This laboratory has as its goal the use of mathematical tools in the study and solution of real world problems  coming  from the applied  sciences. In  particular, we  have  studied  problems  coming  from biophysical and financial applications. In the biophysical sciences we can  cite applications  to image reconstruction & tomography, structured populations, and virus dynamics. In the financial applications we  can mention  the study of risk  management, commodity modelling, volatility estimation, and project evaluation under uncertainty.


Minicourse Announcement:

As part of the 2017 activities of the Thematic Program: "New Trends in Parameter Identification for Mathematical Models" we are happy to announce the short-course: (watch all the videos here)


Uri Ascher (British Columbia, Canada)
"Computational methods in applied inverse problems" (abstract)
From 16/Oct to 27/Oct (2 weeks) (click here for the video)


Bernd Hofmann (TU Chemnitz, Germany)
"Regularization methods in Banach spaces" (abstract)
From 16/Oct to 27/Oct (2 weeks) (click here for the video)


Samuli Siltanen (University of Helsinki, Finland)
"Reconstruction methods for sparse-data X-ray tomography" (abstract)
From 23/Oct to 27/Oct (1 week) (click here for the video)


Ville Kolehmainen (University of Eastern Finland)
"Solution of Inverse Problems within the Bayesian Framework of Statistics" (abstract)
From 06/Nov to 10/Nov (1 week)


Philippe Le-Masson (Bretagne-Sud Univ., France)
"Thermal Characterization of Materials at High-Temperatures: Design of Experiment and Multiphysics Inverse Analysis (abstract)
06/Nov - 10/Nov (1 week)

Wellington Betencurte and Julio Dutra (Federal Univ. Espirito Santo, Brazil) and Henrique Fonseca and Cesar Pacheco (Federal Univ. Rio de Janeiro, Brazil)
"Kalman Particle Filters" (abstract)
06/Nov - 10/Nov (1 week)

Diego Estumano (Federal Univ. Para, Brazil)
"ABC - Approximate Bayesian Computation" (abstractvideo)
06/Nov - 10/Nov (1 week)


We are happy to announce the upcoming events:  


Upcoming text "New Trends in Parameter Identification for Mathematical Models" edited by B. Hofmann, A. Leitão and J.P. Zubelli announced by Springer.

INVERSE PROBLEMS AT WORK!!!  The importance of Inverse Problems in the Applied Sciences is once more confirmed by the Nobel prize award to Prof. Joachim Frank" of Columbia University for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution" jointly with Jacques Dubochet and Richard Henderson.
The methodology behind such technique involves the solution of a difficult inverse problem and has been the subject of intense investigation by many groups. It is in the cross roads of many research areas including numerical analysis, computer science and optimization.
We at LAMCA have been actively working in inverse problems and in 2003 published jointly with the group of Prof. Gabor T. Herman  the article
"Three-dimensional reconstruction by Chahine's method from electron microscopic projections corrupted by instrumental aberrations" in the journal Inverse Problems where we studied the issue of high-resolution imaging for cryo-microscopy and proposed a class of algorithms based on a classical method of Chahine's. 

More details in Portuguese


LAMCA participates at the CEMRACS 2017 at the CIRM in Luminy, France.
See Talk:  "Project Evaluation under Uncertainty" by J.P. Zubelli


Paper published in  Physical Review B:
"Theory and measurements of harmonic generation in semiconductor superlattices with applications in the 100 GHz to 1 THz range"
 by M. F. Pereira, J. P. Zubelli, D. Winge, et al.


Manuscript accepted in the SIAM Journal on Numerical Analysis:
"A non-intrusive stratified resampler for regression Monte Carlo:
application to solving non-linear equations"

 by E. Gobet, G. Liu, and J.P. Zubelli


Paper published (online first)
Data driven recovery of local volatility surfaces 

on Inverse Problems and Imaging.
by V. Albani, U. Ascher, Xu. Yang, and J.P. Zubelli.


Discussion group on the Statistical PlanAb for the OTIM-PBR project.
March 13-15, 2017


Project Evaluation under Uncertainty: The Hedged Monte Carlo Approach.

Jorge P. Zubelli - IMPA 

24/04/2017,  19:00  - room 232


Abstract :  Industrial strategic decisions have evolved tremendously in the last decades towards a higher degree of quantitative analysis. Such decisions require taking into account a large number of uncertain variables and volatile scenarios, much like financial market investments. Furthermore, they can be evaluated by comparing to portfolios of investments in financial assets such as in stocks, derivatives and commodity futures. This revolution led to the development of a new field of managerial science known as Real Options.  The use of Real Option techniques incorporates also the value of flexibility and gives a broader view of many business decisions that brings in techniques from quantitative finance and risk management. Such techniques are now part of the decision making process of many corporations and require a substantial amount of mathematical background. Yet, there has been substantial debate concerning the use of risk neutral pricing and hedging arguments to the context of project evaluation. We discuss some alternatives to risk neutral pricing that could be suitable to evaluation of projects in a realistic context with special attention to projects dependent on commodities and non-hedgeable uncertainties. More precisely, we make use of a variant of the hedged Monte-Carlo method of Potters, Bouchaud and Sestovic to tackle strategic decisions. This  is joint work with E.Brigatti (UFRJ), F.Macias (BTG Chile) and M.O.Souza (UFF).