Nonlinear characterizations of stochastic completeness

We prove that conservation of probability for the free heat semigroup on a Riemannian manifold M (namely stochastic completeness), hence a linear property, is equivalent to uniqueness of positive, bounded solutions to nonlinear evolution equations of fast diffusion type on M of the form ut=Δϕ(u), ϕ being an arbitrary concave, increasing, positive function, regular outside the origin and with ϕ(0)=0. Either property is also equivalent to nonexistence of nonnegative, nontrivial, bounded solutions to the elliptic equation ΔW=ϕ−1(W), with ϕ as above. As a consequence, explicit criteria for uniqueness or nonuniqueness of bounded solutions to fast diffusion-type equations on manifolds are given, these being the first results on such issues

Application of multivariate statistical methods to the modelling of a flue gas treatment stage in a waste-to-energy plant

Among all the macro-pollutants released by waste combustion, acid contaminants such as sulphur dioxide, hydrogen chloride and hydrogen fluoride have the lowest emission standards in environmental regulations in EU, USA and China. Their removal is thus a key step of flue gas treatment in waste-to-energy (WtE) plants. A widespread approach for acid gas removal is by in-duct injection of dry powdered sorbents, which neutralize the acid pollutants by gas-solid reaction. However, systems based on dry injection, albeit cost-effective and easy to operate, suffer from a limited knowledge of the gas-solid reaction process at industrial operating conditions. High excess of sorbent feed rate is generally required to obtain high acid gas removal efficiencies. The present study proposes a multivariate statistical approach to the modelling of acid gas treatment units, with the aim of extracting information from real process data in order to derive a predictive model of dynamic acid gas removal efficiency. Specifically, process data regarding the composition of the flue gas, the sorbent feed and other operating conditions were elaborated to characterise the different phenomena that influence acid gas abatement. Eventually, a partial least squares (PLS) regression was set up to predict the outlet concentration of hydrogen chloride as a function of the measured process variables. The resulting model is a step forward with respect to previously available stationary models. Its simplicity and low computational cost could make PLS a promising candidate for model-based process control. Nonetheless, a linear approach such as PLS still comes short of predicting large instantaneous deviations from the typical range of operation (e.g. abrupt peaks in inlet acid gas load), for which a modification of the PLS model to incorporate non-linear behaviour is envisaged

Tonsillectomy and residents: a safe match?

Letter to the Edito

Cost analysis in oral cavity and oropharyngeal reconstructions with microvascular and pedicled flaps.

Reconstructive surgery of the head and neck region has undergone tremendous advancement over the past three decades, and the success rate of free tissue transfers has risen to greater than 95\%. It must always be considered that not all patients are ideal candidates for free flap reconstruction, and also that not every defect strictly requires a free flap transfer to achieve good functional results. At our institution, free flap reconstruction is first choice, although we use pedicled alternative flaps for most weak patients suffering from severe comorbidities, and for pretreated patients presenting a second primary or a recurrent cancer. From July 2006 to May 2010, 54 consecutive patients underwent soft tissue reconstruction of oral cavity and oropharyngeal defects. We divided the cohort in three groups: Group 1 (G1): 16 patients in good general conditions that received free radial forearm flap reconstruction; Group 2 (G2): 18 high-risk patients that received a reconstruction with infrahyoid flap; Group 3 (G3): 20 patients that received temporal flap (10 cases) or pectoral flap (10 cases) reconstruction. We must highlight that pedicled alternative flaps were used in elderly, unfavourable and weak patients, where usually the medical costs tend to rise rather than decrease. We compared the healthcare costs of the three groups, calculating real costs in each group from review of medical records and operating room registers, and calculating the corresponding DRG system reimbursement. For real costs, we found a statistically significant difference among groups: in G1 the average total cost per patient was € 22,924, in G2 it was € 18,037 and in G3 was € 19,872 (p = 0.043). The amount of the refund, based on the DRG system, was € 7,650 per patient, independently of the type of surgery. Our analysis shows that the use of alternative non-microvascular techniques, in high-risk patients, is functionally and oncologically sound, and can even produce a cost savings. In particular, the infrahyoid flap (G2) ensures excellent functional results, accompanied by the best economic savings in the worst group of patients. Our data reflect a large disconnection between the DRG system and actual treatment costs.Abstract available from the publisher

On non-L2L^2 solutions to the Seiberg-Witten equations

We show that a previous paper of Freund describing a solution to the Seiberg-Witten equations has a sign error rendering it a solution to a related but different set of equations. The non-$L^2$ nature of Freund's solution is discussed and clarified and we also construct a whole class of solutions to the Seiberg-Witten equations.Comment: 8 pages, Te

Electrosensitization Assists Cell Ablation by Nanosecond Pulsed Electric Field in 3D Cultures

Previous studies reported a delayed increase of sensitivity to electroporation (termed electrosensitization ) in mammalian cells that had been subjected to electroporation. Electrosensitization facilitated membrane permeabilization and reduced survival in cell suspensions when the electric pulse treatments were split in fractions. The present study was aimed to visualize the effect of sensitization and establish its utility for cell ablation. We used KLN 205 squamous carcinoma cells embedded in an agarose gel and cell spheroids in Matrigel. A local ablation was created by a train of 200 to 600 of 300-ns pulses (50 Hz, 300-600 V) delivered by a two-needle probe with 1-mm inter-electrode distance. In order to facilitate ablation by engaging electrosensitization, the train was split in two identical fractions applied with a 2- to 480-s interval. At 400-600 V (2.9-4.3 kV/cm), the split-dose treatments increased the ablation volume and cell death up to 2-3-fold compared to single-train treatments. Under the conditions tested, the maximum enhancement of ablation was achieved when two fractions were separated by 100 s. The results suggest that engaging electrosensitization may assist in vivo cancer ablation by reducing the voltage or number of pulses required, or by enabling larger inter-electrode distances without losing the ablation efficiency