Tropical Geometry of Statistical Models

This paper presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are coordinates of a point in the variety, and the sum-product algorithm is an efficient tool for evaluating specific coordinates. The question addressed here is how the solutions to various inference problems depend on the model parameters. The proposed answer is expressed in terms of tropical algebraic geometry. A key role is played by the Newton polytope of a statistical model. Our results are applied to the hidden Markov model and to the general Markov model on a binary tree.Comment: 14 pages, 3 figures. Major revision. Applications now in companion paper, "Parametric Inference for Biological Sequence Analysis

Parametric Inference for Biological Sequence Analysis

One of the major successes in computational biology has been the unification, using the graphical model formalism, of a multitude of algorithms for annotating and comparing biological sequences. Graphical models that have been applied towards these problems include hidden Markov models for annotation, tree models for phylogenetics, and pair hidden Markov models for alignment. A single algorithm, the sum-product algorithm, solves many of the inference problems associated with different statistical models. This paper introduces the \emph{polytope propagation algorithm} for computing the Newton polytope of an observation from a graphical model. This algorithm is a geometric version of the sum-product algorithm and is used to analyze the parametric behavior of maximum a posteriori inference calculations for graphical models.Comment: 15 pages, 4 figures. See also companion paper "Tropical Geometry of Statistical Models" (q-bio.QM/0311009

Potential Structural Materials and Design Concepts for Light Airplanes

Potential structural materials and design considerations for helicopters and light general aircraf

Potential structural materials and design concepts for light airplanes Final report

Potential structural materials and design concepts evaluated for light aircraft application

Explanation of the Tao effect

In a series of experiments Tao and coworkers\cite{tao1,tao2,tao3} found that superconducting microparticles in the presence of a strong electrostatic field aggregate into balls of macroscopic dimensions. No explanation of this phenomenon exists within the conventional theory of superconductivity. We show that this effect can be understood within an alternative electrodynamic description of superconductors recently proposed that follows from an unconventional theory of superconductivity. Experiments to test the theory are discussed.Comment: Submitted to Science January 2nd, declined January 6th; to Nature January 7th, declined January 13th; to PRL January 14th, declined February 25t

Testing of molded high temperature plastic actuator road seals for use in advanced aircraft hydraulic systems

Molded high temperature plastic first and second stage rod seal elements were evaluated in seal assemblies to determine performance characteristics. These characteristics were compared with the performance of machined seal elements. The 6.35 cm second stage Chevron seal assembly was tested using molded Chevrons fabricated from five molding materials. Impulse screening tests conducted over a range of 311 K to 478 K revealed thermal setting deficiencies in the aromatic polyimide molding materials. Seal elements fabricated from aromatic copolyester materials structurally failed during impulse cycle calibration. Endurance testing of 3.85 million cycles at 450 K using MIL-H-83283 fluid showed poorer seal performance with the unfilled aromatic polyimide material than had been attained with seals machined from Vespel SP-21 material. The 6.35 cm first stage step-cut compression loaded seal ring fabricated from copolyester injection molding material failed structurally during impulse cycle calibration. Molding of complex shape rod seals was shown to be a potentially controllable technique, but additional molding material property testing is recommended

Enumeration of RNA structures by Matrix Models

We enumerate the number of RNA contact structures according to their genus, i.e. the topological character of their pseudoknots. By using a recently proposed matrix model formulation for the RNA folding problem, we obtain exact results for the simple case of an RNA molecule with an infinitely flexible backbone, in which any arbitrary pair of bases is allowed. We analyze the distribution of the genus of pseudoknots as a function of the total number of nucleotides along the phosphate-sugar backbone.Comment: RevTeX, 4 pages, 2 figure

Use of a Self-Fed, Small-Package Protein Supplement for Beef Cows Post-Weaning

A 2-year supplementation study conducted at Miles City, MT from mid-October to mid-December in 2007 and 2008 evaluated responses of beef cows (n = 141 in 2007, n = 138 in 2008; avg BW = 546 ± 5.2 kg) grazing dormant native range (8.8% CP, 64% NDF, 71% IVDMD) to two different supplementation strategies. Each year, cows were stratified by age and weight at weaning and then assigned to one of two supplements: 1) self-fed loose mineral mix (MIN) or 2) self-fed mineral plus high-bypass protein sources (MIN+PRO; 50% mineral mix, 25% feather meal, 25% fish meal). Target intakes were 70 g/d for MIN and 140 g/d for MIN+PRO. Cows were weighed and hip height and girth measurements were taken at the beginning and end of the 60-d studies. Weight-to-height and weight-to-girth ratio changes were calculated. Data were analyzed with supplement, cow age (2, 3, and 4+), year, and their interactions in the model. In 2007, cows fed MIN consumed 28 g/d and MIN+PRO cows consumed 93 g/d, which was lower than the target amount for both supplements. In 2008, MIN cows again failed to consume the target amount (13 g/d), while MIN+PRO cows consumed just over target amount (160 g/d). Cows lost similar (P = 0.70) amounts of weight during the study regardless of supplement treatment (-22 and -25 ± 5 kg for MIN and MIN+PRO, respectively). Likewise, weight-toheight ratio change (-0.25 and -0.25 ± 0.04) and weight-togirth ratio change (-0.10 and -0.12 ± 0.02) were similar (P ≥ 0.60) for MIN and MIN+PRO cows, respectively. Year × cow age interactions (P ≤ 0.08) were observed for weight change and weight-to-height ratio change. Two- and 3-yrold cows lost less weight in 2008 than in 2007, while mature cows lost similar amounts of weight in both years. All cows exhibited less change in weight-to-height ratio in 2008 compared to 2007, with the difference between years most pronounced in younger cows. Protein supplementation at this level did not impact cow performance; however, forage quality was higher than expected, which may have contributed to the lack of response to supplementation with the mineral-protein mix

