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We demonstrate a quantum walk with time-dependent coin bias. With this technique we realize an experimental single-photon one-dimensional quantum walk with a linearly-ramped time-dependent coin flip operation and thereby demonstrate two periodic revivals of the walker distribution. In our beam-displacer interferometer, the walk corresponds to movement between discretely separated transverse modes of the field serving as lattice sites, and the time-dependent coin flip is effected by implementing a different angle between the optical axis of half-wave plate and the light propagation at each step. Each of the quantum-walk steps required to realize a revival comprises two sequential orthogonal coin-flip operators, with one coin having constant bias and the other coin having a time-dependent ramped coin bias, followed by a conditional translation of the walker. [4][5][6] plus the fundamental interest of being a natural quantized version of the ubiquitous random walk that appears in statistics, computer science, finance, physics, and chemistry. QW research has focused on evolution due to repeated applications of a time-independent unitary step operator U , but a QW with time-dependent unitary steps U (t), with discrete time t ∈ N := {0, 1, 2, . . . }, opens a much richer array of phenomena including localization and quasiperiodicity [7,8]. Here we demonstrate a time-dependent QW and use this technique to demonstrate a revival of the walker's position distribution.Rather than employing direct time-dependent control, we simulate time-dependent coin control by setting different coin parameters for different steps, which are effected in different locations along the longitudinal axis within our photonic beam-displacer interferometer (BDI) [9]. The quantum walker within the BDI is a single heralded photon produced by spontaneous parametric down conversion, and its walking degree of freedom is the set of discretely spaced transverse beam modes. The coin flip is effected by employing quarter-and half-wave plates.Our method for realizing the first time-dependent QW demonstrates the phenomenon of revivals and also opens the door to realizing a multitude of time-dependent QWs experimentally. Compared to prior work employing position-dependent control [10][11][12], our new technique decreases experimental complexity by relaxing the requirement of optical compensation. Our QW revival displays a different characteristic than typical QW properties such as ballistic spreading and localization of the walker distribution.The QW with a coin proceeds as a sequence of coin flips and then walker-coin entangling operations whereby the walker's position is displaced according to the coin state. We explain the QW now in full generality so the coin operator admits both spatial and temporal dependence. Spatially-dependent coin operations have dramatically demonstrated the realization of topological phases by QWs [4][5][6], but the time-dependent QW is, until now, only a theoretical construct and not yet explored experimentally.We employ a two...

BackgroundCommunity-level analysis of the human microbiota has culminated in the discovery of relationships between overall shifts in the microbiota and a wide range of diseases and conditions. However, existing work has primarily focused on analysis of relatively simple dichotomous or quantitative outcomes, for example, disease status or biomarker levels. Recently, there is also considerable interest in the relationship between the microbiota and censored survival outcomes, such as in clinical trials. How to conduct community-level analysis with censored survival outcomes is unclear, since standard dissimilarity-based tests cannot accommodate censored survival times and no alternative methods exist.MethodsWe develop a new approach, MiRKAT-S, for community-level analysis of microbiome data with censored survival times. MiRKAT-S uses ecologically informative distance metrics, such as the UniFrac distances, to generate matrices of pairwise distances between individuals’ taxonomic profiles. The distance matrices are transformed into kernel (similarity) matrices, which are used to compare similarity in the microbiota to similarity in survival times between individuals.ResultsSimulation studies using synthetic microbial communities demonstrate correct control of type I error and adequate power. We also apply MiRKAT-S to examine the relationship between the gut microbiota and survival after allogeneic blood or bone marrow transplant.ConclusionsWe present MiRKAT-S, a method that facilitates community-level analysis of the association between the microbiota and survival outcomes and therefore provides a new approach to analysis of microbiome data arising from clinical trials.Electronic supplementary materialThe online version of this article (doi:10.1186/s40168-017-0239-9) contains supplementary material, which is available to authorized users.

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Objective To examine associations between the composition of the vaginal microbiota and genitourinary menopausal symptoms, serum estrogen, and vaginal glycogen. Methods For this cross-sectional study, 88 women ages 40–62 enrolled in a hot flash treatment trial provided vaginal swabs and a blood sample at enrollment. Bacterial communities were characterized using 16S rRNA PCR and deep sequencing targeting the V3-V4 region. Quantities of Lactobacillus crispatus and L. iners were measured using qPCR. Self-reported genitourinary symptoms included: 1) presence and severity of individual symptoms and 2) identification of most bothersome symptom. Glycogen was measured fluorometrically in swab eluate. Serum estradiol (E2) and estrone (E1) were measured by liquid chromatography/mass spectrometry. Associations between bacteria, symptoms, glycogen, and serum estrogens were tested by linear regression or Wilcoxon signed-rank test, adjusted for multiple comparisons. Comparisons between groups used Kruskall-Wallis or Fisher’s exact test. Results Of the 88 women, 33 (38%) had a majority of Lactobacillus species, while 58 (66%) had any Lactobacillus detected. Over half (53%) reported ≥ 1 vulvovaginal symptom (most commonly dryness), but symptoms were not associated with the presence of Lactobacillus species. Women with Lactobacillus dominant communities had higher unconjugated serum estrone, but no difference in vaginal glycogen levels, compared to those with non-Lactobacillus dominant communities. Higher serum E2 and E1 were not associated with higher vaginal glycogen, nor detection of individual genera. Conclusions Presence of Lactobacillus-dominant vaginal microbiota was not associated with fewer vulvovaginal symptoms. Serum estrone was higher in women with Lactobacillus-dominance, but vaginal free glycogen was not associated with composition of the vaginal microbiota.

