# Vinicius AlbaniFederal University of Santa Catarina | UFSC · Departamento de Matemática

Vinicius Albani

PhD in Mathematics

Inverse Problems and Mathematical Modelling

## About

51

Publications

5,070

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299

Citations

Citations since 2017

Introduction

I am an assistant professor of Mathematics at the Federal University of Santa Catarina (UFSC). My major research interests are the Regularization of Inverse Problems, Parameter Estimation Techniques, and Mathematical Modeling. I have a special interest in calibration problems arising in Quantitative Finance, Mathematical Biology, and Fluid Dynamics.

## Publications

Publications (51)

In this paper we calculate the variation of the estimated vaccine efficacy (VE) due to the time-dependent force of infection resulting from the difference between the moment the Clinical Trial (CT) begins and the peak in the outbreak intensity. Using a simple mathematical model we tested the hypothesis that the time difference between the moment th...

Understanding and predicting power consumption behavior helps estimate costs, seek actions to save energy and plan affirmative actions that raise people's awareness. Organized civil society has made efforts in this context. Our contribution is a framework that first extracts knowledge about consumption through an extensive time series analysis of t...

We present a methodology to identify multiple pollutant sources in the atmosphere that combines a data-driven dispersion model with Bayesian inference and uncertainty quantification. The dispersion model accounts for a realistic wind field based on the output of a multivariate dynamic linear model (DLM), estimated from measured wind components time...

Recent empirical evidence suggests that the transmission coefficient in susceptible-exposed-infected-removed-like (SEIR-like) models evolves with time, presenting random patterns, and some stylized facts, such as mean-reversion and jumps. To address such observations we propose the use of jump-diffusion stochastic processes to parameterize the tran...

In this work, the inverse problem of identification of pollution sources location and intensity in a river is studied considering the advection-dispersion equation, along with a Neural Network approach. In the direct problem, the location and the intensity of the source terms are known as well as the PDE coefficients and then it is solved by classi...

Source identification methodologies use inverse problems techniques combined with a dispersion model and observational data to estimate relevant source parameters. This work proposes a time-dependent model to estimate source parameters of multiple point releases. The forward problem or dispersion model accounts for the time variation of the wind fi...

Dry deposition removal process is a major environmental concern, especially because the material deposited over a surface may react with underling substances producing potential harmful substances. Dry deposition rates can be obtained from observational data, though it may be a hard task. The computational modeling using atmospheric dispersion mode...

We propose a generalized susceptible-exposed-infected-removed (SEIR) model to track COVID-19 in Canadian provinces, taking into account the impact of the pandemics on unemployment. The model is based on a network representing provinces, where the contact between individuals from different locations is defined by a data-driven mixing matrix. Moreove...

We present a new methodology to estimate multiple source parameters in the framework of Bayesian Inference. In the Bayesian inference technique, the estimation problem is modeled as the determination of the full conditional probability density of the unknown parameters. In turn, the full conditionals are the product of the likelihood function, whic...

Background
During 2020, there were no effective treatments or vaccines against SARS-CoV-2. The most common disease contention measures were social distance (social isolation), the use of face masks and lockdowns. In the beginning, numerous countries have succeeded to control and reduce COVID-19 infections at a high economic cost. Thus, to alleviate...

We propose a parsimonious, yet effective, susceptible–exposed–infected–removed-type model that incorporates the time change in the transmission and death rates. The model is calibrated by Tikhonov-type regularization from official reports from New York City (NYC), Chicago, the State of São Paulo, in Brazil and British Columbia, in Canada. To foreca...

We propose a parsimonious, yet effective, susceptible-exposed-infected-removed-type model that incorporates the time change in the transmission and death rates. The model is calibrated by Tikhonov-type regularization from official reports from New York City (NYC), Chicago, the State of São Paulo, in Brazil, and British Columbia, in Canada. To forec...

