The transition between stochastic and deterministic behavior in an excitable gene circuit

We explore the connection between a stochastic simulation model and an ordinary differential equations (ODEs) model of the dynamics of an excitable gene circuit that exhibits noise-induced oscillations. Near a bifurcation point in the ODE model, the stochastic simulation model yields behavior dramatically different from that predicted by the ODE model. We analyze how that behavior depends on the gene copy number and find very slow convergence to the large number limit near the bifurcation point. The implications for understanding the dynamics of gene circuits and other birth-death dynamical systems with small numbers of constituents are discussed.Comment: PLoS ONE: Research Article, published 11 Apr 201

Reliability of a 1-week recall period for the Medical Outcomes Study Sleep Scale (MOS-SS) in patients with fibromyalgia

<p>Abstract</p> <p>Objective</p> <p>To evaluate the reliability of a one-week versus a four-week recall period of the Medical Outcomes Study Sleep Scale (MOS-SS) in patients with fibromyalgia (FM).</p> <p>Methods</p> <p>The MOS-SS was administered by mail to patients with a confirmed diagnosis of FM and a current pain rating of > 2 (0–10 point numerical rating scale) recruited through newspapers, support groups, and the Internet. Reliability of MOS-SS subscale domains was evaluated using test-retest methodology separated by a 1–3 day interval for the 4-week recall period and a 7-day interval for the 1-week recall period. Patient Impression of Change was evaluated for sleep, and for patients with no change, the intraclass correlation coefficient (ICC) and the Pearson correlation coefficient was calculated for MOS-SS subscales.</p> <p>Results</p> <p>Of 129 patients enrolled, 91.3% were female, mean age was 49.4 ± 11.0 years; self-rated FM severity was moderate-to-severe in 88.1% of patients. MOS-SS subscale scores were similar for both recall periods with little variation between test-retest. The 9-item Sleep Problems Index scores ranged from 57.2 ± 14.5 to 61.9 ± 15.8 across all assessments and demonstrated high reliability which was similar for the 1-week (ICC 0.81) and 4-week (ICC 0.89) recall periods. For the other MOS-SS subscales, the 1-week recall period also showed good reliability, which was consistent for the ICC and Pearson correlation coefficients.</p> <p>Conclusion</p> <p>A 1-week recall period is adequately reliable for use of the MOS-SS in studies evaluating sleep disturbance in patients with FM.</p

An effective theory for jet propagation in dense QCD matter: jet broadening and medium-induced bremsstrahlung

Two effects, jet broadening and gluon bremsstrahlung induced by the propagation of a highly energetic quark in dense QCD matter, are reconsidered from effective theory point of view. We modify the standard Soft Collinear Effective Theory (SCET) Lagrangian to include Glauber modes, which are needed to implement the interactions between the medium and the collinear fields. We derive the Feynman rules for this Lagrangian and show that it is invariant under soft and collinear gauge transformations. We find that the newly constructed theory SCET$_{\rm G}$ recovers exactly the general result for the transverse momentum broadening of jets. In the limit where the radiated gluons are significantly less energetic than the parent quark, we obtain a jet energy-loss kernel identical to the one discussed in the reaction operator approach to parton propagation in matter. In the framework of SCET$_{\rm G}$ we present results for the fully-differential bremsstrahlung spectrum for both the incoherent and the Landau-Pomeranchunk-Migdal suppressed regimes beyond the soft-gluon approximation. Gauge invariance of the physics results is demonstrated explicitly by performing the calculations in both the light-cone and covariant $R_{\xi}$ gauges. We also show how the process-dependent medium-induced radiative corrections factorize from the jet production cross section on the example of the quark jets considered here.Comment: 52 pages, 15 pdf figures, as published in JHE

The role of chaotic resonances in the solar system

Our understanding of the Solar System has been revolutionized over the past decade by the finding that the orbits of the planets are inherently chaotic. In extreme cases, chaotic motions can change the relative positions of the planets around stars, and even eject a planet from a system. Moreover, the spin axis of a planet-Earth's spin axis regulates our seasons-may evolve chaotically, with adverse effects on the climates of otherwise biologically interesting planets. Some of the recently discovered extrasolar planetary systems contain multiple planets, and it is likely that some of these are chaotic as well.Comment: 28 pages, 9 figure

Three-dimensional coherent X-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms

Ultra-low density polymers, metals, and ceramic nanofoams are valued for their high strength-to-weight ratio, high surface area and insulating properties ascribed to their structural geometry. We obtain the labrynthine internal structure of a tantalum oxide nanofoam by X-ray diffractive imaging. Finite element analysis from the structure reveals mechanical properties consistent with bulk samples and with a diffusion limited cluster aggregation model, while excess mass on the nodes discounts the dangling fragments hypothesis of percolation theory.Comment: 8 pages, 5 figures, 30 reference

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

IMPULSE: the impact of gender on the presentation and management of aortic stenosis across Europe.

