Chiral symmetry breaking, instantons and the ultimate quenched calculation

We calculate the spectral density of the Dirac operator over an ensemble of configurations composed of overlapping instantons and anti-instantons. We find evidence that the spectral density diverges in the limit of small eigenvalues. This indicates the breaking of chiral symmetry and also provides evidence that quenched QCD may be pathological in nature.Comment: LATTICE98(confine

Topology and chiral symmetry breaking in QCD

We construct a model to study the impact of instantons on the low lying eigenvalue spectrum of the Dirac operator. The model is by necessity, approximate, though it does incorporate the important symmetries of the underlying field theory. The model also reproduces classical results in the appropriate limits. We find that generic instanton ensembles lead to an accumulation of eigenvalues around zero, and hence, break chiral symmetry. The eigenvalue spectrum is divergent however, as the eigenvalue approaches zero. This leads to a divergent chiral condensate in quenched QCD, and hence, shows the theory to be pathological. In full QCD we find the novel result of a divergent spectral density leading to chiral symmetry breaking, but, with a finite condensate. This result holds for both $N_{f}=1$ and $N_{f}=2$. We also compute correlation functions and find a massive $\eta^{'}$ and $\sigma$ in the chiral limit. Whilst the divergence follows a power law, the strength of the divergence is inversely proportional to the instanton density. To investigate the impact of the divergence further, we analyse instanton ensembles derived by "cooling" lattice gauge configurations. An important negative result is that the chiral condensate is strongly dependent upon the number of cooling sweeps performed. Whether the problem lies with cooling or with the identification of topological objects is yet to be resolved.Comment: 164 pages, D.Phil. thesi

Pseudo-forces in quantum mechanics

Dynamical evolution is described as a parallel section on an infinite dimensional Hilbert bundle over the base manifold of all frames of reference. The parallel section is defined by an operator-valued connection whose components are the generators of the relativity group acting on the base manifold. In the case of Galilean transformations we show that the property that the curvature for the fundamental connection must be zero is just the Heisenberg equations of motion and the canonical commutation relation in geometric language. We then consider linear and circular accelerating frames and show that pseudo-forces must appear naturally in the Hamiltonian.Comment: 6 pages, 1 figure, revtex, new section added, to appear in PR

Results of an Indo-Swiss programme for qualification and testing of a 300-kW IISc-Dasag gasifier

The paper describes the performance and operational experience in India on a high efficiency, low tar, woody biomass gasifier developed at Indian Institute of Science, Bangalore. This development is also of interest to Switzerland, which has a substantial potential of biomass energy. The test scheme included measurements on tar and particulates and the effluents along with necessary measurements for the mass and energy balance. The results indicate a low tar level to meet the engine specifications and the effluents issuing out of the system could be treated using simpler techniques, as the levels are low

On the spectral density from instantons in quenched QCD

We investigate the contribution of instantons to the eigenvalue spectrum of the Dirac operator in quenched QCD. The instanton configurations that we use have been derived, elsewhere, from cooled SU(3) lattice gauge fields and, for comparison, we also analyse a random `gas' of instantons. Using a set of simplifying approximations, we find a non-zero chiral condensate. However we also find that the spectral density diverges for small eigenvalues, so that the chiral condensate, at zero quark mass, diverges in quenched QCD. The degree of divergence decreases with the instanton density, so that it is negligible for the smallest number of cooling sweeps but becomes substantial for larger number of cools. We show that the spectral density scales, that finite volume corrections are small and we see evidence for the screening of topological charges. However we also find that the spectral density and chiral condensate vary rapidly with the number of cooling sweeps -- unlike, for example, the topological susceptibility. Whether the problem lies with the cooling or with the identification of the topological charges is an open question. This problem needs to be resolved before one can determine how important is the divergence we have found for quenched QCD.Comment: 33 pages, 16 figures (RevTex), substantial revisions; to appear in Phys.Rev.

