Quantum Fourier transform revisited

The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a particular matrix decomposition of the discrete Fourier transform (DFT) matrix. In this paper, we show that the quantum Fourier transform (QFT) can be derived by further decomposing the diagonal factors of the FFT matrix decomposition into products of matrices with Kronecker product structure. We analyze the implication of this Kronecker product structure on the discrete Fourier transform of rank-1 tensors on a classical computer. We also explain why such a structure can take advantage of an important quantum computer feature that enables the QFT algorithm to attain an exponential speedup on a quantum computer over the FFT algorithm on a classical computer. Further, the connection between the matrix decomposition of the DFT matrix and a quantum circuit is made. We also discuss a natural extension of a radix-2 QFT decomposition to a radix-d QFT decomposition. No prior knowledge of quantum computing is required to understand what is presented in this paper. Yet, we believe this paper may help readers to gain some rudimentary understanding of the nature of quantum computing from a matrix computation point of view

Acoustic black holes for relativistic fluids

We derive a new acoustic black hole metric from the Abelian Higgs model. In the non-relativistic limit, while the Abelian Higgs model becomes the Ginzburg-Landau model, the metric reduces to an ordinary Unruh type. We investigate the possibility of using (type I and II) superconductors as the acoustic black holes. We propose to realize experimental acoustic black holes by using spiral vortices solutions from the Navier-stokes equation in the non-relativistic classical fluids.Comment: 16 pages. typos corrected, contents expande

The Complete Star Formation History of the Universe

The determination of the star-formation history of the Universe is a key goal of modern cosmology, as it is crucial to our understanding of how structure in the Universe forms and evolves. A picture has built up over recent years, piece-by-piece, by observing young stars in distant galaxies at different times in the past. These studies indicated that the stellar birthrate peaked some 8 billion years ago, and then declined by a factor of around ten to its present value. Here we report on a new study which obtains the complete star formation history by analysing the fossil record of the stellar populations of 96545 nearby galaxies. Broadly, our results support those derived from high-redshift galaxies elsewhere in the Universe. We find, however, that the peak of star formation was more recent - around 5 billion years ago. Our study also shows that the bigger the stellar mass of the galaxy, the earlier the stars were formed. This striking result indicates a very different formation history for high- and low-mass formation.Comment: Accepted by Nature. Press embargo until publishe

"Engaging with birth stories in pregnancy: a hermeneutic phenomenological study of women's experiences across two generations"

BACKGROUND: The birth story has been widely understood as a crucial source of knowledge about childbirth. What has not been reported is the effect that birth stories may have on primigravid women's understandings of birth. Findings are presented from a qualitative study exploring how two generations of women came to understand birth in the milieu of other's stories. The prior assumption was that birth stories must surely have a positive or negative influence on listeners, steering them towards either medical or midwifery-led models of care. METHODS: A Heideggerian hermeneutic phenomenological approach was used. Twenty UK participants were purposively selected and interviewed. Findings from the initial sample of 10 women who were pregnant in 2012 indicated that virtual media was a primary source of birth stories. This led to recruitment of a second sample of 10 women who gave birth in the 1970s-1980s, to determine whether they were more able to translate information into knowledge via stories told through personal contact and not through virtual technologies RESULTS: Findings revealed the experience of 'being-in-the-world' of birth and of stories in that world. From a Heideggerian perspective, the birth story was constructed through 'idle talk' (the taken for granted assumptions of things, which come into being through language). Both oral stories and those told through technology were described as the 'modern birth story'. The first theme 'Stories are difficult like that', examines the birth story as problematic and considers how stories shape meaning. The second 'It's a generational thing', considers how women from two generations came to understand what their experience might be. The third 'Birth in the twilight of certainty,' examines women's experience of Being in a system of birth as constructed, portrayed and sustained in the stories being shared. CONCLUSIONS: The women pregnant in 2012 framed their expectations in the language of choice, whilst the women who birthed in the 1970s-1980s framed their experience in the language of safety. For both, however, the world of birth was the same; saturated with, and only legitimised by the birth of a healthy baby. Rather than creating meaningful understanding, the 'idle talk' of birth made both cohorts fearful of leaving the relative comfort of the 'system', and of claiming an alternative birth

Sub-Sets of Cancer Stem Cells Differ Intrinsically in Their Patterns of Oxygen Metabolism

PMCID: PMC3640080This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Paternal obesity is associated with IGF2 hypomethylation in newborns: results from a Newborn Epigenetics Study (NEST) cohort

