Modulated Chaos as a Source of Images for Numbers

Classificação de imagens de Markus-Lyapounof

Fragments Intimes d'un Savant Oublié

Explicação do "ser matemático não arbitrário" Posições sobre a história dos povos semitas. Atitude perante a história da arte. Poema de amor à Esposa

Bethe lattice solution of a model of SAW's with up to 3 monomers per site and no restriction

In the multiple monomers per site (MMS) model, polymeric chains are represented by walks on a lattice which may visit each site up to K times. We have solved the unrestricted version of this model, where immediate reversals of the walks are allowed (RA) for K = 3 on a Bethe lattice with arbitrary coordination number in the grand-canonical formalism. We found transitions between a non-polymerized and two polymerized phases, which may be continuous or discontinuous. In the canonical situation, the transitions between the extended and the collapsed polymeric phases are always continuous. The transition line is partly composed by tricritical points and partially by critical endpoints, both lines meeting at a multicritical point. In the subspace of the parameter space where the model is related to SASAW's (self-attracting self-avoiding walks), the collapse transition is tricritical. We discuss the relation of our results with simulations and previous Bethe and Husimi lattice calculations for the MMS model found in the literature.Comment: 25 pages, 9 figure

Structural shifts of aldehyde dehydrogenase enzymes were instrumental for the early evolution of retinoiddependent axial patterning in metazoans

Aldehyde dehydrogenases (ALDHs) catabolize toxic aldehydes and process the vitamin A-derived retinaldehyde into retinoic acid (RA), a small diffusible molecule and a pivotal chordate morphogen. In this study, we combine phylogenetic, structural, genomic, and developmental gene expression analyses to examine the evolutionary origins of ALDH substrate preference. Structural modeling reveals that processing of small aldehydes, such as acetaldehyde, by ALDH2, versus large aldehydes, including retinaldehyde, by ALDH1A is associated with small versus large substrate entry channels (SECs), respectively. Moreover, we show that metazoan ALDH1s and ALDH2s are members of a single ALDH1/2 clade and that during evolution, eukaryote ALDH1/2s often switched between large and small SECs after gene duplication, transforming constricted channels into wide opened ones and vice versa. Ancestral sequence reconstructions suggest that during the evolutionary emergence of RA signaling, the ancestral, narrow-channeled metazoan ALDH1/2 gave rise to large ALDH1 channels capable of accommodating bulky aldehydes, such as retinaldehyde, supporting the view that retinoid-dependent signaling arose from ancestral cellular detoxification mechanisms. Our analyses also indicate that, on a more restricted evolutionary scale, ALDH1 duplicates from invertebrate chordates (amphioxus and ascidian tunicates) underwent switches to smaller and narrower SECs. When combined with alterations in gene expression, these switches led to neofunctionalization from ALDH1-like roles in embryonic patterning to systemic, ALDH2-like roles, suggesting functional shifts from signaling to detoxification

Glycation potentiates α-synuclein-associated neurodegeneration in synucleinopathies

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