The curious nonexistence of Gaussian 2-designs

2-designs -- ensembles of quantum pure states whose 2nd moments equal those of the uniform Haar ensemble -- are optimal solutions for several tasks in quantum information science, especially state and process tomography. We show that Gaussian states cannot form a 2-design for the continuous-variable (quantum optical) Hilbert space L2(R). This is surprising because the affine symplectic group HWSp (the natural symmetry group of Gaussian states) is irreducible on the symmetric subspace of two copies. In finite dimensional Hilbert spaces, irreducibility guarantees that HWSp-covariant ensembles (such as mutually unbiased bases in prime dimensions) are always 2-designs. This property is violated by continuous variables, for a subtle reason: the (well-defined) HWSp-invariant ensemble of Gaussian states does not have an average state because the averaging integral does not converge. In fact, no Gaussian ensemble is even close (in a precise sense) to being a 2-design. This surprising difference between discrete and continuous quantum mechanics has important implications for optical state and process tomography.Comment: 9 pages, no pretty figures (sorry!

Maximum Running Speed of Captive Bar-Headed Geese Is Unaffected by Severe Hypoxia

While bar-headed geese are renowned for migration at high altitude over the Himalayas, previous work on captive birds suggested that these geese are unable to maintain rates of oxygen consumption while running in severely hypoxic conditions. To investigate this paradox, we re-examined the running performance and heart rates of bar-headed geese and barnacle geese (a low altitude species) during exercise in hypoxia. Bar-headed geese (n = 7) were able to run at maximum speeds (determined in normoxia) for 15 minutes in severe hypoxia (7% O2; simulating the hypoxia at 8500 m) with mean heart rates of 466±8 beats min�1. Barnacle geese (n = 10), on the other hand, were unable to complete similar trials in severe hypoxia and their mean heart rate (316 beats.min�1) was significantly lower than bar-headed geese. In bar-headed geese, partial pressures of oxygen and carbon dioxide in both arterial and mixed venous blood were significantly lower during hypoxia than normoxia, both at rest and while running. However, measurements of blood lactate in bar-headed geese suggested that anaerobic metabolism was not a major energy source during running in hypoxia. We combined these data with values taken from the literature to estimate (i) oxygen supply, using the Fick equation and (ii) oxygen demand using aerodynamic theory for bar-headed geese flying aerobically, and under their own power, at altitude. This analysis predicts that the maximum altitude at which geese can transport enough oxygen to fly without environmental assistance ranges from 6,800 m to 8,900 m altitude, depending on the parameters used in the model but that such flights should be rare

Characterization of the Positivity of the Density Matrix in Terms of the Coherence Vector Representation

A parameterization of the density operator, a coherence vector representation, which uses a basis of orthogonal, traceless, Hermitian matrices is discussed. Using this parameterization we find the region of permissible vectors which represent a density operator. The inequalities which specify the region are shown to involve the Casimir invariants of the group. In particular cases, this allows the determination of degeneracies in the spectrum of the operator. The identification of the Casimir invariants also provides a method of constructing quantities which are invariant under {\it local} unitary operations. Several examples are given which illustrate the constraints provided by the positivity requirements and the utility of the coherence vector parameterization.Comment: significantly rewritten and submitted for publicatio

Evaluation of the Theoretical Uncertainties in the Z to ll Cross Sections at the LHC

We study the sources of systematic errors in the measurement of the Z to ll cross-sections at the LHC. We consider the systematic errors in both the total cross-section and acceptance for anticipated experimental cuts. We include the best available analysis of QCD effects at NNLO in assessing the effect of higher order corrections and PDF and scale uncertainties on the theoretical acceptance. In addition, we evaluate the error due to missing NLO electroweak corrections and propose which MC generators and computational schemes should be implemented to best simulate the events.Comment: 23 pages, 52 eps figures, LaTeX with JHEP3.cls, epsfig. Added a reference, acknowledgment, and a few clarifying comments. 4/29: Changes in references, minor rewordings and misprint corrections, and one new table (Table 4) comparing CTEQ and MRST PDFs in the NNLO calculation. Version 6 adds email addresses and corrects one referenc

Limitations of Self-Assembly at Temperature One (extended abstract)

We prove that if a subset X of the integer Cartesian plane weakly self-assembles at temperature 1 in a deterministic (Winfree) tile assembly system satisfying a natural condition known as *pumpability*, then X is a finite union of doubly periodic sets. This shows that only the most simple of infinite shapes and patterns can be constructed using pumpable temperature 1 tile assembly systems, and gives strong evidence for the thesis that temperature 2 or higher is required to carry out general-purpose computation in a tile assembly system. Finally, we show that general-purpose computation is possible at temperature 1 if negative glue strengths are allowed in the tile assembly model

Physics, Topology, Logic and Computation: A Rosetta Stone

In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much like a "cobordism". Similar diagrams can be used to reason about logic, where they represent proofs, and computation, where they represent programs. With the rise of interest in quantum cryptography and quantum computation, it became clear that there is extensive network of analogies between physics, topology, logic and computation. In this expository paper, we make some of these analogies precise using the concept of "closed symmetric monoidal category". We assume no prior knowledge of category theory, proof theory or computer science.Comment: 73 pages, 8 encapsulated postscript figure

Enhancing the Social Capital of Learning Communities by Using an Ad Hoc Transient Communities Service

