Existence and Besov regularity of the density for a class of SDEs with Volterra noise

By using a simple method based on the fractional integration by parts, we prove the existence and the Besov regularity of the density for solutions to stochastic differential equations driven by an additive Gaussian Volterra process. We assume weak regularity conditions on the drift. Several examples of Gaussian Volterra noises are discussed.     

Thermal analysis and calorimetry in the study of materials and processes for fundamental sciences and various applications in Central and Eastern Europe

We investigated the influence of B substitution for Al₂W₃O₁₂ on thermal changes of UV–Vis and Raman spectra, and colors. First, B-substituted Al₂W₃O₁₂ powder was synthesized by a solid-state reaction method. Single-phase Al_2?xB_xW₃O₁₂ powders with x = 0, 0.10 and 0.20 were successively prepared. B substitution promoted thermal changes of the UV–Vis spectra, resulting in a more pronounced color change of Al₂W₃O₁₂ in the range of 30–150 °C. Raman spectra of the Al_2?xB_xW₃O₁₂ powders with x = 0 and 0.20 indicated that the lattice vibrations of Al_2?xB_xW₃O₁₂ with x = 0.20 were larger than those of Al₂W₃O₁₂. The thermal change of the color phase (ΔE) in the range 30–150 °C of Al₂W₃O₁₂ was increased by B substitution. The color of the B-substituted Al₂W₃O₁₂ powders changed reversibly from pale white at 30 °C to light yellowish green at 150 °C.     

MTD-ADJ: A multiconformational minimal topologic difference for determining bioactive conformers using adjusted biological activities

The active conformation is part of a conformational mixture with experimental activity Yexp, and is used in QSAR studies to extract more information regarding the ligand-receptor interaction. To reflect the relative amount () of the active conformation, we adjust Yexp : Yadj = Yexp - log . We establish a quantitative structure-activity relationship (QSAR) between Yadj and 3D conformational characteristics for the acetylcholinesterase (AChE) hydrolysis rates of 25 acetic esters. The 3D-QSAR model was obtained using the adjusted multiconformational minimal steric/topologic difference (MTD-ADJ) method, optimizing the receptor map based on Yadj for each conformer. Yadj was updated during each step of the optimization process. and Yadj are based on the Boltzmann distribution calculated using AM1 (MOPAC 6.0) relative energies of the COSMIC 90 derived conformers. The MTD-ADJ results are: (i) the 3D-QSAR models obtained by this procedure have significant statistical parameters and are similar to the unadjusted (MTD-MC, using Yexp) models; (ii) the selected bioactive conformations are extended, occupy cavity vertices and, for the same structures, have the same MTD value; and (iii) the optimized conformational map of the neutral ligands obtained from the MTD-ADJ model fits well in the active site of the crystallographic structure of AChE (from Torpedo californica). We propose a neutral ligands binding site model for AchE. Our results show that MTD-ADJ, which can be implemented in any 3D-QSAR method, is capable of providing additional information regarding the active conformations, and can be used to gain further insight into the ligand-receptor models for which no structural data are available.     

Scaffold topologies. 2. Analysis of chemical databases

We have systematically enumerated graph representations of scaffold topologies for up to eight-ring molecules and four-valence atoms, thus providing coverage of the lower portion of the chemical space of small molecules (Pollock et al. J. Chem. Inf. Model., this issue). Here, we examine scaffold topology distributions for several databases: ChemNavigator and PubChem for commercially available chemicals, the Dictionary of Natural Products, a set of 2742 launched drugs, WOMBAT, a database of medicinal chemistry compounds, and two subsets of PubChem, "actives" and DSSTox comprising toxic substances. We also examined a virtual database of exhaustively enumerated small organic molecules, GDB (Fink et al. Angew. Chem., Int. Ed. 2005, 44, 1504-1508), and we contrast the scaffold topology distribution from these collections to the complete coverage of up to eight-ring molecules. For reasons related, perhaps, to synthetic accessibility and complexity, scaffolds exhibiting six rings or more are poorly represented. Among all collections examined, PubChem has the greatest scaffold topological diversity, whereas GDB is the most limited. More than 50% of all entries (13 000 000+ actual and 13 000 000+ virtual compounds) exhibit only eight distinct topologies, one of which is the nonscaffold topology that represents all treelike structures. However, most of the topologies are represented by a single or very small number of examples. Within topologies, we found that three-way scaffold connections (3-nodes) are much more frequent compared to four-way (4-node) connections. Fused rings have a slightly higher frequency in biologically oriented databases. Scaffold topologies can be the first step toward an efficient coarse-grained classification scheme of the molecules found in chemical databases.     

