A mean square chain rule and its application in solving the random Chebyshev differential equation

[EN] In this paper a new version of the chain rule for calculat- ing the mean square derivative of a second-order stochastic process is proven. This random operational calculus rule is applied to construct a rigorous mean square solution of the random Chebyshev differential equation (r.C.d.e.) assuming mild moment hypotheses on the random variables that appear as coefficients and initial conditions of the cor- responding initial value problem. Such solution is represented through a mean square random power series. Moreover, reliable approximations for the mean and standard deviation functions to the solution stochastic process of the r.C.d.e. are given. Several examples, that illustrate the theoretical results, are included.This work was completed with the support of our TEX-pert.Cortés, J.; Villafuerte, L.; Burgos-Simon, C. (2017). A mean square chain rule and its application in solving the random Chebyshev differential equation. Mediterranean Journal of Mathematics. 14(1):14-35. https://doi.org/10.1007/s00009-017-0853-6S1435141Calbo, G., Cortés, J.C., Jódar, L., Villafuerte, L.: Analytic stochastic process solutions of second-order random differential equations. Appl. Math. Lett. 23(12), 1421–1424 (2010). doi: 10.1016/j.aml.2010.07.011El-Tawil, M.A., El-Sohaly, M.: Mean square numerical methods for initial value random differential equations. Open J. Discret. Math. 1(1), 164–171 (2011). doi: 10.4236/ojdm.2011.12009Khodabin, M., Maleknejad, K., Rostami, K., Nouri, M.: Numerical solution of stochastic differential equations by second order Runge Kutta methods. Math. Comp. Model. 59(9–10), 1910–1920 (2010). doi: 10.1016/j.mcm.2011.01.018Santos, 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). doi: 10.1016/j.amc.2010.03.001González Parra, G., Chen-Charpentier, B.M., Arenas, A.J.: Polynomial Chaos for random fractional order differential equations. Appl. Math. Comput. 226(1), 123–130 (2014). doi: 10.1016/j.amc.2013.10.51El-Beltagy, M.A., El-Tawil, M.A.: Toward a solution of a class of non-linear stochastic perturbed PDEs using automated WHEP algorithm. Appl. Math. Model. 37(12–13), 7174–7192 (2013). doi: 10.1016/j.apm.2013.01.038Nouri, K., Ranjbar, H.: Mean square convergence of the numerical solution of random differential equations. Mediterran. J. Math. 12(3), 1123–1140 (2015). doi: 10.1007/s00009-014-0452-8Villafuerte, L., Braumann, C.A., Cortés, J.C., Jódar, L.: Random differential operational calculus: theory and applications. Comp. Math. Appl. 59(1), 115–125 (2010). doi: 10.1016/j.camwa.2009.08.061Øksendal, B.: Stochastic differential equations: an introduction with applications, 6th edn. Springer, Berlin (2007)Soong, T.T.: Random differential equations in science and engineering. Academic Press, New York (1973)Wong, B., Hajek, B.: Stochastic processes in engineering systems. Springer Verlag, New York (1985)Arnold, L.: Stochastic differential equations. Theory and applications. John Wiley, New York (1974)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). doi: 10.1016/j.camwa.2010.05.046Calbo, G., Cortés, J.C., Jódar, L.: Random Hermite differential equations: mean square power series solutions and statistical properties. Appl. Math. Comp. 218(7), 3654–3666 (2011). doi: 10.1016/j.amc.2011.09.008Calbo, G., Cortés, J.C., Jódar, L., Villafuerte, L.: Solving the random Legendre differential equation: Mean square power series solution and its statistical functions. Comp. Math. Appl. 61(9), 2782–2792 (2010). doi: 10.1016/j.camwa.2011.03.045Cortés, J.C., Jódar, L., Company, R., Villafuerte, L.: Laguerre random polynomials: definition, differential and statistical properties. Utilit. Math. 98, 283–293 (2015)Cortés, J.C., Jódar, L., Villafuerte, L.: Mean square solution of Bessel differential equation with uncertainties. J. Comp. Appl. Math. 309, 383–395 (2017). doi: 10.1016/j.cam.2016.01.034Golmankhaneh, A.K., Porghoveh, N.A., Baleanu, D.: Mean square solutions of second-order random differential equations by using homotopy analysis method. Romanian Reports Physics 65(2), 1237–1244 (2013)Khalaf, S.L.: Mean square solutions of second-order random differential equations by using homotopy perturbation method. Int. Math. Forum 6(48), 2361–2370 (2011)Khudair, A.R., Ameen, A.A., Khalaf, S.L.: Mean square solutions of second-order random differential equations by using Adomian decomposition method. Appl. Math. Sci. 5(49), 2521–2535 (2011)Agarwal, R.P., O’Regan, D.: Ordinary and partial differential equations. Springer, New York (2009

