Incremental complexity of a bi-objective hypergraph transversal problem

The hypergraph transversal problem has been intensively studied, from both a theoretical and a practical point of view. In particular , its incremental complexity is known to be quasi-polynomial in general and polynomial for bounded hypergraphs. Recent applications in computational biology however require to solve a generalization of this problem, that we call bi-objective transversal problem. The instance is in this case composed of a pair of hypergraphs (A, B), and the aim is to find minimal sets which hit all the hyperedges of A while intersecting a minimal set of hyperedges of B. In this paper, we formalize this problem, link it to a problem on monotone boolean $\land$ -- $\lor$ formulae of depth 3 and study its incremental complexity

A model for gene deregulation detection using expression data

In tumoral cells, gene regulation mechanisms are severely altered, and these modifications in the regulations may be characteristic of different subtypes of cancer. However, these alterations do not necessarily induce differential expressions between the subtypes. To answer this question, we propose a statistical methodology to identify the misregulated genes given a reference network and gene expression data. Our model is based on a regulatory process in which all genes are allowed to be deregulated. We derive an EM algorithm where the hidden variables correspond to the status (under/over/normally expressed) of the genes and where the E-step is solved thanks to a message passing algorithm. Our procedure provides posterior probabilities of deregulation in a given sample for each gene. We assess the performance of our method by numerical experiments on simulations and on a bladder cancer data set

NMR Relaxivities of Paramagnetic Lanthanide-Containing Polyoxometalates

The current trend for ultra-high-field magnetic resonance imaging (MRI) technologies opens up new routes in clinical diagnostic imaging as well as in material imaging applications. MRI selectivity is further improved by using contrast agents (CAs), which enhance the image contrast and improve specificity by the paramagnetic relaxation enhancement (PRE) mechanism. Generally, the efficacy of a CA at a given magnetic field is measured by its longitudinal and transverse relaxivities r(1) and r(2), i.e., the longitudinal and transverse relaxation rates T(1)(−1) and T(2)(−1) normalized to CA concentration. However, even though basic NMR sensitivity and resolution become better in stronger fields, r(1) of classic CA generally decreases, which often causes a reduction of the image contrast. In this regard, there is a growing interest in the development of new contrast agents that would be suitable to work at higher magnetic fields. One of the strategies to increase imaging contrast at high magnetic field is to inspect other paramagnetic ions than the commonly used Gd(III)-based CAs. For lanthanides, the magnetic moment can be higher than that of the isotropic Gd(III) ion. In addition, the symmetry of electronic ground state influences the PRE properties of a compound apart from diverse correlation times. In this work, PRE of water (1)H has been investigated over a wide range of magnetic fields for aqueous solutions of the lanthanide containing polyoxometalates [Dy(III)(H(2)O)(4)GeW(11)O(39)](5–) (Dy-W(11)), [Er(III)(H(2)O)(3)GeW(11)O(39)](5–) (Er-W(11)) and [{Er(III)(H(2)O)(CH(3)COO)(P(2)W(17)O(61))}(2)](16−) (Er(2)-W(34)) over a wide range of frequencies from 20 MHz to 1.4 GHz. Their relaxivities r(1) and r(2) increase with increasing applied fields. These results indicate that the three chosen POM systems are potential candidates for contrast agents, especially at high magnetic fields

NMR Relaxivities of Paramagnetic Lanthanide-Containing Polyoxometalates

The current trend for ultra-high-field magnetic resonance imaging (MRI) technologies opens up new routes in clinical diagnostic imaging as well as in material imaging applications. MRI selectivity is further improved by using contrast agents (CAs), which enhance the image contrast and improve specificity by the paramagnetic relaxation enhancement (PRE) mechanism. Generally, the efficacy of a CA at a given magnetic field is measured by its longitudinal and transverse relaxivities r1 and r2, i.e., the longitudinal and transverse relaxation rates T1−1 and T2−1 normalized to CA concentration. However, even though basic NMR sensitivity and resolution become better in stronger fields, r1 of classic CA generally decreases, which often causes a reduction of the image contrast. In this regard, there is a growing interest in the development of new contrast agents that would be suitable to work at higher magnetic fields. One of the strategies to increase imaging contrast at high magnetic field is to inspect other paramagnetic ions than the commonly used Gd(III)-based CAs. For lanthanides, the magnetic moment can be higher than that of the isotropic Gd(III) ion. In addition, the symmetry of electronic ground state influences the PRE properties of a compound apart from diverse correlation times. In this work, PRE of water 1H has been investigated over a wide range of magnetic fields for aqueous solutions of the lanthanide containing polyoxometalates [DyIII(H2O)4GeW11O39]5– (Dy-W11), [ErIII(H2O)3GeW11O39]5– (Er-W11) and [{ErIII(H2O)(CH3COO)(P2W17O61)}2]16− (Er2-W34) over a wide range of frequencies from 20 MHz to 1.4 GHz. Their relaxivities r1 and r2 increase with increasing applied fields. These results indicate that the three chosen POM systems are potential candidates for contrast agents, especially at high magnetic fields