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Standard methods of structural dynamic analysis assume that the structural characteristics are deterministic. Recognizing that these characteristics are actually statistical in nature, researchers have recently developed a variety of methods that use this information to determine probabilities of a desired response characteristic, such as natural frequency, without using expensive Monte Carlo simulations. One of the problems in these methods is correctly identifying the statistical properties of primitive variables such as geometry, stiffness, and mass. This paper presents a method where the measured dynamic properties of substructures are used instead as the random variables. The residual flexibility method of component mode synthesis is combined with the probabilistic methods to determine the cumulative distribution function of the system eigenvalues. A simple cantilever beam test problem is presented that illustrates the theory.

Accounting for the statistical geometric and material variability of structures in analysis has been a topic of considerable research for the last 30 years. The determination of quantifiable measures of statistical probability of a desired response variable, such as natural frequency, maximum displacement, or stress, to replace experience-based ''safety factors'' has been a primary goal of these studies. There are, however, several problems associated with their satisfactory application to realistic structures, such as bladed disks in turbomachinery. These include the accurate definition of the input random variables (rv's), the large size of the finite element models frequently used to simulate these structures, which makes even a single deterministic analysis expensive, and accurate generation of the cumulative distribution function (CDF) necessary to obtain the probability of the desired response variables. The research presented here applies a methodology called probabilistic dynamic synthesis (PDS) to solve these problems. The PDS method uses dynamic characteristics of substructures measured from modal test as the input rv's, rather than ''primitive'' rv's such as material or geometric uncertainties. These dynamic characteristics, which are the free-free eigenvalues, eigenvectors, and residual flexibility (RF), are readily measured and for many substructures, a reasonable sample set of these measurements can be obtained. The statistics for these rv's accurately account for the entire random character of the substructure. Using the RF method of component mode synthesis, these dynamic characteristics are used to generate reduced-size sample models of the substructures, which are then coupled to form system models. These sample models are used to obtain the CDF of the response variable by either applying Monte Carlo simulation or by generating data points for use in the response surface reliability method, which can perform the probabilistic analysis with an order of magnitude less computational effort. Both free- and forced-response analyses have been performed, and the results indicate that, while there is considerable room for improvement, the method produces usable and more representative solutions for the design of realistic structures with a substantial savings in computer time.

In 1990 Bender, Canfield and McKay gave an asymptotic formula for the number of connected graphs on $[n]$ with $m$ edges, whenever $n$ and the nullity $m-n+1$ tend to infinity. Asymptotic formulae for the number of connected $r$-uniform hypergraphs on $[n]$ with $m$ edges and so nullity $t=(r-1)m-n+1$ were proved by Karo\'nski and \L uczak for the case $t=o(\log n/\log\log n)$, and Behrisch, Coja-Oghlan and Kang for $t=\Theta(n)$. Here we prove such a formula for any $r\ge 3$ fixed, and any $t=t(n)$ satisfying $t=o(n)$ and $t\to\infty$ as $n\to\infty$. This leaves open only the (much simpler) case $t/n\to\infty$, which we will consider in future work. ( arXiv:1511.04739 ) Our approach is probabilistic. Let $H^r_{n,p}$ denote the random $r$-uniform hypergraph on $[n]$ in which each edge is present independently with probability $p$. Let $L_1$ and $M_1$ be the numbers of vertices and edges in the largest component of $H^r_{n,p}$. We prove a local limit theorem giving an asymptotic formula for the probability that $L_1$ and $M_1$ take any given pair of values within the `typical' range, for any $p=p(n)$ in the supercritical regime, i.e., when $p=p(n)=(1+\epsilon(n))(r-2)!n^{-r+1}$ where $\epsilon^3n\to\infty$ and $\epsilon\to 0$; our enumerative result then follows easily. Taking as a starting point the recent joint central limit theorem for $L_1$ and $M_1$, we use smoothing techniques to show that `nearby' pairs of values arise with about the same probability, leading to the local limit theorem. Behrisch et al used similar ideas in a very different way, that does not seem to work in our setting. Independently, Sato and Wormald have recently proved the special case $r=3$, with an additional restriction on $t$. They use complementary, more enumerative methods, which seem to have a more limited scope, but to give additional information when they do work.

