Reconstruction of Network Evolutionary History from Extant Network Topology and Duplication History

Genome-wide protein-protein interaction (PPI) data are readily available thanks to recent breakthroughs in biotechnology. However, PPI networks of extant organisms are only snapshots of the network evolution. How to infer the whole evolution history becomes a challenging problem in computational biology. In this paper, we present a likelihood-based approach to inferring network evolution history from the topology of PPI networks and the duplication relationship among the paralogs. Simulations show that our approach outperforms the existing ones in terms of the accuracy of reconstruction. Moreover, the growth parameters of several real PPI networks estimated by our method are more consistent with the ones predicted in literature.Comment: 15 pages, 5 figures, submitted to ISBRA 201

Solutions to Maxwell's Equations using Spheroidal Coordinates

Analytical solutions to the wave equation in spheroidal coordinates in the short wavelength limit are considered. The asymptotic solutions for the radial function are significantly simplified, allowing scalar spheroidal wave functions to be defined in a form which is directly reminiscent of the Laguerre-Gaussian solutions to the paraxial wave equation in optics. Expressions for the Cartesian derivatives of the scalar spheroidal wave functions are derived, leading to a new set of vector solutions to Maxwell's equations. The results are an ideal starting point for calculations of corrections to the paraxial approximation

Generalizing the autonomous Kepler Ermakov system in a Riemannian space

We generalize the two dimensional autonomous Hamiltonian Kepler Ermakov dynamical system to three dimensions using the sl(2,R) invariance of Noether symmetries and determine all three dimensional autonomous Hamiltonian Kepler Ermakov dynamical systems which are Liouville integrable via Noether symmetries. Subsequently we generalize the autonomous Kepler Ermakov system in a Riemannian space which admits a gradient homothetic vector by the requirements (a) that it admits a first integral (the Riemannian Ermakov invariant) and (b) it has sl(2,R) invariance. We consider both the non-Hamiltonian and the Hamiltonian systems. In each case we compute the Riemannian Ermakov invariant and the equations defining the dynamical system. We apply the results in General Relativity and determine the autonomous Hamiltonian Riemannian Kepler Ermakov system in the spatially flat Friedman Robertson Walker spacetime. We consider a locally rotational symmetric (LRS) spacetime of class A and discuss two cosmological models. The first cosmological model consists of a scalar field with exponential potential and a perfect fluid with a stiff equation of state. The second cosmological model is the f(R) modified gravity model of {\Lambda}_{bc}CDM. It is shown that in both applications the gravitational field equations reduce to those of the generalized autonomous Riemannian Kepler Ermakov dynamical system which is Liouville integrable via Noether integrals.Comment: Reference [25] update, 21 page

Anomalies of ac driven solitary waves with internal modes: Nonparametric resonances induced by parametric forces

We study the dynamics of kinks in the $\phi^4$ model subjected to a parametric ac force, both with and without damping, as a paradigm of solitary waves with internal modes. By using a collective coordinate approach, we find that the parametric force has a non-parametric effect on the kink motion. Specifically, we find that the internal mode leads to a resonance for frequencies of the parametric driving close to its own frequency, in which case the energy of the system grows as well as the width of the kink. These predictions of the collective coordinate theory are verified by numerical simulations of the full partial differential equation. We finally compare this kind of resonance with that obtained for non-parametric ac forces and conclude that the effect of ac drivings on solitary waves with internal modes is exactly the opposite of their character in the partial differential equation.Comment: To appear in Phys Rev

Applications of Lie systems in dissipative Milne--Pinney equations

We use the geometric approach to the theory of Lie systems of differential equations in order to study dissipative Ermakov systems. We prove that there is a superposition rule for solutions of such equations. This fact enables us to express the general solution of a dissipative Milne--Pinney equation in terms of particular solutions of a system of second-order linear differential equations and a set of constants.Comment: To be published in the Int. J. Geom. Methods Mod. Phy

