Microwave Gaseous Discharges

Contains reports on six research projects.Atomic Energy Commission under Contract AT(30-1) 184

Triangle-Free Penny Graphs: Degeneracy, Choosability, and Edge Count

We show that triangle-free penny graphs have degeneracy at most two, list coloring number (choosability) at most three, diameter $D=\Omega(\sqrt n)$, and at most $\min\bigl(2n-\Omega(\sqrt n),2n-D-2\bigr)$ edges.Comment: 10 pages, 2 figures. To appear at the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Global phosphoproteomic profiling reveals perturbed signaling in a mouse model of dilated cardiomyopathy

Phospholamban (PLN) plays a central role in Ca2+ homeostasis in cardiac myocytes through regulation of the sarco(endo)plasmic reticulum Ca2+-ATPase 2A (SERCA2A) Ca2+ pump. An inherited mutation converting arginine residue 9 in PLN to cysteine (R9C) results in dilated cardiomyopathy (DCM) in humans and transgenic mice, but the downstream signaling defects leading to decompensation and heart failure are poorly understood. Here we used precision mass spectrometry to study the global phosphorylation dynamics of 1,887 cardiac phosphoproteins in early affected heart tissue in a transgenic R9C mouse model of DCM compared with wild-type littermates. Dysregulated phosphorylation sites were quantified after affinity capture and identification of 3,908 phosphopeptides from fractionated whole-heart homogenates. Global statistical enrichment analysis of the differential phosphoprotein patterns revealed selective perturbation of signaling pathways regulating cardiovascular activity in early stages of DCM. Strikingly, dysregulated signaling through the Notch-1 receptor, recently linked to cardiomyogenesis and embryonic cardiac stem cell development and differentiation but never directly implicated in DCM before, was a prominently perturbed pathway. We verified alterations in Notch-1 downstream components in early symptomatic R9C transgenic mouse cardiomyocytes compared with wild type by immunoblot analysis and confocal immunofluorescence microscopy. These data reveal unexpected connections between stress-regulated cell signaling networks, specific protein kinases, and downstream effectors essential for proper cardiac function

Finding 2-Edge and 2-Vertex Strongly Connected Components in Quadratic Time

We present faster algorithms for computing the 2-edge and 2-vertex strongly connected components of a directed graph, which are straightforward generalizations of strongly connected components. While in undirected graphs the 2-edge and 2-vertex connected components can be found in linear time, in directed graphs only rather simple $O(m n)$-time algorithms were known. We use a hierarchical sparsification technique to obtain algorithms that run in time $O(n^2)$. For 2-edge strongly connected components our algorithm gives the first running time improvement in 20 years. Additionally we present an $O(m^2 / \log{n})$-time algorithm for 2-edge strongly connected components, and thus improve over the $O(m n)$ running time also when $m = O(n)$. Our approach extends to k-edge and k-vertex strongly connected components for any constant k with a running time of $O(n^2 \log^2 n)$ for edges and $O(n^3)$ for vertices

Pixel and Voxel Representations of Graphs

We study contact representations for graphs, which we call pixel representations in 2D and voxel representations in 3D. Our representations are based on the unit square grid whose cells we call pixels in 2D and voxels in 3D. Two pixels are adjacent if they share an edge, two voxels if they share a face. We call a connected set of pixels or voxels a blob. Given a graph, we represent its vertices by disjoint blobs such that two blobs contain adjacent pixels or voxels if and only if the corresponding vertices are adjacent. We are interested in the size of a representation, which is the number of pixels or voxels it consists of. We first show that finding minimum-size representations is NP-complete. Then, we bound representation sizes needed for certain graph classes. In 2D, we show that, for $k$-outerplanar graphs with $n$ vertices, $\Theta(kn)$ pixels are always sufficient and sometimes necessary. In particular, outerplanar graphs can be represented with a linear number of pixels, whereas general planar graphs sometimes need a quadratic number. In 3D, $\Theta(n^2)$ voxels are always sufficient and sometimes necessary for any $n$-vertex graph. We improve this bound to $\Theta(n\cdot \tau)$ for graphs of treewidth $\tau$ and to $O((g+1)^2n\log^2n)$ for graphs of genus $g$. In particular, planar graphs admit representations with $O(n\log^2n)$ voxels

Containment and equivalence of weighted automata: Probabilistic and max-plus cases

This paper surveys some results regarding decision problems for probabilistic and max-plus automata, such as containment and equivalence. Probabilistic and max-plus automata are part of the general family of weighted automata, whose semantics are maps from words to real values. Given two weighted automata, the equivalence problem asks whether their semantics are the same, and the containment problem whether one is point-wise smaller than the other one. These problems have been studied intensively and this paper will review some techniques used to show (un)decidability and state a list of open questions that still remain

Joint analysis of stressors and ecosystem services to enhance restoration effectiveness

With increasing pressure placed on natural systems by growing human populations, both scientists and resource managers need a better understanding of the relationships between cumulative stress from human activities and valued ecosystem services. Societies often seek to mitigate threats to these services through large-scale, costly restoration projects, such as the over one billion dollar Great Lakes Restoration Initiative currently underway. To help inform these efforts, we merged high-resolution spatial analyses of environmental stressors with mapping of ecosystem services for all five Great Lakes. Cumulative ecosystem stress is highest in near-shore habitats, but also extends offshore in Lakes Erie, Ontario, and Michigan. Variation in cumulative stress is driven largely by spatial concordance among multiple stressors, indicating the importance of considering all stressors when planning restoration activities. In addition, highly stressed areas reflect numerous different combinations of stressors rather than a single suite of problems, suggesting that a detailed understanding of the stressors needing alleviation could improve restoration planning. We also find that many important areas for fisheries and recreation are subject to high stress, indicating that ecosystem degradation could be threatening key services. Current restoration efforts have targeted high-stress sites almost exclusively, but generally without knowledge of the full range of stressors affecting these locations or differences among sites in service provisioning. Our results demonstrate that joint spatial analysis of stressors and ecosystem services can provide a critical foundation for maximizing social and ecological benefits from restoration investments. www.pnas.org/lookup/suppl/doi:10.1073/pnas.1213841110/-/DCSupplementa

Schur Q-functions and degeneracy locus formulas for morphisms with symmetries

We give closed-form formulas for the fundamental classes of degeneracy loci associated with vector bundle maps given locally by (not necessary square) matrices which are symmetric (resp. skew-symmetric) w.r.t. the main diagonal. Our description uses essentially Schur Q-polynomials of a bundle, and is based on a certain push-forward formula for these polynomials in a Grassmann bundle.Comment: 22 pages, AMSTEX, misprints corrected, exposition improved. to appear in the Proceedings of Intersection Theory Conference in Bologna, "Progress in Mathematics", Birkhause

Diffusion tensor imaging of frontal lobe white matter tracts in schizophrenia

We acquired diffusion tensor and structural MRI images on 103 patients with schizophrenia and 41 age-matched normal controls. The vector data was used to trace tracts from a region of interest in the anterior limb of the internal capsule to the prefrontal cortex. Patients with schizophrenia had tract paths that were significantly shorter in length from the center of internal capsule to prefrontal white matter. These tracts, the anterior thalamic radiations, are important in frontal-striatal-thalamic pathways. These results are consistent with findings of smaller size of the anterior limb of the internal capsule in patients with schizophrenia, diffusion tensor anisotropy decreases in frontal white matter in schizophrenia and hypothesized disruption of the frontal-striatal-thalamic pathway system