On the additivity of block designs

We show that symmetric block designs \({\mathcal {D}}=({\mathcal {P}},{\mathcal {B}})\) can be embedded in a suitable commutative group \({\mathfrak {G}}_{\mathcal {D}}\) in such a way that the sum of the elements in each block is zero, whereas the only Steiner triple systems with this property are the point-line designs of \({\mathrm {PG}}(d,2)\) and \({\mathrm {AG}}(d,3)\). In both cases, the blocks can be characterized as the only k-subsets of \(\mathcal {P}\) whose elements sum to zero. It follows that the group of automorphisms of any such design \(\mathcal {D}\) is the group of automorphisms of \({\mathfrak {G}}_\mathcal {D}\) that leave \(\mathcal {P}\) invariant. In some special cases, the group \({\mathfrak {G}}_\mathcal {D}\) can be determined uniquely by the parameters of \(\mathcal {D}\). For instance, if \(\mathcal {D}\) is a 2-\((v,k,\lambda )\) symmetric design of prime order p not dividing k, then \({\mathfrak {G}}_\mathcal {D}\) is (essentially) isomorphic to \(({\mathbb {Z}}/p{\mathbb {Z}})^{\frac{v-1}{2}}\), and the embedding of the design in the group can be described explicitly. Moreover, in this case, the blocks of \(\mathcal {B}\) can be characterized also as the v intersections of \(\mathcal {P}\) with v suitable hyperplanes of \(({\mathbb {Z}}/p{\mathbb {Z}})^{\frac{v-1}{2}}\).     

New phosphorylating reagents for deoxyribonucleosides and oligonucleotides

New phosphorylating reagents 1 and 2 were prepared in three steps from 4-hydroxybenzaldehyde. They showed good efficiency in the solid phase synthesis of 5′-phosphate monoester nucleosides. End-phosphate DNA sequence synthesis demonstrated the efficiency of the new reagents (1 and 2) according to the general procedure of automated DNA synthesis. The oxidation of P(III) to P(V) and the removal of benzyl protecting groups were achieved in a single step by treatment with a 0.02 M I₂/pyridine/H₂O solution. Due to this one-pot treatment, it is possible to use the phosphorylating reagents (1 and 2) for the synthesis of base-sensitive ODNs. The reagents 1 and 2 are unique among phosphorylating reagents.     

A sharp eigenvalue theorem for fractional elliptic equations

The invisibility graph I(X) of a set X ? R ^d is a (possibly infinite) graph whose vertices are the points of X and two vertices are connected by an edge if and only if the straight-line segment connecting the two corresponding points is not fully contained in X. We consider the following three parameters of a set X: the clique number ω(I(X)), the chromatic number χ(I(X)) and the convexity number γ(X), which is the minimum number of convex subsets of X that cover X.We settle a conjecture of Matou?ek and Valtr claiming that for every planar set X, γ(X) can be bounded in terms of χ(I(X)). As a part of the proof we show that a disc with n one-point holes near its boundary has χ(I(X)) ≥ log log(n) but ω(I(X)) = 3.We also find sets X in R⁵ with χ(X) = 2, but γ(X) arbitrarily large.     

Conjugate Direction Methods and Polarity for Quadratic Hypersurfaces

We use some results from polarity theory to recast several geometric properties of Conjugate Gradient-based methods, for the solution of nonsingular symmetric linear systems. This approach allows us to pursue three main theoretical objectives. First, we can provide a novel geometric perspective on the generation of conjugate directions, in the context of positive definite systems. Second, we can extend the above geometric perspective to treat the generation of conjugate directions for handling indefinite linear systems. Third, by exploiting the geometric insight suggested by polarity theory, we can easily study the possible degeneracy (pivot breakdown) of Conjugate Gradient-based methods on indefinite linear systems. In particular, we prove that the degeneracy of the standard Conjugate Gradient on nonsingular indefinite linear systems can occur only once in the execution of the Conjugate Gradient.     

Exploiting damped techniques for nonlinear conjugate gradient methods

In this paper we propose the use of damped techniques within Nonlinear Conjugate Gradient (NCG) methods. Damped techniques were introduced by Powell and recently reproposed by Al-Baali and till now, only applied in the framework of quasi-Newton methods. We extend their use to NCG methods in large scale unconstrained optimization, aiming at possibly improving the efficiency and the robustness of the latter methods, especially when solving difficult problems. We consider both unpreconditioned and Preconditioned NCG. In the latter case, we embed damped techniques within a class of preconditioners based on quasi-Newton updates. Our purpose is to possibly provide efficient preconditioners which approximate, in some sense, the inverse of the Hessian matrix, while still preserving information provided by the secant equation or some of its modifications. The results of an extensive numerical experience highlights that the proposed approach is quite promising.     

