Isospectral Graph Reductions and Improved Estimates of Matrices' Spectra

Via the process of isospectral graph reduction the adjacency matrix of a graph can be reduced to a smaller matrix while its spectrum is preserved up to some known set. It is then possible to estimate the spectrum of the original matrix by considering Gershgorin-type estimates associated with the reduced matrix. The main result of this paper is that eigenvalue estimates associated with Gershgorin, Brauer, Brualdi, and Varga improve as the matrix size is reduced. Moreover, given that such estimates improve with each successive reduction, it is also possible to estimate the eigenvalues of a matrix with increasing accuracy by repeated use of this process.Comment: 32 page

Uncovering Hierarchical Structure in Social Networks using Isospectral Reductions

We employ the recently developed theory of isospectral network reductions to analyze multi-mode social networks. This procedure allows us to uncover the hierarchical structure of the networks we consider as well as the hierarchical structure of each mode of the network. Additionally, by performing a dynamical analysis of these networks we are able to analyze the evolution of their structure allowing us to find a number of other network features. We apply both of these approaches to the Southern Women Data Set, one of the most studied social networks and demonstrate that these techniques provide new information, which complements previous findings.Comment: 17 pages, 5 figures, 5 table

A TiO study of the black-hole binary GRO J0422+32 in a very low state

We present 53 simultaneous photometric (I band) and spectroscopic (6900-9500 Angstroms) observations of J0422+32, taken during December 1997. From these we determine that J0422+32 was in its lowest state yet observed, at I=20.44+/-0.08. Using relative spectrophotometry, we show that it is possible to correct very accurately for telluric absorption. Following this, we use the TiO bands at 7055 Angstroms and 7589 Angstroms for a radial velocity study and thereby obtain a semi-amplitude of 378+/-16kms-1, which yields f(M)=1.191+/-0.021M_solar and q=9.0+2.2-2.7, consistent with previous observations. We further demonstrate that this little explored method is very powerful for such systems. We also determine a new orbital ephemeris of HJD=2450274.4156+/-0.0009 + 0.2121600+/-0.0000002E. We see some evidence for an ellipsoidal modulation, from which we determine the orbital inclination of J0422+32 to be less than 45 degrees. We therefore calculate a minimum mass for the primary of 2.22M_solar, consistent with a black hole, but not necessarily the super-massive one proposed by Beekman et al (1997). We obtain an M4-5 spectral type for the secondary star and determine that the secondary contributes 38+/-2% of the flux that we observe from J0422+32 over the range 6950-8400 Angstroms. From this we calculate the distance to the system to be 1.39+/-0.15kpc.Comment: (1) Department of Physics, Keele University, Keele, Staffordshire, ST5 5BG (2) Department of Astrophysics, Nuclear Physics Laboratory, Keble Road, Oxfo rd, OX1 3RH Accepted, to appear in MNRAS 8 pages, 5 figure

Spatial imaging of Zn and other elements in Huanglongbing-affected grapefruit by synchrotron-based micro X-ray fluorescence investigation

Huanglongbing (HLB) is a highly destructive, fast-spreading disease of citrus, causing substantial economic losses to the citrus industry worldwide. Nutrient levels and their cellular distribution patterns in stems and leaves of grapefruit were analysed after graft-inoculation with lemon scions containing 'Candidatus Liberibacter asiaticus' (Las), the heat-tolerant Asian type of the HLB bacterium. After 12 months, affected plants showed typical HLB symptoms and significantly reduced Zn concentrations in leaves. Micro-XRF imaging of Zn and other nutrients showed that preferential localization of Zn to phloem tissues was observed in the stems and leaves collected from healthy grapefruit plants, but was absent from HLB-affected samples. Quantitative analysis by using standard references revealed that Zn concentration in the phloem of veins in healthy leaves was more than 10 times higher than that in HLB-affected leaves. No significant variation was observed in the distribution patterns of other elements such as Ca in stems and leaves of grapefruit plants with or without graft-inoculation of infected lemon scions. These results suggest that reduced phloem transport of Zn is an important factor contributing to HLB-induced Zn deficiency in grapefruit. Our report provides the first in situ, cellular level visualization of elemental variations within the tissues of HLB-affected citrus. © 2014 © The Author 2014. Published by Oxford University Press on behalf of the Society for Experimental Biology

Universal computation by multi-particle quantum walk

A quantum walk is a time-homogeneous quantum-mechanical process on a graph defined by analogy to classical random walk. The quantum walker is a particle that moves from a given vertex to adjacent vertices in quantum superposition. Here we consider a generalization of quantum walk to systems with more than one walker. A continuous-time multi-particle quantum walk is generated by a time-independent Hamiltonian with a term corresponding to a single-particle quantum walk for each particle, along with an interaction term. Multi-particle quantum walk includes a broad class of interacting many-body systems such as the Bose-Hubbard model and systems of fermions or distinguishable particles with nearest-neighbor interactions. We show that multi-particle quantum walk is capable of universal quantum computation. Since it is also possible to efficiently simulate a multi-particle quantum walk of the type we consider using a universal quantum computer, this model exactly captures the power of quantum computation. In principle our construction could be used as an architecture for building a scalable quantum computer with no need for time-dependent control