Rodrigo Treviño

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The aim of this paper is to introduce a method for computing rigorous lower bounds for topological entropy. The topological entropy of a dynamical system measures the number of trajectories that separate in finite time and quantifies the complexity of the system. Our method relies on extending existing computational Conley index techniques for constructing(More)
The NH2-terminal sequence of rhodanese influences many of its properties, ranging from mitochondrial import to folding. Rhodanese truncated by >9 residues is degraded in Escherichia coli. Mutant enzymes with lesser truncations are recoverable and active, but they show altered active site reactivities (Trevino, R. J., Tsalkova, T., Dramer, G., Hardesty, B.,(More)
We present new methods of automating the construction of index pairs, essential ingredients of discrete Conley index theory. These new algorithms are further steps in the direction of automating computer-assisted proofs of semiconjugacies from a map on a manifold to a subshift of finite type. We apply these new algorithms to the standard map at different(More)
We prove some ergodic theorems for flat surfaces of finite area. The first result concerns such surfaces whose Teichmüller orbits are recurrent to a compact set of SL(2, R)/SL(S, α), where SL(S, α) is the Veech group of the surface. In this setting, this means that the translation flow on a flat surface can be renormalized through its Veech group. This(More)
Rhodanese mutants containing sequential NH2-terminal deletions were constructed to test the distinct contributions of this region of the protein to expression, folding, and stability. The results indicate that the first 11 residues are nonessential for folding to the active conformation, but they are necessary for attaining an active, stable structure when(More)
In the first part, we prove the non-uniform hyperbolicity of the Kontsevich-Zorich cocycle for a measure supported on abelian differentials which come from non-orientable quadratic differentials. The proof uses Forni's criterion for non-uniform hyperbolicity of the cocycle for SL(2, R)-invariant measures. We apply these results to the study of deviations in(More)
Let (S, α) be a flat surface. By that I mean that S is a Riemann surface and α a 1-form on S which is holomorphic. That this defines a flat surface is a standard fact; one can consult Zorich's excellent introduction to the area to see how this is done [7]. The form α defines two dynamical systems on S, called the horizontal and vertical flows. One obtains(More)
We prove the non-uniform hyperbolicity of the Kontsevich-Zorich cocycle for a measure supported on abelian differentials which come from non-orientable quadratic differentials through a standard orienting, double cover construction. The proof uses Forni's criterion [For11] for non-uniform hyper-bolicity of the cocycle for SL(2, R)-invariant measures. We(More)
We describe a cDNA from Chinese hamster ovary cells which encodes a protein 91 and 96% identical to bovine and rat mitochondrial rhodaneses, respectively. Recombinant protein was expressed from the cDNA in Escherichia coli, purified to homogeneity, and found to have kinetic properties nearly indistinguishable from those of the bovine enzyme, the only cloned(More)