Crosslinked Hyaluronic Acid with Liposomes and Crocin Confers Cytoprotection in an Experimental Model of Dry Eye

Dry eye disease (DED) is a multifactorial condition caused by tear deficiency and accompanied by ocular surface damage. Recent data support a key role of oxidative and inflammatory processes in the pathogenesis of DED. Hyaluronic acid (HA) is widely used in artificial tears to treat DED by improving ocular hydration and reducing surface friction. Crocin (Cr), the main constituent of saffron, is a renowned compound that exhibits potent antioxidant and anti-inflammatory effects. The present study was undertaken to assess the viscosity and muco-adhesiveness of a photoactivated formulation with crosslinked HA (cHA), Cr, and liposomes (cHA-Cr-L). Our aim was also to evaluate whether cHA-Cr-L may exert cytoprotective effects against oxidative and inflammatory processes in human corneal epithelial cells (HCECs). Viscosity was measured using a rotational rheometer, and then the muco-adhesiveness was evaluated. Under hyperosmolarity (450 mOsm), the HCECs were treated with cHA-Cr-L. Interleukin-1β (IL-1β) and tumor necrosis factor α (TNFα) were quantified by quantitative real-time polymerase chain reaction (RT-qPCR). The levels of reactive oxygen species (ROS) were measured using the DCF assay. The combined action of cHA-Cr-L produced a higher viscosity and muco-adhesiveness compared to the control. The anti-inflammatory effect of cHA-Cr-L was achieved through a significant reduction of IL-1β and TNFα (p < 0.001). The results also showed that cHA-Cr-L reduces ROS production under conditions of hyperosmolarity (p < 0.001). We conclude that cHA-Cr-L has potential as a therapeutic agent in DED, which should be further investigated.     

Preliminary Study of a 1,5-Benzodiazepine-Derivative Labelled with Indium-111 for CCK-2 Receptor Targeting

The cholecystokinin-2 receptor (CCK-2R) is overexpressed in several human cancers but displays limited expression in normal tissues. For this reason, it is a suitable target for developing specific radiotracers. In this study, a nastorazepide-based ligand functionalized with a 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid (DOTA) chelator (IP-001) was synthesized and labelled with indium-111. The radiolabeling process yielded >95% with a molar activity of 10 MBq/nmol and a radiochemical purity of >98%. Stability studies have shown a remarkable resistance to degradation (>93%) within 120 h of incubation in human blood. The in vitro uptake of [¹¹¹In]In-IP-001 was assessed for up to 24 h on a high CCK-2R-expressing tumor cell line (A549) showing maximal accumulation after 4 h of incubation. Biodistribution and single photon emission tomography (SPECT)/CT imaging were evaluated on BALB/c nude mice bearing A549 xenograft tumors. Implanted tumors could be clearly visualized after only 4 h post injection (2.36 ± 0.26% ID/cc), although a high amount of radiotracer was also found in the liver, kidneys, and spleen (8.25 ± 2.21%, 6.99 ± 0.97%, and 3.88 ± 0.36% ID/cc, respectively). Clearance was slow by both hepatobiliary and renal excretion. Tumor retention persisted for up to 24 h, with the tumor to organs ratio increasing over-time and ending with a tumor uptake (1.52 ± 0.71% ID/cc) comparable to liver and kidneys.     

Structures and Bioactivities of Steroidal Saponins Isolated from the Genera Dracaena and Sansevieria

The species Dracaena and Sansevieria, that are well-known for different uses in traditional medicines and as indoor ornamental plants with air purifying property, are rich sources of bioactive secondary metabolites. In fact, a wide variety of phytochemical constituents have been isolated so far from about seventeen species. This paper has reviewed the literature of about 180 steroidal saponins, isolated from Dracaena and Sansevieria species, as a basis for further studies. Saponins are among the most characteristic metabolites isolated from the two genera. They show a great variety in structural motifs and a wide range of biological activities, including anti-inflammatory, anti-microbial, anti-proliferative effects and, in most case, remarkable cytotoxic properties.