A Class of Integrable Flows on the Space of Symmetric Matrices

For a given skew symmetric real n × n matrix N, the bracket [X, Y] _N = XNY − YNX defines a Lie algebra structure on the space Sym(n, N) of symmetric n × n real matrices and hence a corresponding Lie-Poisson structure. The purpose of this paper is to investigate the geometry, integrability, and linearizability of the Hamiltonian system , or equivalently in Lax form, the equation on this space along with a detailed study of the Poisson geometry itself. If N has distinct eigenvalues, it is proved that this system is integrable on a generic symplectic leaf of the Lie-Poisson structure of Sym(n, N). This is established by finding another compatible Poisson structure. If N is invertible, several remarkable identifications can be implemented. First, (Sym(n, N), [·, ·]) is Lie algebra isomorphic with the symplectic Lie algebra associated to the symplectic form on given by N ⁻¹. In this case, the system is the reduction of the geodesic flow of the left invariant Frobenius metric on the underlying symplectic group Sp(n, N ⁻¹). Second, the trace of the product of matrices defines a non-invariant non-degenerate inner product on Sym(n, N) which identifies it with its dual. Therefore Sym(n, N) carries a natural Lie-Poisson structure as well as a compatible “frozen bracket” structure. The Poisson diffeomorphism from Sym(n, N) to maps our system to a Mischenko-Fomenko system, thereby providing another proof of its integrability if N is invertible with distinct eigenvalues. Third, there is a second ad-invariant inner product on Sym(n, N); using it to identify Sym(n, N) with itself and composing it with the dual of the Lie algebra isomorphism with , our system becomes a Mischenko- Fomenko system directly on Sym(n, N). If N is invertible and has distinct eigenvalues, it is shown that this geodesic flow on Sym(n, N) is linearized on the Prym subvariety of the Jacobian of the spectral curve associated to a Lax pair formulation with parameter of the system. If, on the other hand, N has nullity one and distinct eigenvalues, in spite of the fact that the system is completely integrable, it is shown that the flow does not linearize on the Jacobian of the spectral curve. Research partially supported by NSF grants CMS-0408542 and DMS-0604307. Research partially supported by the Swiss SCOPES grant IB7320-110721/1, 2005-2008, and MEdC Contract 2-CEx 06-11-22/25.07.2006. Research partially supported by the California Institute of Technology and NSF-ITR Grant ACI-0204932. Research partially supported by the Swiss NSF and the Swiss SCOPES grant IB7320-110721/1.     

Synthesis and structural characterization of amino-functionalized polysaccharides

A variety of carbohydrates, in particular polysaccharides can be subjected to chemical modification to obtain derivatives with amphiphilic properties, which enable biochemical or biological reactions at the polymer surface. In the present work, a polydisperse maltodextrin mixture of average molecular weight 3000 was coupled with 1,6-hexamethylenediamine (HMD) via reductive amination reaction. Resulting products were characterized by thermal analysis and positive nanoelectrospray quadrupole time-of-flight (Q-TOF) mass spectrometry (MS) and tandem mass spectrometry (MS/MS). Both thermal analysis and MS screening confirmed the formation of the HMD-polysaccharide coupling products. Moreover, HMD-linked polysaccharide chains containing 2 to 26 glucose building blocks were identified by nanoESI Q-TOF MS. MS/MS fragmentation using collision-induced dissociation (CID) at low ion acceleration energies provided strong evidence for HMD-maltodextrin linkage formation and the set of sequence ions diagnostic for the composition and structure of a HMD-linked chain containing 18 glucose residues.