On the approximation of the subgrid scale for systems of equations

Postprint (published version)

On periodic solutions of 2-periodic Lyness difference equations

We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n} is a cycle with positive values a,b and with positive initial conditions. It is known that for a=b=1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a,b) different from (1,1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a is not equal to b, then any odd period, except 1, appears.

Prediction of Childhood Asthma Using Conditional Probability and Discrete Event Simulation

Abstract: Asthma prevalence in children and adolescents in Spain is 10-17%. It is the most common chronic illness during childhood. Prevalence has been increasing over the last 40 years and there is considerable evidence that, among other factors, continued exposure to cigarette smoke results in asthma in children. No statistical or simulation model exist to forecast the evolution of childhood asthma in Europe. Such a model needs to incorporate the main risk factors that can be managed by medical authorities, such as tobacco (OR = 1.44), to establish how they affect the present generation of children. A simulation model using conditional probability and discrete event simulation for childhood asthma was developed and validated by simulating realistic scenario. The parameters used for the model (input data) were those found in the bibliography, especially those related to the incidence of smoking in Spain. We also used data from a panel of experts from the Hospital del Mar (Barcelona) related to actual evolution and asthma phenotypes. The results obtained from the simulation established a threshold of a 15-20% smoking population for a reduction in the prevalence of asthma. This is still far from the current level in Spain, where 24% of people smoke. We conclude that more effort must be made to combat smoking and other childhood asthma risk factors, in order to significantly reduce the number of cases. Once completed, this simulation methodology can realistically be used to forecast the evolution of childhood asthma as a function of variation in different risk factors.

Investigation of Rapid Thermal Analysis Procedures for Prediction of the Service Life of PCCP Carbonate Coarse Aggregate, HR-337, 1993

The major objective of this research project was to use thermal analysis techniques in conjunction with x-ray analysis methods to identify and explain chemical reactions that promote aggregate related deterioration in portland cement concrete. Twenty-two different carbonate aggregate samples were subjected to a chemical testing scheme that included: • bulk chemistry (major, minor and selected trace elements) • bulk mineralogy (minor phases concentrated by acid extraction) • solid-solution in the major carbonate phases • crystallite size determinations for the major carbonate phases • a salt treatment study to evaluate the impact of deicer salts Test results from these different studies were then compared to information that had been obtained using thermogravimetric analysis techniques. Since many of the limestones and dolomites that were used in the study had extensive field service records it was possible to correlate many of the variables with service life. The results of this study have indicated that thermogravimetric analysis can play an important role in categorizing carbonate aggregates. In fact, with modern automated thermal analysis systems it should be possible to utilize such methods on a quality control basis. Strong correlations were found between several of the variables that were monitored in this study. In fact, several of the variables exhibited significant correlations to concrete service life. When the full data set was utilized (n = 18), the significant correlations to service life can be summarized as follows ( a = 5% level): • Correlation coefficient, r, = -0.73 for premature TG loss versus service life. • Correlation coefficient, r, = 0.74 for relative crystallite size versus service life. • Correlation coefficient, r, = 0.53 for ASTM C666 durability factor versus service life. • Correlation coefficient, r, = -0.52 for acid-insoluble residue versus service life. Separation of the carbonate aggregates into their mineralogical categories (i.e., calcites and dolomites) tended to increase the correlation coefficients for some specific variables (r sometimes approached 0.90); however, the reliability of such correlations was questionable because of the small number of samples that were present in this study.

Prediction of cottonseed longevity

The objective of this work was to determine the viability equation constants for cottonseed and to detect the occurrence and depletion of hardseededness. Three seedlots of Brazilian cultivars IAC-19 and IAC-20 were tested, using 12 moisture content levels, ranging from 2.2 to 21.7% and three storage temperatures, 40, 50 and 65ºC. Seed moisture content level was reached from the initial value (around 8.8%) either by rehydration, in a closed container, or by drying in desiccators containing silica gel, both at 20ºC. Twelve seed subsamples for each moisture content/temperature treatment were sealed in laminated aluminium-foil packets and stored in incubators at those temperatures, until complete survival curves were obtained. Seed equilibrium relative humidity was recorded. Hardseededness was detected at moisture content levels below 6% and its releasing was achieved either naturally, during storage period, or artificially through seed coat removal. The viability equation quantified the response of seed longevity to storage environment well with K E = 9.240, C W = 5.190, C H = 0.03965 and C Q = 0.000426. The lower limit estimated for application of this equation at 65ºC was 3.6% moisture content.