Many genetic association studies collect a wide range of complex traits. As these traits may be correlated and share a common genetic mechanism, joint analysis can be statistically more powerful and biologically more meaningful. However, most existing tests for multiple traits cannot be used for high-dimensional and possibly structured traits, such as network-structured transcriptomic pathway expressions. To overcome potential limitations, in this article we propose the dual kernel-based association test (DKAT) for testing the association between multiple traits and multiple genetic variants, both common and rare. In DKAT, two individual kernels are used to describe the phenotypic and genotypic similarity, respectively, between pairwise subjects. Using kernels allows for capturing structure while accommodating dimensionality. Then, the association between traits and genetic variants is summarized by a coefficient which measures the association between two kernel matrices. Finally, DKAT evaluates the hypothesis of nonassociation with an analytical -value calculation without any computationally expensive resampling procedures. By collapsing information in both traits and genetic variants using kernels, the proposed DKAT is shown to have a correct type-I error rate and higher power than other existing methods in both simulation studies and application to a study of genetic regulation of pathway gene expressions.

Summary To fully understand the role of microbiome in human health and diseases, researchers are increasingly interested in assessing the relationship between microbiome composition and host genomic data. The dimensionality of the data as well as complex relationships between microbiota and host genomics pose considerable challenges for analysis. In this paper, we apply a kernel RV coefficient (KRV) test to evaluate the overall association between host gene expression and microbiome composition. The KRV statistic can capture non-linear correlations and complex relationships among the individual data types and between gene expression and microbiome composition through measuring general dependency. Testing proceeds via a similar route as existing tests of the generalized RV coefficients and allows for rapid p-value calculation. Strategies to allow adjustment for confounding effects, which is crucial for avoiding misleading results, and to alleviate the problem of selecting the most favorable kernel are considered. Simulation studies show that KRV is useful in testing statistical independence with finite samples given the kernels are appropriately chosen, and can powerfully identify existing associations between microbiome composition and host genomic data while protecting type I error. We apply the KRV to a microbiome study examining the relationship between host transcriptome and microbiome composition within the context of inflammatory bowel disease and are able to derive new biological insights and provide formal inference on prior qualitative observations.

We perform generalized measurements of a qubit by realizing the qubit as a coin in a photonic quantum walk and subjecting the walker to projective measurements. Our experimental technique can be used to realize photonically any rank-1 single-qubit positive operator-valued measure via constructing an appropriate interferometric quantum-walk network and then projectively measuring the walker's position at the final step.PACS numbers: 42.50. Ex, 42.50.Dv, 03.67.Lx, 03.67.Ac Quantum walks (QWs) exhibit distinct features compared to classical random walks with applications to quantum algorithms [1, 2]. The discrete-time QW is a process in which the evolution of a quantum particle on a lattice depends on a state of a coin, typically a twolevel system, or qubit. Controlling the coin degree of freedom indirectly controls the walker, and, through this indirect control, the walker's state can be measured to infer the coin state. Rigorously speaking, walker-coin entanglement and projective measurement of the walker yields a positive operator-valued measure (POVM) on a single qubit [3]. Furthermore any rank-1 and rank-2 single-qubit POVM can be generated by a judiciously engineered QW. Here we demonstrate experimentally the capability of performing such generalized measurements of a qubit by realizing the walker in the path degree of freedom of a photon and the coin state as polarization and performing optical interferometry with path-based photodetector to perform a POVM on the photon's polarization state.Realizing a POVM is important as a POVM is needed for generalized acquisition of information thereby associated with a multitude of quantum information tasks such as quantum state estimation and tomography [4] Our goal is to realize experimentally a single-qubit POVM and to discriminate between non-orthogonal initial coin states via executing a properly engineered QW whose projective walker measurement is sometimes inconclusive [3]. To achieve a site-specific POVM, we control the internal degree of freedom of the measured twolevel coin. Here we report our successful experimental realization of POVMs, including unambiguous state discrimination of two equally probable single-qubit states and a single-qubit SIC-POVM, via a one-dimensional photonic QW.We focus on rank-1 POVMs, as higher-rank POVMs can be constructed as a convex combination of rank-1 elements [3]. Our experimental technique can be used to realize photonically any rank-1 single-qubit POVM via constructing an interferometric QW and projectively measuring the walker's position at the final step. We characterize experimental performance by the 1-norm distance [18] between the walker distribution obtained experimentally P exp (x) vs theoretically P th (x) over integervalued position x. This distance isand a small distance indicates a successful experimental realization.A standard model of a one-dimensional (1D) discretetime QW consists of a walker carrying a coin that is flipped before each step. In the coin-state basis {|0 , |1 }, the site-dependent coin rotati...