Polynomials on Banach spaces with unconditional bases

We study the classes of homogeneous polynomials on a Banach space with unconditional Schauder basis that have unconditionally convergent monomial expansions relative to this basis. We extend some results of Matos, and we show that the homogeneous polynomials with unconditionally convergent expansions coincide with the polynomials that are regular with respect to the Banach lattices structure of the domain.

Geometry in preduals of spaces of 2-homogeneous polynomials on Hilbert spaces

Let H be a (real or complex) Hilbert space. Using spectral theory and properties of the Schatten–Von Neumann operators, we prove that every symmetric tensor of unit norm in HoH is an infinite absolute convex combination of points of the form xox with x in the unit sphere of the Hilbert space. We use this to obtain explicit characterizations of the smooth points of the unit ball of HoH .

Controllable Gaussian-Qubit Interface for Extremal Quantum State Engineering

We study state engineering through bilinear interactions between two remote qubits and two-mode Gaussian light fields. The attainable two-qubit states span the entire physically allowed region in the entanglement-versus-global-purity plane. Two-mode Gaussian states with maximal entanglement at fixed global and marginal entropies produce maximally entangled two-qubit states in the corresponding entropic diagram. We show that a small set of parameters characterizing extremally entangled two-mode Gaussian states is sufficient to control the engineering of extremally entangled two-qubit states, which can be realized in realistic matter-light scenarios.

Algorithmic computation of knot polynomials of secondary structure elements of proteins

The classification of protein structures is an important and still outstanding problem. The purpose of this paper is threefold. First, we utilize a relation between the Tutte and homfly polynomial to show that the Alexander-Conway polynomial can be algorithmically computed for a given planar graph. Second, as special cases of planar graphs, we use polymer graphs of protein structures. More precisely, we use three building blocks of the three-dimensional protein structure-alpha-helix, antiparallel beta-sheet, and parallel beta-sheet-and calculate, for their corresponding polymer graphs, the Tutte polynomials analytically by providing recurrence equations for all three secondary structure elements. Third, we present numerical results comparing the results from our analytical calculations with the numerical results of our algorithm-not only to test consistency, but also to demonstrate that all assigned polynomials are unique labels of the secondary structure elements. This paves the way for an automatic classification of protein structures.

Faithful nonclassicality indicators and extremal quantum correlations in two-qubit states

The state disturbance induced by locally measuring a quantum system yields a signature of nonclassical correlations beyond entanglement. Here, we present a detailed study of such correlations for two-qubit mixed states. To overcome the asymmetry of quantum discord and the unfaithfulness of measurement-induced disturbance (severely overestimating quantum correlations), we propose an ameliorated measurement-induced disturbance as nonclassicality indicator, optimized over joint local measurements, and we derive its closed expression for relevant two-qubit states. We study its analytical relation with discord, and characterize the maximally quantum-correlated mixed states, that simultaneously extremize both quantifiers at given von Neumann entropy: among all two-qubit states, these states possess the most robust quantum correlations against noise.

Extremal quantum correlations: Experimental study with two-qubit states

We explore experimentally the space of two-qubit quantum-correlated mixed states, including frontier states as defined by the use of quantum discord and von Neumann entropy. Our experimental setup is flexible enough to allow for high-quality generation of a vast variety of states. We address quantitatively the relation between quantum discord and a recently suggested alternative measure of quantum correlations.

Lipoprotein-associated phospholipase A2 (Lp-PLA2) as a therapeutic target to prevent retinal vasopermeability during diabetes

Lipoprotein-associated phospholipase A2 (Lp-PLA2) hydrolyses oxidized low-density lipoproteins into proinflammatory products, which can have detrimental effects on vascular function. As a specific inhibitor of Lp-PLA2, darapladib has been shown to be protective against atherogenesis and vascular leakage in diabetic and hypercholesterolemic animal models. This study has investigated whether Lp-PLA2 and its major enzymatic product, lysophosphatidylcholine (LPC), are involved in blood-retinal barrier (BRB) damage during diabetic retinopathy. We assessed BRB protection in diabetic rats through use of species-specific analogs of darapladib. Systemic Lp-PLA2 inhibition using SB-435495 at 10 mg/kg (i.p.) effectively suppressed BRB breakdown in streptozotocin-diabetic Brown Norway rats. This inhibitory effect was comparable to intravitreal VEGF neutralization, and the protection against BRB dysfunction was additive when both targets were inhibited simultaneously. Mechanistic studies in primary brain and retinal microvascular endothelial cells, as well as occluded rat pial microvessels, showed that luminal but not abluminal LPC potently induced permeability, and that this required signaling by the VEGF receptor 2 (VEGFR2). Taken together, this study demonstrates that Lp-PLA2 inhibition can effectively prevent diabetes-mediated BRB dysfunction and that LPC impacts on the retinal vascular endothelium to induce vasopermeability via VEGFR2. Thus, Lp-PLA2 may be a useful therapeutic target for patients with diabetic macular edema (DME), perhaps in combination with currently administered anti-VEGF agents.