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Parkinson's disease (PD) is a common progressive neurodegenerative disorder caused by the loss of dopaminergic neurons in the substantia nigra. Although mutations in alpha-synuclein have been identified in autosomal dominant PD, the mechanism by which dopaminergic neural cell death occurs remains unknown. Proteins encoded by two other genes in which(More)
We have recently identified a protein we called synphilin-1, which interacts in vivo with alpha-synuclein. Mutations in alpha-synuclein cause familial Parkinson's disease (PD). Alpha-synuclein protein is present in the pathologic lesions of familial and sporadic PD, and diffuse Lewy body disease, indicating an important pathogenic role for alpha-synuclein.(More)
Phase separation processes in compound materials can produce intriguing and complicated patterns. Yet, characterizing the geometry of these patterns quantitatively can be quite challenging. In this paper we use computational algebraic topology to obtain such a characterization. Our method is illustrated for the complex microstructures observed during(More)
Homology has long been accepted as an important computable tool for quantifying complex structures. In many applications these structures arise as nodal domains of real-valued functions and are therefore amenable only to a numerical study, based on suitable discretizations. Such an approach immediately raises the question of how accurate the resulting(More)
We present a new variational approach for proving exponentially slow motion in singularly-perturbed partial differential equations in one space dimension, which builds on the energy approach due to Bronsard and Kohn (Comm. As well as covering the known applications, this approach is also capable of proving slow motion in equations whose corresponding(More)
We present an algorithm for computing the homology of inclusion maps which is based on the idea of coreductions and leads to significant speed improvements over current algorithms. It is shown that this algorithm can be extended to compute both persistent homology and an extension of the persistence concept to two-sided filtrations. In addition to(More)
This paper gives theoretical results on spinodal decomposition for the Cahn-Hillard equation. We prove a mechanism which explains why most solutions for the Cahn-Hilliard equation which start near a homogeneous equilibrium within the spinodal interval exhibit phase separation with a characteristic wavelength when exiting a ball of radius R. Namely, most(More)
Cytosine arabinoside (ara-C) is one of the most active compounds in the treatment of acute leukemias. In the majority of current protocols ara-C is combined with other cytotoxic agents in an attempt to increase antileukemic activity. The present study investigated the impact of etoposide, teniposide, amsacrine, mitoxantrone, anthracyclines, and asparaginase(More)