Measured Thoracic Gas Volume Versus Two Predictions

Body composition, or one’s fat mass relative to total mass, is important to a person’s health and physical performance. One method to measure body composition is the Bod Pod air displacement plethysmograph. To determine body volume from the Bod Pod, thoracic gas volume (TGV), or the volume of air in the lungs during a normal breath, must be measured or predicted. PURPOSE: The intent of this study was to compare measured TGV to two predictions: one from the Bod Pod (TGVBP) that makes assumptions about functional residual capacity and tidal volume, and one from a recent publication (TGVDucharme) that relies on measures of height and body mass rather than lung volumes. METHODS: Bod Pod data from university club sport athletes participating in a larger study were used. TGV was measured following the Bod Pod manufacturer’s instructions. Comparisons of mean data were made between the measured test and the two predictions with a one-way repeated-measures ANOVA. Individual error scores were evaluated with Bland-Altman plots. RESULTS: Data from 26 club sport athletes (18 male, 8 female) revealed a statistically significant difference (p = .001) between the three TGV measures. The measured TGV (4.108 ± 0.850 L) and TGVDucharme (4.092 ± 0.655 L) were not significantly different from one another (p = .851), but TGVBP (3.724 ± 0.409 L) significantly underestimated the measured TGV (p = .002) and Ducharme’s prediction (p \u3c .001). A clear bias exists for TGVBP (r = -0.799, p \u3c .001), such that the Bod Pod prediction overestimates athletes with a small TGV (\u3c 3.3 L) and underestimates athletes with a large TGV (\u3e 3.3 L). The bias for TGVDucharme is statistically significant (r = -0.460, p = .018), but much smaller than the bias from the Bod Pod prediction. CONCLUSION: When possible, measure TGV. If TGV must be predicted, use the Ducharme prediction rather than the TGV prediction from the Bod Pod

Thermodynamics of an interacting trapped Bose-Einstein gas in the classical field approximation

We present a convenient technique describing the condensate in dynamical equilibrium with the thermal cloud, at temperatures close to the critical one. We show that the whole isolated system may be viewed as a single classical field undergoing nonlinear dynamics leading to a steady state. In our procedure it is the observation process and the finite detection time that allow for splitting the system into the condensate and the thermal cloud.Comment: 4 pages, 4 eps figures, final versio

Critical Temperature of a Trapped Interacting Bose Gas in the Local Density Approximation

The Bose gas in an external potential is studied by means of the local density approximation. An analytical result is derived for the dependence of the critical temperature of Bose-Einstein condensation on the mutual interaction in a generic power-law potential.Comment: 6 pages, latex, no figure

Probing the classical field approximation - thermodynamics and decaying vortices

We review our version of the classical field approximation to the dynamics of a finite temperature Bose gas. In the case of a periodic box potential, we investigate the role of the high momentum cut-off, essential in the method. In particular, we show that the cut-off going to infinity limit decribes the particle number going to infinity with the scattering length going to zero. In this weak interaction limit, the relative population of the condensate tends to unity. We also show that the cross-over energy, at which the probability distribution of the condensate occupation changes its character, grows with a growing scattering length. In the more physical case of the condensate in the harmonic trap we investigate the dissipative dynamics of a vortex. We compare the decay time and the velocities of the vortex with the available analytic estimates.Comment: 7 pages, 8 eps figures, submitted to J. Optics B for the proceedings of the "Atom Optics and Interferometry" Lunteren 2002 worksho

Principal null directions of perturbed black holes

The properties of principal null directions of a perturbed black hole are investigated. It shown that principal null directions are directly observable quantities characterizing the space-time. A definition of a perturbed space-time, generalizing that given by Stewart and Walker is proposed. This more general framework allows one to include descriptions of a given space-time other than by a pair $(M,g)$ where $M$ is a four-dimensional differential manifold and $g$ a Lorentz metric. Examples of alternative characterizations are the curvature representation of Karlhede and others, the Newman-Penrose representation or observable quantities involving principal null directions. The conditions are studied under which the various alternative choices of observables provide equivalent descriptions of the space-time.Comment: To appear in Class. Quantum Gra

The extensions of gravitational soliton solutions with real poles

We analyse vacuum gravitational "soliton" solutions with real poles in the cosmological context. It is well known that these solutions contain singularities on certain null hypersurfaces. Using a Kasner seed solution, we demonstrate that these may contain thin sheets of null matter or may be simple coordinate singularities, and we describe a number of possible extensions through them.Comment: 14 pages, LaTeX, 6 figures included using graphicx; to appear in Gen. Rel. Gra

