Compression of Correlation Matrices and an Efficient Method for Forming Matrix Product States of Fermionic Gaussian States

Here we present an efficient and numerically stable procedure for compressing a correlation matrix into a set of local unitary single-particle gates, which leads to a very efficient way of forming the matrix product state (MPS) approximation of a pure fermionic Gaussian state, such as the ground state of a quadratic Hamiltonian. The procedure involves successively diagonalizing subblocks of the correlation matrix to isolate local states which are purely occupied or unoccupied. A small number of nearest neighbor unitary gates isolates each local state. The MPS of this state is formed by applying the many-body version of these gates to a product state. We treat the simple case of compressing the correlation matrix of spinless free fermions with definite particle number in detail, though the procedure is easily extended to fermions with spin and more general BCS states (utilizing the formalism of Majorana modes). We also present a DMRG-like algorithm to obtain the compressed correlation matrix directly from a hopping Hamiltonian. In addition, we discuss a slight variation of the procedure which leads to a simple construction of the multiscale entanglement renormalization ansatz (MERA) of a fermionic Gaussian state, and present a simple picture of orthogonal wavelet transforms in terms of the gate structure we present in this paper. As a simple demonstration we analyze the Su-Schrieffer-Heeger model (free fermions on a 1D lattice with staggered hopping amplitudes).Comment: 15 pages, 17 figure

Using a Cubic Equation of State to Identify Optimal Working Fluids for an ORC Operating with Two-Phase Expansion Using a Twin-Screw Expander

For waste-heat recovery applications, operating an organic Rankine cycle (ORC) with two-phase expansion has been shown to increase the utilisation of the waste-heat stream, leading to a higher power output compared to a conventional ORC with single-phase expansion. However, unlike the conventional ORC, working-fluid selection for an ORC operating with two-phase expansion has not been explored in detail within the literature. Therefore, the aim of this paper is to explore which working-fluid parameters make a particular working fluid suitable for this type of cycle. This is conducted by coupling a thermodynamic model of the cycle with the Peng-Robinson cubic equation of state. Moreover, the effect of the expander volumetric ratio on the expander isentropic efficiency is accounted for using a performance model for a twin-screw expander. Ultimately, the adopted approach allows the effect of the working-fluid parameters, namely the critical temperature and ideal specific-heat capacity, on both the expander performance and the cycle to be evaluated in a generalised way. For the investigation, 15 theoretical working fluids are defined, covering five different critical temperatures, with a negatively-sloped, vertical and positively-sloped saturated vapour line respectively. The 15 working fluids are selected as they represent the feasible design space occupied by existing ORC working fluids. For each fluid, a cycle optimisation is completed for different heat-source temperatures ranging between 80 and 200 °C. The objective is to identify the optimal cycle operating conditions that result in maximum power output from the system. By analysing the results, the optimal characteristics of a working fluid are obtained, and this information can be used to identify physical working fluids which are good candidates for a particular heat-source temperature. In the final part of this paper, the cycle optimisation is repeated for the physical working fluids identified, thus validating the suitability of the approach developed. Ultimately, the results can help to narrow down the search space when considering working fluids for an ORC operating with two-phase expansion

The identification of mitochondrial DNA variants in glioblastoma multiforme

Background: Mitochondrial DNA (mtDNA) encodes key proteins of the electron transfer chain (ETC), which produces ATP through oxidative phosphorylation (OXPHOS) and is essential for cells to perform specialised functions. Tumor-initiating cells use aerobic glycolysis, a combination of glycolysis and low levels of OXPHOS, to promote rapid cell proliferation and tumor growth. Glioblastoma multiforme (GBM) is an aggressively malignant brain tumor and mitochondria have been proposed to play a vital role in GBM tumorigenesis. Results: Using next generation sequencing and high resolution melt analysis, we identified a large number of mtDNA variants within coding and non-coding regions of GBM cell lines and predicted their disease-causing potential through in silico modeling. The frequency of variants was greatest in the D-loop and origin of light strand replication in non-coding regions. ND6 was the most susceptible coding gene to mutation whilst ND4 had the highest frequency of mutation. Both genes encode subunits of complex I of the ETC. These variants were not detected in unaffected brain samples and many have not been previously reported. Depletion of HSR-GBM1 cells to varying degrees of their mtDNA followed by transplantation into immunedeficient mice resulted in the repopulation of the same variants during tumorigenesis. Likewise, de novo variants identified in other GBM cell lines were also incorporated. Nevertheless, ND4 and ND6 were still the most affected genes. We confirmed the presence of these variants in high grade gliomas. Conclusions: These novel variants contribute to GBM by rendering the ETC. partially dysfunctional. This restricts metabolism to anaerobic glycolysis and promotes cell proliferation

