Online Local Volatility Calibration by Convex Regularization with Morozov's Principle and Convergence Rates

We address the inverse problem of local volatility surface calibration from market given option prices. We integrate the ever-increasing flow of option price information into the well-accepted local volatility model of Dupire. This leads to considering both the local volatility surfaces and their corresponding prices as indexed by the observed underlying stock price as time goes by in appropriate function spaces. The resulting parameter to data map is defined in appropriate Bochner-Sobolev spaces. Under this framework, we prove key regularity properties. This enable us to build a calibration technique that combines online methods with convex Tikhonov regularization tools. Such procedure is used to solve the inverse problem of local volatility identification. As a result, we prove convergence rates with respect to noise and a corresponding discrepancy-based choice for the regularization parameter. We conclude by illustrating the theoretical results by means of numerical tests.Comment: 23 pages, 5 figure

Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces

In this paper, we prove optimal convergence rates results for regularisation methods for solving linear ill-posed operator equations in Hilbert spaces. The result generalises existing convergence rates results on optimality to general source conditions, such as logarithmic source conditions. Moreover, we also provide optimality results under variational source conditions and show the connection to approximative source conditions

Field coverage and weed mapping by UAV swarms

The demands from precision agriculture (PA) for high-quality information at the individual plant level require to re-think the approaches exploited to date for remote sensing as performed by unmanned aerial vehicles (UAVs). A swarm of collaborating UAVs may prove more efficient and economically viable compared to other solutions. To identify the merits and limitations of a swarm intelligence approach to remote sensing, we propose here a decentralised multi-agent system for a field coverage and weed mapping problem, which is efficient, intrinsically robust and scalable to different group sizes. The proposed solution is based on a reinforced random walk with inhibition of return, where the information available from other agents (UAVs) is exploited to bias the individual motion pattern. Experiments are performed to demonstrate the efficiency and scalability of the proposed approach under a variety of experimental conditions, accounting also for limited communication range and different routing protocols. © 2017 IEEE

Holocene regional gradients of dust provenance and flux between Talos Dome and Dome C, East Antarctica.

Aeolian sequences from Central East Antarctic ice cores provide climate and environmental information of hemispheric significance. Close to the margins of the ice sheet, high-elevation ice-free terrains protruding above the ice sheet surface can provide an additional input of fine dust particles to the atmosphere, making peripheral locations particularly interesting for the study of the regional climate evolution. In the Talos Dome area of East Antarctica, entrainment and transport of local mineral particles is merely influenced by local wind direction and strength, which in turn is tuned by regional climate changes. We investigate the spatial variability of modern and Holocene dust flux, grain size and isotopic (Sr-Nd) composition along a hypothetic transect from Talos Dome all through the interior of the ice sheet (Dome C/Vostok area), and compare the geochemical fingerprint of dust extracted from firn and ice cores to the equivalent size fraction of regolith and glacial deposits from high altitude Victoria Land sources. This study aims to better understand the environmental gradients of dust flux and provenance from the marginal Talos Dome site to the higher Dome C drainage area, with implications for the regional atmospheric circulation, while documenting the isotopic composition of local exposed sediments

Differential Density Statistics of Galaxy Distribution and the Luminosity Function

This paper uses data obtained from the galaxy luminosity function (LF) to calculate two types of radial number densities statistics of the galaxy distribution as discussed in Ribeiro (2005), namely the differential density $\gamma$ and the integral differential density $\gamma^\ast$. By applying the theory advanced by Ribeiro and Stoeger (2003), which connects the relativistic cosmology number counts with the astronomically derived LF, the differential number counts $dN/dz$ are extracted from the LF and used to calculate both $\gamma$ and $\gamma^\ast$ with various cosmological distance definitions, namely the area distance, luminosity distance, galaxy area distance and redshift distance. LF data are taken from the CNOC2 galaxy redshift survey and $\gamma$ and $\gamma^\ast$ are calculated for two cosmological models: Einstein-de Sitter and an $\Omega_{m_0}=0.3$, $\Omega_{\Lambda_0}=0.7$ standard cosmology. The results confirm the strong dependency of both statistics on the distance definition, as predicted in Ribeiro (2005), as well as showing that plots of $\gamma$ and $\gamma^\ast$ against the luminosity and redshift distances indicate that the CNOC2 galaxy distribution follows a power law pattern for redshifts higher than 0.1. These findings bring support to Ribeiro's (2005) theoretical proposition that using different cosmological distance measures in statistical analyses of galaxy surveys can lead to significant ambiguity in drawing conclusions about the behavior of the observed large scale distribution of galaxies.Comment: LaTeX, 37 pages, 6 tables, 10 figures. Accepted for publication in "The Astrophysical Journal

Proteomic profile of maternal-aged blastocoel fluid suggests a novel role for ubiquitin system in blastocyst quality

Purpose: The etiology of maternal aging, a common cause of female factor infertility and a rate-limiting step in vitro fertilization (IVF) success, remains still unclear. Proteomic changes responsible for the impaired successful pregnancy outcome after IVF with aged blastocysts have not been yet evaluated. The objective of this prospective study was to employ proteomic techniques and bioinformatic tools to enlight differences at the protein level in blastocoel fluid of aged and younger woman. Methods: Protein composition of human blastocoel fluid isolated by micromanipulation from 46 blastocysts of women aged <37 years (group A) and 29 of women aged 6537 years (group B) have been identified by a shotgun proteomic approach based on high-resolution nano-liquid chromatography electrospray-ionization-tandem mass spectrometry (nLC-ESI-MS/MS) using label free for the relative quantification of their expression levels. Results: The proteomic analysis leads to the identification and quantification of 148 proteins; 132 and 116 proteins were identified in groups A and B, respectively. Interestingly, the identified proteins are mainly involved in processes aimed at fine tuning embryo implantation and development. Among the 100 proteins commonly expressed in both groups, 17 proteins are upregulated and 44 downregulated in group B compared to group A. Overall, the analysis identified 33 proteins, which were increased or present only in B while 76 were decreased in B or present only in A. Conclusions: Data revealed that maternal aging mainly affects blastocyst survival and implantation through unbalancing the equilibrium of the ubiquitin system known to play a crucial role in fine-tuning several aspects required to ensure successful pregnancy outcome