The latent process decomposition of cDNA microarray data sets

We present a new computational technique (a software implementation, data sets, and supplementary information are available at http://www.enm.bris.ac.uk/lpd/) which enables the probabilistic analysis of cDNA microarray data and we demonstrate its effectiveness in identifying features of biomedical importance. A hierarchical Bayesian model, called latent process decomposition (LPD), is introduced in which each sample in the data set is represented as a combinatorial mixture over a finite set of latent processes, which are expected to correspond to biological processes. Parameters in the model are estimated using efficient variational methods. This type of probabilistic model is most appropriate for the interpretation of measurement data generated by cDNA microarray technology. For determining informative substructure in such data sets, the proposed model has several important advantages over the standard use of dendrograms. First, the ability to objectively assess the optimal number of sample clusters. Second, the ability to represent samples and gene expression levels using a common set of latent variables (dendrograms cluster samples and gene expression values separately which amounts to two distinct reduced space representations). Third, in contrast to standard cluster models, observations are not assigned to a single cluster and, thus, for example, gene expression levels are modeled via combinations of the latent processes identified by the algorithm. We show this new method compares favorably with alternative cluster analysis methods. To illustrate its potential, we apply the proposed technique to several microarray data sets for cancer. For these data sets it successfully decomposes the data into known subtypes and indicates possible further taxonomic subdivision in addition to highlighting, in a wholly unsupervised manner, the importance of certain genes which are known to be medically significant. To illustrate its wider applicability, we also illustrate its performance on a microarray data set for yeast

Phase decorrelation, streamwise vortices and acoustic radiation in mixing layers

Several direct numerical simulations were performed and analyzed to study various aspects of the early development of mixing layers. Included are the phase jitter of the large-scale eddies, which was studied using a 2-D spatially-evolving mixing layer simulation; the response of a time developing mixing layer to various spanwise disturbances; and the sound radiation from a 2-D compressible time developing mixing layer

Vitrification and determination of the crystallization time scales of the bulk-metallic-glass-forming liquid Zr58.5Nb2.8Cu15.6Ni12.8Al10.3

The crystallization kinetics of Zr58.5Nb2.8Cu15.6Ni12.8Al10.3 were studied in an electrostatic levitation (ESL) apparatus. The measured critical cooling rate is 1.75 K/s. Zr58.5Nb2.8Cu15.6Ni12.8Al10.3 is the first bulk-metallic-glass-forming liquid that does not contain beryllium to be vitrified by purely radiative cooling in the ESL. Furthermore, the sluggish crystallization kinetics enable the determination of the time-temperature-transformation (TTT) diagram between the liquidus and the glass transition temperatures. The shortest time to reach crystallization in an isothermal experiment; i.e., the nose of the TTT diagram is 32 s. The nose of the TTT diagram is at 900 K and positioned about 200 K below the liquidus temperature

Vacuum-UV negative photoion spectroscopy of CH3F, CH3Cl and CH3Br

Using tunable vacuum-UV radiation from a synchrotron, negative ions are detected by quadrupolar mass spectrometry following photoexcitation of three gaseous halogenated methanes CH$_3$X (X = F,Cl,Br). The anions X$^-$, H$^-$, CX$^-$, CHX$^-$ and CH$_2$X$^-$ are observed, and their ion yields recorded in the range 8-35 eV. The anions show a linear dependence of signal with pressure, showing that they arise from unimolecular ion-pair dissociation, generically described as AB + h$v$ $\rightarrow$ A$^-$ + B$^+$ (+ neutrals). Absolute cross sections for ion-pair formation are obtained by calibrating the signal intensities with those of F$^-$ from both SF$_6$ and CF$_4$. The cross sections for formation of X$^-$ + CH$_3$$^+$ are much greater than for formation of CH$_2$X$^-$ + H$^+$. In common with many quadrupoles, the spectra of $m$/$z$ 1 (H$^-$) anions show contributions from all anions, and only for CH$_3$Br is it possible to perform the necessary subtraction to obtain the true H$^-$ spectrum. The anion cross sections are normalised to vacuum-UV absorption cross sections to obtain quantum yields for their production. The appearance energies of X$^-$ and CH$_2$X$^-$ are used to calculate upper limits to 298 K bond dissociation energies for D$^o$ (H$_3$C-X) and D$^o$ (XH$_2$C-H) which are consistent with literature values. The spectra suggest that most of the anions are formed indirectly by crossing of Rydberg states of the parent molecule onto an ion-pair continuum. The one exception is the lowest-energy peak of F$^-$ from CH$_3$F at 13.4 eV, where its width and lack of structure suggest it may correspond to a direct ion-pair transition