Spatial Curvature Falsifies Eternal Inflation

Inflation creates large-scale cosmological density perturbations that are characterized by an isotropic, homogeneous, and Gaussian random distribution about a locally flat background. Even in a flat universe, the spatial curvature measured within one Hubble volume receives contributions from long wavelength perturbations, and will not in general be zero. These same perturbations determine the Cosmic Microwave Background (CMB) temperature fluctuations, which are O(10^-5). Consequently, the low-l multipole moments in the CMB temperature map predict the value of the measured spatial curvature \Omega_k. On this basis we argue that a measurement of |\Omega_k| > 10^-4 would rule out slow-roll eternal inflation in our past with high confidence, while a measurement of \Omega_k < -10^-4 (which is positive curvature, a locally closed universe) rules out false-vacuum eternal inflation as well, at the same confidence level. In other words, negative curvature (a locally open universe) is consistent with false-vacuum eternal inflation but not with slow-roll eternal inflation, and positive curvature falsifies both. Near-future experiments will dramatically extend the sensitivity of \Omega_k measurements and constitute a sharp test of these predictions.Comment: 16+2 pages, 2 figure

Modelling the impact of local reactive school closures on critical care provision during an influenza pandemic

Despite the fact that the 2009 H1N1 pandemic influenza strain was less severe than had been feared, both seasonal epidemics of influenza-like-illness and future influenza pandemics have the potential to place a serious burden on health services. The closure of schools has been postulated as a means of reducing transmission between children and hence reducing the number of cases at the peak of an epidemic; this is supported by the marked reduction in cases during school holidays observed across the world during the 2009 pandemic. However, a national policy of long-duration school closures could have severe economic costs. Reactive short-duration closure of schools in regions where health services are close to capacity offers a potential compromise, but it is unclear over what spatial scale and time frame closures would need to be made to be effective. Here, using detailed geographical information for England, we assess how localized school closures could alleviate the burden on hospital intensive care units (ICUs) that are reaching capacity. We show that, for a range of epidemiologically plausible assumptions, considerable local coordination of school closures is needed to achieve a substantial reduction in the number of hospitals where capacity is exceeded at the peak of the epidemic. The heterogeneity in demand per hospital ICU bed means that even widespread school closures are unlikely to have an impact on whether demand will exceed capacity for many hospitals. These results support the UK decision not to use localized school closures as a control mechanism, but have far wider international public-health implications. The spatial heterogeneities in both population density and hospital capacity that give rise to our results exist in many developed countries, while our model assumptions are sufficiently general to cover a wide range of pathogens. This leads us to believe that when a pandemic has severe implications for ICU capacity, only widespread school closures (with their associated costs and organizational challenges) are sufficient to mitigate the burden on the worst-affected hospitals

The WARPS Survey: VI. Galaxy Cluster and Source Identifications from Phase I

We present in catalog form the optical identifications for objects from the first phase of the Wide Angle ROSAT Pointed Survey (WARPS). WARPS is a serendipitous survey of relatively deep, pointed ROSAT observations for clusters of galaxies. The X-ray source detection algorithm used by WARPS is Voronoi Tessellation and Percolation (VTP), a technique which is equally sensitive to point sources and extended sources of low surface brightness. WARPS-I is based on the central regions of 86 ROSAT PSPC fields, covering an area of 16.2 square degrees. We describe here the X-ray source screening and optical identification process for WARPS-I, which yielded 34 clusters at 0.06<z<0.75. Twenty-two of these clusters form a complete, statistically well defined sample drawn from 75 of these 86 fields, covering an area of 14.1 square degrees, with a flux limit of F (0.5-2.0 keV) = 6.5 \times 10^{-14} erg cm^{-2} s^{-1}}. This sample can be used to study the properties and evolution of the gas, galaxy and dark matter content of clusters, and to constrain cosmological parameters. We compare in detail the identification process and findings of WARPS to those from other recently published X-ray surveys for clusters, including RDCS, SHARC-Bright, SHARC-south and the CfA 160 deg$^2$ survey.Comment: v3 reflects minor updates to tables 2 and