Learn More
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 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)
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)
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)
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)
  • 1