Quantum Chi-Squared and Goodness of Fit Testing

The density matrix in quantum mechanics parameterizes the statistical properties of the system under observation, just like a classical probability distribution does for classical systems. The expectation value of observables cannot be measured directly, it can only be approximated by applying classical statistical methods to the frequencies by which certain measurement outcomes (clicks) are obtained. In this paper, we make a detailed study of the statistical fluctuations obtained during an experiment in which a hypothesis is tested, i.e. the hypothesis that a certain setup produces a given quantum state. Although the classical and quantum problem are very much related to each other, the quantum problem is much richer due to the additional optimization over the measurement basis. Just as in the case of classical hypothesis testing, the confidence in quantum hypothesis testing scales exponentially in the number of copies. In this paper, we will argue 1) that the physically relevant data of quantum experiments is only contained in the frequencies of the measurement outcomes, and that the statistical fluctuations of the experiment are essential, so that the correct formulation of the conclusions of a quantum experiment should be given in terms of hypothesis tests, 2) that the (classical) $\chi^2$ test for distinguishing two quantum states gives rise to the quantum $\chi^2$ divergence when optimized over the measurement basis, 3) present a max-min characterization for the optimal measurement basis for quantum goodness of fit testing, find the quantum measurement which leads both to the maximal Pitman and Bahadur efficiency, and determine the associated divergence rates.Comment: 22 Pages, with a new section on parameter estimatio

Quantum state estimation and large deviations

In this paper we propose a method to estimate the density matrix \rho of a d-level quantum system by measurements on the N-fold system. The scheme is based on covariant observables and representation theory of unitary groups and it extends previous results concerning the estimation of the spectrum of \rho. We show that it is consistent (i.e. the original input state \rho is recovered with certainty if N \to \infty), analyze its large deviation behavior, and calculate explicitly the corresponding rate function which describes the exponential decrease of error probabilities in the limit N \to \infty. Finally we discuss the question whether the proposed scheme provides the fastest possible decay of error probabilities.Comment: LaTex2e, 40 pages, 2 figures. Substantial changes in Section 4: one new subsection (4.1) and another (4.2 was 4.1 in the previous version) completely rewritten. Minor changes in Sect. 2 and 3. Typos corrected. References added. Accepted for publication in Rev. Math. Phy

Two quantum analogues of Fisher information from a large deviation viewpoint of quantum estimation

We discuss two quantum analogues of Fisher information, symmetric logarithmic derivative (SLD) Fisher information and Kubo-Mori-Bogoljubov (KMB) Fisher information from a large deviation viewpoint of quantum estimation and prove that the former gives the true bound and the latter gives the bound of consistent superefficient estimators. In another comparison, it is shown that the difference between them is characterized by the change of the order of limits.Comment: LaTeX with iopart.cls, iopart12.clo, iopams.st

Asymptotic estimation theory for a finite dimensional pure state model

The optimization of measurement for n samples of pure sates are studied. The error of the optimal measurement for n samples is asymptotically compared with the one of the maximum likelihood estimators from n data given by the optimal measurement for one sample.Comment: LaTeX, 23 pages, Doctoral Thesi

Low-Dose Imaging in a New Preclinical Total-Body PET/CT Scanner.

Ionizing radiation constitutes a health risk to imaging scientists and study animals. Both PET and CT produce ionizing radiation. CT doses in pre-clinical in vivo imaging typically range from 50 to 1,000 mGy and biological effects in mice at this dose range have been previously described. [ <sup>18</sup> F]FDG body doses in mice have been estimated to be in the range of 100 mGy for [ <sup>18</sup> F]FDG. Yearly, the average whole body doses due to handling of activity by PET technologists are reported to be 3-8 mSv. A preclinical PET/CT system is presented with design features which make it suitable for small animal low-dose imaging. The CT subsystem uses a X-source power that is optimized for small animal imaging. The system design incorporates a spatial beam shaper coupled with a highly sensitive flat-panel detector and very fast acquisition (<10 s) which allows for whole body scans with doses as low as 3 mGy. The mouse total-body PET subsystem uses a detector architecture based on continuous crystals, coupled to SiPM arrays and a readout based in rows and columns. The PET field of view is 150 mm axial and 80 mm transaxial. The high solid-angle coverage of the sample and the use of continuous crystals achieve a sensitivity of 9% (NEMA) that can be leveraged for use of low tracer doses and/or performing rapid scans. The low-dose imaging capabilities of the total-body PET subsystem were tested with NEMA phantoms, in tumor models, a mouse bone metabolism scan and a rat heart dynamic scan. The CT imaging capabilities were tested in mice and in a low contrast phantom. The PET low-dose phantom and animal experiments provide evidence that image quality suitable for preclinical PET studies is achieved. Furthermore, CT image contrast using low dose scan settings was suitable as a reference for PET scans. Total-body mouse PET/CT studies could be completed with total doses of <10 mGy

