A mathematical model of aging-related and cortisol induced hippocampal dysfunction

Background  

The hippocampus is essential for declarative memory synthesis and is a core pathological substrate for Alzheimer's disease (AD), the most common aging-related dementing disease. Acute increases in plasma cortisol are associated with transient hippocampal inhibition and retrograde amnesia, while chronic cortisol elevation is associated with hippocampal atrophy. Thus, cortisol levels could be monitored and managed in older people, to decrease their risk of AD type hippocampal dysfunction. We generated an in silicomodel of the chronic effects of elevated plasma cortisol on hippocampal activity and atrophy, using the systems biology mark-up language (SBML). We further challenged the model with biologically based interventions to ascertain if cortisol associated hippocampal dysfunction could be abrogated.     

Polynomial solutions to Dirichlet problems

The Dirichlet problem

is considered where the functions and are polynomials. The authors study the problem of determining which functions will admit polynomial solutions for any polynomial . When one additionally requires the classical condition , this forces , and a complete classification is obtained. Some necessary conditions are obtained for the case 2$">.

     

Concise total synthesis of phidianidine A and B

The shortest total synthesis of cytotoxic indole alkaloids phidianidine A and B is described. Rapid assembly of the 1,2,4-oxadiazole core from a novel N-hydroxyguanidine and the corresponding indole-3-acetic acid chloride led to formal syntheses of phidianidine A and B in only three steps from known compounds. Deprotection under standard conditions provided the trifluoroacetate salts of phidianidine A and B in quantitative yield.     

Nilpotent Jacobians in dimension three

In this paper we completely classify all polynomial maps of the form H=(u(x,y),v(x,y,z),h(u(x,y),v(x,y,z))) with JH nilpotent.     

The magnetic phase diagram of La2−x Sr x CuQ4+y observed via111In PAC

We report perturbed angular correlation studies of¹¹¹In diffused into La_2−x Sr _x CuO_4+y . We determine the Néel temperature, T_N, as a function of x for y ≈ 0 and provide an empirical calibration of the charge defect concentration via the PAC linewidth.     

Structural evidence that alkoxy substituents adopt electronically preferred pseudoaxial orientations in six-membered ring dioxocarbenium ions

Nucleophilic substitution reactions of monosubstituted tetrahydropyran acetals give opposite selectivities when a remote alkyl or alkoxy substituent is present at C-4. Coupled with earlier computational reports on the intermediates of glycosylation reactions, these results are consistent with the preference for the oxocarbenium ion intermediate derived from alkoxy-substituted tetrahydropyran acetals to occupy a pseudoaxial conformation. Theoretical, spectroscopic, and X-ray crystallographic evidence of this conformational preference in an analogous and more stable dioxocarbenium ion are provided. This contrasteric preference for an axial orientation of an alkoxy substituent likely derives from the electronically favored pseudoaxial orientation of remote electronegative substituents in neutral six-membered rings possessing electron-deficient carbon atoms.     

A duality theorem for an overdetermined eigenvalue problem

We prove an equivalent integral formulation of an eigenvalue problem for the Laplacian operator, with overdetermined boundary conditions. A special case of this problem, that with homogeneous Neumann condition, is known in the literature as Schiffer's problem, due to the still open conjecture, attributed to him, that the only domains possessing nontrivial solutions aren-balls. It is hoped that this integral formulation may provide a new tool with which to analyse Schiffer's conjecture.Research sponsored by NSERC of Canada via a post-doctoral fellowship.