Preliminary calibration of a generic scramjet combustor

The results of a preliminary investigation of the combustion of hydrogen fuel at hypersonic flow conditions are provided. The tests were performed in a generic, constant-area combustor model with test gas supplied by a free-piston-driven reflected-shock tunnel. Static pressure measurements along the combustor wall indicated that burning did occur for combustor inlet conditions of P(static) approximately equal to 19kPa, T(static) approximately equal to 1080 K, and U approximately equal to 3630 m/s with a fuel equivalence ratio approximately equal to 0.9. These inlet conditions were obtained by operating the tunnel with stagnation enthalpy approximately equal to 8.1 MJ/kg, stagnation pressure approximately equal to 52 MPa, and a contoured nozzle with a nominal exit Mach number of 5.5

An Alternative Parameterization of R-matrix Theory

An alternative parameterization of R-matrix theory is presented which is mathematically equivalent to the standard approach, but possesses features which simplify the fitting of experimental data. In particular there are no level shifts and no boundary-condition constants which allows the positions and partial widths of an arbitrary number levels to be easily fixed in an analysis. These alternative parameters can be converted to standard R-matrix parameters by a straightforward matrix diagonalization procedure. In addition it is possible to express the collision matrix directly in terms of the alternative parameters.Comment: 8 pages; accepted for publication in Phys. Rev. C; expanded Sec. IV, added Sec. VI, added Appendix, corrected typo

TMDlib and TMDplotter: library and plotting tools for transverse-momentum-dependent parton distributions

Transverse-momentum-dependent distributions (TMDs) are central in high-energy physics from both theoretical and phenomenological points of view. In this manual we introduce the library, TMDlib, of fits and parameterisations for transverse-momentum-dependent parton distribution functions (TMD PDFs) and fragmentation functions (TMD FFs) together with an online plotting tool, TMDplotter. We provide a description of the program components and of the different physical frameworks the user can access via the available parameterisations.Comment: version 2, referring to TMDlib 1.0.2 - comments and references adde

Optical fiber interferometer for the study of ultrasonic waves in composite materials

The possibility of acoustic emission detection in composites using embedded optical fibers as sensing elements was investigated. Optical fiber interferometry, fiber acoustic sensitivity, fiber interferometer calibration, and acoustic emission detection are reported. Adhesive bond layer dynamical properties using ultrasonic interface waves, the design and construction of an ultrasonic transducer with a two dimensional Gaussian pressure profile, and the development of an optical differential technique for the measurement of surface acoustic wave particle displacements and propagation direction are also examined

A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces

A Wasserstein spaces is a metric space of sufficiently concentrated probability measures over a general metric space. The main goal of this paper is to estimate the largeness of Wasserstein spaces, in a sense to be precised. In a first part, we generalize the Hausdorff dimension by defining a family of bi-Lipschitz invariants, called critical parameters, that measure largeness for infinite-dimensional metric spaces. Basic properties of these invariants are given, and they are estimated for a naturel set of spaces generalizing the usual Hilbert cube. In a second part, we estimate the value of these new invariants in the case of some Wasserstein spaces, as well as the dynamical complexity of push-forward maps. The lower bounds rely on several embedding results; for example we provide bi-Lipschitz embeddings of all powers of any space inside its Wasserstein space, with uniform bound and we prove that the Wasserstein space of a d-manifold has "power-exponential" critical parameter equal to d.Comment: v2 Largely expanded version, as reflected by the change of title; all part I on generalized Hausdorff dimension is new, as well as the embedding of Hilbert cubes into Wasserstein spaces. v3 modified according to the referee final remarks ; to appear in Journal of Topology and Analysi