Use of a Self-Fed, Small-Package Protein Supplement for Beef Cows Post-Weaning

A 2-year supplementation study conducted at Miles City, MT from mid-October to mid-December in 2007 and 2008 evaluated responses of beef cows (n = 141 in 2007, n = 138 in 2008; avg BW = 546 ± 5.2 kg) grazing dormant native range (8.8% CP, 64% NDF, 71% IVDMD) to two different supplementation strategies. Each year, cows were stratified by age and weight at weaning and then assigned to one of two supplements: 1) self-fed loose mineral mix (MIN) or 2) self-fed mineral plus high-bypass protein sources (MIN+PRO; 50% mineral mix, 25% feather meal, 25% fish meal). Target intakes were 70 g/d for MIN and 140 g/d for MIN+PRO. Cows were weighed and hip height and girth measurements were taken at the beginning and end of the 60-d studies. Weight-to-height and weight-to-girth ratio changes were calculated. Data were analyzed with supplement, cow age (2, 3, and 4+), year, and their interactions in the model. In 2007, cows fed MIN consumed 28 g/d and MIN+PRO cows consumed 93 g/d, which was lower than the target amount for both supplements. In 2008, MIN cows again failed to consume the target amount (13 g/d), while MIN+PRO cows consumed just over target amount (160 g/d). Cows lost similar (P = 0.70) amounts of weight during the study regardless of supplement treatment (-22 and -25 ± 5 kg for MIN and MIN+PRO, respectively). Likewise, weight-toheight ratio change (-0.25 and -0.25 ± 0.04) and weight-togirth ratio change (-0.10 and -0.12 ± 0.02) were similar (P ≥ 0.60) for MIN and MIN+PRO cows, respectively. Year × cow age interactions (P ≤ 0.08) were observed for weight change and weight-to-height ratio change. Two- and 3-yrold cows lost less weight in 2008 than in 2007, while mature cows lost similar amounts of weight in both years. All cows exhibited less change in weight-to-height ratio in 2008 compared to 2007, with the difference between years most pronounced in younger cows. Protein supplementation at this level did not impact cow performance; however, forage quality was higher than expected, which may have contributed to the lack of response to supplementation with the mineral-protein mix

Protein Kinase D-Mediated Anterograde Membrane Trafficking Is Required for Fibroblast Motility

AbstractBackground: Locomoting cells exhibit a constant retrograde flow of plasma membrane (PM) proteins from the leading edge lamellipodium backward, which when coupled to substrate adhesion, may drive forward cell movement. However, the intracellular source of these PM components and whether their continuous retrograde flow is required for cell motility is unknown.Results: To test the hypothesis that the anterograde secretion pathway supplies PM components for retrograde flow that are required for lamellipodial activity and cell motility, we specifically inhibited transport of cargo from the trans-Golgi network (TGN) to the PM in Swiss 3T3 fibroblasts and monitored cell motility using time-lapse microscopy. TGN-to-PM trafficking was inhibited with a dominant-negative, kinase-dead (kd) mutant of protein kinase D1 (PKD) that specifically blocks budding of secretory vesicles from the TGN and does not affect other transport pathways. Inhibition of PKD on the TGN inhibited directed cell motility and retrograde flow of surface markers and filamentous actin, while inhibition of PKD elsewhere in the cell neither blocked anterograde membrane transport nor cell motile functions. Exogenous activation of Rac1 in PKD-kd-expressing cells restored lamellipodial dynamics independent of membrane traffic. However, lamellipodial activity was delocalized from a single leading edge, and directed cell motility was not fully recovered.Conclusions: These results indicate that PKD-mediated anterograde membrane traffic from the TGN to the PM is required for fibroblast locomotion and localized Rac1-dependent leading edge activity. We suggest that polarized secretion transmits cargo that directs localized signaling for persistent leading edge activity necessary for directional migration