Local trace formulae and scaling asymptotics in Toeplitz quantization, II

In the spectral theory of positive elliptic operators, an important role is played by certain smoothing kernels, related to the Fourier transform of the trace of a wave operator, which may be heuristically interpreted as smoothed spectral projectors asymptotically drifting to the right of the spectrum. In the setting of Toeplitz quantization, we consider analogues of these, where the wave operator is replaced by the Hardy space compression of a linearized Hamiltonian flow, possibly composed with a family of zeroth order Toeplitz operators. We study the local asymptotics of these smoothing kernels, and specifically how they concentrate on the fixed loci of the linearized dynamics.Comment: Typos corrected. Slight expository change

Scaling asymptotics for quantized Hamiltonian flows

In recent years, the near diagonal asymptotics of the equivariant components of the Szeg\"{o} kernel of a positive line bundle on a compact symplectic manifold have been studied extensively by many authors. As a natural generalization of this theme, here we consider the local scaling asymptotics of the Toeplitz quantization of a Hamiltonian symplectomorphism, and specifically how they concentrate on the graph of the underlying classical map

Local trace formulae and scaling asymptotics in Toeplitz quantization

A trace formula for Toeplitz operators was proved by Boutet de Monvel and Guillemin in the setting of general Toeplitz structures. Here we give a local version of this result for a class of Toeplitz operators related to continuous groups of symmetries on quantizable compact symplectic manifolds. The local trace formula involves certain scaling asymptotics along the clean fixed locus of the Hamiltonian flow of the symbol, reminiscent of the scaling asymptotics of the equivariant components of the Szeg\"o kernel along the diagonal

Ground Beetles From a Remnant Oak-Maple-Beech Forest and Its Surroundings in Northeastern Ohio (Coleoptera: Carabidae)

We report 66 ground beetle species in 14 tribes from a natural preserve in northeastern Ohio (Stark County). Six species are new state records. Data from pitfall trap transects across adjoining habitats suggest narrow habitat preferences in some species and broad tolerances in others. Trends toward flightlessness in forest species and macroptery in the fauna of disturbed agricultural sites are apparent

Silicon photomultiplers in Very High Energy gamma-ray astrophysics

In the last ten years silicon photomultipliers (SiPMs) have gained terrain in experiments and applications in which photomultiplier tubes have been the dominant photosensors during decades. Imaging Atmospheric Cherenkov Telescopes (IACTs) for very high energy (VHE, E$>$50 GeV) gamma-ray astronomy are experiencing the same process. Until now FACT was the only IACT using SiPMs. In the Cherenkov Telescope Array (CTA), the next-generation VHE gamma-ray observatory, at least 70 telescopes equipped with SiPMs are planned to be built. The first prototypes have already been constructed and are now being commissioned. Here we discuss some of the advantages and drawbacks of using SiPMs in VHE gamma-ray astronomy and provide a brief overview of different developments related to the use of SiPMs in IACTs.Comment: Accepted for publication in JINST. 9 pages, 7 figures. Proceedings of the 5th INFIER

A parametric-assisted method for 3D generation of as-built BIM models for the built heritage

The paper outlines a parametric-assisted method for the 3D reconstruction and creation of BIM models for the built heritage. The research implements the emerging paradigms of open sourcing, cloud computing and interoperability, employing low-cost technologies (digital photogrammetry) and open source software (Grasshopper for Rhinoceros) which can ease the accessibility to a potential reuse of heritage, typically requiring high specialists and expensive equipment. The research examines the abandoned Albergo Diurno “Venezia” in Milan, heritage with a unique architectural value – a blend of Liberty and Art Deco styles. The process of 3D reconstruction of the ceiling is described. Custom algorithms have been developed to automatically rebuild the complex and irregular geometry from mesh, towards the creation of a NURBS-based 3D model. It is shown how the proposed methodology can streamline the process of data elaboration by reducing arbitrary operations and improve accuracy to preserve geometric irregularities. The associative model allows the automatic improvement in the model definition when more precise input data is feeding the algorithm, offering the opportunity to relate the precision of BIM models in accordance with the needed level of detail (LOD)

Multiple verification in computational modeling of bone pathologies

We introduce a model checking approach to diagnose the emerging of bone pathologies. The implementation of a new model of bone remodeling in PRISM has led to an interesting characterization of osteoporosis as a defective bone remodeling dynamics with respect to other bone pathologies. Our approach allows to derive three types of model checking-based diagnostic estimators. The first diagnostic measure focuses on the level of bone mineral density, which is currently used in medical practice. In addition, we have introduced a novel diagnostic estimator which uses the full patient clinical record, here simulated using the modeling framework. This estimator detects rapid (months) negative changes in bone mineral density. Independently of the actual bone mineral density, when the decrease occurs rapidly it is important to alarm the patient and monitor him/her more closely to detect insurgence of other bone co-morbidities. A third estimator takes into account the variance of the bone density, which could address the investigation of metabolic syndromes, diabetes and cancer. Our implementation could make use of different logical combinations of these statistical estimators and could incorporate other biomarkers for other systemic co-morbidities (for example diabetes and thalassemia). We are delighted to report that the combination of stochastic modeling with formal methods motivate new diagnostic framework for complex pathologies. In particular our approach takes into consideration important properties of biosystems such as multiscale and self-adaptiveness. The multi-diagnosis could be further expanded, inching towards the complexity of human diseases. Finally, we briefly introduce self-adaptiveness in formal methods which is a key property in the regulative mechanisms of biological systems and well known in other mathematical and engineering areas.Comment: In Proceedings CompMod 2011, arXiv:1109.104

Preferential utilization of endogenous arachidonate by cyclo-oxygenase in incubations of human platelets

AbstractThromboxane B2 (TXB2) and 12-hydroxy-5,8,10,14-eicosatetraenoic acid (12-HETE) formed from the endogenous and exogenous arachidonate during human platelet incubation, was evaluated by selected ion monitoring (SIM). TXB2 formed from endogenous substrate accounted for about one third of the total, whereas the great part of 12-HETE derived from exogenous arachidonate. These data indicate that under the tested conditions the pool of arachidonate that acts as substrate for cyclo-oxygenase is different from the pool that acts as substrate for lipoxygenase and that the arachidonate released from phospholipids is preferentially utilized by cyclo-oxygenase