A Variational Procedure for Time-Dependent Processes

A simple variational Lagrangian is proposed for the time development of an arbitrary density matrix, employing the "factorization" of the density. Only the "kinetic energy" appears in the Lagrangian. The formalism applies to pure and mixed state cases, the Navier-Stokes equations of hydrodynamics, transport theory, etc. It recaptures the Least Dissipation Function condition of Rayleigh-Onsager {\bf and in practical applications is flexible}. The variational proposal is tested on a two level system interacting that is subject, in one instance, to an interaction with a single oscillator and, in another, that evolves in a dissipative mode.Comment: 25 pages, 4 figure

Parenting practices and adolescent eating behaviors in African American families.

Parents play an important role in developing the eating behaviors of their children by adopting specific parenting practices. As the prevalence of obesity is high amongst African American adolescents, investigations into associations of specific parenting practices and adolescents' eating behaviors are essential. In this exploratory study, 14 African American parent-adolescent dyads were interviewed to characterize the influence of eight different parenting practices on the consumption of three main food categories (dairy, fruits and vegetables, and unhealthy snacks). The results revealed that authoritarian parenting practices were correlated with a higher BMI percentile in adolescents, whereas modeling and monitoring are correlated with a higher parent BMI. In addition, reasoning, monitoring, modeling, and authoritative parenting practices were associated with less unhealthy snack consumption among adolescents. Reasoning and monitoring were the only parenting practices associated with higher fruit and vegetable consumption. Finally, a significant correlation was found between eating fruits and vegetables and unhealthy snacks and the location of eating. In conclusion, different parenting practices and environmental factors may impact BMI and food consumption of African American dyads. The results of this study can be used to guide improvement in, and/or development of, nutritional education interventions considering the cultural differences of racial minorities

Relationship between family racial/ethnic backgrounds, parenting practices and styles, and adolescent eating behaviors.

Obesity is more prevalent among racial minority children in the United States, as compared to White children. Parenting practices can impact the development of children's eating behaviors and habits. In this study, we investigated the relationships among racial/ethnic backgrounds, parenting practices and styles, and eating behaviors in adolescents. Fifty-one parent-adolescent dyads were interviewed to characterize parenting practices and styles, as well as the consumption of dairy, fruits and vegetables, and unhealthy snacks. Height and weight were measured to calculate parent BMI and adolescent BMI-for-age percentiles. Three parenting practice categories-modeling, authoritative, and authoritarian-were found to be related to race/ethnicity. A higher score in authoritarian parenting practices was related to higher BMI percentiles among African American adolescents, whereas a higher score in monitoring practices was related to lower BMI percentiles among non-Hispanic White adolescents. Modeling, reasoning, and monitoring led to higher consumption of fruits and vegetables among adolescents; however, the consumption of unhealthy snacks was higher with rule-setting and lower with reasoning and authoritative practices. Finally, an analysis of the relationships between environmental factors and snack intake showed that adolescents consumed significantly more unhealthy snacks when performing other activities while eating. In conclusion, the findings from this study suggest that families' racial heritages are related to their parenting practices, BMI percentiles, and their adolescents' food consumption and eating behaviors. The results of this study can be used to develop and improve adolescent nutrition education and interventions with consideration of their racial/ethnic backgrounds

Describing independent eating occasions among low-income adolescents.

The purpose of this formative, cross-sectional study was to describe independent eating occasions (iEOs) among a convenience sample of low-income early adolescents (10-13 years, n = 46) in 10 U.S. states, including environmental context, foods selected and reasons for selection, and parental rules about foods consumed. Participants took pictures of all foods consumed over 24 h and participated in semi-structured interviews to describe the context of each eating occasion using the pictures as a guide. Responses based on a total of 304 eating occasions were coded to classify foods based on United States Department of Agriculture (USDA) MyPlate food groups and to characterize parental rules and reasons for food selection. Average age was 10.9 ± 1.1 years and 60% were female. Approximately 58% of eating occasions were classified as iEOs with approximately 65% as snacks. Most iEOs took place at home. Foods frequently consumed during iEOs were from the sweets, total fruit, dairy, and whole fruit food categories. Primary parental rules for iEOs focused on avoiding certain foods and not eating too much. Early adolescents selected foods for convenience, taste preferences, and availability. Foods selected during iEOs were based on parent, household and early adolescent factors, which could be addressed to influence overall diet qualit