The release of toxic gases into the atmosphere is a subject of great environmental concern. Such releases might occur in several ways, including in regular industrial activities and accidents. The proper identification of the origin and the quantity of released harmful materials is essential particularly in emergencies to avoid or reduce possible d...

This work proposes the use of a Monte Carlo Markov Chain technique to estimate the location and strength of multiple pollutant emissions in the atmosphere. The corresponding dispersion problem is numerically solved by the stabilezed Galerkin/Least-Square finite element method. The sources parameters are estimated simultaneously to the so-called pre...

We calculate the impact of a socioeconomic program during 2020 as a measure to mitigate the Coronavirus Disease 2019 (COVID-19) outbreak in Brazil. For each Brazilian State, we estimate the time-dependent reproduction number from daily reports of COVID-19 infections and deaths using a Susceptible-Exposed-Infected-Recovered-like (SEIR-like) model. T...

Background
Underreporting cases of infectious diseases poses a major challenge in the analysis of their epidemiological characteristics and dynamical aspects. Without accurate numerical estimates it is difficult to precisely quantify the proportions of severe and critical cases, as well as the mortality rate. Such estimates can be provided for inst...

We address the source characterization of atmospheric releases using adaptive strategies in Bayesian inference in combination with the numerical solution of the dispersion problem by a stabilized finite element method and uncertainty quantification in the measurements. The adaptive techniques accelerate the convergence of Monte Carlo Markov Chain (...

Background
By the beginning of December 2020, some vaccines against COVID-19 already presented efficacy and security, which qualify them to be used in mass vaccination campaigns. Thus, setting up strategies of vaccination became crucial to control the COVID-19 pandemic.
Methods
We use daily COVID-19 reports from Chicago and New York City (NYC) fro...

We propose a susceptible-exposed-infective-recovered-type (SEIR-type) meta-population model to simulate and monitor the (COVID-19) epidemic evolution. The basic model consists of seven categories, namely, susceptible (S), exposed (E), three infective classes, recovered (R), and deceased (D). We define these categories for n age and sex groups in m...

Background: By the beginning of December 2020, some vaccines against COVID-19 already presented efficacy and security, which qualify them to be used in mass vaccination campaigns. Thus, setting up strategies of vaccination became crucial to control the COVID19 pandemic. Methods: We use daily COVID-19 reports from Chicago and NYC from 01-Mar2020 to...

We present a novel methodology for the stable rate estimation of hospitalization and death related to the Corona Virus Disease 2019 (COVID-19) using publicly available reports from various distinct communities. These rates are then used to estimate underreported infections on the corresponding areas by making use of reported daily hospitalizations...

We propose an SEIR-type meta-population model to simulate and monitor the Covid-19 epidemic evolution. The basic model consists of seven compartments, namely susceptible (S), exposed (E), three infective classes, recovered (R), and deceased (D). We define these compartments for n age and gender groups in m different spatial locations. So, the resul...

This work proposes an inverse modeling technique to estimate point source emissions in the atmosphere. Tikhonov-type regularization with composite misfits functions is used to identify the emission sources, and the corresponding minimization problem is solved by Particle Swarm Optimization (PSO). The regularization parameter in the Tikhonov-type fu...

We propose a Susceptible-Exposed-Infected-Recovered-type model to describe the dynamics of Covid-19 in a population. The population is distributed into seven compartments, namely, susceptible (S), exposed (E), three infective classes (I M , I S , and I C), recovered (R), and deceased D. The disease severity is accounted for by the infective classes...

We propose a methodology to estimate single and multiple emission sources of atmospheric contaminants. It combines hybrid metaheuristic/gradient-descent optimization techniques and Tikhonov-type regularization. The dispersion problem is solved by the Galerkin/Least-squares finite element formulation, which allows more realistic modeling. The accura...

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 integr...

We propose a new methodology to retrieve multiple point emission sources in the atmosphere. To allow more realistic modelling, the dispersion problem is solved by a stabilized finite element formulation. The simultaneous estimation of the source strengths, their locations and the total number of sources is made employing Tikhonov-type regularizatio...

