to implement pilot discipleship groups at Front Range Christian Church (FRCC). Taking into account the mobility of both the congregation and the surrounding community, the project aimed at people development over a short period of time rather than the establishment of a new church program. Three pilot groups with varying composition, meeting logistics, and resource utilization were used for comparison in determining the most effective means of equipping and catalyzing disciple makers at FRCC. Jesus’ example with the first disciples was normative in determining the means and method of discipleship in the project. Through an examination of Scripture, four primary areas of development were extrapolated from Jesus’ discipleship model: biblical worldview, integrated mission, intentional relationships, and habits and rhythms of life conducive for ongoing growth. These four areas comprised the subject matter for each pilot group to varying degrees. The project also took into account the multipliable nature of discipleship in the New Testament. Thus, the invitation to participate in the pilot groups included a full life cycle—from beginning (as disciples) to beginning (as disciple makers). The assessment of the project consists of three distinct phases. The initial assessment took place midway through the project in order to allow for needed adjustments to increase the likelihood of equipping and catalyzing disciple makers. The second assessment will take place at the conclusion of the pilot project. It is designed to facilitate discussion amongst FRCC leadership as to the potential for ongoing church- wide discipleship efforts. The final assessment will occur over time as it becomes clear whether or not subsequent generations of disciple makers are resulting

Inventory and Analysis of Plankton in Green River within Mammoth Cave National Park

National Park Service biological staff are charged with preserving and protecting all creatures within a park’s boundaries. It is only a matter of time before exotic zebra mussels (Dreissena polymorpha) invade all eastern waterways including Green River within Mammoth Cave National Park, Kentucky. The National Park Service, in cooperation with University of Tennessee, initiated this inventory of plankton within Mammoth Cave National Park to establish baseline data prior to zebra mussel invasion. During this two year study (2000-2002), 180 plankton samples were collected at three sampling sites which encompassed all major riverine habitat types within the three flow zones (free-flow, transitional, impounded) created by Lock and Dam #6. Duplicate plankton samples were taken on all six occasions at these sites. Each year one sample was collected in June/July (base flow), another in August/September (base flow), and the other in November/December (enhanced flow). Zooplankton were sampled using both vertical (4/site) and horizontal (4/site) tows with 153-micron and 80-micron mesh plankton nets. Samples were fixed in the field with a 10% sugared formalin solution for later examination in the laboratory. A 1.0-L polycarbonate water bottle was used to collect phytoplankton samples at a depth just above the Secchi disk transparency level; samples were fixed in a 1% Lugol’s solution and stored in an opaque container for analysis. Water temperature, conductivity, dissolved oxygen, pH, and water transparency were also measured and recorded at each sample site. Water quality data were similar among sites and the variation among dates was consistent with climatic conditions. Dissolved oxygen ranged from 10.96 (mg/L) in iv December 2001 to 6.20 (mg/L) in July 2002. Temperature ranged from 25.9o C in July 2002 to 6.4o C in November 2000. The pH ranged from 8.05 (su) in November 2000 to 5.72 (su) in July 2002. Conductivity ranged from 282 (mS/cm) in November 2000 to 383 (mS/cm) in July 2002. A paucity of zooplankton was observed in Green River while phytoplankton densities were similar to levels measured upstream in Green River Lake. The dominant zooplankton groups were Cladocera (Bosmina longirostrus) and Copepoda (Mesocyclops edax). Densities of Bosmina ranged from 0.01/L in September 2000 to 0.46/L in December 2001; M. edax densities ranged from 0.01/L to 0.53/L during the same period. Aquatic insects were collected at densities equal to or greater than the zooplankton during the study, with the family Chironomidae as the dominant aquatic insect taxon collected. Chlorophyta (green algae) was the dominant phytoplankton phylum present during all samples with approximately 97% of the species composition; the genus Cholorella comprised over 95% of all cells in every sample. Other filamentous Chlorophyta genera, like Ulothrix, contributed minor portions of the population. Also, Cyanophyta (blue-greens) and Chrysophyta (golden-brown algae) were found in relatively low numbers. Only limited evidence of zooplankton reproduction was found at the downstream sample site. We concluded that, during the study period, Green River did not exhibit a true plankton community, potamoplankton, but rather a tachyplankton (transient) community. A digital reference collection of zooplankton and phytoplankton was created to provide baseline data for future studies. A long-term plankton data set should be developed if future mussel propagation projects are to be successful in the river