Superposition rules for higher-order systems and their applications

Superposition rules form a class of functions that describe general solutions of systems of first-order ordinary differential equations in terms of generic families of particular solutions and certain constants. In this work we extend this notion and other related ones to systems of higher-order differential equations and analyse their properties. Several results concerning the existence of various types of superposition rules for higher-order systems are proved and illustrated with examples extracted from the physics and mathematics literature. In particular, two new superposition rules for second- and third-order Kummer--Schwarz equations are derived.Comment: (v2) 33 pages, some typos corrected, added some references and minor commentarie

On A Cosmological Invariant as an Observational Probe in the Early Universe

k-essence scalar field models are usually taken to have lagrangians of the form ${\mathcal L}=-V(\phi)F(X)$ with $F$ some general function of $X=\nabla_{\mu}\phi\nabla^{\mu}\phi$. Under certain conditions this lagrangian in the context of the early universe can take the form of that of an oscillator with time dependent frequency. The Ermakov invariant for a time dependent oscillator in a cosmological scenario then leads to an invariant quadratic form involving the Hubble parameter and the logarithm of the scale factor. In principle, this invariant can lead to further observational probes for the early universe. Moreover, if such an invariant can be observationally verified then the presence of dark energy will also be indirectly confirmed.Comment: 4 pages, Revte

Measuring CP violation and mass ordering in joint long baseline experiments with superbeams

We propose to measure the CP phase $\delta_{\rm CP}$, the magnitude of the neutrino mixing matrix element $|U_{e3}|$ and the sign of the atmopheric scale mass--squared difference $\Delta{\rm m}^2_{31}$ with a superbeam by the joint analysis of two different long baseline neutrino oscillation experiments. One is a long baseline experiment (LBL) at 300 km and the other is a very long baseline (VLBL) experiment at 2100 km. We take the neutrino source to be the approved high intensity proton synchrotron, HIPA. The neutrino beam for the LBL is the 2-degree off-axis superbeam and for the VLBL, a narrow band superbeam. Taking into account all possible errors, we evaluate the event rates required and the sensitivities that can be attained for the determination of $\delta_{\rm CP}$ and the sign of $\Delta m^2_{31}$. We arrive at a representative scenario for a reasonably precise probe of this part of the neutrino physics.Comment: 25 RevTEX pages, 16 PS figures, revised figure captions and references adde

Exact Formulas and Simple CP dependence of Neutrino Oscillation Probabilities in Matter with Constant Density

We investigate neutrino oscillations in constant matter within the context of the standard three neutrino scenario. We derive an exact and simple formula for the oscillation probability applicable to all channels. In the standard parametrization, the probability for $\nu_e$ $\to$ $\nu_{\mu}$ transition can be written in the form $P(\nu_e \to \nu_{\mu})=A_{e\mu}\cos\delta+B_{e\mu}\sin\delta+C_{e\mu}$ without any approximation using CP phase $\delta$. For $\nu_{\mu}$ $\to$ $\nu_{\tau}$ transition, the linear term of $\cos 2\delta$ is added and the probability can be written in the form $P(\nu_{\mu} \to \nu_{\tau})=A_{\mu\tau}\cos\delta+B_{\mu\tau} \sin\delta+C_{\mu\tau}+D_{\mu\tau}\cos 2\delta$. We give the CP dependences of the probability for other channels. We show that the probability for each channel in matter has the same form with respect to $\delta$ as in vacuum. It means that matter effects just modify the coefficients $A$, $B$, $C$ and $D$. We also give the exact expression of the coefficients for each channel. Furthermore, we show that our results with respect to CP dependences are reproduced from the effective mixing angles and the effective CP phase calculated by Zaglauer and Schwarzer. Through the calculation, a new identity is obtained by dividing the Naumov-Harrison-Scott identity by the Toshev identity.Comment: 12 pages, RevTeX4 style, changed title, minor correction