Structural identifiability of viscoelastic mechanical systems

We solve the local and global structural identifiability problems for viscoelastic mechanical models represented by networks of springs and dashpots. We propose a very simple characterization of both local and global structural identifiability based on identifiability tables, with the purpose of providing a guideline for constructing arbitrarily complex, identifiable spring-dashpot networks. We illustrate how to use our results in a number of examples and point to some applications in cardiovascular modeling.Comment: 3 figure

Identifiable reparametrizations of linear compartment models

Identifiability concerns finding which unknown parameters of a model can be quantified from given input-output data. Many linear ODE models, used in systems biology and pharmacokinetics, are unidentifiable, which means that parameters can take on an infinite number of values and yet yield the same input-output data. We use commutative algebra and graph theory to study a particular class of unidentifiable models and find conditions to obtain identifiable scaling reparametrizations of these models. Our main result is that the existence of an identifiable scaling reparametrization is equivalent to the existence of a scaling reparametrization by monomial functions. We also provide partial results beginning to classify graphs which possess an identifiable scaling reparametrization.Comment: 5 figure

Maximum Angular Separation Epochs for Exoplanet Imaging Observations

Direct imaging of exoplanets presents both significant challenges and significant gains. The advantages primarily lie in receiving emitted and, with future instruments, reflected photons at phase angles not accessible by other techniques, enabling the potential for atmospheric studies and the detection of rotation and surface features. The challenges are numerous and include coronagraph development and achieving the necessary contrast ratio. Here, we address the specific challenge of determining epochs of maximum angular separation for the star and planet. We compute orbital ephemerides for known transiting and radial velocity planets, taking Keplerian orbital elements into account. We provide analytical expressions for angular star--planet separation as a function of the true anomaly, including the locations of minimum and maximum. These expressions are used to calculate uncertainties for maximum angular separation as a function of time for the known exoplanets, and we provide strategies for improving ephemerides with application to proposed and planned imaging missions.Comment: 7 pages, 3 figures, 1 table, accepted for publication in the Astronomical Journa

Joining and decomposing reaction networks

In systems and synthetic biology, much research has focused on the behavior and design of single pathways, while, more recently, experimental efforts have focused on how cross-talk (coupling two or more pathways) or inhibiting molecular function (isolating one part of the pathway) affects systems-level behavior. However, the theory for tackling these larger systems in general has lagged behind. Here, we analyze how joining networks (e.g., cross-talk) or decomposing networks (e.g., inhibition or knock-outs) affects three properties that reaction networks may possess---identifiability (recoverability of parameter values from data), steady-state invariants (relationships among species concentrations at steady state, used in model selection), and multistationarity (capacity for multiple steady states, which correspond to multiple cell decisions). Specifically, we prove results that clarify, for a network obtained by joining two smaller networks, how properties of the smaller networks can be inferred from or can imply similar properties of the original network. Our proofs use techniques from computational algebraic geometry, including elimination theory and differential algebra.Comment: 44 pages; extensive revision in response to referee comment

Johnson’s Relations: visions of global order, 1601-1630

This paper investigates the seven English editions of Giovanni Botero’s Relationi Universali, produced by London merchant Robert Johnson in the context of the growing rivalry between Britain and Spain concerning international expansion, imperialism and trade. By examining each edition in its unique historical context, two important conclusions can be drawn. First, it becomes immediately clear that Johnson was doing much more than translating Botero; he was making a specific intervention in these debates, arguing for a British international presence to rival and curb that of the Spanish. Second, Johnson made elaborate changes to Botero’s work in order to present his case, and as such to treat these texts as translations of the Relationi, as many historians have done, obscures their rich contextual history

Optimized Principal Component Analysis on Coronagraphic Images of the Fomalhaut System

We present the results of a study to optimize the principal component analysis (PCA) algorithm for planet detection, a new algorithm complementing ADI and LOCI for increasing the contrast achievable next to a bright star. The stellar PSF is constructed by removing linear combinations of principal components, allowing the flux from an extrasolar planet to shine through. The number of principal components used determines how well the stellar PSF is globally modelled. Using more principal components may decrease the number of speckles in the final image, but also increases the background noise. We apply PCA to Fomalhaut VLT NaCo images acquired at 4.05 micron with an apodized phase plate. We do not detect any companions, with a model dependent upper mass limit of 13-18 M_Jup from 4-10 AU. PCA achieves greater sensitivity than the LOCI algorithm for the Fomalhaut coronagraphic data by up to 1 magnitude. We make several adaptations to the PCA code and determine which of these prove the most effective at maximizing the signal-to-noise from a planet very close to its parent star. We demonstrate that optimizing the number of principal components used in PCA proves most effective for pulling out a planet signal.Comment: Accepted for publication in ApJ, 7 pages, 9 figure