A transient homotypic interaction model for the influenza A virus NS1 protein effector domain

Influenza A virus NS1 protein is a multifunctional virulence factor consisting of an RNA binding domain (RBD), a short linker, an effector domain (ED), and a C-terminal 'tail'. Although poorly understood, NS1 multimerization may autoregulate its actions. While RBD dimerization seems functionally conserved, two possible apo ED dimers have been proposed (helix-helix and strand-strand). Here, we analyze all available RBD, ED, and full-length NS1 structures, including four novel crystal structures obtained using EDs from divergent human and avian viruses, as well as two forms of a monomeric ED mutant. The data reveal the helix-helix interface as the only strictly conserved ED homodimeric contact. Furthermore, a mutant NS1 unable to form the helix-helix dimer is compromised in its ability to bind dsRNA efficiently, implying that ED multimerization influences RBD activity. Our bioinformatical work also suggests that the helix-helix interface is variable and transient, thereby allowing two ED monomers to twist relative to one another and possibly separate. In this regard, we found a mAb that recognizes NS1 via a residue completely buried within the ED helix-helix interface, and which may help highlight potential different conformational populations of NS1 (putatively termed 'helix-closed' and 'helix-open') in virus-infected cells. 'Helix-closed' conformations appear to enhance dsRNA binding, and 'helix-open' conformations allow otherwise inaccessible interactions with host factors. Our data support a new model of NS1 regulation in which the RBD remains dimeric throughout infection, while the ED switches between several quaternary states in order to expand its functional space. Such a concept may be applicable to other small multifunctional proteins

Retrospective observational RT-PCR analyses on 688 babies born to 843 SARS-CoV-2 positive mothers, placental analyses and diagnostic analyses limitations suggest vertical transmission is possible

Research question: Is there vertical transmission (from mother to baby antenatally or intrapartum) after SARS-CoV-2 (COVID-19) infected pregnancy? Study design: A systematic search related to SARS-CoV-2 (COVID-19), pregnancy, neonatal complications, viral and vertical transmission. The duration was from December 2019 to May 2020. Results: A total of 84 studies with 862 COVID positive women were included. Two studies had ongoing pregnancies while 82 studies included 705 babies, 1 miscarriage and 1 medical termination of pregnancy (MTOP). Most publications (50/84, 59.5%), reported small numbers (<5) of positive babies. From 75 studies, 18 babies were COVID-19 positive. The first reverse transcription polymerase chain reaction (RT-PCR) diagnostic test was done in 449 babies and 2 losses, 2nd RT-PCR was done in 82 babies, IgM tests were done in 28 babies, and IgG tests were done in 28 babies. On the first RT-PCR, 47 studies reported time of testing while 28 studies did not. Positive results in the first RT-PCR were seen in 14 babies. Earliest tested at birth and the average time of the result was 22 hours. Three babies with negative first RT-PCR became positive on the second RT-PCR at day 6, day 7 and at 24 hours which continued to be positive at 1 week. Four studies with a total of 4 placental swabs were positive demonstrating SARS-CoV-2 localised in the placenta. In 2 studies, 10 tests for amniotic fluid were positive for SARS-CoV-2. These 2 babies were found to be positive on RT-PCR on serial testing. Conclusion: Diagnostic testing combined with incubation period and placental pathology indicate a strong likelihood that intrapartum vertical transmission of SARS-CoV-2 (COVID-19) from mother to baby is possible

New Forms of Development: Branding Innovative Ideas and Bidding for Foreign Aid in the Maternal and Child Health Service in Nepal

Nepal has been receiving foreign aid since the early 1950s. Currently, the country’s health care systemis heavily dependent on aid, even for the provision of basic health services to its people. Globally, the mechanismfor the dispersal of foreign aid is becoming increasingly complex. Numerous stakeholders are involved at variouslevels: donors, intermediary organisations, project-implementing partners and the beneficiaries, engaging not onlyin Nepal but also globally. To illustrate how branding and bidding occurs, and to discuss how this process hasbecome increasingly vital in securing foreign aid to run MCH activities in Nepal

Exploiting structural and topological information to improve prediction of RNA-protein binding sites

The breast and ovarian cancer susceptibility gene BRCA1 encodes a multifunctional tumor suppressor protein BRCA1, which is involved in regulating cellular processes such as cell cycle, transcription, DNA repair, DNA damage response and chromatin remodeling. BRCA1 protein, located primarily in cell nuclei, interacts with multiple proteins and various DNA targets. It has been demonstrated that BRCA1 protein binds to damaged DNA and plays a role in the transcriptional regulation of downstream target genes. As a key protein in the repair of DNA double-strand breaks, the BRCA1-DNA binding properties, however, have not been reported in detail

Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.