Angiosarcoma of the nasal cavity: a case report

Angiosarcomas are malignant neoplasias of rapid growth that develop from endothelial cells. They represent 2% of all sarcomas and only 1–4% are located in the aerodigestive tract. Since 1977, only 16 cases have been reported

Excessive TV viewing and cardiovascular disease risk factors in adolescents. The AVENA cross-sectional study

<p>Abstract</p> <p>Background</p> <p>Excessive television (TV) viewing might play an important role in the development of cardiovascular disease (CVD). The aim of this study was to examine the independent associations between TV viewing and CVD risk factors in adolescents.</p> <p>Methods</p> <p>A sample of 425 adolescents, aged 13- to 18.5-year-old, was included in this study. Body mass index (BMI), waist circumference (WC), glucose, total cholesterol, triglycerides, HDL-cholesterol, LDL-cholesterol, apolipoprotein (apo) A-1, apo B-100, and lipoprotein(a) levels were determined. A composite CVD risk score was computed based on age-, sex-, sexual maturation- and race-standardized triglycerides, HDL-cholesterol, LDL-cholesterol and glucose. TV viewing was self-reported.</p> <p>Results</p> <p>Two hundred and twenty-five adolescents (53%) who spent >3 hrs/day watching TV were considered as the "high TV viewing" group. Ninety-nine adolescents (23%) from the total sample were classified as overweight according to International age- and sex-specific BMI values. The high TV viewing group had significantly less favorable values of HDL-cholesterol, glucose, apo A1 and CVD score, independent of age, sex, sexual maturation, race and weight status. There was a significant interaction effect of TV viewing × weight status (P = 0.002) on WC, and the negative influence of TV viewing on WC persisted in the overweight group (P = 0.031) but was attenuated in non-overweight adolescents (P > 0.05).</p> <p>Conclusion</p> <p>Excessive TV viewing seems to be related to an unfavorable CVD risk factors profile in adolescence. Reducing TV viewing in overweight adolescents might be beneficial to decrease abdominal body fat.</p

The Evolution of Compact Binary Star Systems

We review the formation and evolution of compact binary stars consisting of white dwarfs (WDs), neutron stars (NSs), and black holes (BHs). Binary NSs and BHs are thought to be the primary astrophysical sources of gravitational waves (GWs) within the frequency band of ground-based detectors, while compact binaries of WDs are important sources of GWs at lower frequencies to be covered by space interferometers (LISA). Major uncertainties in the current understanding of properties of NSs and BHs most relevant to the GW studies are discussed, including the treatment of the natal kicks which compact stellar remnants acquire during the core collapse of massive stars and the common envelope phase of binary evolution. We discuss the coalescence rates of binary NSs and BHs and prospects for their detections, the formation and evolution of binary WDs and their observational manifestations. Special attention is given to AM CVn-stars -- compact binaries in which the Roche lobe is filled by another WD or a low-mass partially degenerate helium-star, as these stars are thought to be the best LISA verification binary GW sources.Comment: 105 pages, 18 figure

Observation of associated near-side and away-side long-range correlations in √sNN=5.02 TeV proton-lead collisions with the ATLAS detector

Two-particle correlations in relative azimuthal angle (Δϕ) and pseudorapidity (Δη) are measured in √sNN=5.02  TeV p+Pb collisions using the ATLAS detector at the LHC. The measurements are performed using approximately 1  μb-1 of data as a function of transverse momentum (pT) and the transverse energy (ΣETPb) summed over 3.1<η<4.9 in the direction of the Pb beam. The correlation function, constructed from charged particles, exhibits a long-range (2<|Δη|<5) “near-side” (Δϕ∼0) correlation that grows rapidly with increasing ΣETPb. A long-range “away-side” (Δϕ∼π) correlation, obtained by subtracting the expected contributions from recoiling dijets and other sources estimated using events with small ΣETPb, is found to match the near-side correlation in magnitude, shape (in Δη and Δϕ) and ΣETPb dependence. The resultant Δϕ correlation is approximately symmetric about π/2, and is consistent with a dominant cos⁡2Δϕ modulation for all ΣETPb ranges and particle pT