Mechanical property characterization experiments have been carried out on a 2-D, woven, carbon-carbon composite. These were followed by tests to determine statistical variability and size effects. Tension, compression, in plane and interlaminar shear tests, unnotched and notched four point beam and plate (with and without holes) tests were performed. Weibull distribution parameters are reported.

High temperature and long duration applications of monolithic ceramics can place their failure mode in the creep rupture regime. A previous model advanced by the authors described a methodology by which the creep rupture life of a loaded component can be predicted. That model was based on the life fraction damage accumulation rule in association with the modified Monkman-Grant creep ripture criterion However, that model did not take into account the deteriorating state of the material due to creep damage (e.g., cavitation) as time elapsed. In addition, the material creep parameters used in that life prediction methodology, were based on uniaxial creep curves displaying primary and secondary creep behavior, with no tertiary regime. The objective of this paper is to present a creep life prediction methodology based on a modified form of the Kachanov-Rabotnov continuum damage mechanics (CDM) theory. In this theory, the uniaxial creep rate is described in terms of stress, temperature, time, and the current state of material damage. This scalar damage state parameter is basically an abstract measure of the current state of material damage due to creep deformation. The damage rate is assumed to vary with stress, temperature, time, and the current state of damage itself. Multiaxial creep and creep rupture formulations of the CDM approach are presented in this paper. Parameter estimation methodologies based on nonlinear regression analysis are also described for both, isothermal constant stress states and anisothermal variable stress conditions This creep life prediction methodology was preliminarily added to the integrated design code CARES/Creep (Ceramics Analysis and Reliability Evaluation of Structures/Creep), which is a postprocessor program to commercially available finite element analysis (FEA) packages. Two examples, showing comparisons between experimental and predicted creep lives of ceramic specimens, are used to demonstrate the viability of this methodology and the CARES/Creep program.

Inverse problems are of great importance in astrophysics for deriving information about the physical characteristics of hot optically thin plasma sources from their EUV and X-ray spectra. We describe and test an iterative method developed within the framework of a probabilistic approach to the spectral inverse problem for determining the thermal structures of the emitting plasma. We also demonstrate applications of this method to both high resolution line spectra and broadband imaging data. Our so-called Bayesian iterative method (BIM) is an iterative procedure based on Bayes' theorem and is used to reconstruct differential emission measure (DEM) distributions. To demonstrate the abilities of the BIM, we performed various numerical tests and model simulations establishing its robustness and usefulness. We then applied the BIM to observable data for several active regions (AR) previously analyzed with other DEM diagnostic techniques: both SUMER/SOHO (Landi and Feldman, 2008) and SPIRIT/CORONAS-F (Shestov et al., 2010) line spectra data, and XRT/Hinode (Reale et al., 2009) broadband imaging data. The BIM results show that this method is an effective tool for determining the thermal structure of emitting plasma and can be successfully used for the DEM analysis of both line spectra and broadband imaging data. The BIM calculations correlate with recent studies confirming the existence of hot plasma in solar ARs. The BIM results also indicate that the coronal plasma may have the continuous distributions predicted by the nanoflare paradigm.

The strength of brittle materials is characterized by a wide scatter. Such materials are also afflicted by size effects. Size effects in brittle composite structures such as beams and plates with and without stress raisers are investigated experimentally and analytically. A methodology for reliability analysis of carbon-carbon composites is presented. The model is based on Weibull statistics which was extended to account for the three-dimensional stress field including interlaminar stresses. Failure criteria for bi-directional orthotropic lamina are developed and failure analysis in the non-probabilistic sense (i.e., First-ply-failure analysis) is performed. Comparisons are made with existing failure criteria, with the results of the reliability analysis and also with experiments.

