A centerless representation of the Virasoro algebra associated with the unitary circular ensemble

We consider the 2-dimensional Toda lattice tau functions τ_n(t,s;η,θ) deforming the probabilities τ_n(η,θ) that a randomly chosen matrix from the unitary group U(n), for the Haar measure, has no eigenvalues within an arc (η,θ) of the unit circle. We show that these tau functions satisfy a centerless Virasoro algebra of constraints, with a boundary part in the sense of Adler, Shiota and van Moerbeke. As an application, we obtain a new derivation of a differential equation due to Tracy and Widom, satisfied by these probabilities, linking it to the Painlevé VI equation.     

Redox strategy for reversible attachment of biomolecules using bifunctional linkers

Soft attachment of streptavidin to β-cyclodextrin-modified pegylated SAMs was efficiently performed in a reversible and repetitive way via orthogonal bifunctional linkers involving streptavidin-biotin recognition and redox-driven multivalent host-guest (β-cyclodextrin-ferrocene) interactions.     

Molecular clusters in aqueous solutions of pyridine and its methyl derivatives

Small-angle neutron scattering proved that molecules in aqueous solutions of pyridine, 2-methylpyridine and 2,6-dimethylpyridine form clusters. The clusters are dynamic aggregates consisting of hydrogen-bonded water-amine complexes. Strengthening of the hydrogen bonds between water and amine molecules due to the methyl groups in the ortho position in the pyridine ring makes the structures more stable, as was evidenced by relatively long times of the structural relaxation. The strong intermolecular forces affect the thermal expansion of the systems. No aggregates similar to those in aqueous systems are present in the methanolic ones. That points to the crucial role of water in the molecular clustering. A molecule of methanol, although capable of hydrogen bonding with the amines, cannot participate in larger structures because of the lack of protons that could form the enhanced network. Thus, even if the amine-methanol complexes occur, they are incapable of further association. It was shown that the co-operative nature of hydrogen bonds and the propensity of water to association are the main factors that determine the properties of aqueous systems.     

A novel ruthenium(II) complex for two-photon absorption-based optical power limiting in the near-IR range

In this article, the synthesis of a novel high-conjugated ligand and its corresponding Ru(II) complex PTFTF:Ru is reported, along with the linear and nonlinear optical characterizations. Two-photon absorption based optical power limiting properties (OPL), especially in the near infrared, are described and compared to those of the analogous complexes previously published. Combined with a preliminary theoretical approach, this allows us to highlight several key parameters for OPL optimization in such molecular systems and more particularly the spectral overlap between TPA and excited-state absorption.     

On mean-field limits and quantitative estimates with a large class of singular kernels: Application to the Patlak–Keller–Segel model

In this note, we propose a modulated free energy combination of the methods developed by P.-E. Jabin and Z. Wang [Inventiones (2018)] and by S. Serfaty [Proc. Int. Cong. Math. (2018) and references therein] to treat more general kernels in mean-field limit theory. This modulated free energy may be understood as introducing appropriate weights in the relative entropy developed by P.-E. Jabin and Z. Wang (in the spirit of what has been recently developed by D. Bresch and P.-E. Jabin [Ann. of Math. (2) (2018)]) to cancel the most singular terms involving the divergence of the flow. Our modulated free energy allows us to treat singular potentials that combine large smooth part, small attractive singular part, and large repulsive singular part. As an example, a full rigorous derivation (with quantitative estimates) of some chemotaxis models, such as the Patlak–Keller–Segel system in subcritical regimes, is obtained.     

