Natural Formulations Based on Olea europaea L. Fruit Extract for the Topical Treatment of HSV-1 Infections

In the present study, a hydroxytyrosol-rich Olea europaea L. fruit extract (OFE) was added to three thoroughly green formulations—hydrogel, oleogel, and cream—in order to evaluate their antiviral activity against HSV-1. The extract was characterized by different analytical techniques, i.e., FT-IR, XPS, and TGA. HPLC analyses were carried out to monitor the content and release of hydroxytyrosol in the prepared formulations. The total polyphenol content and antioxidant activity were investigated through Folin–Ciocâlteu’s reagent, DPPH, and ABTS assays. The ability of the three formulations to convey active principles to the skin was evaluated using a Franz cell, showing that the number of permeated polyphenols in the hydrogel (272.1 ± 1.8 GAE/g) was significantly higher than those in the oleogel and cream (174 ± 10 and 179.6 ± 2 GAE/g, respectively), even if a negligible amount of hydroxytyrosol crossed the membrane for all the formulations. The cell viability assay indicated that the OFE and the three formulations were not toxic to cultured Vero cells. The antiviral activity tests highlighted that the OFE had a strong inhibitory effect against HSV-1 with a 50% inhibitory concentration (IC50) at 25 µg/mL, interfering directly with the viral particles. Among the three formulations, the hydrogel exhibited the highest antiviral activity also against the acyclovir-resistant strain.     

Gaussian Amplitude Amplification for Quantum Pathfinding

We study an oracle operation, along with its circuit design, which combined with the Grover diffusion operator boosts the probability of finding the minimum or maximum solutions on a weighted directed graph. We focus on the geometry of sequentially connected bipartite graphs, which naturally gives rise to solution spaces describable by Gaussian distributions. We then demonstrate how an oracle that encodes these distributions can be used to solve for the optimal path via amplitude amplification. And finally, we explore the degree to which this algorithm is capable of solving cases that are generated using randomized weights, as well as a theoretical application for solving the Traveling Salesman problem.     

Long Term Stability of Proper Rotations of the Perturbed Euler Rigid Body

We study the long term stability of the proper rotations of the perturbed Euler rigid body, in the framework of Nekhoroshev theory. For simplicity we treat here in detail only the kinetically symmetric case (the potential needs not to be symmetric), but we indicate how to extend the results to the triaxial case. We show that the proper rotations around the symmetry axis are Nekhoroshev stable: more precisely, if the initial datum is sufficiently close to a proper rotation, then for a very long time it remains such, and the tip of the unit vector parallel to the angular momentum precesses, up to a small noise, along the level curves of a regular function on the unit sphere. If the proper rotations are resonant, chaotic motions with positive Lyapunov exponents are possible, but chaos (unlike the case of ordinary motions, that is motions not close to proper rotations) is always localized, and does not affect in an essential way the motion of the angular momentum in space. Preliminary numerical results indicate that the theory is, in many aspects, optimal, although in some points it can still be improved.     

Next-to-next-to-leading-order subtraction formalism in hadron collisions and its application to Higgs-boson production at the large hadron collider

We consider higher-order QCD corrections to the production of colorless high-mass systems (lepton pairs, vector bosons, Higgs bosons, etc.) in hadron collisions. We propose a new formulation of the subtraction method to numerically compute arbitrary infrared-safe observables for this class of processes. To cancel the infrared divergences, we exploit the universal behavior of the associated transverse-momentum (qT) distributions in the small-qT region. The method is illustrated in general terms up to the next-to-next-to-leading order in QCD perturbation theory. As a first explicit application, we study Higgs-boson production through gluon fusion. Our calculation is implemented in a parton level Monte Carlo program that includes the decay of the Higgs boson into two photons. We present selected numerical results at the CERN Large Hadron Collider.     

The rate matching effect: A hidden property of aperiodic stochastic resonance

We study a system S generating Poisson events, and a corresponding dichotomous signal as well, perturbed by a system P, also generating Poisson events and a corresponding dichotomous signal. The rates of events productions for system and perturbation are gS and gP, respectively. We call S events the events produced by the system S and P events those produced by the perturbation P. We show that this simple model reproduces the essence of recent experimental and theoretical results on aperiodic stochastic resonance. More remarkably, this simplified version of aperiodic stochastic resonance allows us to discover a property that has been overlooked by the earlier research work. The rate matching condition gS=gP is the border between two distinctly different conditions: For gS<gP, the P events are attractors of the S events and for gS>gP they become repellers of the S events. The transition from the former to the latter condition is very marked and takes place in a short region of either gS or gP, depending on which is the parameter changed, thereby resulting in a discontinuous transition.     

On optimal regularity of free boundary problems and a conjecture of De Giorgi

We present a general theory to study optimal regularity for a large class of nonlinear elliptic systems satisfying general boundary conditions and in the presence of a geometric transmission condition on the free boundary. As an application we give a full positive answer to a conjecture of De Giorgi on the analyticity of local minimizers of the Mumford‐Shah functional. © 2004 Wiley Periodicals, Inc.