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Physical Sciences and Mathematics Commons™

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Selected Works

Mathematics

2015

Eduardo Cabral Balreira

Articles 1 - 7 of 7

Full-Text Articles in Physical Sciences and Mathematics

Foliations And Global Inversion, Eduardo C. Balreira Aug 2015

Foliations And Global Inversion, Eduardo C. Balreira

Eduardo Cabral Balreira

We consider topological conditions under which a locally invertible map admits a global inverse. Our main theorem states that a local diffeomorphism f : M → Rn is bijective if and only if Hn−1(M) = 0 and the pre-image of every affine hyperplane is non-empty and acyclic. The proof is based on some geometric constructions involving foliations and tools from intersection theory. This topological result generalizes in finite dimensions the classical analytic theorem of Hadamard-Plastock, including its recent improvement by Nollet-Xavier. The main theorem also relates to a conjecture of the aforementioned authors, involving the well known Jacobian Conjecture in …

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Incompressibility And Global Inversion, Eduardo C. Balreira Jul 2015

Incompressibility And Global Inversion, Eduardo C. Balreira

Eduardo Cabral Balreira

Given a local diffeomorphism f : ℝn → ℝn, we consider certain in- compressibility conditions on the parallelepiped D f (x) ([0, 1]n) which imply that the pre-image of an affine subspace is non-empty and has trivial homotopy groups. These conditions are then used to establish criteria for f to be globally invertible, generalizing in all dimensions the previous results of M. Sabatini.

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Global Dynamics Of Triangular Maps, Eduardo C. Balreira, Saber Elaydi, Rafael Luis Jul 2015

Global Dynamics Of Triangular Maps, Eduardo C. Balreira, Saber Elaydi, Rafael Luis

Eduardo Cabral Balreira

We consider continuous triangular maps on IN, where I is a compact interval in the Euclidean space R. We show, under some conditions, that the orbit of every point in a triangular map converges to a fixed point if and only if there is no periodic orbit of prime period two. As a consequence we obtain a result on global stability, namely, if there are no periodic orbits of prime period 2 and the triangular map has a unique fixed point, then the fixed point is globally asymptotically stable. We also discuss examples and applications of our results to competition …

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Local Stability Implies Global Stability For The Planar Ricker Competition Model, Eduardo C. Balreira, Saber Elaydi, Rafael Luis Jul 2015

Local Stability Implies Global Stability For The Planar Ricker Competition Model, Eduardo C. Balreira, Saber Elaydi, Rafael Luis

Eduardo Cabral Balreira

Under certain analytic and geometric assumptions we show that local stability of the coexistence (positive) fixed point of the planar Ricker competition model implies global stability with respect to the interior of the positive quadrant. This result is a confluence of ideas from Dynamical Systems, Geometry, and Topology that provides a framework to the study of global stability for other planar competition models.

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Mathematical Classification Of Tight Junction Protein Images, Katherine Ogawa, Caitlin Troyer, Robert Doss, Farzan Aminian, Eduardo Balreira, Jonathan King Jul 2015

Mathematical Classification Of Tight Junction Protein Images, Katherine Ogawa, Caitlin Troyer, Robert Doss, Farzan Aminian, Eduardo Balreira, Jonathan King

Eduardo Cabral Balreira

We present the rationale for the development of mathematical features used for classification of images stained for selected tight junction proteins. The project examined localization of zonula occludens-1, claudin-1 and F-actin in a model epithelium, Madin-Darby canine kidney II cells. Cytochalasin D exposure was used to perturb junctional localization by actin cytoskeleton disruption. Mathematical features were extracted from images to reliably reveal characteristic information of the pattern of protein localization. Features, such as neighborhood standard deviation, gradient of pixel intensity measurement and conditional probability, provided meaningful information to classify complex image sets. The newly developed mathematical features were used as …

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An Oracle Method To Predict Nfl Games, Eduardo C. Balreira, Brian K. Miceli, Thomas Tegtmeyer Jul 2015

An Oracle Method To Predict Nfl Games, Eduardo C. Balreira, Brian K. Miceli, Thomas Tegtmeyer

Eduardo Cabral Balreira

Multiple models are discussed for ranking teams in a league and introduce a new model called the Oracle method. This is a Markovian method that can be customized to incorporate multiple team traits into its ranking. Using a foresight prediction of NFL game outcomes for the 2002–2013 seasons, it is shown that the Oracle method correctly picked 64.1% of the games under consideration, which is higher than any of the methods compared, including ESPN Power Rankings, Massey, Colley, and PageRank.

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A Generalization Of The Fujisawa–Kuh Global Inversion Theorem, Marius Radulescu, Sorin Radulescu, Eduardo C. Balreira Jul 2015

A Generalization Of The Fujisawa–Kuh Global Inversion Theorem, Marius Radulescu, Sorin Radulescu, Eduardo C. Balreira

Eduardo Cabral Balreira

We discuss the problem of global invertibility of nonlinear maps defined on the finitedimensional Euclidean space via differential tests. We provide a generalization of theFujisawa-Kuh global inversion theorem and introduce a generalized ratio conditionwhich detects when the pre-image of a certain class of linear manifolds is non-emptyand connected. In particular, we provide conditions that also detect global injectivity.

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