Fitting a geometric graph to a protein-protein interaction network

Finding a good network null model for protein-protein interaction (PPI) networks is a fundamental issue. Such a model would provide insights into the interplay between network structure and biological function as well as into evolution. Also, network (graph) models are used to guide biological experiments and discover new biological features. It has been proposed that geometric random graphs are a good model for PPI networks. In a geometric random graph, nodes correspond to uniformly randomly distributed points in a metric space and edges (links) exist between pairs of nodes for which the corresponding points in the metric space are close enough according to some distance norm. Computational experiments have revealed close matches between key topological properties of PPI networks and geometric random graph models. In this work, we push the comparison further by exploiting the fact that the geometric property can be tested for directly. To this end, we develop an algorithm that takes PPI interaction data and embeds proteins into a low-dimensional Euclidean space, under the premise that connectivity information corresponds to Euclidean proximity, as in geometric-random graphs.We judge the sensitivity and specificity of the fit by computing the area under the Receiver Operator Characteristic (ROC) curve. The network embedding algorithm is based on multi-dimensional scaling, with the square root of the path length in a network playing the role of the Euclidean distance in the Euclidean space. The algorithm exploits sparsity for computational efficiency, and requires only a few sparse matrix multiplications, giving a complexity of O(N2) where N is the number of proteins.The algorithm has been verified in the sense that it successfully rediscovers the geometric structure in artificially constructed geometric networks, even when noise is added by re-wiring some links. Applying the algorithm to 19 publicly available PPI networks of various organisms indicated that: (a) geometric effects are present and (b) two-dimensional Euclidean space is generally as effective as higher dimensional Euclidean space for explaining the connectivity. Testing on a high-confidence yeast data set produced a very strong indication of geometric structure (area under the ROC curve of 0.89), with this network being essentially indistinguishable from a noisy geometric network. Overall, the results add support to the hypothesis that PPI networks have a geometric structure

Fitting a geometric graph to a protein-protein interaction network

Finding a good network null model for protein-protein interaction (PPI) networks is a fundamental issue. Such a model would provide insights into the interplay between network structure and biological function as well as into evolution. Also, network (graph) models are used to guide biological experiments and discover new biological features. It has been proposed that geometric random graphs are a good model for PPI networks. In a geometric random graph, nodes correspond to uniformly randomly distributed points in a metric space and edges (links) exist between pairs of nodes for which the corresponding points in the metric space are close enough according to some distance norm. Computational experiments have revealed close matches between key topological properties of PPI networks and geometric random graph models. In this work, we push the comparison further by exploiting the fact that the geometric property can be tested for directly. To this end, we develop an algorithm that takes PPI interaction data and embeds proteins into a low-dimensional Euclidean space, under the premise that connectivity information corresponds to Euclidean proximity, as in geometric-random graphs.We judge the sensitivity and specificity of the fit by computing the area under the Receiver Operator Characteristic (ROC) curve. The network embedding algorithm is based on multi-dimensional scaling, with the square root of the path length in a network playing the role of the Euclidean distance in the Euclidean space. The algorithm exploits sparsity for computational efficiency, and requires only a few sparse matrix multiplications, giving a complexity of O(N2) where N is the number of proteins.The algorithm has been verified in the sense that it successfully rediscovers the geometric structure in artificially constructed geometric networks, even when noise is added by re-wiring some links. Applying the algorithm to 19 publicly available PPI networks of various organisms indicated that: (a) geometric effects are present and (b) two-dimensional Euclidean space is generally as effective as higher dimensional Euclidean space for explaining the connectivity. Testing on a high-confidence yeast data set produced a very strong indication of geometric structure (area under the ROC curve of 0.89), with this network being essentially indistinguishable from a noisy geometric network. Overall, the results add support to the hypothesis that PPI networks have a geometric structure

Time evolution of condensed state of interacting bosons with reduced number fluctuation in a leaky box

We study the time evolution of the Bose-Einstein condensate of interacting bosons confined in a leaky box, when its number fluctuation is initially (t=0) suppressed. We take account of quantum fluctuations of all modes, including k = 0. We identify a ``natural coordinate'' b_0 of the interacting bosons, by which many physical properties can be simply described. Using b_0, we successfully define the cosine and sine operators for interacting many bosons. The wavefunction, which we call the ``number state of interacting bosons'' (NSIB), of the ground state that has a definite number N of interacting bosons can be represented simply as a number state of b_0. We evaluate the time evolution of the reduced density operator \rho(t) of the bosons in the box with a finite leakage flux J, in the early time stage for which Jt << N. It is shown that \rho(t) evolves from a single NSIB at t = 0, into a classical mixture of NSIBs of various values of N at t > 0. We define a new state called the ``number-phase squeezed state of interacting bosons'' (NPIB). It is shown that \rho(t) for t>0 can be rewritten as the phase-randomized mixture (PRM) of NPIBs. It is also shown that the off-diagonal long-range order (ODLRO) and the order parameter defined by it do not distinguish the NSIB and NPIB. On the other hand, the other order parameter \Psi, defined as the expectation value of the boson operator, has different values among these states. For each element of the PRM of NPIBs, we show that \Psi evolves from zero to a finite value very quickly. Namely, after the leakage of only two or three bosons, each element acquires a full, stable and definite (non-fluctuating) value of \Psi.Comment: 25 pages including 3 figures. To appear in Phys. Rev. A (1999). The title is changed to stress the time evolution. Sections II, III and IV of the previous manuscript have been combined into one section. The introduction and summary of the previous manuscript have been combined into the Introduction and Summary. The names and abbreviations of quantum states are changed to stress that they are for interacting many bosons. More references are cite

Testing Broken U(1) Symmetry in a Two-Component Atomic Bose-Einstein Condensate

We present a scheme for determining if the quantum state of a small trapped Bose-Einstein condensate is a state with well defined number of atoms, a Fock state, or a state with a broken U(1) gauge symmetry, a coherent state. The proposal is based on the observation of Ramsey fringes. The population difference observed in a Ramsey fringe experiment will exhibit collapse and revivals due to the mean-field interactions. The collapse and revival times depend on the relative strength of the mean-field interactions for the two components and the initial quantum state of the condensate.Comment: 20 Pages RevTex, 3 Figure