In this article, we introduce the parametrix technique in order to construct fundamental solutions as a general method based on semigroups and their generators. This leads to a probabilistic interpretation of the parametrix method that is amenable to Monte Carlo simulation. We consider the explicit examples of continuous diffusions and jump driven stochastic differential equations with H\"{o}lder continuous coefficients.

In this article, we introduce the parametrix technique in order to construct fundamental solutions as a general method based on semigroups and their generators. This leads to a probabilistic interpretation of the parametrix method that is amenable to Monte Carlo simulation. We consider the explicit examples of continuous diffusions and jump driven stochastic differential equations with H\"{o}lder continuous coefficients.

In this article, we introduce the parametrix technique in order to construct fundamental solutions as a general method based on semigroups and their generators. This leads to a probabilistic interpretation of the parametrix method that is amenable to Monte Carlo simulation. We consider the explicit examples of continuous diffusions and jump driven stochastic differential equations with H\"{o}lder continuous coefficients.

We propose an accurate method for counting states of close to zero and positive cosmological constant in the Bousso-Polchinski Landscape. This method is based on simple geometrical considerations on the high-dimensional lattice of quantized fluxes and on a probabilistic model (the "random hyperplane" model) that provides a distribution of the values of the cosmological constant. Justification of the assumptions made in this model are given by means of numerical experiments.

In this paper we introduce a probabilistic approach to show the existence of initial data with arbitrarily large $L^2(\mathbb{R}^3)$, $\dot{H}^{1/2}(\mathbb{R}^3)$ and $\mathcal{PM}^2$-norms for which a Generalized Navier-Stokes system generate a global regular solution. More precisely, we show that from a certain family of possible large initial data most of them give raise to global regular solutions to a given Generalized Navier-Stokes system.

In this paper we describe a general framework for incorporating tidal uncertainty into probabilistic tsunami hazard assessment and propose the Pattern Method and a simpler special case called the $\Delta t$ Method as effective approaches. The general framework also covers the method developed by Mofjeld et.al in 2007 that was used for the 2009 Seaside, Oregon probabilistic study by Gonzalez et.al. We show the Pattern Method is superior to past approaches because it takes advantage of our ability to run the tsunami simulation at multiple tide stages and uses the time history of flow depth at strategic gauge locations to infer the temporal pattern of waves that is unique to each tsunami source. Combining these patterns with knowledge of the tide cycle at a particular location improves the ability to estimate the probability that a wave will arrive at a time when the tidal stage is sufficiently large that a quantity of interest such as the maximum flow depth exceeds a specified level.

The construction of torsion-free abelian groups with prescribed endomorphism rings starting with Corner's seminal work is a well-studied subject in the theory of abelian groups. Usually these construction work by adding elements from a (topological) completion in order to get rid of (kill) unwanted homomorphisms. The critical part is to actually prove that every unwanted homomorphism can be killed by adding a suitable element. We will demonstrate that some of those constructions can be significantly simplified by choosing the elements at random. As a result, the endomorphism ring will be almost surely prescribed, i.e., with probability one.

The Probabilistic Dynamic Synthesis method is a technique for obtaining the statistics of a desired response engineering quantity for a structure with non-deterministic parameters. The method uses measured data from modal testing of the structure as the input random variables, rather than more "primitive" quantities like geometry or material variation. This modal information is much more comprehensive and easily measured than the "primitive" information. The probabilistic analysis is carried out using either response surface reliability methods or Monte Carlo simulation. In previous work, the feasibility of the PDS method applied to a simple seven degree-of-freedom spring-mass system was verified. In this paper, extensive issues involved with applying the method to a realistic three-substructure system are examined, and free and forced response analyses are performed. The results from using the method are promising, especially when the lack of alternatives for obtaining quantitative output for probabilistic structures is considered.

We introduce a new method, combination of random testing and abstract interpretation, for the analysis of programs featuring both probabilistic and non-probabilistic nondeterminism. After introducing "ordinary" testing, we show how to combine testing and abstract interpretation and give formulas linking the precision of the results to the number of iterations. We then discuss complexity and optimization issues and end with some experimental results.