This work is concerned with the source identification problem in air pollution modeling. The forward problem is described by an advection-diffusion equation with physically realistic coefficients. It is solved by the combination of adaptive meshes and a stabilized finite element method. The source is estimated by Tikhonov-type regularization with a...

This work is concerned with the source identification problem in air pollution modeling. The forward problem is described by an advection-diffusion equation with physically realistic coefficients. It is solved by the combination of adaptive meshes and a stabilized finite element method. The source is estimated by Tikhonov-type regularization with a...

We state sufficient conditions for the uniqueness of minimizers of Tikhonov-type functionals. We further explore a connection between such results and the well-posedness of Morozov-like discrepancy principle. Moreover, we find appropriate conditions to apply such results to the local volatility surface calibration problem.

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...

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 locati...

We apply convex regularization techniques to the problem of calibrating Dupire’s local volatility surface model taking into account the practical requirement of discrete grids and noisy data. Such requirements are the consequence of bid and ask spreads, quantization of the quoted prices and lack of liquidity of option prices for strikes far away fr...

We introduce a local volatility model for the valuation of options on commodity futures by using European vanilla option prices. The corresponding calibration problem is addressed within an online framework, allowing the use of multiple price surfaces. Since uncertainty in the observation of the underlying future prices translates to uncertainty in...

div class="title">Within-person stability and responsiveness to dietary change of C15:0 and C17:0 concentrations in dry blood spots in the Food4Me Study
- Volume 75 Issue OCE3 - V. Albani, M. C. Walsh, M. J. Gibney, J. C. Mathers, A. Adamson, C. Celis-Morales, L. Brennan

We address the classical issue of appropriate choice of the regularization and discretization level for the Tikhonov regularization of an inverse problem with imperfectly measured data. We focus on the fact that the proper choice of the discretization level in the domain together with the regularization parameter is a key feature in adequate regula...

We introduce a local volatility model for the valuation of options on commodity futures by using European vanilla option prices. The corresponding calibration problem is addressed within an online framework, allowing the use of multiple price surfaces. Since uncertainty in the observation of the underlying future prices translates to uncertainty in...

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 of [10] to general source conditions, such as logarithmic source conditions. Moreover, we also provide optimality results unde...

Structured population models in biology lead to integro-differential equations that describe the evolution in time of the population density taking into account a given feature such as the age, the size, or the volume. These models possess interesting analytic properties and have been used extensively in a number of areas. In this article, we consi...

We calibrate the Schwartz-Smith commodity pricing model using CBOT soybean futures. The results allows us to identify the properties that characterize the equilibrium in agricultural commodity prices, and, in particular, backwardation. This phenomenon has been attributed to effects on replication of prices on the term structure of commodities due t...

In this article we address the regularization of the ill-posed problem of
determining the local volatility surface (as a function of time to maturity and
price) 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 th...

We apply convex regularization techniques to the problem of calibrating Dupire's local volatility surface model taking into account the practical requirement of discrete grids and noisy data. Such requirements are the consequence of bid and ask spreads, quantization of the quoted prices and lack of liquidity of option prices for strikes far way fro...

We propose a theoretical approach to solve the inverse problem of local volatility calibration from quoted European option prices in Equity and Commodity markets. Based on the assumption that local volatility surface evolves with the initial state, and varies with time, we achieve a term structure calibration procedure for such surface. Thus, combi...

We address the inverse problem of local volatility surface calibration from market given option prices. We integrate the ever-increasing ow 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 underl...

This paper uses data obtained from the galaxy luminosity function (LF) to calculate two types of radial number density statistics of the galaxy distribution as discussed in Ribeiro, namely, the differential density γ and the integral differential density γ*. By applying the theory advanced by Ribeiro & Stoeger, which connects the relativistic cosmo...