Inference of Circadian Regulatory Networks

Abstract. We assess the accuracy of various state-of-the-art methods for reconstructing gene and protein regulatory networks in the context of circadian regulation. Gene expression and protein concentration time series are simulated from a recently published regulatory network of the circadian clock in A. thaliana, which is mathematically described by a Markov jump process based on Michaelis-Menten kinetics. Our study provides relative network reconstruction accuracy scores for a critical comparative performance evaluation, quantifies the influence of systematically missing values related to unknown protein concentrations and mRNA transcription rates, and investigates the dependence of the performance on the network topology and the degree of recurrency. An application to recent gene expression time series from qPCR experiments suggests new hypotheses about the structure of the central circadian gene regulatory network in A. thaliana

Uniform random generation of large acyclic digraphs

Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of the structure itself is of great interest. As well as for the assessment of different structure learning algorithms in simulation studies, a uniform sample from the space of directed acyclic graphs is required to evaluate the prevalence of certain structural features. Here we analyse how to sample acyclic digraphs uniformly at random through recursive enumeration, an approach previously thought too computationally involved. Based on complexity considerations, we discuss in particular how the enumeration directly provides an exact method, which avoids the convergence issues of the alternative Markov chain methods and is actually computationally much faster. The limiting behaviour of the distribution of acyclic digraphs then allows us to sample arbitrarily large graphs. Building on the ideas of recursive enumeration based sampling we also introduce a novel hybrid Markov chain with much faster convergence than current alternatives while still being easy to adapt to various restrictions. Finally we discuss how to include such restrictions in the combinatorial enumeration and the new hybrid Markov chain method for efficient uniform sampling of the corresponding graphs.Comment: 15 pages, 2 figures. To appear in Statistics and Computin

The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation

In this paper we revisit one of the rst models of analog computation, Shannon's General Purpose Analog Computer (GPAC). The GPAC has often been argued to be weaker than computable analysis. As main contribution, we show that if we change the notion of GPACcomputability in a natural way, we compute exactly all real computable functions (in the sense of computable analysis). Moreover, since GPACs are equivalent to systems of polynomial di erential equations then we show that all real computable functions can be de ned by such models

Solving analytic differential equations in polynomial time over unbounded domains

In this paper we consider the computational complexity of solving initial-value problems de ned with analytic ordinary diferential equations (ODEs) over unbounded domains of Rn and Cn, under the Computable Analysis setting. We show that the solution can be computed in polynomial time over its maximal interval of de nition, provided it satis es a very generous bound on its growth, and that the function admits an analytic extension to the complex plane

Interparticle interactions:Energy potentials, energy transfer, and nanoscale mechanical motion in response to optical radiation

In the interactions between particles of material with slightly different electronic levels, unusually large shifts in the pair potential can result from photoexcitation, and on subsequent electronic excitation transfer. To elicit these phenomena, it is necessary to understand the fundamental differences between a variety of optical properties deriving from dispersion interactions, and processes such as resonance energy transfer that occur under laser irradiance. This helps dispel some confusion in the recent literature. By developing and interpreting the theory at a deeper level, one can anticipate that in suitable systems, light absorption and energy transfer will be accompanied by significant displacements in interparticle separation, leading to nanoscale mechanical motion

Protection against LPS-induced cartilage inflammation and degradation provided by a biological extract of Mentha spicata

<p>Abstract</p> <p>Background</p> <p>A variety of mint [<it>Mentha spicata</it>] has been bred which over-expresses Rosmarinic acid (RA) by approximately 20-fold. RA has demonstrated significant anti-inflammatory activity <it>in vitro </it>and in small rodents; thus it was hypothesized that this plant would demonstrate significant anti-inflammatory activity <it>in vitro</it>. The objectives of this study were: a) to develop an <it>in vitro </it>extraction procedure which mimics digestion and hepatic metabolism, b) to compare anti-inflammatory properties of High-Rosmarinic-Acid <it>Mentha spicata </it>(HRAM) with wild-type control <it>M. spicata </it>(CM), and c) to quantify the relative contributions of RA and three of its hepatic metabolites [ferulic acid (FA), caffeic acid (CA), coumaric acid (CO)] to anti-inflammatory activity of HRAM.</p> <p>Methods</p> <p>HRAM and CM were incubated in simulated gastric and intestinal fluid, liver microsomes (from male rat) and NADPH. Concentrations of RA, CA, CO, and FA in simulated digest of HRAM (HRAM_sim) and CM (CM_sim) were determined (HPLC) and compared with concentrations in aqueous extracts of HRAM and CM. Cartilage explants (porcine) were cultured with LPS (0 or 3 μg/mL) and test article [HRAM_sim(0, 8, 40, 80, 240, or 400 μg/mL), or CM_sim(0, 1, 5 or 10 mg/mL), or RA (0.640 μg/mL), or CA (0.384 μg/mL), or CO (0.057 μg/mL) or FA (0.038 μg/mL)] for 96 h. Media samples were analyzed for prostaglandin E₂(PGE₂), interleukin 1β (IL-1), glycosaminoglycan (GAG), nitric oxide (NO) and cell viability (differential live-dead cell staining).</p> <p>Results</p> <p>RA concentration of HRAM_simand CM_simwas 49.3 and 0.4 μg/mL, respectively. CA, FA and CO were identified in HRAM_simbut not in aqueous extract of HRAM. HRAM_sim(≥ 8 μg/mL) inhibited LPS-induced PGE₂and NO; HRAM_sim(≥ 80 μg/mL) inhibited LPS-induced GAG release. RA inhibited LPS-induced GAG release. No anti-inflammatory or chondroprotective effects of RA metabolites on cartilage explants were identified.</p> <p>Conclusions</p> <p>Our biological extraction procedure produces a substance which is similar in composition to post-hepatic products. HRAM_simis an effective inhibitor of LPS-induced inflammation in cartilage explants, and effects are primarily independent of RA. Further research is needed to identify bioactive phytochemical(s) in HRAM_sim.</p

Squeezing and expanding light without reflections via transformation optics

This paper was published in OPTICS EXPRESS and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://dx.doi.org/10.1364/OE.19.003562. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law[EN] We study the reflection properties of squeezing devices based on transformation optics. An analytical expression for the angle-dependent reflection coefficient of a generic three-dimensional squeezer is derived. In contrast with previous studies, we find that there exist several conditions that guarantee no reflections so it is possible to build transformation-optics-based reflectionless squeezers. Moreover, it is shown that the design of antireflective coatings for the non-reflectionless case can be reduced to matching the impedance between two dielectrics. We illustrate the potential of these devices by proposing two applications in which a reflectionless squeezer is the key element: an ultra-short perfect coupler for high-index nanophotonic waveguides and a completely flat reflectionless hyperlens. We also apply our theory to the coupling of two metallic waveguides with different cross-section. Finally, we show how the studied devices can be implemented with non-magnetic isotropic materials by using a quasi-conformal mapping technique. © 2011 Optical Society of America.Financial support by the Spanish MICINN under contract CONSOLIDER EMET (CSD2008-00066) and PROMETEO-2010-087 R&D Excellency Program (NANOMET) is gratefully acknowledged. C. G.-M., R. O. and F.J. R.-F. acknowledge financial support from grants FPU of MICINN, FPI of U.P.V. and FPI of Generalitat Valenciana, respectively.García Meca, C.; Tung, MM.; Galán Conejos, JV.; Ortuño Molinero, R.; Rodríguez Fortuño, FJ.; Martí Sendra, J.; Martínez Abietar, AJ. (2011). 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