Big bounce from spin and torsion

The Einstein-Cartan-Sciama-Kibble theory of gravity naturally extends general relativity to account for the intrinsic spin of matter. Spacetime torsion, generated by spin of Dirac fields, induces gravitational repulsion in fermionic matter at extremely high densities and prevents the formation of singularities. Accordingly, the big bang is replaced by a bounce that occurred when the energy density $\epsilon\propto gT^4$ was on the order of $n^2/m_\textrm{Pl}^2$ (in natural units), where $n\propto gT^3$ is the fermion number density and $g$ is the number of thermal degrees of freedom. If the early Universe contained only the known standard-model particles ($g\approx 100$), then the energy density at the big bounce was about 15 times larger than the Planck energy. The minimum scale factor of the Universe (at the bounce) was about $10^{32}$ times smaller than its present value, giving \approx 50 \mum. If more fermions existed in the early Universe, then the spin-torsion coupling causes a bounce at a lower energy and larger scale factor. Recent observations of high-energy photons from gamma-ray bursts indicate that spacetime may behave classically even at scales below the Planck length, supporting the classical spin-torsion mechanism of the big bounce. Such a classical bounce prevents the matter in the contracting Universe from reaching the conditions at which a quantum bounce could possibly occur.Comment: 6 pages; published versio

Shadowing in Inelastic Scattering of Muons on Carbon, Calcium and Lead at Low XBj

Nuclear shadowing is observed in the per-nucleon cross-sections of positive muons on carbon, calcium and lead as compared to deuterium. The data were taken by Fermilab experiment E665 using inelastically scattered muons of mean incident momentum 470 GeV/c. Cross-section ratios are presented in the kinematic region 0.0001 < XBj <0.56 and 0.1 < Q**2 < 80 GeVc. The data are consistent with no significant nu or Q**2 dependence at fixed XBj. As XBj decreases, the size of the shadowing effect, as well as its A dependence, are found to approach the corresponding measurements in photoproduction.Comment: 22 pages, incl. 6 figures, to be published in Z. Phys.

Exploring the Underdiagnosis and Prevalence of Autism Spectrum Conditions in Beijing

Previous studies reported that the prevalence of Autism Spectrum Conditions (ASC) in mainland China is much lower than estimates from developed countries (around 1%). The aim of the study is to apply current screening and standardized diagnostic instruments to a Chinese population to establish a prevalence estimate of ASC in an undiag-nosed population in mainland China. We followed the design development used previously in the UK published in 2009 by Baron-Cohen and colleagues. The Mandarin Childhood Autism Spectrum Test (CAST) was validated by screening primary school pupils (n = 737 children age 6–10 years old) in Beijing and by conducting diagnostic assessments using the Autism Diagnostic Observation Schedule and the Autism Diagnostic Interview-Revised. The prevalence estimate was generated after adjusting and imputing for missing values using the inverse probability weighting. Response was high (97%). Using the UK cutoff (≥15), CAST performance has 84 % sensitivity and 96 % specificity (95 % confidence interval [CI]: 46, 98, and 96, 97, respectively). Six out of 103 children, not previously diagnosed, were found to the meet diagnostic criteria (8.5 after adjustment, 95 % CI: 1.6, 15.4). The preliminary prevalence in an undiagnosed primary school population in mainland China was 119 per 10,000 (95 % CI: 53, 265). The utility of CAST is acceptable as a screening instrument for ASC in large epidemiological studies in China. Using a comparable method, the preliminary prevalence estimate of ASC in mainland China is similar to that of those from developed countries. Autism Res 2015

Early Atomic Models - From Mechanical to Quantum (1904-1913)

A complete history of early atomic models would fill volumes, but a reasonably coherent tale of the path from mechanical atoms to the quantum can be told by focusing on the relevant work of three great contributors to atomic physics, in the critically important years between 1904 and 1913: J. J. Thomson, Ernest Rutherford and Niels Bohr. We first examine the origins of Thomson's mechanical atomic models, from his ethereal vortex atoms in the early 1880's, to the myriad "corpuscular" atoms he proposed following the discovery of the electron in 1897. Beyond predictions for the periodicity of the elements, the application of Thomson's atoms to problems in scattering and absorption led to quantitative predictions that were confirmed by experiments with high-velocity electrons traversing thin sheets of metal. Still, the much more massive and energetic {\alpha}-particles being studied by Rutherford were better suited for exploring the interior of the atom, and careful measurements on the angular dependence of their scattering eventually allowed him to infer the existence of an atomic nucleus. Niels Bohr was particularly troubled by the radiative instability inherent to any mechanical atom, and succeeded in 1913 where others had failed in the prediction of emission spectra, by making two bold hypotheses that were in contradiction to the laws of classical physics, but necessary in order to account for experimental facts.Comment: 58 Pages + References, 8 Figures. Accepted for publication in the European Physical Journal H (Historical Perspectives on Contemporary Physics). V2 - minor typos corrected and a footnote added to p.2

