A two-phasemathematical model describing the dynamics of a substance between two coupled media of different properties and dimensions is presented. A system of partial differential equations describes the diffusion and the binding/unbinding processes in both layers. Additional flux continuity at the interface and clearance conditions into systemic circulation are imposed. An eigenvalue problem with discontinuous coefficients is solved and an analytical solution is given in the form of an infinite series expansion. The model points out the role of the diffusion and reaction parameters, which control the complex transfer mechanism and the drug kinetics across the two layers.

Transcriptome studies have shown the pervasive nature of transcription, demonstrating almost all the genes undergo alternative splicing. Accurately annotating all transcripts of a gene is crucial. It is needed to understand the impact of mutations on phenotypes, to shed light on genetic and epigenetic regulation of mRNAs and more generally to widen our knowledge about cell functionality and tissue diversity. RNA-sequencing (RNA-Seq), and the other applications of the next-generation sequencing, provides precious data to improve annotations' accuracy, simultaneously creating issues related to the variety, complexity and the size of produced data. In this 'scenario', the lack of user-friendly resources, easily accessible to researchers with low skills in bioinformatics, makes difficult to retrieve complete information about one or few genes without browsing a jungle of databases. Concordantly, the increasing amount of data from 'omics' technologies imposes to develop integrated databases merging different data formats coming from distinct but complementary sources. In light of these considerations, and given the wide interest in studying Down syndrome-a genetic condition due to the trisomy of human chromosome 21 (HSA21)-we developed an integrated relational database and a web interface, named ALE-HSA21 (AnaLysis of Expression on HSA21), accessible at http://bioinfo.na.iac.cnr.it/ALE-HSA21. This comprehensive and user-friendly web resource integrates-for all coding and noncoding transcripts of chromosome 21-existing gene annotations and transcripts identified de novo through RNA-Seq analysis with predictive computational analysis of regulatory sequences. Given the role of noncoding RNAs and untranslated regions of coding genes in key regulatory mechanisms, ALE-HSA21 is also an interesting web-based platform to investigate such processes. The 'transcript-centric' and easily-accessible nature of ALE-HSA21 makes this resource a valuable tool to rapidly retrieve data at the isoform level, rather than at gene level, useful to investigate any disease, molecular pathway or cell process involving chromosome 21 genes.

We review recent advances on the mesoscopic modeling of water-like fluids, based on the lattice Boltzmann (LB) methodology. The main idea is to enrich the basic LB (hydro)-dynamics with angular degrees of freedom responding to suitable directional potentials between water-like molecules. The model is shown to reproduce some microscopic features of liquid water, such as an average number of hydrogen bonds per molecules (HBs) between 3 and 4, as well as a qualitatively correct statistics of the hydrogen bond angle as a function of the temperature. Future developments, based on the coupling the present water-like LB model with the dynamics of suspended bodies, such as biopolymers, may open new angles of attack to the simulation of complex biofluidic problems, such as protein folding and aggregation, and the motion of large biomolecules in complex cellular environments.

We present the results of a computational study of coronary trees obtained from CT acquisition at resolution of 0.35mm x 0.35mm x 0.4mm and presenting significant stenotic plaques. We analyze the cardiovascular implications of stenotic plaques for a sizeable number of patients and show that the standard clinical criterion for surgical or percutaneous intervention, based on the Fractional Flow Reserve (FFR), is well reproduced by simulations in a range of inflow conditions that can be finely controlled. The relevance of the present study is related to the reproducibility of FFR data by simulating the coronary trees at global level via high performance simulation methods together with an independent assessment based on in vitro hemodynamics. The data show that controlling the flow Reynolds number is a viable procedure to account for FFR as heart-cycle time averages and maximal hyperemia, as measured in vivo. The reproducibility of the clinical data with simulation offers a systematic approach to measuring the functional implications of stenotic plaques. © 2014 SPIE.