Data from epidemiological and animal model studies suggest that nutrition during pregnancy may affect the health status of subsequent generations. These transgenerational effects are now being explained by disruptions at the level of the epigenetic machinery. Besides in vitro environmental exposures, the possible impact on the reprogramming of methylation profiles at imprinted genes at a much earlier time point, such as during spermatogenesis or oogenesis, has not previously been considered. In this study, our aim was to determine associations between preconceptional obesity and DNA methylation profiles in the offspring, particularly at the differentially methylated regions (DMRs) of the imprinted Insulin-like Growth Factor 2 (IGF2) gene

Polynomial diffeomorphisms of C^2, IV: The measure of maximal entropy and laminar currents

This paper concerns the dynamics of polynomial automorphisms of ${\bf C}^2$. One can associate to such an automorphism two currents $\mu^\pm$ and the equilibrium measure $\mu=\mu^+\wedge\mu^-$. In this paper we study some geometric and dynamical properties of these objects. First, we characterize $\mu$ as the unique measure of maximal entropy. Then we show that the measure $\mu$ has a local product structure and that the currents $\mu^\pm$ have a laminar structure. This allows us to deduce information about periodic points and heteroclinic intersections. For example, we prove that the support of $\mu$ coincides with the closure of the set of saddle points. The methods used combine the pluripotential theory with the theory of non-uniformly hyperbolic dynamical systems

Deuteron and antideuteron production in Au+Au collisions at sqrt(s_NN)=200 GeV

The production of deuterons and antideuterons in the transverse momentum range 1.1 < p_T < 4.3 GeV/c at mid-rapidity in Au + Au collisions at sqrt(s_NN)=200 GeV has been studied by the PHENIX experiment at RHIC. A coalescence analysis comparing the deuteron and antideuteron spectra with those of protons and antiprotons, has been performed. The coalescence probability is equal for both deuterons and antideuterons and increases as a function of p_T, which is consistent with an expanding collision zone. Comparing (anti)proton yields p_bar/p = 0.73 +/- 0.01, with (anti)deuteron yields: d_bar/d = 0.47 +/- 0.03, we estimate that n_bar/n = 0.64 +/- 0.04.Comment: 326 authors, 6 pages text, 5 figures, 1 Table. Submitted to PRL. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm

Single Electrons from Heavy Flavor Decays in p+p Collisions at sqrt(s) = 200 GeV

The invariant differential cross section for inclusive electron production in p+p collisions at sqrt(s) = 200 GeV has been measured by the PHENIX experiment at the Relativistic Heavy Ion Collider over the transverse momentum range $0.4 <= p_T <= 5.0 GeV/c at midrapidity (eta <= 0.35). The contribution to the inclusive electron spectrum from semileptonic decays of hadrons carrying heavy flavor, i.e. charm quarks or, at high p_T, bottom quarks, is determined via three independent methods. The resulting electron spectrum from heavy flavor decays is compared to recent leading and next-to-leading order perturbative QCD calculations. The total cross section of charm quark-antiquark pair production is determined as sigma_(c c^bar) = 0.92 +/- 0.15 (stat.) +- 0.54 (sys.) mb.Comment: 329 authors, 6 pages text, 3 figures. Submitted to Phys. Rev. Lett. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm

A HIF-independent, CD133-mediated mechanism of cisplatin resistance in glioblastoma cells

Purpose Glioblastoma Multiforme (GBM) is the commonest brain tumour in adults. A population of cells, known as cancer stem cells (CSCs), is thought to mediate chemo/radiotherapy resistance. CD133 is a cell surface marker to identify and isolate CSCs. However, its functional significance and the relevant microenvironment in which to study CD133 remain unknown. We examined the influence of hypoxia on CD133 expression and the potential functional significance of CD133 in glioblastoma chemoresistance. Methods Gene expression was analysed by qRT-PCR. siRNA technique was used to downregulate genes and confirmed by flow cytometry. IC50 values was evaluated with the Alamar blue assay. Results CD133 expression was upregulated in hypoxia in 2D and 3D models. There was increased resistance to chemotherapeutics, cisplatin, temozolomide and etoposide, in cells cultured in hypoxia compared to normoxia. siRNA knockdown of either HIF1a or HIF2a resulted in reduced CD133 mRNA expression with HIF2a having a more prolonged effect on CD133 expression. HIF2a downregulation sensitized GBM cells to cisplatin to a greater extent than HIF1a but CD133 knockdown had a much more marked effect on cisplatin sensitisation than knockdown of either of the HIFs suggesting a HIF-independent mechanism of cisplatin resistance mediated via CD133. The same mechanism was not involved in temozolomide resistance since downregulation of HIF1a but not HIF2a or CD133 sensitized GBM cells to temozolomide. Conclusion Knowledge of the mechanisms involved in the novel hypoxia-induced CD133-mediated resistance to cisplatin observed might lead to identification of new strategies that enable more effective use of current therapeutic agents