Quenched divergences in the deconfined phase of SU(2) gauge theory

The spectrum of the overlap Dirac operator in the deconfined phase of quenched gauge theory is known to have three parts: exact zeros arising from topology, small nonzero eigenvalues that result in a non-zero chiral condensate, and the dense bulk of the spectrum, which is separated from the small eigenvalues by a gap. In this paper, we focus on the small nonzero eigenvalues in an SU(2) gauge field background at $\beta=2.4$ and $N_T=4$. This low-lying spectrum is computed on four different spatial lattices ($12^3$, $14^3$, $16^3$, and $18^3$). As the volume increases, the small eigenvalues become increasingly concentrated near zero in such a way as to strongly suggest that the infinite volume condensate diverges.Comment: 12 pages, 3 figures, version to appear in Physical Review

Topology and chiral symmetry breaking in SU(N) gauge theories

We study the low-lying eigenmodes of the lattice overlap Dirac operator for SU(N) gauge theories with N=2,3,4 and 5 colours. We define a fermionic topological charge from the zero-modes of this operator and show that, as N grows, any disagreement with the topological charge obtained by cooling the fields, becomes rapidly less likely. By examining the fields where there is a disagreement, we are able to show that the Dirac operator does not resolve instantons below a critical size of about rho = 2.5 a, but resolves the larger, more physical instantons. We investigate the local chirality of the near-zero modes and how it changes as we go to larger N. We observe that the local chirality of these modes, which is prominent for SU(2) and SU(3), becomes rapidly weaker for larger N and is consistent with disappearing entirely in the limit of N -> infinity. We find that this is not due to the observed disappearance of small instantons at larger N.Comment: 41 pages, 12 figures, RevTe

Associating Genes and Protein Complexes with Disease via Network Propagation

A fundamental challenge in human health is the identification of disease-causing genes. Recently, several studies have tackled this challenge via a network-based approach, motivated by the observation that genes causing the same or similar diseases tend to lie close to one another in a network of protein-protein or functional interactions. However, most of these approaches use only local network information in the inference process and are restricted to inferring single gene associations. Here, we provide a global, network-based method for prioritizing disease genes and inferring protein complex associations, which we call PRINCE. The method is based on formulating constraints on the prioritization function that relate to its smoothness over the network and usage of prior information. We exploit this function to predict not only genes but also protein complex associations with a disease of interest. We test our method on gene-disease association data, evaluating both the prioritization achieved and the protein complexes inferred. We show that our method outperforms extant approaches in both tasks. Using data on 1,369 diseases from the OMIM knowledgebase, our method is able (in a cross validation setting) to rank the true causal gene first for 34% of the diseases, and infer 139 disease-related complexes that are highly coherent in terms of the function, expression and conservation of their member proteins. Importantly, we apply our method to study three multi-factorial diseases for which some causal genes have been found already: prostate cancer, alzheimer and type 2 diabetes mellitus. PRINCE's predictions for these diseases highly match the known literature, suggesting several novel causal genes and protein complexes for further investigation

Twin reversed arterial perfusion (TRAP) sequence in association with VACTERL association: a case report

<p>Abstract</p> <p>Introduction</p> <p>Twin reversed arterial perfusion (TRAP) sequence is a rare complication of multiple pregnancy caused by defects in early embryogenesis. The pump twin supplies the acardiac recipient twin with blood, and although the pump twin is usually structurally normal, congenital anomalies have sometimes been reported. We report a unique case of twin reversed arterial perfusion sequence with a prenatal diagnosis of VACTERL association in the surviving pump twin.</p> <p>Case presentation</p> <p>A 24-year-old Caucasian woman presented at 11 weeks' gestation with a monochorionic, monoamniotic twin pregnancy. A reversed arterial flow was noted on a Doppler imaging study coming from the larger, apparently normal twin to the smaller, grossly abnormal twin, and a diagnosis of twin reversed arterial perfusion sequence was made. Cardiac activity was undetectable in the recipient twin by 16 weeks' gestation. Further detailed assessment at 18 weeks' gestation revealed multiple congenital anomalies of the surviving pump twin, in keeping with a diagnosis of VACTERL association. A live infant girl was delivered at 39 weeks by elective cesarean section. She underwent extensive surgery with subsequent normal development at the age of two years.</p> <p>Conclusion</p> <p>The co-existence of two rare and complex conditions in this unique case raises interesting questions about the role of early defects in embryogenesis and their subsequent effects on fetal development. This case also highlights the importance of prenatal diagnosis of major congenital anomalies to the plan treatment, reduce morbidity and aid the survival of affected children.</p