We present a detailed analysis and implementation of a splitting strategy to identify simultaneously the local-volatility surface and the jump-size distribution from quoted European prices. The underlying model consists of a jump-diffusion driven asset with time and price dependent volatility. Our approach uses a forward Dupire-type partial-integro-differential equations for the option prices to produce a parameter-to-solution map. The ill-posed inverse problem for such map is then solved by means of a Tikhonov-type convex regularization. The proofs of convergence and stability of the algorithm are provided together with numerical examples that substantiate the robustness of the method both for synthetic and real data.

Vinicius Albani Jorge Zubelli

This paper examines issues of data completion and location uncertainty, popular in many practical PDE-based inverse problems, in the context of option calibration via recovery of local volatility surfaces. While real data is usually more accessible for this application than for many others, the data is often given only at a restricted set of locations. We show that attempts to "complete missing data" by approximation or interpolation, proposed in the literature, may produce results that are inferior to treating the data as scarce. Furthermore, model uncertainties may arise which translate to uncertainty in data locations, and we show how a model-based adjustment of the asset price may prove advantageous in such situations. We further compare a carefully calibrated Tikhonov-type regularization approach against a similarly adapted EnKF method, in an attempt to fine-tune the data assimilation process. The EnKF method offers reassurance as a different method for assessing the solution in a problem where information about the true solution is difficult to come by. However, additional advantage in the latter approach turns out to be limited in our context.

Vinicius Albani Uri M. Ascher Xu Yang Jorge P. Zubelli

We introduce a notion of sensitivity, with respect to a continuous bounded observable, which provides a sufficient condition for a continuous map, acting on a Baire metric space, to exhibit a Baire generic subset of points with historic behavior. The applications of this criterion recover, and extend, several known theorems on the genericity of the irregular set, besides yielding a number of new results, including information on the irregular set of geodesic flows, in both negative and non-positive curvature, and semigroup actions.

M. Carvalho V. Coelho L. Salgado P. Varandas

We bound several quantities related to the packing density of the patterns 1(L+1)L...2. These bounds sharpen results of B\'ona, Sagan, and Vatter and give a new proof of the packing density of these patterns, originally computed by Stromquist in the case L=2 and by Price for larger L. We end with comments and conjectures.

Martin Hildebrand Bruce E. Sagan Vincent Vatter

In the present work, we theoretically investigate light deflection in the weak and strong field regimes for two regular spacetimes with corrections from loop quantum gravity. We treat analytically the expansions for both limits and use them as a basis for investigating gravitational lensing observables. We analyze and provide reasonable values for observables related to the second model that observational tools may be able to detect.

A. R. Soares C. F. S. Pereira R. L. L. Vitória Marcos V. de S. Silva H. Belich

A catalogue of superclusters of galaxies is used to investigate the influence of the supercluster environment on galaxy populations, considering galaxies brighter than M$_r<$-21+5$\log$ h. Empirical spectral synthesis techniques are applied to obtain the stellar population properties of galaxies which belong to superclusters and representative values of stellar population parameters are attributed to each supercluster. We show that richer superclusters present denser environments and older stellar populations. The galaxy populations of superclusters classified as filaments and pancakes are statistically similar, indicating that the morphology of superclusters does not have a significative influence on the stellar populations. Clusters of galaxies within superclusters are also examined in order to evaluate the influence of the supercluster environment on their galaxy properties. Our results suggest that the environment affects galaxy properties but its influence should operate on scales of groups and clusters, more than on the scale of superclusters.

M. V. Costa-Duarte L. Sodre Jr F. Durret

Correctly interpreting observations of sources such as type Ia supernovae (SNe Ia) require knowledge of the power spectrum of matter on AU scales - which is very hard to model accurately. Because under-dense regions account for much of the volume of the universe, light from a typical source probes a mean density significantly below the cosmic mean. The relative sparsity of sources implies that there could be a significant bias when inferring distances of SNe Ia, and consequently a bias in cosmological parameter estimation. While the weak lensing approximation should in principle give the correct prediction for this, linear perturbation theory predicts an effectively infinite variance in the convergence for ultra-narrow beams. We attempt to quantify the effect typically under-dense lines of sight might have in parameter estimation by considering three alternative methods for estimating distances, in addition to the usual weak lensing approximation. We find in each case this not only increases the errors in the inferred density parameters, but also introduces a bias in the posterior value.

V. C. Busti R. F. L. Holanda C. Clarkson

The most recent Hubble constant ($H_0)$ estimates from local methods (z << 1), $H_0=73.8\pm 2.4$ km s$^{-1}$ Mpc$^{-1}$, and the one from high redshifts $H_0=67.3\pm 1.2$ km s$^{-1}$ Mpc$^{-1}$, are discrepant at $2.4 \sigma$ confidence level. Within this context, Lima & Cunha (LC) derived a new determination of $H_0$ using four cosmic probes at intermediate redshifts ($0.1<z<1.8$) based on the so-called flat $\Lambda$CDM model. They obtained $H_0=74.1\pm 2.2$ km s$^{-1}$ Mpc$^{-1}$, in full agreement with local measurements. In this Letter, we explore the robustness of the LC result searching for systematic errors and its dependence from the cosmological model used. We find that the $H_0$ value from this joint analysis is very weakly dependent on the underlying cosmological model, but the morphology adopted to infer the distance to galaxy clusters changes the result sizeably, being the main source of systematic errors. Therefore, a better understanding of the cluster morphology is paramount to transform this method into a powerful cross-check for $H_0$.

R. F. L. Holanda V. C. Busti G. Pordeus da Silva

This work presents a proposal for a wireless sensor network for participatory sensing, with IoT sensing devices developed especially for monitoring and predicting air quality, as alternatives of high cost meteorological stations. The system, called pmSensing, aims to measure particulate material. A validation is done by comparing the data collected by the prototype with data from stations. The comparison shows that the results are close, which can enable low-cost solutions to the problem. The system still presents a predictive analysis using recurrent neural networks, in this case the LSTM-RNN, where the predictions presented high accuracy in relation to the real data.

Lucas L. S. Sachetti Enzo B. Cussuol José Marcos S. Nogueira Vinicius F. S. Mota

The flavor is the focal point in the flavor industry, which follows social tendencies and behaviors. The research and development of new flavoring agents and molecules are essential in this field. On the other hand, the development of natural flavors plays a critical role in modern society. In light of this, the present work proposes a novel framework based on Scientific Machine Learning to undertake an emerging problem in flavor engineering and industry. Therefore, this work brings an innovative methodology to design new natural flavor molecules. The molecules are evaluated regarding the synthetic accessibility, the number of atoms, and the likeness to a natural or pseudo-natural product.

Luana P. Queiroz Carine M. Rebello Erbet A. Costa Vinícius V. Santana Bruno C. L. Rodrigues Alírio E. Rodrigues Ana M. Ribeiro Idelfonso B. R. Nogueira