Diagnostic value of exome and whole genome sequencing in craniosynostosis

Background Craniosynostosis, the premature fusion of one or more cranial sutures, occurs in ~1 in 2250 births, either in isolation or as part of a syndrome. Mutations in at least 57 genes have been associated with craniosynostosis, but only a minority of these are included in routine laboratory genetic testing. Methods We used exome or whole genome sequencing to seek a genetic cause in a cohort of 40 subjects with craniosynostosis, selected by clinical or molecular geneticists as being high-priority cases, and in whom prior clinically driven genetic testing had been negative. Results We identified likely associated mutations in 15 patients (37.5%), involving 14 different genes. All genes were mutated in single families, except for IL11RA (two families). We classified the other positive diagnoses as follows: commonly mutated craniosynostosis genes with atypical presentation (EFNB1, TWIST1); other core craniosynostosis genes (CDC45, MSX2, ZIC1); genes for which mutations are only rarely associated with craniosynostosis (FBN1, HUWE1, KRAS, STAT3); and known disease genes for which a causal relationship with craniosynostosis is currently unknown (AHDC1, NTRK2). In two further families, likely novel disease genes are currently undergoing functional validation. In 5 of the 15 positive cases, the (previously unanticipated) molecular diagnosis had immediate, actionable consequences for either genetic or medical management (mutations in EFNB1, FBN1, KRAS, NTRK2, STAT3). Conclusions This substantial genetic heterogeneity, and the multiple actionable mutations identified, emphasises the benefits of exome/whole genome sequencing to identify causal mutations in craniosynostosis cases for which routine clinical testing has yielded negative results

Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties

[EN] In this paper we study random non-autonomous second order linear differential equations by taking advantage of the powerful theory of random difference equations. The coefficients are assumed to be stochastic processes, and the initial conditions are random variables both defined in a common underlying complete probability space. Under appropriate assumptions established on the data stochastic processes and on the random initial conditions, and using key results on difference equations, we prove the existence of an analytic stochastic process solution in the random mean square sense. Truncating the random series that defines the solution process, we are able to approximate the main statistical properties of the solution, such as the expectation and the variance. We also obtain error a priori bounds to construct reliable approximations of both statistical moments. We include a set of numerical examples to illustrate the main theoretical results established throughout the paper. We finish with an example where our findings are combined with Monte Carlo simulations to model uncertainty using real data.This work has been supported by the Spanish Ministerio de Economia y Competitividad grant MTM2017-89664-P. Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia.Calatayud-Gregori, J.; Cortés, J.; Jornet-Sanz, M.; Villafuerte, L. (2018). Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties. Advances in Difference Equations. (3):1-29. https://doi.org/10.1186/s13662-018-1848-8S1293Apostol, T.M.: Mathematical Analysis, 2nd edn. Pearson, New York (1976)Boyce, W.E.: Probabilistic Methods in Applied Mathematics I. Academic Press, New York (1968)Calbo, G., Cortés, J.C., Jódar, L.: Random Hermite differential equations: mean square power series solutions and statistical properties. Appl. Math. Comput. 218(7), 3654–3666 (2011)Calbo, G., Cortés, J.C., Jódar, L., Villafuerte, L.: Solving the random Legendre differential equation: mean square power series solution and its statistical functions. Comput. Math. Appl. 61(9), 2782–2792 (2011)Casabán, M.C., Cortés, J.C., Navarro-Quiles, A., Romero, J.V., Roselló, M.D., Villanueva, R.J.: Computing probabilistic solutions of the Bernoulli random differential equation. J. Comput. Appl. Math. 309, 396–407 (2017)Casabán, M.C., Cortés, J.C., Romero, J.V., Roselló, M.D.: Solving random homogeneous linear second-order differential equations: a full probabilistic description. Mediterr. J. Math. 13(6), 3817–3836 (2016)Cortés, J.C., Jódar, L., Camacho, J., Villafuerte, L.: Random Airy type differential equations: mean square exact and numerical solutions. Comput. Math. Appl. 60(5), 1237–1244 (2010)Cortés, J.C., Jódar, L., Company, R., Villafuerte, L.: Laguerre random polynomials: definition, differential and statistical properties. Util. Math. 98, 283–295 (2015)Cortés, J.C., Jódar, L., Villafuerte, L.: Random linear-quadratic mathematical models: computing explicit solutions and applications. Math. Comput. Simul. 79(7), 2076–2090 (2009)Cortés, J.C., Jódar, L., Villafuerte, L.: Mean square solution of Bessel differential equation with uncertainties. J. Comput. Appl. Math. 309(1), 383–395 (2017)Cortés, J.C., Sevilla-Peris, P., Jódar, L.: Analytic-numerical approximating processes of diffusion equation with data uncertainty. Comput. Math. Appl. 49(7–8), 1255–1266 (2005)Díaz-Infante, S., Jerez, S.: Convergence and asymptotic stability of the explicit Steklov method for stochastic differential equations. J. Comput. Appl. Math. 291(1), 36–47 (2016)Dorini, F., Cunha, M.: Statistical moments of the random linear transport equation. J. Comput. Phys. 227(19), 8541–8550 (2008)Dorini, F.A., Cecconello, M.S., Dorini, M.B.: On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density. Commun. Nonlinear Sci. Numer. Simul. 33, 160–173 (2016)Golmankhaneh, A.K., Porghoveh, N.A., Baleanu, D.: Mean square solutions of second-order random differential equations by using homotopy analysis method. Rom. Rep. Phys. 65(2), 350–362 (2013)Grimmett, G.R., Stirzaker, D.R.: Probability and Random Processes. Clarendon Press, Oxford (2000)Henderson, D., Plaschko, P.: Stochastic Differential Equations in Science and Engineering. Cambridge Texts in Applied Mathematics. World Scientific, Singapore (2006)Hussein, A., Selim, M.M.: A developed solution of the stochastic Milne problem using probabilistic transformations. Appl. Math. Comput. 216(10), 2910–2919 (2009)Hussein, A., Selim, M.M.: Solution of the stochastic transport equation of neutral particles with anisotropic scattering using RVT technique. Appl. Math. Comput. 213(1), 250–261 (2009)Hussein, A., Selim, M.M.: Solution of the stochastic radiative transfer equation with Rayleigh scattering using RVT technique. Appl. Math. Comput. 218(13), 7193–7203 (2012)Khodabin, M., Maleknejad, K., Rostami, M., Nouri, M.: Numerical solution of stochastic differential equations by second order Runge–Kutta methods. Math. Comput. Model. 53(9–10), 1910–1920 (2011)Khodabin, M., Rostami, M.: Mean square numerical solution of stochastic differential equations by fourth order Runge–Kutta method and its application in the electric circuits with noise. Adv. Differ. Equ. 2015, 62 (2015)Khudair, A.K., Ameen, A.A., Khalaf, S.L.: Mean square solutions of second-order random differential equations by using Adomian decomposition method. Appl. Math. Sci. 51(5), 2521–2535 (2011)Khudair, A.K., Haddad, S.A.M., Khalaf, S.L.: Mean square solutions of second-order random differential equations by using the differential transformation method. Open J. Appl. Sci. 6, 287–297 (2016)Lesaffre, E., Lawson, A.B.: Bayesian Biostatistics. Statistics in Practice. Wiley, New York (2012)Li, X., Fu, X.: Stability analysis of stochastic functional differential equations with infinite delay and its application to recurrent neural networks. J. Comput. Appl. Math. 234(2), 407–417 (2010)Licea, J.A., Villafuerte, L., Chen-Charpentier, B.M.: Analytic and numerical solutions of a Riccati differential equation with random coefficients. J. Comput. Appl. Math. 309(1), 208–219 (2013)Liu, S., Debbouche, A., Wang, J.: On the iterative learning control for stochastic impulsive differential equations with randomly varying trial lengths. J. Comput. Appl. Math. 312, 47–57 (2017)Loève, M.: Probability Theory. Vol. I. Springer, Mineola (1977)Lord, G.J., Powell, C.E., Shardlow, T.: An Introduction to Computational Stochastic PDEs. Cambridge Texts in Applied Mathematics. Dover, New York (2014)Nouri, K., Ranjbar, H.: Mean square convergence of the numerical solution of random differential equations. Mediterr. J. Math. 12(3), 1123–1140 (2015)Rencher, A.C., Schaalje, G.B.: Linear Models in Statistics, 2nd edn. Wiley, New York (2008)Santos, L.T., Dorini, F.A., Cunha, M.C.C.: The probability density function to the random linear transport equation. Appl. Math. Comput. 216(5), 1524–1530 (2010)Seber, G.A.F., Wild, C.J.: Nonlinear Regression. Cambridge Texts in Applied Mathematics. Wiley, New York (2003)Smith, R.C.: Uncertainty Quantification: Theory, Implementation, and Applications. SIAM, Philadelphia (2014)Soheili, A.R., Toutounian, F., Soleymani, F.: A fast convergent numerical method for matrix sign function with application in SDEs (Stochastic Differential Equations). J. Comput. Appl. Math. 282, 167–178 (2015)Soong, T.T.: Random Differential Equations in Science and Engineering. Academic Press, New York (1973)Villafuerte, L., Braumann, C.A., Cortés, J.C., Jódar, L.: Random differential operational calculus: theory and applications. Comput. Math. Appl. 59(1), 115–125 (2010)Xiu, D.: Numerical Methods for Stochastic Computations. A Spectral Method Approach. Cambridge Texts in Applied Mathematics. Princeton University Press, New York (2010