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The protein ubiquitin is an important post-translational modifier that regulates a wide variety of biological processes. In cells, ubiquitin is apportioned among distinct pools, which include a variety of free and conjugated species. Although maintenance of a dynamic and complex equilibrium among ubiquitin pools is crucial for cell survival, the tools… (More)

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 pathogenesis of most neurodegenerative diseases, including transmissible diseases like prion encephalopathy, inherited disorders like Huntington disease, and sporadic diseases like Alzheimer and Parkinson diseases, is intimately linked to the formation of fibrillar protein aggregates. It is becoming increasingly appreciated that prion-like intercellular… (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)

- RODRIGO TREVIÑO
- 2013

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)

- Rodrigo Treviño
- 2014

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)

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)

- RODRIGO TREVIÑO
- 2012

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)

- RODRIGO TREVIÑO
- 2011

This short note is based on a talk I gave at the student dynamical systems seminar about using your computer to figure out what the Lyapunov exponents of a matrix-valued cocycle are. I will focus only on discrete cocycles, that is, cocycles over Z-actions. It is based on [ER85, §V.C], which also treats the continuous-time case. I tried to make it as… (More)

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