A differential geometric approach to nonlinear filtering: theprojection filter

This paper presents a new and systematic method of approximating exact nonlinear filters with finite dimensional filters, using the differential geometric approach to statistics. The projection filter is defined rigorously in the case of exponential families. A convenient exponential family is proposed which allows one to simplify the projection filter equation and to define an a posteriori measure of the local error of the projection filter approximation. Finally, simulation results are discussed for the cubic sensor problem     

On the nice behaviour of the Gaussian projection filter with small observation noise

When projecting on the manifold of Gaussian densities, the projection filter has been shown to be equal to a McShane-Fisk-Stratonovich (MFS) derivation of the Gaussian assumed density filter. Starting from this point, we study the asymptotic behaviour of the Gaussian projection filter when the covariance of the observation noise tends to zero. We prove that the mean square difference between the true state of the system and the estimate given by the projection filter is bounded by a constant which is proportional to the magnitude of the observation noise.     

Lithiasic, congenital, choledochal dilatation: problems of diagnosis and therapy

We report a case of a 30-year old female with congenital lithiasic choledochal dilatation which was not diagnosed at the ultrasonographic examination. Congenital biliary dilatation abnormalities are rare and may clinically present with episodic biliary colics or more rarely with recurrent pancreatis. Ultrasound, CT-scanning and ERCP usually make these anatomic alterations evident but in some cases there may be some doubt despite the vast range of radiological techniques available (PTC, Tc99m-Isida scinti-scan). The best results from a diagnostic point of view are obtained from the ERCP that may in fact visualize an anomalous pancreatico-biliary junction, rule out carcinoma, accurately define the cyst dimensions or show the intrahepatic ductal radicals. Furthermore, the extraction of intracystic stones or the treatment of choledochocele through a papillostomy may be performed. However the ERCP may cause traumatic pancreatitis, above all in youngster as was verified in our patient. During surgical exploration, the definitive diagnosis can be achieved via intraoperative cholangiography. We emphasize that in patients with congenital choledochal dilatation, the dilated choledochus should be excised even in young children to avoid the risk of malignancy which may occur also following cyso-duodeno- or cystojejunostomy treatment. In our patient an hepatiocojejunostomy on a Roux-en-Y limb was performed. This single case has been oresented along with a review of the literature to recall such anomalies in differential diagnosis of biliary colics and to stress that the choice treatment is surgical resection.     

New results on the Gaussian projection filter with small observation noise

In this paper we define a one dimensional Gaussian projection filter (GPF) for a one dimensional diffusion and show that it behaves as nicely as the previously studied two dimensional GPF w.r.t. the true state. We extend part of the results on its nice behaviour to systems with bounded but not necessarily Lipschitz drift, and observe that in this case the resulting efficient filter does not depend on the drift itself.     

New hybrid organic–inorganic sol–gel positive resist

The direct nanopatterning of a novel hybrid organic–inorganic sol–gel film based on bridged polysilsesquioxanes (BPS) using X-ray synchrotron radiation is reported. The main advantages of a direct fabrication technique with respect to conventional photolithography are represented by the possibility to bypass some typical post-exposure lithographic steps and to avoid the use of a sacrificial layer. The distinctive features rendering hybrid BPS-based material innovative for photolithographic applications are: the patternability as resist, the positive tone behaviour exhibited under X-ray irradiation, the porous structure demonstrated at low temperature, and the possibility to widely tailor material electro-optical and structural properties to experimental needs. A systematic investigation of the interactions between sol–gel BPS films based on the bis(triethoxysilyl)benzene precursor and soft X-rays is conducted. Under X-ray exposure, BPS-based films suffer structural changes attributed to the organic bridge breaking, and become soluble in suitable acidic aqueous solutions, producing final lithographies of sub-micron resolution, high contrast and good edge definition.     

Hybrid porous resist with sensing functionality

Natively porous hybrid organic-inorganic sol-gel systems have been engineered to be used as functional positive photoresists, aimed to the realization of microsensors in a single-step process.Interesting results have been obtained combing three main sol-gel system features: the direct patternability through X-ray lithography, being processable without the addition of a photocatalyst; the functionalizability, properly designing the organic component of the hybrid network or incorporating active species; the open micro or mesoporosity, tailored by the synthesis process and precursor choice.The photoprocessable porous films have been synthesized starting from a Bridged Polysilsesquioxane (BPS) precursor, 1,4-bis(triethoxysilyl)benzene. The correlation between chemical properties of the sol-gel material and its patternability is described in detail. X-ray exposure leads to a progressive alkyl and aromatic compound elimination and promotes inorganic condensation in the system, allowing the selective dissolution of irradiated cross-linked films in suitable etchants. Patterns of final resolution lower than 100 nm have been realized on BPS-based films synthesized in acid conditions, a procedure that allows to take advantage of a straightforward embedding protocol for active species in the sol-gel matrix. The BPS-based system has been doped with a covalently linked quinolinium dye, obtaining thin sensing films patternable by X-ray lithography. A feasibility test for the fabrication of optical microdevices, where fluorescence properties are obtained directly on the patterned coatings, has been provided.