We consider stochastic differential games with N nearly identical players, linear-Gaussian dynamics, and infinite horizon discounted quadratic cost. Admissible controls are feedbacks for which the system is ergodic. We first study the existence of affine Nash equilibria by means of an associated system of N Hamilton-Jacobi-Bellman and N Kolmogorov-Fokker-Planck partial differential equations, proving that for small discount factors quadratic-Gaussian solutions exist and are unique. Then, we prove the convergence of such solutions to the unique quadratic-Gaussian solution of the pair of Mean Field equations. We also discuss some singular limits, such as vanishing discount, vanishing noise, and cheap control.

The world lines of null particles admit arbitrary parametrizations. In the presence of a family of observers one may introduce along a null world line an extension of the so-called Cattaneo's relative standard time parameter (valid for massive particles) which plays a special role. Another possibility is to use the coordinate time itself as a parameter. The relation between relative standard time and coordinate time allows for the introduction of an observer-dependent optical path and associated refraction index. Both these quantities are studied here working out explicit examples concerning familiar null orbits and observers in black hole spacetimes.

The optical medium analogy of a given spacetime was developed decades ago and has since then been widely applied to different gravitational contexts. Here we consider the case of a colliding gravitational wave spacetime, generalizing previous results concerning single gravitational pulses. Given the complexity of the nonlinear interaction of two gravitational waves in the framework of general relativity, typically leading to the formation of either horizons or singularities, the optical medium analogy proves helpful to simply capture some interesting effects of photon propagation.

The deviation from geodesic motion of the world line of an extended body endowed with multipolar structure up to the mass quadrupole moment is studied in the Kerr background according to the Mathisson-Papapetrou-Dixon model. The properties of the quadrupole tensor are clarified by identifying the relevant components which enter the equations of motion, leading to the definition of an effective quadrupole tensor sharing its own algebraic symmetries, but also obeying those implied by the Mathisson-Papapetrou-Dixon model itself. The equations of motion are then solved analytically in the limit of small values of the characteristic length scales associated with the spin and quadrupole variables in comparison with the one associated with the background curvature and under special assumptions on the body's structure and motion. The resulting quasicircular orbit is parametrized in a Keplerian-like form, so that temporal, radial, and azimuthal eccentricities as well as semimajor axis, period, and periastron advance are explicitly computed and expressed in terms of gauge-invariant variables in the weak field and slow motion limit. A companion numerical study of the equations of motion is performed too.

Some strong field effects on test particle motion associated with the propagation of a plane electromagnetic wave in the exact theory of general relativity are investigated. Two different profiles of the associated radiation flux are considered in comparison, corresponding to either constant or oscillating electric and magnetic fields with respect to a natural family of observers. These are the most common situations to be experimentally explored, and have a well known counterpart in the flat spacetime limit. The resulting line elements are determined by a single metric function, which turns out to be expressed in terms of standard trigonometric functions in the case of a constant radiation flux, and in terms of special functions in the case of an oscillating flux, leading to different features of test particle motion. The world line deviation between both uncharged and charged particles on different spacetime trajectories due to the combined effect of gravitational and electromagnetic forces is studied. The interaction of charged particles with the background radiation field is also discussed through a general relativistic description of the inverse Compton effect. Motion as well as deviation effects on particles endowed with spin are studied too. Special situations may occur in which the direction of the spin vector changes during the interaction, leading to observable effects like spin flip.

We extend the analytical determination of the main radial potential describing (within the effective one-body formalism) the gravitational interaction of two bodies beyond the fourth post-Newtonian approximation recently obtained by us. This extension is done to linear order in the mass ratio by applying analytical gravitational self-force theory (for a particle in circular orbit around a Schwarzschild black hole) to Detweiler's gauge-invariant redshift variable. By using the version of black hole perturbation theory developed by Mano, Suzuki and Takasugi, we have pushed the analytical determination of the (linear in mass ratio) radial potential to the sixth post-Newtonian order (passing through 5 and 5.5 post-Newtonian terms). In principle, our analytical method can be extended to arbitrarily high post-Newtonian orders.

