Guessing probability distributions from small samples

We propose a new method for the calculation of the statistical properties, as e.g. the entropy, of unknown generators of symbolic sequences. The probability distribution $p(k)$ of the elements $k$ of a population can be approximated by the frequencies $f(k)$ of a sample provided the sample is long enough so that each element $k$ occurs many times. Our method yields an approximation if this precondition does not hold. For a given $f(k)$ we recalculate the Zipf--ordered probability distribution by optimization of the parameters of a guessed distribution. We demonstrate that our method yields reliable results.Comment: 10 pages, uuencoded compressed PostScrip

Validity and reliability of seismocardiography for the estimation of cardiorespiratory fitness

BACKGROUND: Low cardiorespiratory fitness (ie, peak oxygen consumption [V.O2peak]) is associated with cardiovascular disease and all-cause mortality and is recognized as an important clinical tool in the assessment of patients. Cardiopulmonary exercise test (CPET) is the gold standard procedure for determination of V.O2peak but has methodological challenges as it is time-consuming and requires specialized equipment and trained professionals. Seismofit is a chest-mounted medical device for estimating V.O2peak at rest using seismocardiography.OBJECTIVE: The purpose of this study was to investigate the validity and reliability of Seismofit V.O2peak estimation in a healthy population.METHODS: On 3 separate days, 20 participants (10 women) underwent estimations of V.O2peak with Seismofit (×2) and Polar Fitness Test (PFT) in randomized order and performed a graded CPET on a cycle ergometer with continuous pulmonary gas exchange measurements.RESULTS: Seismofit V.O2peak showed a significant bias of -3.1 ± 2.4 mL·min-1·kg-1 (mean ± 95% confidence interval) and 95% limits of agreement (LoA) of ±10.8 mL·min-1·kg-1 compared to CPET. The mean absolute percentage error (MAPE) was 12.0%. Seismofit V.O2peak had a coefficient of variation of 4.5% ± 1.3% and an intraclass correlation coefficient of 0.95 between test days and a bias of 0.0 ± 0.4 mL·min-1·kg-1 with 95% LoA of ±1.6 mL·min-1·kg-1 in test-retest. In addition, Seismofit showed a 2.4 mL·min-1·kg-1 smaller difference in 95% LoA than PFT compared to CPET.CONCLUSION: The Seismofit is highly reliable in its estimation of V.O2peak. However, based on the measurement error and MAPE &gt;10%, the Seismofit V.O2peak estimation model needs further improvement to be considered for use in clinical settings.</p

The strength of frustration and quantum fluctuations in LiVCuO4

For the 1D-frustrated ferromagnetic J_1-J_2 model with interchain coupling added, we analyze the dynamical and static structure factor S(k,omega), the pitch angle phi of the magnetic structure, the magnetization curve of edge-shared chain cuprates, and focus on LiCuVO4 for which neither a perturbed spinon nor a spin wave approach can be applied. phi is found to be most sensitive to the interplay of frustration and quantum fluctuations. For LiVCuO4 the obtained exchange parameters J are in accord with the results for a realistic 5-band extended Hubbard model and LSDA + U predictions yielding alpha=J_2/|J_1| about 0.75 in contrast to 5.5 > alpha > 1.42 suggested in the literature. The alpha-regime of the empirical phi-values in NaCu2O2 and linarite are considered, too.Comment: 7 pages, 7 figures, (1 figure added), improved text including also the abstract (the present second version has been submitted to EPL 26.10.2011, so far with one missing first referee report

Inverse Problems in a Bayesian Setting

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. We give a detailed account of this approach via conditional approximation, various approximations, and the construction of filters. Together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update in form of a filter is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and nonlinear Bayesian update in form of a filter on some examples.Comment: arXiv admin note: substantial text overlap with arXiv:1312.504

Fluxes and fate of dissolved methane released at the seafloor at the landward limit of the gas hydrate stability zone offshore western Svalbard

Widespread seepage of methane from seafloor sediments offshore Svalbard close to the landward limit of the gas hydrate stability zone (GHSZ) may, in part, be driven by hydrate destabilization due to bottom water warming. To assess whether this methane reaches the atmosphere where it may contribute to further warming, we have undertaken comprehensive surveys of methane in seawater and air on the upper slope and shelf region. Near the GHSZ limit at ?400 m water depth, methane concentrations are highest close to the seabed, reaching 825 nM. A simple box model of dissolved methane removal from bottom waters by horizontal and vertical mixing and microbially mediated oxidation indicates that ?60% of methane released at the seafloor is oxidized at depth before it mixes with overlying surface waters. Deep waters are therefore not a significant source of methane to intermediate and surface waters; rather, relatively high methane concentrations in these waters (up to 50 nM) are attributed to isopycnal turbulent mixing with shelf waters. On the shelf, extensive seafloor seepage at &lt;100 m water depth produces methane concentrations of up to 615 nM. The diffusive flux of methane from sea to air in the vicinity of the landward limit of the GHSZ is ?4–20 ?mol m?2 d?1, which is small relative to other Arctic sources. In support of this, analyses of mole fractions and the carbon isotope signature of atmospheric methane above the seeps do not indicate a significant local contribution from the seafloor source