THE PHOTOREACTIONS OF 8-METHOXYPSORALEN WITH TRYPTOPHAN AND LENS PROTEINS*

Abstract— We have previously demonstrated that 8-methoxypsoralen (8-MOP) can be found in the lenses of rats injected (i.p.) with this drug, and that its presence can lead to a photosensitized enhancement of lenticular fluorescence. The cutaneous photosensitizing properties of psoralens are thought to be mediated via their excited triplet states, resulting in photoaddition cyclobutane products between pyri-midine bases and 8-MOP. We have now investigated the possibility that similar types of photoadducts could be generated between 8-MOP and the aromatic amino acid residues in lens proteins. Our experiments involved in vitro irradiation (at 360 nm) of aqueous solutions of 0.1 mM 8-MOP plus purified alpha, beta, or gamma crystallins from calf or normal human (under 20 years of age) lenses. UV absorption and fluorescence emission spectra were measured before and after radiation, and aliquots from all experiments were frozen and kept in the dark for subsequent phosphorescence and EPR spectroscopy. Similar experiments were performed with irradiated aqueous solutions of tryptophan or thymine plus 8-MOP. All controls consisted of solutions kept in the dark. NMR spectra demonstrated that the hydrogen atoms at the 3,4 and 4',5' positions of the 8-MOP molecule were lost following irradiation, suggesting that these two sites were involved in the photoproduct formed between tryptophan and 8-MOP. These studies strongly suggest that 8-MOP is capable of forming photoaddition products with tryptophan and with lens proteins as well as DNA in vivo, resulting in its permanent retention within the ocular lens.     

Tight focusing of spatially variant vector optical fields with elliptical symmetry of linear polarization

We study the tight-focusing properties of spatially variant vector optical fields with elliptical symmetry of linear polarization. We found the eccentricity of the incident polarized light to be an important parameter providing an additional degree of freedom assisting in controlling the field properties at the focus and allowing matching of the field distribution at the focus to the specific application. Applications of these space-variant polarized beams vary from lithography and optical storage to particle beam trapping and material processing.     

Functional neural network analysis in frontotemporal dementia and Alzheimer's disease using EEG and graph theory

Background  

Although a large body of knowledge about both brain structure and function has been gathered over the last decades, we still have a poor understanding of their exact relationship. Graph theory provides a method to study the relation between network structure and function, and its application to neuroscientific data is an emerging research field. We investigated topological changes in large-scale functional brain networks in patients with Alzheimer's disease (AD) and frontotemporal lobar degeneration (FTLD) by means of graph theoretical analysis of resting-state EEG recordings. EEGs of 20 patients with mild to moderate AD, 15 FTLD patients, and 23 non-demented individuals were recorded in an eyes-closed resting-state. The synchronization likelihood (SL), a measure of functional connectivity, was calculated for each sensor pair in 0.5–4 Hz, 4–8 Hz, 8–10 Hz, 10–13 Hz, 13–30 Hz and 30–45 Hz frequency bands. The resulting connectivity matrices were converted to unweighted graphs, whose structure was characterized with several measures: mean clustering coefficient (local connectivity), characteristic path length (global connectivity) and degree correlation (network 'assortativity'). All results were normalized for network size and compared with random control networks.     

Slow-fast hamiltonian dynamics near a ghost separatix loop

We study the behavior of a slow-fast (singularly perturbed) Hamiltonian system with two degrees of freedom, losing one degree of freedom at the singular limit = 0, near its ghost separatrix loop, i.e., a homoclinic orbit to a saddle equilibrium of the slow (one degree of freedom) system. We show that, for small > 0, the system has an equilibrium of the saddle-center type and prove, using the method of Delatte, that the Moser normal form exists in an O()-neighborhood of the equilibrium. Then we show that one-dimensional separatrices of the equilibria are generically split with exponentially small splitting. Also, we demonstrate that out of some exponentially thin neighborhood of the ghost separatrix loop in the level of a Hamiltonian containing a saddle-center, the major part of the phase space is foliated into Diophantine invariant tori.Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 8 , Suzdal Conference—2, 2003.This revised version was published online in April 2005 with a corrected cover date.     

Theories of mathematics education: Is plurality a problem?

In this developed contribution to the Research Forum, held at the recent meeting of the International Group for the Psychology of Mathematics Education, the theme being “Theories of Mathematics Education”, I focus on the call by the organisers: ‘the time seems ripe for our community to take stock of the multiple and widely diverging mathematical theories’. I examine empirically the diversity of theories and I draw on the sociological theories of Basil Bernstein to relate the developments to the nature of intellectual communities and their productions. In particular, I suggest that the multiplicity and divergence are not surprising nor are they necessarily damaging to the field. I end by discussing concerns about accountability in relation to research in education.     

Contact cuts

We describe a contact analog of the symplectic cut construction [L]. As an application we show that the group of contactomorphisms for certain overtwisted contact structures on lens spaces contains countably many non-conjugate two tori. Supported by the NSF grant DMS-980305.     

Harmonic Vibrations of Shells with Cutouts Under Kinematic Conditions at Their Periphery

Problems on harmonic vibrations of shells with openings are considered for the case where displacements and angles of turn are specified at their periphery. A technique for determination of the natural frequencies and modes of vibrations is stated. The technique replaces the unknown peripheral forces and moments by a system of local statically equivalent loads. The intensity of these loads is found from the boundary conditions at the opening periphery. The solutions of the equations of shell theory for local loads are constructed by expanding the sought-for quantities into series in terms of the natural modes of the shell without openings. The performance of the approach developed is illustrated by calculating the natural frequencies and modes of shallow shells with a rectangular planform and various Gaussian curvatures