3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries

Recent advances in electron microscopy have enabled the imaging of single cells in 3D at nanometer length scale resolutions. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed geometries. Enabling such simulations requires watertight meshing of electron micrograph images into 3D volume meshes, which can then form the basis of computer simulations of such processes using numerical techniques such as the Finite Element Method. In this paper, we describe the use of our recently rewritten mesh processing software, GAMer 2, to bridge the gap between poorly conditioned meshes generated from segmented micrographs and boundary marked tetrahedral meshes which are compatible with simulation. We demonstrate the application of a workflow using GAMer 2 to a series of electron micrographs of neuronal dendrite morphology explored at three different length scales and show that the resulting meshes are suitable for finite element simulations. This work is an important step towards making physical simulations of biological processes in realistic geometries routine. Innovations in algorithms to reconstruct and simulate cellular length scale phenomena based on emerging structural data will enable realistic physical models and advance discovery at the interface of geometry and cellular processes. We posit that a new frontier at the intersection of computational technologies and single cell biology is now open.Comment: 39 pages, 14 figures. High resolution figures and supplemental movies available upon reques

An Open Source Mesh Generation Platform for Biophysical Modeling Using Realistic Cellular Geometries

ABSTRACT Advances in imaging methods such as electron microscopy, tomography, and other modalities are enabling high-resolution reconstructions of cellular and organelle geometries. Such advances pave the way for using these geometries for biophysical and mathematical modeling once these data can be represented as a geometric mesh, which, when carefully conditioned, enables the discretization and solution of partial differential equations. In this study, we outline the steps for a naïve user to approach GAMer 2 , a mesh generation code written in C++ designed to convert structural datasets to realistic geometric meshes, while preserving the underlying shapes. We present two example cases, 1) mesh generation at the subcellular scale as informed by electron tomography, and 2) meshing a protein with structure from x-ray crystallography. We further demonstrate that the meshes generated by GAMer are suitable for use with numerical methods. Together, this collection of libraries and tools simplifies the process of constructing realistic geometric meshes from structural biology data. SIGNIFICANCE As biophysical structure determination methods improve, the rate of new structural data is increasing. New methods that allow the interpretation, analysis, and reuse of such structural information will thus take on commensurate importance. In particular, geometric meshes, such as those commonly used in graphics and mathematics, can enable a myriad of mathematical analysis. In this work, we describe GAMer 2 , a mesh generation library designed for biological datasets. Using GAMer 2 and associated tools PyGAMer and BlendGAMer , biologists can robustly generate computer and algorithm friendly geometric mesh representations informed by structural biology data. We expect that GAMer 2 will be a valuable tool to bring realistic geometries to biophysical models

Plasma Analogy and Non-Abelian Statistics for Ising-type Quantum Hall States

We study the non-Abelian statistics of quasiparticles in the Ising-type quantum Hall states which are likely candidates to explain the observed Hall conductivity plateaus in the second Landau level, most notably the one at filling fraction nu=5/2. We complete the program started in Nucl. Phys. B 506, 685 (1997) and show that the degenerate four-quasihole and six-quasihole wavefunctions of the Moore-Read Pfaffian state are orthogonal with equal constant norms in the basis given by conformal blocks in a c=1+1/2 conformal field theory. As a consequence, this proves that the non-Abelian statistics of the excitations in this state are given by the explicit analytic continuation of these wavefunctions. Our proof is based on a plasma analogy derived from the Coulomb gas construction of Ising model correlation functions involving both order and (at most two) disorder operators. We show how this computation also determines the non-Abelian statistics of collections of more than six quasiholes and give an explicit expression for the corresponding conformal block-derived wavefunctions for an arbitrary number of quasiholes. Our method also applies to the anti-Pfaffian wavefunction and to Bonderson-Slingerland hierarchy states constructed over the Moore-Read and anti-Pfaffian states.Comment: 68 pages, 3 figures; v2: substantial revisions and additions for clarity, minor correction

An Open Source Mesh Generation Platform for Biophysical Modeling Using Realistic Cellular Geometries

