A mathematical formulation for the cell-cycle model in somitogenesis: analysis, parameter constraints and numerical solutions

In this work we present an analysis, supported by numerical simulations, of the formulation of the cell-cycle model for somitogenesis proposed in Collier et al.(J. Theor. Biol. 207 (2000), 305–316). The analysis indicates that by introducing appropriate parameter constraints on model parameters the cell-cycle mechanism can indeed give rise to the periodic pattern of somites observed in normal embryos. The analysis also provides a greater understanding of the signalling process controlling somite formation and allows us to understand which parameters influence somite length

Modeling round-off error in the fast gradient method for predictive control

We present a method for determining the smallest precision required to have algorithmic stability of an implementation of the Fast Gradient Method (FGM) when solving a linear Model Predictive Control (MPC) problem in fixed-point arithmetic. We derive two models for the round-off error present in fixed-point arithmetic. The first is a generic model with no assumptions on the predicted system or weight matrices. The second is a parametric model that exploits the Toeplitz structure of the MPC problem for a Schur-stable system. We also propose a metric for measuring the amount of round-off error the FGM iteration can tolerate before becoming unstable. This metric is combined with the round-off error models to compute the minimum number of fractional bits needed for the fixed-point data type. Using these models, we show that exploiting the MPC problem structure nearly halves the number of fractional bits needed to implement an example problem. We show that this results in significant decreases in resource usage, computational energy and execution time for an implementation on a Field Programmable Gate Array

Horizon-independent preconditioner design for linear predictive control

First-order optimization solvers, such as the Fast Gradient Method, are increasingly being used to solve Model Predictive Control problems in resource-constrained environments. Unfortunately, the convergence rate of these solvers is significantly affected by the conditioning of the problem data, with ill-conditioned problems requiring a large number of iterations. To reduce the number of iterations required, we present a simple method for computing a horizon-independent preconditioning matrix for the Hessian of the condensed problem. The preconditioner is based on the block Toeplitz structure of the Hessian. Horizon-independence allows one to use only the predicted system and cost matrices to compute the preconditioner, instead of the full Hessian. The proposed preconditioner has equivalent performance to an optimal preconditioner in numerical examples, producing speedups between 2x and 9x for the Fast Gradient Method. Additionally, we derive horizon-independent spectral bounds for the Hessian in terms of the transfer function of the predicted system, and show how these can be used to compute a novel horizon-independent bound on the condition number for the preconditioned Hessian

Survey of inorganic polymers

A literature search was carried out in order to identify inorganic, metallo-organic, and hybrid inorganic-organic polymers that could serve as potential matrix resins for advanced composites. The five most promising candidates were critically reviewed and recommendations were made for the achievement of their potential in terms of performance and cost. These generic polymer classes comprise: (1) Poly(arylsil sesquioxanes); (2) Poly(silyl arylene siloxanes); (3) Poly(silarylenes); (4) Poly(silicon-linked ferrocenes); and (5) Poly(organo phosphazenes). No single candidate currently possesses the necessary combination of physicomechanical properties, thermal stability, processability, and favorable economics. The first three classes exhibit the best thermal performance. On the other hand, poly (organo phosphazenes), the most extensively studied polymer class, exhibit the best combination of structure-property control, processability, and favorable economics

Heterogeneous models place the root of the placental mammal phylogeny

Heterogeneity among life traits in mammals has resulted in considerable phylogenetic conflict, particularly concerning the position of the placental root. Layered upon this are gene- and lineage-specific variation in amino acid substitution rates and compositional biases. Life trait variations that may impact upon mutational rates are longevity, metabolic rate, body size, and germ line generation time. Over the past 12 years, three main conflicting hypotheses have emerged for the placement of the placental root. These hypotheses place the Atlantogenata (common ancestor of Xenarthra plus Afrotheria), the Afrotheria, or the Xenarthra as the sister group to all other placental mammals. Model adequacy is critical for accurate tree reconstruction and by failing to account for these compositional and character exchange heterogeneities across the tree and data set, previous studies have not provided a strongly supported hypothesis for the placental root. For the first time, models that accommodate both tree and data set heterogeneity have been applied to mammal data. Here, we show the impact of accurate model assignment and the importance of data sets in accommodating model parameters while maintaining the power to reject competing hypotheses. Through these sophisticated methods, we demonstrate the importance of model adequacy, data set power and provide strong support for the Atlantogenata over other competing hypotheses for the position of the placental root

Genome sequence of Acetomicrobium hydrogeniformans OS1

Acetomicrobium hydrogeniformans, an obligate anaerobe of the phylum Synergistetes, was isolated from oil production water. It has the unusual ability to produce almost 4 molecules H2/molecule glucose. The draft genome of A. hydrogeniformans OS1 (DSM 22491T) is 2,123,925 bp, with 2,068 coding sequences and 60 RNA genes

Fast and accurate method for computing non-smooth solutions to constrained control problems

Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems with constraints. State-of-the-art methods use fixed mesh schemes, which cannot achieve superlinear convergence in the presence of non-smooth solutions. In this paper, we propose using a flexible mesh in an integrated residual method. The locations of the mesh nodes are introduced as decision variables, and constraints are added to set upper and lower bounds on the size of the mesh intervals. We compare our approach to a uniform fixed mesh on a real-world satellite reorientation example. This example demonstrates that the flexible mesh enables the solver to automatically locate the discontinuities in the solution, has superlinear convergence and faster solve time

Delineation of a unique protein-protein interaction site on the surface of the estrogen receptor

Recent studies have identified a series of estrogen receptor (ER)interacting peptides that recognize sites that are distinct from the classic coregulator recruitment (AF2) region. Here, we report the structural and functional characterization of an ER alpha-specific peptide that binds to the liganded receptor in an AF2-independent manner. The 2-angstrom crystal structure of the ER/peptide complex reveals a binding site that is centered on a shallow depression on the beta-hairpin face of the ligand-binding domain. The peptide binds in an unusual extended conformation and makes multiple contacts with the ligand-binding domain. The location and architecture of the binding site provides an insight into the peptide's ER subtype specificity and ligand interaction preferences. In vivo, an engineered coactivator containing the peptide motif is able to strongly enhance the transcriptional activity of liganded ER alpha, particularly in the presence of 4-hydroxytamoxifen. Furthermore, disruption of this binding surface alters ER's response to the coregulator TIF2. Together, these results indicate that this previously unknown interaction site represents a bona fide control surface involved in regulating receptor activity