With the global proliferation of wind power, accurate short-term forecasts of wind resources at wind energy sites are becoming paramount. Regime-switching space-time (RST) models merge meteorological and statistical expertise to obtain accurate and calibrated, fully probabilistic forecasts of wind speed and wind power. The model formulation is parsimonious, yet takes account of all the salient features of wind speed: alternating atmospheric regimes, temporal and spatial correlation, diurnal and seasonal non-stationarity, conditional heteroscedasticity, and non-Gaussianity. The RST method identifies forecast regimes at the wind energy site and fits a conditional predictive model for each regime. Geographically dispersed meteorological observations in the vicinity of the wind farm are used as off-site predictors. The RST technique was applied to 2-hour ahead forecasts of hourly average wind speed at the Stateline wind farm in the US Pacific Northwest. In July 2003, for instance, the RST forecasts had root-mean-square error (RMSE) 28.6% less than the persistence forecasts. For each month in the test period, the RST forecasts had lower RMSE than forecasts using state-of-the-art vector time series techniques. The RST method provides probabilistic forecasts in the form of predictive cumulative distribution functions, and those were well calibrated and sharp. The RST prediction intervals were substantially shorter on average than prediction intervals derived from univariate time series techniques. These results suggest that quality meteorological data from sites upwind of wind farms can be efficiently used to improve short-term forecasts of wind resources. It is anticipated that the RST technique can be successfully applied at wind energy sites all over the world.

A formal procedure for the probabilistic design assessment of a composite structure is described. The uncertainties in all aspects of a composite structure (constituent material properties, fabrication variables, structural geometry, service environments, etc.), which result in the uncertain behavior in the composite structural responses, are included in the assessment. The probabilistic assessment consists of design criteria, modeling of composite structures and uncertainties, simulation methods, and the decision making process. A sample case is presented to illustrate the formal procedure and to demonstrate that composite structural designs can be probabilistically assessed with accuracy and efficiency.

A formal procedure for the probabilistic design assessment of a composite structure is described. The uncertainties in all aspects of a composite structure (constituent material properties, fabrication variables, structural geometry, service environments, etc.), which result in the uncertain behavior in the composite structural responses, are included in the assessment. The probabilistic assessment consists of design criteria, modeling of composite structures and uncertainties, simulation methods, and the decision making process. A sample case is presented to illustrate the formal procedure and to demonstrate that composite structural designs can be probabilistically assessed with accuracy and efficiency.

Standard methods of structural dynamic analysis assume that the structural characteristics are deterministic. Recognizing that these characteristics are actually statistical in nature, researchers have recently developed a variety of methods that use this information to determine probabilities of a desired response characteristic, such as natural frequency, without using expensive Monte Carlo simulations. One of the problems in these methods is correctly identifying the statistical properties of primitive variables such as geometry, stiffness, and mass. This paper presents a method where the measured dynamic properties of substructures are used instead as the random variables. The residual flexibility method of component mode synthesis is combined with the probabilistic methods to determine the cumulative distribution function of the system eigenvalues. A simple cantilever beam test problem is presented that illustrates the theory.

In the framework of parametric modeling, the paper provides the analysis of a unique system «object of waste disposal – protection – locality» from the perspective of its potential danger. It establishes the vertex set of the potential outcomes of violations of the rules of operation of waste disposal and develops a logical model for their realization. Based on the data the authors have tested the logic-probabilistic method of rapid assessment system "object of waste disposal – protection – locality" and got the resulting values of probabilistic realization of the vertex outcome for the current object of disposal. The scheme for determination of protective measures to reduce nitrate concentrations in groundwater was developed. On its basis, the authors have established the necessity to develop instructions for the collection and transportation of object of waste disposal infiltrate.