Advances in imaging methods such as electron microscopy, tomography and other modalities are enabling high-resolution reconstructions of cellular and organelle geometries. Such advances pave the way for using these geometries for biophysical and mathematical modeling once these data can be represented as a geometric mesh, which, when carefully conditioned, enables the discretization and solution of partial differential equations. In this study, we outline the steps for a na\"ive user to approach GAMer 2, a mesh generation code written in C++ designed to convert structural datasets to realistic geometric meshes, while preserving the underlying shapes. We present two example cases, 1) mesh generation at the subcellular scale as informed by electron tomography, and 2) meshing a protein with structure from x-ray crystallography. We further demonstrate that the meshes generated by GAMer are suitable for use with numerical methods. Together, this collection of libraries and tools simplifies the process of constructing realistic geometric meshes from structural biology data.Comment: 6 pages and 4 figures. Supplemental Movie available upon reques

Theory of spin excitations in undoped and underdoped cuprates

We consider the magnetic properties of high Tc cuprates from a gauge theory point of view, with emphasis on the underdoped regime. Underdoped cuprates possess certain antiferromagnetic correlations, as evidenced, for example, by different temperature dependence of the Cu and O site NMR relaxation rates, that are not captured well by slave boson mean field theories of the t-J model. We show that the inclusion of gauge fluctuations will remedy the deficiencies of the mean field theories. As a concrete illustration of the gauge-fluctuation restoration of the antiferromangetic correlation and the feasibility of the 1/N perturbation theory, the Heisenberg spin chain is analyzed in terms of a 1+1D U(1) gauge theory with massless Dirac fermions. The 1/N-perturbative treatment of the same gauge theory in 2+1D (which can be motivated from the mean field pi-flux phase of the Heisenberg model) leads to a dynamical mass generation corresponding to an antiferromagnetic ordering. On the other hand, it is argued that in a similar gauge theory with an additional coupling to a Bose (holon) field, symmetry breaking does not occur, but antiferromagnetic correlations are enhanced, which is the situation in the underdoped cuprates.Comment: Typos corrected; minor changes made to match the published version. Related (background) materials can be found at "http://www.stanford.edu/~donhkim/physics.html

Scalar transport in compressible flow

Transport of scalar fields in compressible flow is investigated. The effective equations governing the transport at scales large compared to those of the advecting flow are derived by using multi-scale techniques. Ballistic transport generally takes place when both the solenoidal and the potential components of the velocity do not vanish, despite of the fact that it has zero average value. The calculation of the effective ballistic velocity $V_b$ is reduced to the solution of one auxiliary equation. An analytic expression for $V_b$ is derived in some special instances, i.e. flows depending on a single coordinate, random with short correlation times and slightly compressible cellular flow. The effective mean velocity $V_b$ vanishes for velocity fields which are either incompressible or potential and time-independent. For generic compressible flow, the most general conditions ensuring the absence of ballistic transport are isotropy and/or parity invariance. When $V_b$ vanishes (or in the frame of reference moving with velocity $V_b$), standard diffusive transport takes place. It is known that diffusion is always enhanced by incompressible flow. On the contrary, we show that diffusion is depleted in the presence of time-independent potential flow. Trapping effects due to potential wells are responsible for this depletion. For time-dependent potential flow or generic compressible flow, transport rates are enhanced or depleted depending on the detailed structure of the velocity field.Comment: 27 pages, submitted to Physica

SMART: Spatial Modeling Algorithms for Reaction and Transport

Recent advances in microscopy and 3D reconstruction methods have allowed for characterization of cellular morphology in unprecedented detail, including the irregular geometries of intracellular subcompartments such as membrane-bound organelles. These geometries are now compatible with predictive modeling of cellular function. Biological cells respond to stimuli through sequences of chemical reactions generally referred to as cell signaling pathways. The propagation and reaction of chemical substances in cell signaling pathways can be represented by coupled nonlinear systems of reaction-transport equations. These reaction pathways include numerous chemical species that react across boundaries or interfaces (e.g., the cell membrane and membranes of organelles within the cell) and domains (e.g., the bulk cell volume and the interior of organelles). Such systems of multi-dimensional partial differential equations (PDEs) are notoriously difficult to solve because of their high dimensionality, non-linearities, strong coupling, stiffness, and potential instabilities. In this work, we describe Spatial Modeling Algorithms for Reactions and Transport (SMART), a high-performance finite-element-based simulation package for model specification and numerical simulation of spatially-varying reaction-transport processes. SMART is based on the FEniCS finite element library, provides a symbolic representation framework for specifying reaction pathways, and supports geometries in 2D and 3D including large and irregular cell geometries obtained from modern ultrastructural characterization methods.Comment: 5 pages, 2 figures, submitted to the Journal of Open Source Software (JOSS), code available at https://github.com/RangamaniLabUCSD/smar