Techniques for Estimating Flood-Frequency Discharges for Streams in Iowa, HR-395A, 2001

A statewide study was conducted to develop regression equations for estimating flood-frequency discharges for ungaged stream sites in Iowa. Thirty-eight selected basin characteristics were quantified and flood-frequency analyses were computed for 291 streamflow-gaging stations in Iowa and adjacent States. A generalized-skew-coefficient analysis was conducted to determine whether generalized skew coefficients could be improved for Iowa. Station skew coefficients were computed for 239 gaging stations in Iowa and adjacent States, and an isoline map of generalized-skew-coefficient values was developed for Iowa using variogram modeling and kriging methods. The skew map provided the lowest mean square error for the generalized-skew- coefficient analysis and was used to revise generalized skew coefficients for flood-frequency analyses for gaging stations in Iowa. Regional regression analysis, using generalized least-squares regression and data from 241 gaging stations, was used to develop equations for three hydrologic regions defined for the State. The regression equations can be used to estimate flood discharges that have recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years for ungaged stream sites in Iowa. One-variable equations were developed for each of the three regions and multi-variable equations were developed for two of the regions. Two sets of equations are presented for two of the regions because one-variable equations are considered easy for users to apply and the predictive accuracies of multi-variable equations are greater. Standard error of prediction for the one-variable equations ranges from about 34 to 45 percent and for the multi-variable equations range from about 31 to 42 percent. A region-of-influence regression method was also investigated for estimating flood-frequency discharges for ungaged stream sites in Iowa. A comparison of regional and region-of-influence regression methods, based on ease of application and root mean square errors, determined the regional regression method to be the better estimation method for Iowa. Techniques for estimating flood-frequency discharges for streams in Iowa are presented for determining ( 1) regional regression estimates for ungaged sites on ungaged streams; (2) weighted estimates for gaged sites; and (3) weighted estimates for ungaged sites on gaged streams. The technique for determining regional regression estimates for ungaged sites on ungaged streams requires determining which of four possible examples applies to the location of the stream site and its basin. Illustrations for determining which example applies to an ungaged stream site and for applying both the one-variable and multi-variable regression equations are provided for the estimation techniques.

Methods for Estimating Annual Exceedance-Probability Discharges for Streams in Iowa, Based on Data through Water Year 2010, TR-519, 2013

A statewide study was performed to develop regional regression equations for estimating selected annual exceedance- probability statistics for ungaged stream sites in Iowa. The study area comprises streamgages located within Iowa and 50 miles beyond the State’s borders. Annual exceedanceprobability estimates were computed for 518 streamgages by using the expected moments algorithm to fit a Pearson Type III distribution to the logarithms of annual peak discharges for each streamgage using annual peak-discharge data through 2010. The estimation of the selected statistics included a Bayesian weighted least-squares/generalized least-squares regression analysis to update regional skew coefficients for the 518 streamgages. Low-outlier and historic information were incorporated into the annual exceedance-probability analyses, and a generalized Grubbs-Beck test was used to detect multiple potentially influential low flows. Also, geographic information system software was used to measure 59 selected basin characteristics for each streamgage. Regional regression analysis, using generalized leastsquares regression, was used to develop a set of equations for each flood region in Iowa for estimating discharges for ungaged stream sites with 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities, which are equivalent to annual flood-frequency recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years, respectively. A total of 394 streamgages were included in the development of regional regression equations for three flood regions (regions 1, 2, and 3) that were defined for Iowa based on landform regions and soil regions. Average standard errors of prediction range from 31.8 to 45.2 percent for flood region 1, 19.4 to 46.8 percent for flood region 2, and 26.5 to 43.1 percent for flood region 3. The pseudo coefficients of determination for the generalized leastsquares equations range from 90.8 to 96.2 percent for flood region 1, 91.5 to 97.9 percent for flood region 2, and 92.4 to 96.0 percent for flood region 3. The regression equations are applicable only to stream sites in Iowa with flows not significantly affected by regulation, diversion, channelization, backwater, or urbanization and with basin characteristics within the range of those used to develop the equations. These regression equations will be implemented within the U.S. Geological Survey StreamStats Web-based geographic information system tool. StreamStats allows users to click on any ungaged site on a river and compute estimates of the eight selected statistics; in addition, 90-percent prediction intervals and the measured basin characteristics for the ungaged sites also are provided by the Web-based tool. StreamStats also allows users to click on any streamgage in Iowa and estimates computed for these eight selected statistics are provided for the streamgage.

Improvement of walking speed prediction by accelerometry and altimetry, validated by satellite positioning.