The equatorial motion of extended bodies in a Kerr spacetime is investigated in the framework of the Mathisson-Papapetrou-Dixon model, including the full set of effective components of the quadrupole tensor. The numerical integration of the associated equations shows the specific role of the mass and current quadrupole moment components. While most of the literature on this topic is limited to spin-induced (purely electric) quadrupole tensor, the present analysis highlights the effect of a completely general quadrupole tensor on the dynamics. The contribution of the magnetic-type components is indeed related to a number of interesting features, e.g., enhanced inward/outward spiraling behavior of the orbit and spin-flip-like effects, which may have observational counterparts. Finally, the validity limit of the Mathisson-Papapetrou-Dixon model is also discussed through explicit examples.

A scalar field equivalent to a nonideal "dark energy fluid" obeying a Shan-Chen-like equation of state is used as the background source of a flat Friedmann-Robertson-Walker cosmological spacetime to describe the inflationary epoch of our Universe. Within the slow-roll approximation, a number of interesting features are presented, including the possibility to fulfill current observational constraints as well as a graceful exit mechanism from the inflationary epoch.

We analytically compute, to the eight-and-a-half post-Newtonian order, and to linear order in the mass ratio, the radial potential describing (within the effective one-body formalism) the gravitational interaction of two bodies, thereby extending previous analytic results. These results are obtained by applying analytical gravitational self-force theory (for a particle in circular orbit around a Schwarzschild black hole) to Detweiler's gauge-invariant redshift variable. We emphasize the increase in "transcendentality" of the numbers entering the post-Newtonian expansion coefficients as the order increases, in particular we note the appearance of zeta(3) (as well as the square of Euler's constant gamma) starting at the seventh post-Newtonian order. We study the convergence of the post-Newtonian expansion as the expansion parameter u = GM/(c(2)r) leaves the weak-field domain u << 1 to enter the strong field domain u = O(1).

Recent work in the literature has found a suppression or, instead, an enhancement of the cosmic microwave background power spectrum in quantum gravity, although the effect is too small to be observed in both cases. The present paper studies in detail the equations recently proposed for a Born-Oppenheimer-type analysis of the problem. By using a perturbative approach to the analysis of the nonlinear ordinary differential equation obeyed by the two-point function for scalar fluctuations, we find various explicit forms of such a two-point function, with the associated power spectrum. In particular, a new family of power spectra is obtained and studied. The theoretical prediction of power enhancement at large scales is hence confirmed.

We analytically compute, to linear order in the mass ratio, the "geodetic" spin-precession frequency of a small spinning body orbiting a large (nonspinning) body to the eight-and-a-half post-Newtonian order, thereby extending previous analytical knowledge which was limited to the third post-Newtonian level. These results are obtained applying analytical gravitational self-force theory to the first-derivative level generalization of Detweiler's gauge-invariant redshift variable. We compare our analytic results with strong-field numerical data recently obtained by Dolan et al. [Phys. Rev. D 89, 064011 (2014)]. Our new, high-post-Newtonian-order results capture the strong-field features exhibited by the numerical data. We argue that the spin precession will diverge as approximate to -0.14/(1 - 3y) as the light ring is approached. We transcribe our kinematical spin-precession results into a corresponding improved analytic knowledge of one of the two (gauge-invariant) effective gyrogravitomagnetic ratios characterizing spin-orbit couplings within the effective-one-body formalism. We provide simple, accurate analytic fits both for spin precession and the effective gyrogravitomagnetic ratio. The latter fit predicts that the linear-in-mass-ratio correction to the gyrogravitomagnetic ratio changes sign before reaching the light ring. This strong-field prediction might be important for improving the analytic modeling of coalescing spinning binaries.

We investigate the asymptotic behavior of peculiar velocities in certain physically significant time-dependent gravitational fields. Previous studies of the motion of free test particles have focused on the collapse scenario, according to which a double-jet pattern with Lorentz factor gamma -> infinity develops asymptotically along the direction of complete gravitational collapse. In the present work, we identify a second wave scenario, in which a single-jet pattern with Lorentz factor gamma -> infinity develops asymptotically along the direction of wave propagation. The possibility of a connection between the two scenarios for the formation of cosmic jets is critically examined.