Quantitative Darboux theorems in contact geometry

This paper begins the study of relations between Riemannian geometry and contact topology in any dimension and continues this study in dimension 3. Specifically we provide a lower bound for the radius of a geodesic ball in a contact manifold that can be embedded in the standard contact structure on Euclidean space, that is on the size of a Darboux ball. The bound is established with respect to a Riemannian metric compatible with an associated contact form. In dimension three, it further leads us to an estimate of the size for a standard neighborhood of a closed Reeb orbit. The main tools are classical comparison theorems in Riemannian geometry. In the same context, we also use holomorphic curves techniques to provide a lower bound for the radius of a PS-tight ball.Comment: 33 pages, corrects several inaccuracies in earlier versio

Airborne mapping of complex obstacles using 2D Splinegon

This paper describes a recently proposed algorithm in mapping the unknown obstacle in a stationary environment where the obstacles are represented as curved in nature. The focus is to achieve a guaranteed performance of sensor based navigation and mapping. The guaranteed performance is quantified by explicit bounds of the position estimate of an autonomous aerial vehicle using an extended Kalman filter and to track the obstacle so as to extract the map of the obstacle. This Dubins path planning algorithm is used to provide a flyable and safe path to the vehicle to fly from one location to another. This description takes into account the fact that the vehicle is made to fly around the obstacle and hence will map the shape of the obstacle using the 2D-Splinegon technique. This splinegon technique, the most efficient and a robust way to estimate the boundary of a curved nature obstacles, can provide mathematically provable performance guarantees that are achievable in practice

Continuous Workout Mortgages

This paper models Continuous Workout Mortgages (CWMs) in an economic environment with refinancings and prepayments by employing a market-observable variable such as the house price index of the pertaining locality. Our main results include: (a) explicit modelling of repayment and interest-only CWMs; (b) closed form formulae for mortgage payment and mortgage balance of a repayment CWM; (c) a closed form formula for the actuarially fair mortgage rate of an interest-only CWM. For repayment CWMs we extend our analysis to include two negotiable parameters: adjustable "workout proportion" and adjustable "workout threshold." These results are of importance as they not only help understanding the mechanics of CWMs and estimating key contract parameters. These results are of importance as they not only help in the understanding of the mechanics of CWMs and estimating key contract parameters, but they also provide guidance on how to enhance the resilience of the financial architecture and mitigate systemic risk.Continuous Workout Mortgage (CWM), Repayment, Interest-only, House price index, Prepayment intensity, Cap and floor on continuous flow

Continuous Workout Mortgages

This paper models Continuous Workout Mortgages (CWMs) in an economic environment with refinancings and prepayments by employing a market-observable variable such as the house price index of the pertaining locality. Our main results include: (a) explicit modelling of repayment and interest-only CWMs; (b) closed form formulae for mortgage payment and mortgage balance of a repayment CWM; (c) a closed form formula for the actuarially fair mortgage rate of an interest-only CWM. For repayment CWMs we extend our analysis to include two negotiable parameters: adjustable “workout proportion” and adjustable “workout threshold.” These results are of importance as they not only help understanding the mechanics of CWMs and estimating key contract parameters. These results are of importance as they not only help in the understanding of the mechanics of CWMs and estimating key contract parameters, but they also provide guidance on how to enhance the resilience of the financial architecture and mitigate systemic risk

Efficient Non-Viral Ocular Gene Transfer with Compacted DNA Nanoparticles

BACKGROUND: The eye is an excellent candidate for gene therapy as it is immune privileged and much of the disease-causing genetics are well understood. Towards this goal, we evaluated the efficiency of compacted DNA nanoparticles as a system for non-viral gene transfer to ocular tissues. The compacted DNA nanoparticles examined here have been shown to be safe and effective in a human clinical trial, have no theoretical limitation on plasmid size, do not provoke immune responses, and can be highly concentrated. METHODS AND FINDINGS: Here we show that these nanoparticles can be targeted to different tissues within the eye by varying the site of injection. Almost all cell types of the eye were capable of transfection by the nanoparticle and produced robust levels of gene expression that were dose-dependent. Most impressively, subretinal delivery of these nanoparticles transfected nearly all of the photoreceptor population and produced expression levels almost equal to that of rod opsin, the highest expressed gene in the retina. CONCLUSIONS: As no deleterious effects on retinal function were observed, this treatment strategy appears to be clinically viable and provides a highly efficient non-viral technology to safely deliver and express nucleic acids in the retina and other ocular tissues

Imidazole processing of wheat straw and eucalyptus residues: comparison of pre-treatment conditions and their influence on enzymatic hydrolysis

ABSTRACT: Biomass pre-treatment is a key step in achieving the economic competitiveness of biomass conversion. In the present work, an imidazole pre-treatment process was performed and evaluated using wheat straw and eucalyptus residues as model feedstocks for agriculture and forest-origin biomasses, respectively. Results showed that imidazole is an efficient pre-treatment agent; however, better results were obtained for wheat straw due to the recalcitrant behavior of eucalyptus residues. The temperature had a stronger effect than time on wheat straw pre-treatment but at 160 degrees C and 4 h, similar results were obtained for cellulose and hemicellulose content from both biomasses (ca. 54% and 24%, respectively). Lignin content in the pre-treated solid was higher for eucalyptus residues (16% vs. 4%), as expected. Enzymatic hydrolysis, applied to both biomasses after different pre-treatments, revealed that results improved with increasing temperature/time for wheat straw. However, these conditions had no influence on the results for eucalyptus residues, with very low glucan to glucose enzymatic hydrolysis yield (93% for wheat straw vs. 40% for eucalyptus residues). Imidazole can therefore be considered as a suitable solvent for herbaceous biomass pre-treatment.info:eu-repo/semantics/publishedVersio

Continuous Workout Mortgages

Continuous Workout Mortgage (CWM) balance and payments are indexed using market-observable house price index in an economic environment with prepayments. Our main results include: (a) explicit modelling of repayment and interest-only CWMs; (b) closed form formulas for mortgage payment and mortgage balance of a repayment CWM; (c) a closed form formula for the actuarially fair mortgage rate of an interest-only CWM. For repayment CWMs we extend our analysis to include two negotiable parameters: adjustable "workout proportion" and adjustable "workout threshold." These results are of importance as they not only help in the understanding of the mechanics of CWMs and estimating key contract parameters, but they also provide guidance on how to enhance the resilience of the financial architecture and mitigate systemic risk.

Experimental observation of magnetic bobbers for a new concept of magnetic solid-state memory

The use of chiral skyrmions, which are nanoscale vortex-like spin textures, as movable data bit carriers forms the basis of a recently proposed concept for magnetic solid-state memory. In this concept, skyrmions are considered to be unique localized spin textures, which are used to encode data through the quantization of different distances between identical skyrmions on a guiding nanostripe. However, the conservation of distances between highly mobile and interacting skyrmions is difficult to implement in practice. Here, we report the direct observation of another type of theoretically-predicted localized magnetic state, which is referred to as a chiral bobber (ChB), using quantitative off-axis electron holography. We show that ChBs can coexist together with skyrmions. Our results suggest a novel approach for data encoding, whereby a stream of binary data representing a sequence of ones and zeros can be encoded via a sequence of skyrmions and bobbers. The need to maintain defined distances between data bit carriers is then not required. The proposed concept of data encoding promises to expedite the realization of a new generation of magnetic solid-state memory