AIMS: There is an increasing awareness of gender-related differences in patients with severe aortic stenosis and their outcomes after surgical aortic valve replacement (SAVR) and transcatheter aortic valve implantation (TAVI). METHODS: Data from the IMPULSE registry were analysed. Patients with severe aortic stenosis (AS) were enrolled between March 2015 and April 2017 and stratified by gender. A subgroup analysis was performed to assess the impact of age. RESULTS: Overall, 2171 patients were enrolled, and 48.0% were female. Women were characterised by a higher rate of renal impairment (31.7 vs 23.3%; p<0.001), were at higher surgical risk (EuroSCORE II: 4.5 vs 3.6%; p=0.001) and more often in a critical preoperative state (7.0vs 4.2%; p=0.003). Men had an increased rate of previous cardiac surgery (9.4 vs 4.7%; p<0.001) and a reduced left ventricular ejection fraction (4.9 vs 1.3%; p<0.001). Concomitant mitral and tricuspid valve disease was substantially more common among women. Symptoms were highly prevalent in both women and men (83.6 vs 77.3%; p<0.001). AVR was planned in 1379 cases. Women were more frequently scheduled to undergo TAVI (49.3 vs 41.0%; p<0.001) and less frequently for SAVR (20.3 vs 27.5%; p<0.001). CONCLUSIONS: The present data show that female patients with severe AS have a distinct patient profile and are managed in a different way to males. Gender-based differences in the management of patients with severe AS need to be taken into account more systematically to improve outcomes, especially for women

'MRI-negative PET-positive' temporal lobe epilepsy (TLE) and mesial TLE differ with quantitative MRI and PET: a case control study

Background: \u27MRI negative PET positive temporal lobe epilepsy\u27 represents a substantial minority of temporal lobe epilepsy (TLE). Clinicopathological and qualitative imaging differences from mesial temporal lobe epilepsy are reported. We aimed to compare TLE with hippocampal sclerosis (HS+ve) and non lesional TLE without HS (HS-ve) on MRI, with respect to quantitative FDG-PET and MRI measures.Methods: 30 consecutive HS-ve patients with well-lateralised EEG were compared with 30 age- and sex-matched HS+ve patients with well-lateralised EEG. Cerebral, cortical lobar and hippocampal volumetric and co-registered FDG-PET metabolic analyses were performed.Results: There was no difference in whole brain, cerebral or cerebral cortical volumes. Both groups showed marginally smaller cerebral volumes ipsilateral to epileptogenic side (HS-ve 0.99, p = 0.02, HS+ve 0.98, p &lt; 0.001). In HS+ve, the ratio of epileptogenic cerebrum to whole brain volume was less (p = 0.02); the ratio of epileptogenic cerebral cortex to whole brain in the HS+ve group approached significance (p = 0.06). Relative volume deficits were seen in HS+ve in insular and temporal lobes. Both groups showed marked ipsilateral hypometabolism (p &lt; 0.001), most marked in temporal cortex. Mean hypointensity was more marked in epileptogenic-to-contralateral hippocampus in HS+ve (ratio: 0.86 vs 0.95, p &lt; 0.001). The mean FDG-PET ratio of ipsilateral to contralateral cerebral cortex however was low in both groups (ratio: HS-ve 0.97, p &lt; 0.0001; HS+ve 0.98, p = 0.003), and more marked in HS-ve across all lobes except insula.Conclusion: Overall, HS+ve patients showed more hippocampal, but also marginally more ipsilateral cerebral and cerebrocortical atrophy, greater ipsilateral hippocampal hypometabolism but similar ipsilateral cerebral cortical hypometabolism, confirming structural and functional differences between these groups.<br /