Numerical Methods for the QCD Overlap Operator:III. Nested Iterations

The numerical and computational aspects of chiral fermions in lattice quantum chromodynamics are extremely demanding. In the overlap framework, the computation of the fermion propagator leads to a nested iteration where the matrix vector multiplications in each step of an outer iteration have to be accomplished by an inner iteration; the latter approximates the product of the sign function of the hermitian Wilson fermion matrix with a vector. In this paper we investigate aspects of this nested paradigm. We examine several Krylov subspace methods to be used as an outer iteration for both propagator computations and the Hybrid Monte-Carlo scheme. We establish criteria on the accuracy of the inner iteration which allow to preserve an a priori given precision for the overall computation. It will turn out that the accuracy of the sign function can be relaxed as the outer iteration proceeds. Furthermore, we consider preconditioning strategies, where the preconditioner is built upon an inaccurate approximation to the sign function. Relaxation combined with preconditioning allows for considerable savings in computational efforts up to a factor of 4 as our numerical experiments illustrate. We also discuss the possibility of projecting the squared overlap operator into one chiral sector.Comment: 33 Pages; citations adde

Numerical Methods for the QCD Overlap Operator: I. Sign-Function and Error Bounds

The numerical and computational aspects of the overlap formalism in lattice quantum chromodynamics are extremely demanding due to a matrix-vector product that involves the sign function of the hermitian Wilson matrix. In this paper we investigate several methods to compute the product of the matrix sign-function with a vector, in particular Lanczos based methods and partial fraction expansion methods. Our goal is two-fold: we give realistic comparisons between known methods together with novel approaches and we present error bounds which allow to guarantee a given accuracy when terminating the Lanczos method and the multishift-CG solver, applied within the partial fraction expansion methods.Comment: 30 pages, 2 figure

Interactome comparison of human embryonic stem cell lines with the inner cell mass and trophectoderm

Networks of interacting co-regulated genes distinguish the inner cell mass (ICM) from the differentiated trophectoderm (TE) in the preimplantation blastocyst, in a species specific manner. In mouse the ground state pluripotency of the ICM appears to be maintained in murine embryonic stem cells (ESCs) derived from the ICM. This is not the case for human ESCs. In order to gain insight into this phenomenon, we have used quantitative network analysis to identify how similar human (h)ESCs are to the human ICM. Using the hESC lines MAN1, HUES3 and HUES7 we have shown that all have only a limited overlap with ICM specific gene expression, but that this overlap is enriched for network properties that correspond to key aspects of function including transcription factor activity and the hierarchy of network modules. These analyses provide an important framework which highlights the developmental origins of hESCs

Evolving Gene Regulatory Networks with Mobile DNA Mechanisms

This paper uses a recently presented abstract, tuneable Boolean regulatory network model extended to consider aspects of mobile DNA, such as transposons. The significant role of mobile DNA in the evolution of natural systems is becoming increasingly clear. This paper shows how dynamically controlling network node connectivity and function via transposon-inspired mechanisms can be selected for in computational intelligence tasks to give improved performance. The designs of dynamical networks intended for implementation within the slime mould Physarum polycephalum and for the distributed control of a smart surface are considered.Comment: 7 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:1303.722

Renormalization of the asymptotically expanded Yang-Mills spectral action

We study renormalizability aspects of the spectral action for the Yang-Mills system on a flat 4-dimensional background manifold, focusing on its asymptotic expansion. Interpreting the latter as a higher-derivative gauge theory, a power-counting argument shows that it is superrenormalizable. We determine the counterterms at one-loop using zeta function regularization in a background field gauge and establish their gauge invariance. Consequently, the corresponding field theory can be renormalized by a simple shift of the spectral function appearing in the spectral action. This manuscript provides more details than the shorter companion paper, where we have used a (formal) quantum action principle to arrive at gauge invariance of the counterterms. Here, we give in addition an explicit expression for the gauge propagator and compare to recent results in the literature.Comment: 28 pages; revised version. To appear in CMP. arXiv admin note: substantial text overlap with arXiv:1101.480

Parton and Hadron Correlations in Jets

Correlation between shower partons is first studied in high $p_T$ jets. Then in the framework of parton recombination the correlation between pions in heavy-ion collisions is investigated. Since thermal partons play very different roles in central and peripheral collisions, it is found that the correlation functions of the produced hadrons behave very differently at different centralities, especially at intermediate $p_T$. The correlation function that can best exhibit the distinctive features is suggested. There is not a great deal of overlap between what we can calculate and what has been measured. Nevertheless, some aspects of our results compare favorably with experimental data.Comment: 28 pages in Latex + 13 figures. This is a revised version with extended discussions added without quantitative changes in the result