The California Bearing Ratio (CBR) design method for flexible airfield pavements was analyzed using a probabilistic approach. The design parameters considered were the load P (or the equivalent single-wheel load), the sub-grade CBR, the tire contact area A, and the pavement total thickness t. The expected value and variance of the dependent variable performance factor, alpha (which is logarithmically related to the number of passes to failure) were estimated by using the Taylor series expansion and the Rosenblueth method. Differences in computed results between the two methods were found to be small, although the derivation of the expressions for Taylor series expansion was very complicated. A procedure was developed to estimate the reliability of the designed pavement system based on known variabilities of design parameters. Results of the reliability analysis indicate that prediction of pavement performance is most influenced by variations of pavement thickness t and is least influenced by variations of tire contact are A. The effects of variations of wheel load P and subgrade CBR are identical. The weighting factors for parameters t, CBR, P, and A, in general, are approximately 1, 0.34, 0.34, and 0.01, respectively (Table 3).

This article is from Emerging Themes in Epidemiology , volume 11 . Abstract Background: Maternal morbidity is more common than maternal death, and population-based estimates of the burden of maternal morbidity could provide important indicators for monitoring trends, priority setting and evaluating the health impact of interventions. Methods based on lay reporting of obstetric events have been shown to lack specificity and there is a need for new approaches to measure the population burden of maternal morbidity. A computer-based probabilistic tool was developed to estimate the likelihood of maternal morbidity and its causes based on self-reported symptoms and pregnancy/delivery experiences. Development involved the use of training datasets of signs, symptoms and causes of morbidity from 1734 facility-based deliveries in Benin and Burkina Faso, as well as expert review. Preliminary evaluation of the method compared the burden of maternal morbidity and specific causes from the probabilistic tool with clinical classifications of 489 recently-delivered women from Benin, Bangladesh and India. Results: Using training datasets, it was possible to create a probabilistic tool that handled uncertainty of women’s self reports of pregnancy and delivery experiences in a unique way to estimate population-level burdens of maternal morbidity and specific causes that compared well with clinical classifications of the same data. When applied to test datasets, the method overestimated the burden of morbidity compared with clinical review, although possible conceptual and methodological reasons for this were identified. Conclusion: The probabilistic method shows promise and may offer opportunities for standardised measurement of maternal morbidity that allows for the uncertainty of women’s self-reported symptoms in retrospective interviews. However, important discrepancies with clinical classifications were observed and the method requires further development, refinement and evaluation in a range of settings.

We demonstrate an approach for exact sampling of certain discrete combinatorial distributions, which is a hybrid of exact Boltzmann sampling and the recursive method, using probabilistic divide-and-conquer (PDC). The approach specializes to exact Boltzmann sampling in the trivial setting, and specializes to PDC deterministic second half in the first non-trivial application. A large class of examples is given for which this method broadly applies, and several examples are worked out explicitly.

In 1990 Bender, Canfield and McKay gave an asymptotic formula for the number of connected graphs on $[n]=\{1,2,\ldots,n\}$ with $m$ edges, whenever $n\to\infty$ and $n-1\le m=m(n)\le \binom{n}{2}$. We give an asymptotic formula for the number $C_r(n,m)$ of connected $r$-uniform hypergraphs on $[n]$ with $m$ edges, whenever $r\ge 3$ is fixed and $m=m(n)$ with $m/n\to\infty$, i.e., the average degree tends to infinity. This complements recent results of Behrisch, Coja-Oghlan and Kang (the case $m=n/(r-1)+\Theta(n)$) and the present authors (the case $m=n/(r-1)+o(n)$, i.e., `nullity' or `excess' $o(n)$). The proof is based on probabilistic methods, and in particular on a bivariate local limit theorem for the number of vertices and edges in the largest component of a certain random hypergraph. The arguments are much simpler than in the sparse case; in particular, we can use `smoothing' techniques to directly prove the local limit theorem, without needing to first prove a central limit theorem.