Activity monitors based on accelerometry are used to predict the speed and energy cost of walking at 0% slope, but not at other inclinations. Parallel measurements of body accelerations and altitude variation were studied to determine whether walking speed prediction could be improved. Fourteen subjects walked twice along a 1.3 km circuit with substantial slope variations (-17% to +17%). The parameters recorded were body acceleration using a uni-axial accelerometer, altitude variation using differential barometry, and walking speed using satellite positioning (DGPS). Linear regressions were calculated between acceleration and walking speed, and between acceleration/altitude and walking speed. These predictive models, calculated using the data from the first circuit run, were used to predict speed during the second circuit. Finally the predicted velocity was compared with the measured one. The result was that acceleration alone failed to predict speed (mean r = 0.4). Adding altitude variation improved the prediction (mean r = 0.7). With regard to the altitude/acceleration-speed relationship, substantial inter-individual variation was found. It is concluded that accelerometry, combined with altitude measurement, can assess position variations of humans provided inter-individual variation is taken into account. It is also confirmed that DGPS can be used for outdoor walking speed measurements, opening up new perspectives in the field of biomechanics.

Fluid dynamical prediction of changed v1-flow at energies available at the CERN Large Hadron Collider

Substantial collective flow is observed in collisions between lead nuclei at Large Hadron Collider (LHC) as evidenced by the azimuthal correlations in the transverse momentum distributions of the produced particles. Our calculations indicate that the global v1-flow, which at RHIC peaked at negative rapidities (named third flow component or antiflow), now at LHC is going to turn toward forward rapidities (to the same side and direction as the projectile residue). Potentially this can provide a sensitive barometer to estimate the pressure and transport properties of the quark-gluon plasma. Our calculations also take into account the initial state center-of-mass rapidity fluctuations, and demonstrate that these are crucial for v1 simulations. In order to better study the transverse momentum flow dependence we suggest a new"symmetrized" vS1(pt) function, and we also propose a new method to disentangle global v1 flow from the contribution generated by the random fluctuations in the initial state. This will enhance the possibilities of studying the collective Global v1 flow both at the STAR Beam Energy Scan program and at LHC.

V3 net charge: additional tool in HIV-1 tropism prediction.

Genotype-based algorithms are valuable tools for the identification of patients eligible for CCR5 inhibitors administration in clinical practice. Among the available methods, geno2pheno[coreceptor] (G2P) is the most used online tool for tropism prediction. This study was conceived to assess if the combination of G2P prediction with V3 peptide net charge (NC) value could improve the accuracy of tropism prediction. A total of 172 V3 bulk sequences from 143 patients were analyzed by G2P and NC values. A phenotypic assay was performed by cloning the complete env gene and tropism determination was assessed on U87_CCR5(+)/CXCR4(+) cells. Sequences were stratified according to the agreement between NC values and G2P results. Of sequences predicted as X4 by G2P, 61% showed NC values higher than 5; similarly, 76% of sequences predicted as R5 by G2P had NC values below 4. Sequences with NC values between 4 and 5 were associated with different G2P predictions: 65% of samples were predicted as R5-tropic and 35% of sequences as X4-tropic. Sequences identified as X4 by NC value had at least one positive residue at positions known to be involved in tropism prediction and positive residues in position 32. These data supported the hypothesis that NC values between 4 and 5 could be associated with the presence of dual/mixed-tropic (DM) variants. The phenotypic assay performed on a subset of sequences confirmed the tropism prediction for concordant sequences and showed that NC values between 4 and 5 are associated with DM tropism. These results suggest that the combination of G2P and NC could increase the accuracy of tropism prediction. A more reliable identification of X4 variants would be useful for better selecting candidates for Maraviroc (MVC) administration, but also as a predictive marker in coreceptor switching, strongly associated with the phase of infection.

Kinetic equations for difussion in the presence of entropic barriers

We use the mesoscopic nonequilibrium thermodynamics theory to derive the general kinetic equation of a system in the presence of potential barriers. The result is applied to a description of the evolution of systems whose dynamics is influenced by entropic barriers. We analyze in detail the case of diffusion in a domain of irregular geometry in which the presence of the boundaries induces an entropy barrier when approaching the exact dynamics by a coarsening of the description. The corresponding kinetic equation, named the Fick-Jacobs equation, is obtained, and its validity is generalized through the formulation of a scaling law for the diffusion coefficient which depends on the shape of the boundaries. The method we propose can be useful to analyze the dynamics of systems at the nanoscale where the presence of entropy barriers is a common feature.

Towards a diffusion image processing validation and accuracy prediction framework

Validation is the main bottleneck preventing theadoption of many medical image processing algorithms inthe clinical practice. In the classical approach,a-posteriori analysis is performed based on someobjective metrics. In this work, a different approachbased on Petri Nets (PN) is proposed. The basic ideaconsists in predicting the accuracy that will result froma given processing based on the characterization of thesources of inaccuracy of the system. Here we propose aproof of concept in the scenario of a diffusion imaginganalysis pipeline. A PN is built after the detection ofthe possible sources of inaccuracy. By integrating thefirst qualitative insights based on the PN withquantitative measures, it is possible to optimize the PNitself, to predict the inaccuracy of the system in adifferent setting. Results show that the proposed modelprovides a good prediction performance and suggests theoptimal processing approach.