Fetter, S., Berlanga, A. J., & Sloep, P. B. (2009). Enhancing the Social Capital of Learning Communities by Using an Ad Hoc Transient Communities Service. In M. Spaniol, Q. Li, R. Klamma & R. W. H. Lau (Eds.), Proceedings of the 8th International Conference Advances in Web-based Learning - ICWL 2009 (pp. 150-157). August, 19-21, 2009, Aachen, Germany. Lecture Notes in Computer Science 5686; Berlin, Heidelberg: Springer-Verlag.In online learning, communities can help to enhance learning. However, because of the dynamic nature of communities, attaining and sustaining these communities can be difficult. One aspect that has an influence on, and is influenced by these dynamics is the social capital of a community. Features of social capital are the social network structure, the sense of belonging and, the support received and provided. It is hypothesized that these features can be improved by using Ad Hoc Transient Communities (AHTCs). Through an AHTC learners are brought together for a specific, learning-related goal (‘ad hoc’) and for only a limited amount of time (‘transience’). To test whether the use of AHTCs has a positive influence on the social capital, a learner support service which enables the use of AHTCs is proposed. Furthermore, requirements, pre-requisites, and future research are discussed.The work on this publication has been sponsored by the TENCompetence Integrated Project that is funded by the European Commission's 6th Framework Programme, priority IST/Technology Enhanced Learning. Contract 027087 [http://www.tencompetence.org

Cosmological parameters from SDSS and WMAP

We measure cosmological parameters using the three-dimensional power spectrum P(k) from over 200,000 galaxies in the Sloan Digital Sky Survey (SDSS) in combination with WMAP and other data. Our results are consistent with a ``vanilla'' flat adiabatic Lambda-CDM model without tilt (n=1), running tilt, tensor modes or massive neutrinos. Adding SDSS information more than halves the WMAP-only error bars on some parameters, tightening 1 sigma constraints on the Hubble parameter from h~0.74+0.18-0.07 to h~0.70+0.04-0.03, on the matter density from Omega_m~0.25+/-0.10 to Omega_m~0.30+/-0.04 (1 sigma) and on neutrino masses from <11 eV to <0.6 eV (95%). SDSS helps even more when dropping prior assumptions about curvature, neutrinos, tensor modes and the equation of state. Our results are in substantial agreement with the joint analysis of WMAP and the 2dF Galaxy Redshift Survey, which is an impressive consistency check with independent redshift survey data and analysis techniques. In this paper, we place particular emphasis on clarifying the physical origin of the constraints, i.e., what we do and do not know when using different data sets and prior assumptions. For instance, dropping the assumption that space is perfectly flat, the WMAP-only constraint on the measured age of the Universe tightens from t0~16.3+2.3-1.8 Gyr to t0~14.1+1.0-0.9 Gyr by adding SDSS and SN Ia data. Including tensors, running tilt, neutrino mass and equation of state in the list of free parameters, many constraints are still quite weak, but future cosmological measurements from SDSS and other sources should allow these to be substantially tightened.Comment: Minor revisions to match accepted PRD version. SDSS data and ppt figures available at http://www.hep.upenn.edu/~max/sdsspars.htm

Embryonic Morphogen Nodal Promotes Breast Cancer Growth and Progression

Breast cancers expressing human embryonic stem cell (hESC)-associated genes are more likely to progress than well-differentiated cancers and are thus associated with poor patient prognosis. Elevated proliferation and evasion of growth control are similarly associated with disease progression, and are classical hallmarks of cancer. In the current study we demonstrate that the hESC-associated factor Nodal promotes breast cancer growth. Specifically, we show that Nodal is elevated in aggressive MDA-MB-231, MDA-MB-468 and Hs578t human breast cancer cell lines, compared to poorly aggressive MCF-7 and T47D breast cancer cell lines. Nodal knockdown in aggressive breast cancer cells via shRNA reduces tumour incidence and significantly blunts tumour growth at primary sites. In vitro, using Trypan Blue exclusion assays, Western blot analysis of phosphorylated histone H3 and cleaved caspase-9, and real time RT-PCR analysis of BAX and BCL2 gene expression, we demonstrate that Nodal promotes expansion of breast cancer cells, likely via a combinatorial mechanism involving increased proliferation and decreased apopotosis. In an experimental model of metastasis using beta-glucuronidase (GUSB)-deficient NOD/SCID/mucopolysaccharidosis type VII (MPSVII) mice, we show that although Nodal is not required for the formation of small (\u3c100 cells) micrometastases at secondary sites, it supports an elevated proliferation:apoptosis ratio (Ki67:TUNEL) in micrometastatic lesions. Indeed, at longer time points (8 weeks), we determined that Nodal is necessary for the subsequent development of macrometastatic lesions. Our findings demonstrate that Nodal supports tumour growth at primary and secondary sites by increasing the ratio of proliferation:apoptosis in breast cancer cells. As Nodal expression is relatively limited to embryonic systems and cancer, this study establishes Nodal as a potential tumour-specific target for the treatment of breast cancer. © 2012 Quail et al

Observation of Orbitally Excited B_s Mesons

We report the first observation of two narrow resonances consistent with states of orbitally excited (L=1) B_s mesons using 1 fb^{-1} of ppbar collisions at sqrt{s} = 1.96 TeV collected with the CDF II detector at the Fermilab Tevatron. We use two-body decays into K^- and B^+ mesons reconstructed as B^+ \to J/\psi K^+, J/\psi \to \mu^+ \mu^- or B^+ \to \bar{D}^0 \pi^+, \bar{D}^0 \to K^+ \pi^-. We deduce the masses of the two states to be m(B_{s1}) = 5829.4 +- 0.7 MeV/c^2 and m(B_{s2}^*) = 5839.7 +- 0.7 MeV/c^2.Comment: Version accepted and published by Phys. Rev. Let