The Probabilistic Dynamic Synthesis method is a new technique for obtaining the statistics of a desired response engineering quantity for a structure with non-deterministic parameters. The method uses measured data from modal testing of the structure as the input random variables, rather than more "primitive" quantities like geometry or material variation. This modal information is much more comprehensive and easily measured than the "primitive" information. The probabilistic analysis is carried out using either response surface reliability methods or Monte Carlo simulation. A previous work verified the feasibility of the PDS method on a simple seven degree-of-freedom spring-mass system. In this paper, extensive issues involved with applying the method to a realistic three-substructure system are examined, and free and forced response analyses are performed. The results from using the method are promising, especially when the lack of alternatives for obtaining quantitative output for probabilistic structures is considered.

A method is described to computationally simulate probabilistic buckling behavior of multilayered composite shells. The simulation accounts for all naturally-occurring uncertainties including those in constituent (fiber/matrix) material properties, fabrication variables, and structure geometry. The method is demonstrated for probabilistically assessing the buckling survivability of a specific case of a stiffened composite cylindrical shell with and without cutouts. The sensitivities of various uncertain variables on the buckling survivability are evaluated at specified reliability. The results show that the buckling survivability for a shell without cutouts depends primarily on shell skin related uncertainties. However, stringer related uncertainties become important for a shell with cutouts.

High temperature and long duration applications of monolithic ceramics can place their failure mode in the creep rupture regime. A previous model advanced by the authors described a methodology by which the creep rupture life of a loaded component can be predicted. That model was based on the life fraction damage accumulation rule in association with the modified Monkman-Grant creep ripture criterion However, that model did not take into account the deteriorating state of the material due to creep damage (e.g., cavitation) as time elapsed. In addition, the material creep parameters used in that life prediction methodology, were based on uniaxial creep curves displaying primary and secondary creep behavior, with no tertiary regime. The objective of this paper is to present a creep life prediction methodology based on a modified form of the Kachanov-Rabotnov continuum damage mechanics (CDM) theory. In this theory, the uniaxial creep rate is described in terms of stress, temperature, time, and the current state of material damage. This scalar damage state parameter is basically an abstract measure of the current state of material damage due to creep deformation. The damage rate is assumed to vary with stress, temperature, time, and the current state of damage itself. Multiaxial creep and creep rupture formulations of the CDM approach are presented in this paper. Parameter estimation methodologies based on nonlinear regression analysis are also described for both, isothermal constant stress states and anisothermal variable stress conditions This creep life prediction methodology was preliminarily added to the integrated design code CARES/Creep (Ceramics Analysis and Reliability Evaluation of Structures/Creep), which is a postprocessor program to commercially available finite element analysis (FEA) packages. Two examples, showing comparisons between experimental and predicted creep lives of ceramic specimens, are used to demonstrate the viability of this methodology and the CARES/Creep program.

The Probabilistic Dynamic Synthesis method is a new technique for obtaining the statistics of a desired response engineering quantity for a structure with non-deterministic parameters. The method uses measured data from modal testing of the structure as the input random variables, rather than more ''primitive'' quantities like geometry or material variation. This modal information is much more comprehensive and easily measured than the ''primitive'' information. The probabilistic analysis is carried out using either response surface reliability methods or Monte Carlo simulation. A previous work verified the feasibility of the PDS method on a simple seven degree-of-freedom spring-mass system. In this paper, extensive issues involved with applying the method to a realistic three-substructure system are examined, and free and forced response analyses are performed. The results from using the method are promising, especially when the lack of alternatives for obtaining quantitative output for probabilistic structures is considered.

Probabilistic weather forecasting consists of finding a joint probability distribution for future weather quantities or events. It is typically done by using a numerical weather prediction model, perturbing the inputs to the model in various ways, often depending on data assimilation, and running the model for each perturbed set of inputs. The result is then viewed as an ensemble of forecasts, taken to be a sample from the joint probability distribution of the future weather quantities of interest. This is typically not feasible for mesoscale weather prediction carried out locally by organizations without the vast data and computing resources of national weather centers. Instead, we propose a simpler method which breaks with much previous practice by perturbing the outputs, or deterministic forecasts, from the model. Forecast errors are modeled using a geostatistical model, and ensemble members are generated by simulating realizations of the geostatistical model. The method is applied to 48-hour mesoscale forecasts of temperature in the US Pacific Northwest in 2000 and 2002. The resulting forecast intervals turn out to be well calibrated for individual meteorological quantities, to be sharper than those obtained from approximate climatology, and to be consistent with aspects of the spatial correlation structure of the observations.

