# Conferencias Plenarias V MACI 2015

# Estimation of Distributed Parameters in Permittivity Models of

Composite Dielectric Materials Using Reflectance

H.T. Banks,

Center for Research in Scientific Computation

North Carolina State University

**Abstract.**

We investigate the feasibility of quantifying properties of a composite dielectric

material through the reflectance, where the permittivity is described by the

Lorentz model in which an unknown probability measure is placed on the model

parameters. We summarize the computational and theoretical framework (the

Prohorov Metric Framework) developed by our group in the past two decades for

nonparametric estimation of probability measures using a least-squares method,

and point out the limitation of the existing computational algorithms for this

particular application. We then improve the algorithms, and demonstrate the

feasibility of our proposed methods by numerical results obtained for both

simulated data and experimental data for inorganic glass when considering the

resonance wavenumber as a distributed parameter. Finally, in the case where the

distributed parameter is taken as the relaxation time, we show using simulated

data how the addition of derivative measurements improves the accuracy of the

method.

# Non-modular Losses in Structured Prediction with Application to Computer Vision

Matthew B. Blaschko

Chargé de Recherche (Inria) and Associate Professor

Center for Visual Computing

École Centrale Paris

Francia

**Abstract.**

Statistical learning has been a driving force in the development of computer vision applications. While statistical estimation is very well developed for binary classification and regression, it is less so for prediction of structured outputs, such as segmentation of an image, or prediction of object location and interrelated parts. Typically, modular losses such as Hamming loss are applied for such prediction problems. We investigate the use of non-modular loss functions, which may be isomorphic to submodular or supermodular set functions, and explore convex surrogate loss functions in these cases. An important question is the computational complexity of regularized risk minimization using the resulting convex surrogate, and we show polynomial time convex surrogates for both submodular and supermodular loss functions.

# A TWO-STRAIN SPATIO-TEMPORAL MATHEMATICAL MODEL OF TUMOR GROWTH

Prof. Fabio Augusto Milner, STEM Education School of Mathematical and Statistical Sciences. Division of Educational Leadership and Innovation Honors Faculty, Barrett’s Honors College, Arizona State University.

**Abstract.**Cancer in most organs develops in the form of solid tumors that begin as spheroids consisting entirely of cancerous (parenchyma) cells. When the tumor reaches the size of approximately 1 mm, it needs blood vessels (vascularization) to develop in it in order to be able to grow further. A model of vascularized tumor growth with competing parenchyma cells of two dierent strains is presented, consisting of a free boundary value problem for a system of nonlinear parabolic PDEs describing the dynamics of the parenchyma cells and vascular endothelial cells (VECs), coupled with an ODE describing the dynamics of vascular density and an algebraic equation describing a variable used as proxy for local resource availability. The tumor is assumed to have radial symmetry and the mathematical domain is then taken to be a sphere with moving boundary, with the boundary moving at the unique physically determined velocity that changes local tumor volume exactly to maintain density. Some theoretical analytical properties of the model are presented, and results from several simulations are shown and biological interpretations provided, including how selection for increased proliferation or for increased angiogenesis may lead to tumors that are structurally like integrated tissues or like segregated ecological niches, as well as to hypertumors.

# Numerical Solutions of Fractional Stefan Problems

Prof. Vaughan R. Voller, Department of Civil, Environmental, and Geo- Engineering, University of Minnesota,

**Abstract.** The Stefan problem, involving the tracking of a phase change interface, provides the frame work for studying moving boundary problems in a variety of physical situations. The solution of the classical one-dimensional Stefan problem predicts that in time t the phase interface goes as s(t) ∼ t can be observed where the time exponent n write down the governing equations of the Stefan problem in terms of fractional order time (1 ≥ β > 0) and space (1 ≥ α > 0) derivatives.

# A virtual power principle for RVE-based multiscale models

Pablo Javier Blanco

HemoLab LNCC – Brasil

**Abstract:**

The overall theory is presented within a clear, logically structured multiscale framework that provides a rational justification of classical formulations and facilitates

the rigorous development of new multiscale models in systematic, well-defined steps. In addition, due to its variational basis, the format in which resulting models are presented is naturally well suited for discretization by finite element methods or any other numerical approximation. Multiscale models already published in the literature can be cast straightforwardly inside the proposed general theory including coupled multiphysics, high order strains effects, dynamics, localization of deformations at macro and micro level and material failure, among others. Several of the above applications are also discussed.