Constrained minimax approximation and optimal preconditioned for Toeplitz matrices

A good preconditioner is extremely important in order for the conjugate gradients method to converge quickly. In the case of Toeplitz matrices, a number of recent studies were made to relate approximation of functions to good preconditioners. In this paper, we present a new result relating the quality of the Toeplitz preconditionerC for the Toeplitz matrixT to the Chebyshev norm (f– g)/f, wheref and g are the generating functions forT andC, respectively. In particular, the construction of band-Toeplitz preconditioners becomes a linear minimax approximation problem. The case whenf has zeros (but is nonnegative) is especially interesting and the corresponding approximation problem becomes constrained. We show how the Remez algorithm can be modified to handle the constraints. Numerical experiments confirming the theoretical results are presented.     

Gaucher disease-associated glucocerebrosidases show mutation-dependent chemical chaperoning profiles

Gaucher disease is a lysosomal storage disorder caused by deficient glucocerebrosidase activity. We have previously shown that the cellular activity of the most common Gaucher disease-associated glucocerebrosidase variant, N370S, is increased when patient-derived cells are cultured with the chemical chaperone N-nonyl-deoxynojirimycin. Chemical chaperones stabilize proteins against misfolding, enabling their trafficking from the endoplasmic reticulum. Herein, the generality of this therapeutic strategy is evaluated with other glucocerebrosidase variants and with additional candidate chemical chaperones. Improved chemical chaperones are identified for N370S glucocerebrosidase. Moreover, we demonstrate that G202R, a glucocerebrosidase variant that is known to be retained in the endoplasmic reticulum, is also amenable to chemical chaperoning. The L444P variant is not chaperoned by any of the active site-directed molecules tested, likely because this mutation destabilizes a domain distinct from the catalytic domain.     

Supramolecular Metal Complex with Ferrocene-conjugated Macrocyclic Triaza Crown Ether as Ligand and Its Electrochemical Property

LigandscontainingelectrochemicallyresponsivecentrearegoodsubjectsforthestUdyofintfamolecularandhost-guestillteraction.Forthisreason,tYemendousamoulltsofsuchligandsandtheircomplexeshavebeensynthesized.'-'AnobservationfromthestudiesofthesecomPlexesisthattheguestionhasapermrbationonthehostcelltre.2'7-9Forexample,itwasdocumelltedthatintroductionofCo(II)ionontoN-ferrocenylmethyl-l,4,7-triazacyclononane(fcmtacn)causesapositiveshiftintheredoxpotentialofferrocenylgroupfromthatofferrocenegroupinfree…