Artificial intelligence needs methods for object modeling having the set of key points. A novel method of Hurwitz- Radon Matrices (MHR) is used in signature modeling. Proposed method is based on the family of Hurwitz-Radon (HR) matrices which possess columns composed of orthogonal vectors. Two-dimensional curve as signature is modeling via different functions as probability distribution functions: polynomial, sinus, cosine, tangent, cotangent, logarithm, exponent, arc sin, arc cos, arc tan and power function. It is shown how to build the orthogonal matrix OHR operator and how to use it in a process of signature modeling.

This article is from Population Health Metrics , volume 9 . Abstract Background: Verbal autopsy (VA) is a widely used method for analyzing cause of death in absence of vital registration systems. We adapted the InterVA method to extrapolate causes of death for stillbirths and neonatal deaths from verbal autopsy questionnaires, using data from Malawi, Zimbabwe, and Nepal. Methods: We obtained 734 stillbirth and neonatal VAs from recent community studies in rural areas: 169 from Malawi, 385 from Nepal, and 180 from Zimbabwe. Initial refinement of the InterVA model was based on 100 physician-reviewed VAs from Malawi. InterVA indicators and matrix probabilities for cause of death were reviewed for clinical and epidemiological coherence by a pediatrician-researcher and an epidemiologist involved in the development of InterVA. The modified InterVA model was evaluated by comparing population-level cause-specific mortality fractions and individual agreement from two methods of interpretation (physician review and InterVA) for a further 69 VAs from Malawi, 385 from Nepal, and 180 from Zimbabwe. Results: Case-by-case agreement between InterVA and reviewing physician diagnoses for 69 cases from Malawi, 180 cases from Zimbabwe, and 385 cases from Nepal were 83% (kappa 0.76 (0.75 - 0.80)), 71% (kappa 0.41(0.32-0.51)), and 74% (kappa 0.63 (0.60-0.63)), respectively. The proportion of stillbirths identified as fresh or macerated by the different methods of VA interpretation was similar in all three settings. Comparing across countries, the modified InterVA method found that proportions of preterm births and deaths due to infection were higher in Zimbabwe (44%) than in Malawi (28%) or Nepal (20%). Conclusion: The modified InterVA method provides plausible results for stillbirths and newborn deaths, broadly comparable to physician review but with the advantage of internal consistency. The method allows standardized cross-country comparisons and eliminates the inconsistencies of physician review in such comparisons.

Eddy current models have matured to such a degree that it is now possible to simulate realistic nondestructive inspection (NDI) scenarios. Models have been used in the design and analysis of NDI systems and to a limited extent, model-based inverse methods for Nondestructive Evaluation (NDE).The science base is also being established to quantify the reliability systems via Model-Assisted Probability of Detection (MAPOD), In realistic situations, it is more accurate to treat the input model variables as random variables rather than deterministic quantities. Typically a Monte- Carlo simulation is conducted to predict the output of a model when the inputs are random variables. This is a reasonable approach as long as computational time is not to long; however, in most applications, introducing a flaw into the model results in extensive computational time ranging from hours to days, prohibiting Monte-Carlo simulations. Even methods such as Latin-Hypercube sampling do not reduce the number of simulations enough for reasonable use.

The state of stress in a cylindrical structure consisting of multiple layers of carbon-carbon composite and subjected to thermal and pressure shock are analyzed using an elasticity approach. The reliability of the structure based on the weakest link concept and the Weibull distribution is also calculated. Coupled thermo-elasticity is first assumed and is shown to be unnecessary for the material considered. The effects of external and internal thermal shock as well as a superimposed pressure shock are examined. It is shown that for the geometry chosen, the structure may fail when exposed to thermal shock alone while a superimposed pressure shock can mitigate the probability of failure.

