Knots and Classical 3-Geometries

It has been conjectured by Rovelli that there is a correspondence between the space of link classes of a Riemannian 3-manifold and the space of 3-geometries (on the same manifold). An exact statement of his conjecture will be established and then verified for the case when the 3-manifold is compact, orientable and closed.Comment: 14p. type-set in AmS-TeX version 2.

Computational Aspects of Protein Functionality

The purpose of this short article is to examine certain aspects of protein functionality with relation to some key organizing ideas. This is important from a computational viewpoint in order to take account of modelling both biological systems and knowledge of these systems. We look at some of the lexical dimensions of the function and how certain constructs can be related to underlying ideas. The pervasive computational metaphor is then discussed in relation to protein multifunctionality, and the specific case of von Willebrand factor as a ‘smart’ multifunctional protein is briefly considered. Some diagrammatic techniques are then introduced to better articulate protein function

Cell biological mechanisms of activity-dependent synapse to nucleus translocation of CRTC1 in neurons.

Previous studies have revealed a critical role for CREB-regulated transcriptional coactivator (CRTC1) in regulating neuronal gene expression during learning and memory. CRTC1 localizes to synapses but undergoes activity-dependent nuclear translocation to regulate the transcription of CREB target genes. Here we investigate the long-distance retrograde transport of CRTC1 in hippocampal neurons. We show that local elevations in calcium, triggered by activation of glutamate receptors and L-type voltage-gated calcium channels, initiate active, dynein-mediated retrograde transport of CRTC1 along microtubules. We identify a nuclear localization signal within CRTC1, and characterize three conserved serine residues whose dephosphorylation is required for nuclear import. Domain analysis reveals that the amino-terminal third of CRTC1 contains all of the signals required for regulated nucleocytoplasmic trafficking. We fuse this region to Dendra2 to generate a reporter construct and perform live-cell imaging coupled with local uncaging of glutamate and photoconversion to characterize the dynamics of stimulus-induced retrograde transport and nuclear accumulation

A multiple-cut analytic center cutting plane method for semidefinite feasibility problems

10.1137/S1052623400370503SIAM Journal on Optimization1241126-114

Spectral operators of matrices

The class of matrix optimization problems (MOPs) has been recognized in recent years to be a powerful tool to model many important applications involving structured low rank matrices within and beyond the optimization community. This trend can be credited to some extent to the exciting developments in emerging fields such as compressed sensing. The Löwner operator, which generates a matrix valued function via applying a single-variable function to each of the singular values of a matrix, has played an important role for a long time in solving matrix optimization problems. However, the classical theory developed for the Löwner operator has become inadequate in these recent applications. The main objective of this paper is to provide necessary theoretical foundations from the perspectives of designing efficient numerical methods for solving MOPs. We achieve this goal by introducing and conducting a thorough study on a new class of matrix valued functions, coined as spectral operators of matrices. Several fundamental properties of spectral operators, including the well-definedness, continuity, directional differentiability and Fréchet-differentiability are systematically studied. © 2017 Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society

Binding of Basic Dyes by the Algae, Chara aspera

Non-living biomass of the algae Chara aspera is capable of binding two basic dyes, methylene blue and basic blue 3, from aqueous solution. Factors such as dye concentration, contact time, sorbent dosage and pH of solution were studied. Maximum sorption capacities of the algae for methylene blue and basic blue 3 are 139.4 and 17.8 mg/g, respectively, as determined from the Langmuir isothenns