A Grüss Type Discrete Inequality in Inner Product Spaces and Applications

A Grüss type inequality in inner product spaces and applications for the discrete Fourier transform, Mellin transform of sequences, polynomials with coefficients in Hilbert spaces, and Lipschitzian vector valued mappings are given.     

Pharmacophore-based screening and drug repurposing exemplified on glycogen synthase kinase-3 inhibitors

The current study was conducted to elaborate a novel pharmacophore model to accurately map selective glycogen synthase kinase-3 (GSK-3) inhibitors, and perform virtual screening and drug repurposing. Pharmacophore modeling was developed using PHASE on a data set of 203 maleimides. Two benchmarking validation data sets with focus on selectivity were assembled using ChEMBL and PubChem GSK-3 confirmatory assays. A drug repurposing experiment linking pharmacophore matching with drug information originating from multiple data sources was performed. A five-point pharmacophore model was built consisting of a hydrogen bond acceptor (A), hydrogen bond donor (D), hydrophobic (H), and two rings (RR). An atom-based 3D quantitative structure–activity relationship (QSAR) model showed good correlative and satisfactory predictive abilities (training set \({R}^{2}= 0.904\); test set: \({Q}^{2}= 0.676\); whole data set: stability \(s = 0.803\)). Virtual screening experiments revealed that selective GSK-3 inhibitors are ranked preferentially by Hypo-1, but fail to retrieve nonselective compounds. The pharmacophore and 3D QSAR models can provide assistance to design novel, potential GSK-3 inhibitors with high potency and selectivity pattern, with potential application for the treatment of GSK-3-driven diseases. A class of purine nucleoside antileukemic drugs was identified as potential inhibitor of GSK-3, suggesting the reassessment of the target range of these drugs.     

N = 2 Supersymmetric Unconstrained Matrix GNLS Hierarchies are Consistent

We develop a pseudo-differential approach to the N = 2 supersymmetric unconstrained matrix (k|n, m)-generalized nonlinear Schrödinger hierarchies and prove consistency of the corresponding Lax-pair representation (nlin.SI/0201026). Furthermore, we establish their equivalence to the integrable hierarchies derived in the super-algebraic approach of the homogeneously-graded loop superalgebra ${sl(2k{+}n\vert 2k{+}m)\otimes C[{\lambda},{\lambda}^{-1}]}$ (nlin.SI/0206037). We introduce an unconventional definition of N = 2 supersymmetric strictly pseudo-differential operators so as to close their algebra among themselves.     

Local enrichment and its nonlocal consequences for victim-exploiter metapopulations

The stabilizing effects of local enrichment are revisited. Diffusively coupled host-parasitoid and predator-prey metapopulations are shown to admit a stable fixed point, limit cycle or stable torus with a rich bifurcation structure. A linear toy model that yields many of the basic qualitative features of this system is presented. The further nonlinear complications are analyzed in the framework of the marginally stable Lotka-Volterra model, and the continuous time analog of the unstable, host-parasitoid Nicholson-Bailey model. The dependence of the results on the migration rate and level of spatial variations is examined, and the possibility of “nonlocal” effect of enrichment, where local enrichment induces stable oscillations at a distance, is studied. A simple method for basic estimation of the relative importance of this effect in experimental systems is presented and exemplified.     

Branched polymeric labels used as drag-tags in free-solution electrophoresis of ssDNA

In the framework of the classical blob theory of end-labeled free-solution electrophoresis of ssDNA, and based on recent experimental data with linear and branched polymeric labels (or drag-tags), the present study puts forward design principles for the optimal type of branching that would give, for a given total number of monomers, the highest effective frictional drag for ssDNA sequencing purposes. The hydrodynamic radii of the linear and branched labels are calculated using standard models like the freely jointed chain model and the Kratky-Porod worm-like chain model. Based on comparisons of the theory with the experimental data, we propose that the design of new branched labels should use either side chains whose length is comparable to the distance between the branching points or two long branches located near the ends of the molecule's backbone.     

The N = 2 Supersymmetric Unconstrained Matrix GNLS Hierarchies

The generalization of the N = 2 supersymmetric chiral matrix (k | n,m)-GNLS hierarchy (Lett. Math. Phys. 45 (1998) 63, solv-int/9711009) to the case when matrix entries are bosonic and fermionic unconstrained N = 2 superfields is proposed. This is done by exhibiting the corresponding matrix Lax-pair representation in terms of N = 2 unconstrained superfields. It is demonstrated that when matrix entries are chiral and antichiral N = 2 superfields, it reproduces the N = 2 chiral matrix (k | n,m)-GNLS hierarchy, while in the scalar case, k = 1, it is equivalent to the N = 2 supersymmetric multicomponent hierarchy (J. Phys. A 29 (1996) 1281, hep-th/9510185). The simplest example—the N = 2 unconstrained (1 | 1,0)-GNLS hierarchy—and its reduction to the N = 2 supersymmetric = 1 KdV hierarchy are discussed in more detail, and its rich symmetry structure is uncovered.     

Multiple-spin analysis of chemical-shift-selective (13C, 13C) transfer in uniformly labeled biomolecules

Chemical-shift-selective (13C, 13C) polarization transfer is analyzed in uniformly labeled biomolecules. It is shown that the spin system dynamics remain sensitive to the distance of interest and can be well reproduced within a quantum-mechanical multiple-spin analysis. These results lead to a general approach on how to describe chemical-shift-selective transfer in uniformly labeled systems. As demonstrated in the case of ubiquitin, this methodology can be used to detect long-range distance constraints in uniformly labeled proteins.     

Invariant Theory for Non-Associative Real Two-Dimensional Algebras and Its Applications

The set ${\mathcal A}$ of all non-associative algebra structures on a fixed 2-dimensional real vector space $A$ is naturally a ${\mbox{\rm GL}}(2,{\mbox{\bf R}})$-module. We compute the ring of ${\mbox{\rm SL}}(2,{\mbox{\bf R}})$-invariants in the ring of polynomial functions, ${\mathcal P}$, on ${\mathcal A}$. We use invariant theory to compute the exact number of nonzero idempotents of an arbitrary 2-dimensional real division algebra. We show that the absolute invariants (i.e.,the ${\mbox{\rm GL}}(2, {\mbox{\bf R}})$-invariants in the field of fractions of ${\mathcal P}$) distinguish the isomorphism classes of 2-dimensional non-associative real division algebras. We show that the (open) set $\Omega^+\subset{\mathcal A}$ of all division algebra structures on $A$ has four connected components. A similar result is proved for another class of regular 2-dimensional real algebras (the principal isotopes of the algebra ${\mbox{\bf R}}\oplus{\mbox{\bf R}}$).