Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model

We consider Hermitian and symmetric random band matrices H in d ≥ 1 dimensions. The matrix elements H _xy , indexed by \({x,y \in \Lambda \subset \mathbb{Z}^d}\), are independent, uniformly distributed random variables if \({\lvert{x-y}\rvert}\) is less than the band width W, and zero otherwise. We prove that the time evolution of a quantum particle subject to the Hamiltonian H is diffusive on time scales \({t\ll W^{d/3}}\). We also show that the localization length of the eigenvectors of H is larger than a factor W ^d/6 times the band width. All results are uniform in the size \({\lvert{\Lambda}\rvert}\) of the matrix.     

Eigenvalue confinement and spectral gap for random simplicial complexes

We consider the adjacency operator of the Linial‐Meshulam model for random simplicial complexes on n vertices, where each d‐cell is added independently with probability p to the complete ‐skeleton. Under the assumption , we prove that the spectral gap between the smallest eigenvalues and the remaining eigenvalues is with high probability. This estimate follows from a more general result on eigenvalue confinement. In addition, we prove that the global distribution of the eigenvalues is asymptotically given by the semicircle law. The main ingredient of the proof is a Füredi‐Komlós‐type argument for random simplicial complexes, which may be regarded as sparse random matrix models with dependent entries. © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 51, 506–537, 2017     

Synthesis and biomimetic mineralization of l‐proline substituted polyphosphazenes as bulk and nanofiber

This work presents the synthesis of polyphosphazenes bearing L ‐proline methyl ester (ProOMe) and 4‐hydroxy‐l ‐proline methyl ester (HypOMe), aiming for new bioactive polymers for bone repair. The polymers were characterized by ¹H and ³¹P NMR, FTIR, DSC, and TGA. Electrospun fibers were prepared using poly[bis(l ‐proline methyl ester)phosphazene] (PProP), and their potential for biomimetic mineralization, as well as the bulk material, were tested in simulated body fluid (1×SBF). Samples were analyzed between 24 h and 3 weeks of incubation using SEM/EDS and FTIR. After 24 h, spherical and flower‐like shapes of calcium phosphates (CaP) were crystallized on the bulk samples. The nanofibers presented spherical CaP crystals attached to them after 48 h of incubation. The Ca/P molar ratio of the crystals varied from 1.5 to 1.6. According to this study, PProP presents bioactivity in vitro, and its fibers offer sites for CaP nucleation like the collagen fibers in bone. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013 , 51, 1318–1327     

Comparison of structure fingerprint and molecular interaction field based methods in explaining biological similarity of small molecules in cell-based screens

In this work, we calculated the pair wise chemical similarity for a subset of small molecules screened against the NCI60 cancer cell line panel. Four different compound similarity calculation methods were used: Brutus, GRIND, Daylight and UNITY. The chemical similarity scores of each method were related to the biological similarity data set. The same was done also for combinations of methods. In the end, we had an estimate of biological similarity for a given chemical similarity score or combinations thereof. The data from above was used to identify chemical similarity ranges where combining two or more methods (data fusion) led to synergy. The results were also applied in ligand-based virtual screening using the DUD data set. In respect to their ability to enrich biologically similar compound pairs, the ranking of the four methods in descending performance is UNITY, Daylight, Brutus and GRIND. Combining methods resulted always in positive synergy within a restricted range of chemical similarity scores. We observed no negative synergy. We also noted that combining three or four methods had only limited added advantage compared to combining just two. In the virtual screening, using the estimated biological similarity for ranking compounds produced more consistent results than using the methods in isolation.     

Origin of the failure of classical nucleation theory: incorrect description of the smallest clusters

We carry out molecular Monte Carlo simulations of clusters in an imperfect vapor. We show that down to very small cluster sizes, classical nucleation theory built on the liquid drop model can be used very accurately to describe the work required to add a monomer to the cluster. However, the error made in modeling the smallest of clusters as liquid drops results in an erroneous absolute value for the cluster work of formation throughout the size range. We calculate factors needed to correct the cluster formation work given by the liquid drop model. The corrected work of formation results in nucleation rates in good agreement with recent nucleation experiments on argon and water.     

Improving the mechanical properties of CNF films by NMMO partial dissolution with hot calender activation

Reinforcing of cellulose nanofibril (CNF) films by partial dissolution with N-methylmorpholine-N-oxide (NMMO) was investigated. The method investigated is composed of impregnation of CNF film with liquid solution of NMMO followed by dry heat activation. The heat activation of the impregnated film was carried out using a heated calendering nip, which enabled simultaneous heating and compression. The partial dissolution of cellulose by NMMO caused a significant increase in the transparency of CNF film due to the decrease of film porosity and increased surface smoothness. The dry strength of the reinforced film was increased from 122 up to 195 MPa. Furthermore, the wet strength of the reinforced film was up to 70% greater than the dry strength of pure CNF film. The changes in the fibrillar structure were investigated with topographical imaging (SEM and AFM) and spectroscopically using NMR and FTIR. No significant changes in the fibril structure or cellulose morphology were observed. Moreover, the treated film resisted significant water pressure, highlighting CNF film’s permanent water resistance. The partial dissolution process with NMMO was also capable of reinforcing a CNF composite film with macro scale structural elements (lyocell short-cut fibres). The strategy investigated is a robust and fast method to improve the mechanical properties of fibrillary cellulose films, allowing them utilization in applications where improved water resistance and fully cellulosic character are required properties.     

Local Semicircle Law for Random Regular Graphs

We consider random d‐regular graphs on N vertices, with degree d at least (log N)⁴. We prove that the Green's function of the adjacency matrix and the Stieltjes transform of its empirical spectral measure are well approximated by Wigner's semicircle law, down to the optimal scale given by the typical eigenvalue spacing (up to a logarithmic correction). Aside from well‐known consequences for the local eigenvalue distribution, this result implies the complete (isotropic) delocalization of all eigenvectors and a probabilistic version of quantum unique ergodicity.© 2017 Wiley Periodicals, Inc.