Accounting for the statistical geometric and material variability of structures in analysis has been a topic of considerable research for the last 30 years. The determination of quantifiable measures of statistical probability of a desired response variable, such as natural frequency, maximum displacement, or stress, to replace experience-based "safety factors" has been a primary goal of these studies. There are, however, several problems associated with their satisfactory application to realistic structures, such as bladed disks in turbomachinery. These include the accurate definition of the input random variables (rv's), the large size of the finite element models frequently used to simulate these structures, which makes even a single deterministic analysis expensive, and accurate generation of the cumulative distribution function (CDF) necessary to obtain the probability of the desired response variables. The research presented here applies a methodology called probabilistic dynamic synthesis (PDS) to solve these problems. The PDS method uses dynamic characteristics of substructures measured from modal test as the input rv's, rather than "primitive" rv's such as material or geometric uncertainties. These dynamic characteristics, which are the free-free eigenvalues, eigenvectors, and residual flexibility (RF), are readily measured and for many substructures, a reasonable sample set of these measurements can be obtained. The statistics for these rv's accurately account for the entire random character of the substructure. Using the RF method of component mode synthesis, these dynamic characteristics are used to generate reduced-size sample models of the substructures, which are then coupled to form system models. These sample models are used to obtain the CDF of the response variable by either applying Monte Carlo simulation or by generating data points for use in the response surface reliability method, which can perform the probabilistic analysis with an order of magnitude less computational effort. Both free- and forced-response analyses have been performed, and the results indicate that, while there is considerable room for improvement, the method produces usable and more representative solutions for the design of realistic structures with a substantial savings in computer time.

We show that the maximal determinant D(n) for $n \times n$ ${\pm 1}$-matrices satisfies $R(n) := D(n)/n^{n/2} \ge \kappa_d > 0$. Here $n^{n/2}$ is the Hadamard upper bound, and $\kappa_d$ depends only on $d := n-h$, where $h$ is the maximal order of a Hadamard matrix with $h \le n$. Previous lower bounds on R(n) depend on both $d$ and $n$. Our bounds are improvements, for all sufficiently large $n$, if $d > 1$. We give various lower bounds on R(n) that depend only on $d$. For example, $R(n) \ge 0.07 (0.352)^d > 3^{-(d+3)}$. For any fixed $d \ge 0$ we have $R(n) \ge (2/(\pi e))^{d/2}$ for all sufficiently large $n$ (and conjecturally for all positive $n$). If the Hadamard conjecture is true, then $d \le 3$ and $\kappa_d \ge (2/(\pi e))^{d/2} > 1/9$.

Let $D(n)$ be the maximal determinant for $n \times n$ $\{\pm 1\}$-matrices, and ${\mathcal R}(n) = D(n)/n^{n/2}$ be the ratio of $D(n)$ to the Hadamard upper bound. We give several new lower bounds on ${\mathcal R}(n)$ in terms of $d$, where $n = h+d$, $h$ is the order of a Hadamard matrix, and $h$ is maximal subject to $h \le n$. A relatively simple bound is \[{\mathcal R}(n) \ge \left(\frac{2}{\pi e}\right)^{d/2} \left(1 - d^2\left(\frac{\pi}{2h}\right)^{1/2}\right) \;\text{ for all }\; n \ge 1.\] An asymptotically sharper bound is \[{\mathcal R}(n) \ge \left(\frac{2}{\pi e}\right)^{d/2} \exp\left(d\left(\frac{\pi}{2h}\right)^{1/2} + \; O\left(\frac{d^{5/3}}{h^{2/3}}\right)\right).\] We also show that \[{\mathcal R}(n) \ge \left(\frac{2}{\pi e}\right)^{d/2}\] if $n \ge n_0$ and $n_0$ is sufficiently large, the threshold $n_0$ being independent of $d$, or for all $n\ge 1$ if $0 \le d \le 3$ (which would follow from the Hadamard conjecture). The proofs depend on the probabilistic method, and generalise previous results that were restricted to the cases $d=0$ and $d=1$.