Meson spectral functions with chirally symmetric lattice fermions

In order to enhance our understanding of spectral functions in lattice QCD obtained with the help of the Maximum Entropy Method, we study meson spectral functions for lattice fermions with chiral symmetry. In particular we analyse lattice artefacts for standard overlap, overlap hypercube and domain wall fermions in the free field limit. We also present first results for pseudoscalar spectral functions in dynamical QCD with 2+1 flavours of domain wall fermions, using data generated by the UKQCD and RBC collaborations on QCDOC machines.Comment: 25 pages, two sentences added; to appear in JHE

Spectral analysis of the truncated Hilbert transform with overlap

We study a restriction of the Hilbert transform as an operator $H_T$ from $L^2(a_2,a_4)$ to $L^2(a_1,a_3)$ for real numbers $a_1 < a_2 < a_3 < a_4$. The operator $H_T$ arises in tomographic reconstruction from limited data, more precisely in the method of differentiated back-projection (DBP). There, the reconstruction requires recovering a family of one-dimensional functions $f$ supported on compact intervals $[a_2,a_4]$ from its Hilbert transform measured on intervals $[a_1,a_3]$ that might only overlap, but not cover $[a_2,a_4]$. We show that the inversion of $H_T$ is ill-posed, which is why we investigate the spectral properties of $H_T$. We relate the operator $H_T$ to a self-adjoint two-interval Sturm-Liouville problem, for which we prove that the spectrum is discrete. The Sturm-Liouville operator is found to commute with $H_T$, which then implies that the spectrum of $H_T^* H_T$ is discrete. Furthermore, we express the singular value decomposition of $H_T$ in terms of the solutions to the Sturm-Liouville problem. The singular values of $H_T$ accumulate at both $0$ and $1$, implying that $H_T$ is not a compact operator. We conclude by illustrating the properties obtained for $H_T$ numerically.Comment: 24 pages, revised versio

Effects of NMR spectral resolution on protein structure calculation

Adequate digital resolution and signal sensitivity are two critical factors for protein structure determinations by solution NMR spectroscopy. The prime objective for obtaining high digital resolution is to resolve peak overlap, especially in NOESY spectra with thousands of signals where the signal analysis needs to be performed on a large scale. Achieving maximum digital resolution is usually limited by the practically available measurement time. We developed a method utilizing non-uniform sampling for balancing digital resolution and signal sensitivity, and performed a large-scale analysis of the effect of the digital resolution on the accuracy of the resulting protein structures. Structure calculations were performed as a function of digital resolution for about 400 proteins with molecular sizes ranging between 5 and 33 kDa. The structural accuracy was assessed by atomic coordinate RMSD values from the reference structures of the proteins. In addition, we monitored also the number of assigned NOESY cross peaks, the average signal sensitivity, and the chemical shift spectral overlap. We show that high resolution is equally important for proteins of every molecular size. The chemical shift spectral overlap depends strongly on the corresponding spectral digital resolution. Thus, knowing the extent of overlap can be a predictor of the resulting structural accuracy. Our results show that for every molecular size a minimal digital resolution, corresponding to the natural linewidth, needs to be achieved for obtaining the highest accuracy possible for the given protein size using state-of-the-art automated NOESY assignment and structure calculation methods

Spectral Properties of the Overlap Dirac Operator in QCD

We discuss the eigenvalue distribution of the overlap Dirac operator in quenched QCD on lattices of size 8^{4}, 10^{4} and 12^{4} at \beta = 5.85 and \beta = 6. We distinguish the topological sectors and study the distributions of the leading non-zero eigenvalues, which are stereographically mapped onto the imaginary axis. Thus they can be compared to the predictions of random matrix theory applied to the \epsilon-expansion of chiral perturbation theory. We find a satisfactory agreement, if the physical volume exceeds about (1.2 fm)^{4}. For the unfolded level spacing distribution we find an accurate agreement with the random matrix conjecture on all volumes that we considered.Comment: 16 pages, 8 figures, final version published in JHE