Measurements of fiducial and differential cross sections for Higgs boson production in the diphoton decay channel at s√=8 TeV with ATLAS

Measurements of fiducial and differential cross sections are presented for Higgs boson production in proton-proton collisions at a centre-of-mass energy of s√=8 TeV. The analysis is performed in the H → γγ decay channel using 20.3 fb−1 of data recorded by the ATLAS experiment at the CERN Large Hadron Collider. The signal is extracted using a fit to the diphoton invariant mass spectrum assuming that the width of the resonance is much smaller than the experimental resolution. The signal yields are corrected for the effects of detector inefficiency and resolution. The pp → H → γγ fiducial cross section is measured to be 43.2 ±9.4(stat.) − 2.9 + 3.2 (syst.) ±1.2(lumi)fb for a Higgs boson of mass 125.4GeV decaying to two isolated photons that have transverse momentum greater than 35% and 25% of the diphoton invariant mass and each with absolute pseudorapidity less than 2.37. Four additional fiducial cross sections and two cross-section limits are presented in phase space regions that test the theoretical modelling of different Higgs boson production mechanisms, or are sensitive to physics beyond the Standard Model. Differential cross sections are also presented, as a function of variables related to the diphoton kinematics and the jet activity produced in the Higgs boson events. The observed spectra are statistically limited but broadly in line with the theoretical expectations

Tetrahymena Metallothioneins Fall into Two Discrete Subfamilies

BACKGROUND: Metallothioneins are ubiquitous small, cysteine-rich, multifunctional proteins which can bind heavy metals. METHODOLOGY/PRINCIPAL FINDINGS: We report the results of phylogenetic and gene expression analyses that include two new Tetrahymena thermophila metallothionein genes (MTT3 and MTT5). Sequence alignments of all known Tetrahymena metallothioneins have allowed us to rationalize the structure of these proteins. We now formally subdivide the known metallothioneins from the ciliate genus Tetrahymena into two well defined subfamilies, 7a and 7b, based on phylogenetic analysis, on the pattern of clustering of Cys residues, and on the pattern of inducibility by the heavy metals Cd and Cu. Sequence alignment also reveals a remarkably regular, conserved and hierarchical modular structure of all five subfamily 7a MTs, which include MTT3 and MTT5. The former has three modules, while the latter has only two. Induction levels of the three T. thermophila genes were determined using quantitative real time RT-PCR. Various stressors (including heavy metals) brought about dramatically different fold-inductions for each gene; MTT5 showed the highest fold-induction. Conserved DNA motifs with potential regulatory significance were identified, in an unbiased way, upstream of the start codons of subfamily 7a MTs. EST evidence for alternative splicing in the 3′ UTR of the MTT5 mRNA with potential regulatory activity is reported. CONCLUSION/SIGNIFICANCE: The small number and remarkably regular structure of Tetrahymena MTs, coupled with the experimental tractability of this model organism for studies of in vivo function, make it an attractive system for the experimental dissection of the roles, structure/function relationships, regulation of gene expression, and adaptive evolution of these proteins, as well as for the development of biotechnological applications for the environmental monitoring of toxic substances

Highly Efficient Elimination of Colorectal Tumor-Initiating Cells by an EpCAM/CD3-Bispecific Antibody Engaging Human T Cells

With their resistance to genotoxic and anti-proliferative drugs and potential to grow tumors and metastases from very few cells, cancer stem or tumor-initiating cells (TICs) are a severe limitation for the treatment of cancer by conventional therapies. Here, we explored whether human T cells that are redirected via an EpCAM/CD3-bispecific antibody called MT110 can lyse colorectal TICs and prevent tumor growth from TICs. MT110 recognizes EpCAM, a cell adhesion molecule expressed on TICs from diverse human carcinoma, which was recently shown to promote tumor growth through engagement of elements of the wnt pathway. MT110 was highly potent in mediating complete redirected lysis of KRAS-, PI3 kinase- and BRAF-mutated colorectal TICs, as demonstrated in a soft agar assay. In immunodeficient mice, MT110 prevented growth of tumors from a 5,000-fold excess of a minimally tumorigenic TIC dose. T cells engaged by MT110 may provide a potent therapeutic means to eradicate TICs and bulk tumor cells derived thereof