Elaboration of hybrid nanocluster materials by solution chemistry

The [(M₆L₁₂ⁱ)L₆^a]ⁿ⁻ and [(M₆L₈ⁱ)L₆^a] units (a = apical, i = inner) constitute the basic building blocks in the octahedral cluster chemistry. Nano-sized metallic clusters are easily obtained by solid state synthesis with transition elements associated with halogen or chalcogen. The intrinsic properties of M₆ cluster units—one or two electron reversible redox process, magnetism and luminescence—depend on the nature of the metal and ligands. The solubilisation of M₆ solid state compounds provides [(M₆L₁₂ⁱ)L₆^a]ⁿ⁻ or [(M₆L₈ⁱ)L₆^a]ⁿ⁻ building blocks with individual properties that can be further used for the design of hybrid organic/inorganic materials. Several examples of solid state precursors are presented as well as substitution reactions of apical ligands in solution. Indeed, hexacyano M₆ clusters are obtained by direct reaction of solid state precursors in aqueous KCN solutions. Low dimensional frameworks are subsequently obtained by recrystallisation of hexacyano M₆ clusters with transition elements. The functionalisation of cluster proceeds in two steps. The first one consists in the replacement of apical halogens of cluster unit precursors by labile groups as CF₃SO₃ (triflate) or solvent molecules after solution reaction. The second one consists in the substitution of the labile groups by functionalised phenolate or pyridine ligands.     

Superparamagnetic iron oxide particles and positive enhancement for myocardial perfusion studies assessed by subsecond T1-weighted MRI

Superparamagnetic iron oxide particles (SPIOs) are usually referred to as T₂ MR contrast agents, reducing signal intensity (SI) on T₂-weighted MR images (negative enhancement). This study reports the original use of SPIOs as T₁-enhancing contrast agents, primarily assessed in vitro, and then applied to an in vivo investigation of a myocardial perfusion defect. Using a strongly T₁-weighted subsecond MR sequence with SPIOs intravenous (IV) bolus injection, MR imaging of myocardial vascularization after reperfusion was performed, on a dog model of coronary occlusion followed by reperfusion. Immediately after the intravenous bolus injection of 20 μmol/kg of SPIOs, a positive signal intensity enhancement was observed respectively, in the right and left ventricular cavity and in the nonischemic left myocardium. Moreover, compared to normal myocardium, the remaining ischemic myocardial region (anterior wall of the left ventricle) appeared as a lower and delayed SI enhancing area (cold spot). Mean peak SIE in the nonischemic myocardium (posterior wall) was significantly higher than in the ischemic myocardium (anterior wall) (110 ± 23% vs. 74 ± 22%, Mann-Whitney test < 1%, n₁ = 6, n₂ − n₁ = 0, U > 2). In conclusion, the T₁ effect of SPIOs at low dose, during their first intravascular distribution, suggests their potential use as positive markers to investigate the regional myocardial blood flow and some perfusion defects such as the “no-reflow phenomenon”.     

Semiclassical results in the linear response theory

We consider a quantum system of non-interacting fermions at temperature T, in the framework of linear response theory. We show that semiclassical theory is an appropriate framework to describe some of their thermodynamic properties, in particular through asymptotic expansions in ? (Planck constant) of the dynamical susceptibilities. We show how the closed orbits of the classical motion in phase space manifest themselves in these expansions, in the regime where T is of the order of ?.     

Contrast-enhanced magnetic resonance tomoangiography: A new imaging technique for studying thoracic great vessels

The authors propose a new imaging approach for studying thoracic great vessels, using high-speed MR imaging combined with intravenous rapid bolus injection of a paramagnetic contrast media. The decrease of the T₁ relaxation time of flowing blood induced by the contrast agent (Gd-DOTA) caused an increased signal intensity within the vessel lumen for a time period allowing multiplanar imaging of various vascular structures. The intraluminal signal enhancement is mainly related to the blood concentration of the contrast agent as in conventional X-ray angiography. Information on the aorta and pulmonary arteries obtained by the so-called contrast-enhanced magnetic resonance tomoangiography appears complementary to that obtained with other vascular MR imaging procedures such as cine-MRI and magnetic resonance angiography (MRA).     

Fuzzy cardinality and the modeling of imprecise quantification

The concept of cardinality of a fuzzy set has received attention from several researchers and has been defined in several apparently independent manners. A systematic investigation of this notion is performed which unifies and improves previous attempts. The cardinality of a fuzzy set, viewed as a fuzzy integer, is related to scalar cardinality indices. The closely related question of the probability of a fuzzy event is dealt with. Lastly, the usefulness of fuzzy cardinality for meaning representation of statements or queries involving fuzzy linguistic quantifiers is emphasized.