Dynamics and bifurcations in a simple quasispecies model of tumorigenesis

Cancer is a complex disease and thus is complicated to model. However, simple models that describe the main processes involved in tumoral dynamics, e.g., competition and mutation, can give us clues about cancer behaviour, at least qualitatively, also allowing us to make predictions. Here we analyze a simplified quasispecies mathematical model given by differential equations describing the time behaviour of tumor cells populations with different levels of genomic instability. We find the equilibrium points, also characterizing their stability and bifurcations focusing on replication and mutation rates. We identify a transcritical bifurcation at increasing mutation rates of the tumor cells population. Such a bifurcation involves an scenario with dominance of healthy cells and impairment of tumor populations. Finally, we characterize the transient times for this scenario, showing that a slight increase beyond the critical mutation rate may be enough to have a fast response towards the desired state (i.e., low tumor populations) during directed mutagenic therapies

Casimir interaction at liquid nitrogen temperature: Comparison between experiment and theory

We have measured the normalized gradient of the Casimir force between Au-coated surfaces of the sphere and the plate and equivalent Casimir pressure between two parallel Au plates at T=77K. These measurements have been performed by means of dynamic force microscope adapted for operating at low temperatures in the frequency shift technique. It was shown that the measurement results at T=77K are in a very good agreement with those at T=300K and with computations at T=77K using both theoretical approaches to the thermal Casimir force proposed in the literature. No thermal effect in the Casimir pressure was observed in the limit of experimental errors with the increase of temperature from T=77K to T=300K. Taking this into account, we have discussed the possible role of patch potentials in the comparison between measured and calculated Casimir pressures.Comment: 18 pages, 8 figures, to appear in Phys. Rev.

Dissecting the Power Sources of Low-Luminosity Emission-Line Galaxy Nuclei via Comparison of HST-STIS and Ground-Based Spectra

Using a sample of ~100 nearby line-emitting galaxy nuclei, we have built the currently definitive atlas of spectroscopic measurements of H_alpha and neighboring emission lines at subarcsecond scales. We employ these data in a quantitative comparison of the nebular emission in Hubble Space Telescope (HST) and ground-based apertures, which offer an order-of-magnitude difference in contrast, and provide new statistical constraints on the degree to which Transition Objects and low-ionization nuclear emission-line regions (LINERs) are powered by an accreting black hole at <10 pc. We show that while the small-aperture observations clearly resolve the nebular emission, the aperture dependence in the line ratios is generally weak, and this can be explained by gradients in the density of the line-emitting gas: the higher densities in the more nuclear regions potentially flatten the excitation gradients, suppressing the forbidden emission. The Transition Objects show a threefold increase in the incidence of broad H_alpha emission in the high-resolution data, as well as the strongest density gradients, supporting the composite model for these systems as accreting sources surrounded by star-forming activity. The narrow-line LINERs appear to be the weaker counterparts of the Type 1 LINERs, where the low accretion rates cause the disappearance of the broad-line component. The enhanced sensitivity of the HST observations reveals a 30% increase in the incidence of accretion-powered systems at z~0. A comparison of the strength of the broad-line emission detected at different epochs implies potential broad-line variability on a decade-long timescale, with at least a factor of three in amplitude.Comment: 27 pages, 13 figures, 4 tables, accepted for publication in Ap

The Effect of Relative Humidity on Dropwise Condensation Dynamics

Dropwise condensation of atmospheric water vapor is important in multiple practical engineering applications. The roles of environmental factors and surface morphology/chemistry on the condensation dynamics need to be better understood to enable efficient water-harvesting, dehumidification, and other psychrometric processes. Systems and surfaces that may promote faster condensation rates and self-shedding of condensate droplets could lead to improved mass transfer rates and higher water yields in harvesting applications. In the present study, experiments are performed in a facility that allows visualization of the condensation process on a vertically oriented, hydrophobic surface at a controlled relative humidity and surface subcooling temperature. The distribution and growth of water droplets are monitored across the surface at different relative humidities (45%, 50%, 55%, and 70%) at a constant surface subcooling temperature of 15 C below the ambient temperature (20 C). The droplet growth dynamics exhibits a strong dependency on relative humidity in the early stages during which there is a large population of small droplets on the surface and single droplet growth dominates over coalescence effects. At later stages, the dynamics of droplet growth is insensitive to relative humidity due to the dominance of coalescence effects. The overall volumetric rate of condensation on the surface is also assessed as a function of time and ambient relative humidity. Low relative humidity conditions not only slow the absolute rate of condensation, but also prolong an initial transient regime over which the condensation rate remains significantly below the steady-state value

Trading interactions for topology in scale-free networks

Scale-free networks with topology-dependent interactions are studied. It is shown that the universality classes of critical behavior, which conventionally depend only on topology, can also be explored by tuning the interactions. A mapping, $\gamma' = (\gamma - \mu)/(1-\mu)$, describes how a shift of the standard exponent $\gamma$ of the degree distribution $P(q)$ can absorb the effect of degree-dependent pair interactions $J_{ij} \propto (q_iq_j)^{-\mu}$. Replica technique, cavity method and Monte Carlo simulation support the physical picture suggested by Landau theory for the critical exponents and by the Bethe-Peierls approximation for the critical temperature. The equivalence of topology and interaction holds for equilibrium and non-equilibrium systems, and is illustrated with interdisciplinary applications.Comment: 4 pages, 5 figure

On the Quantum Mechanics for One Photon

This paper revisits the quantum mechanics for one photon from the modern viewpoint and by the geometrical method. Especially, besides the ordinary (rectangular) momentum representation, we provide an explicit derivation for the other two important representations, called the cylindrically symmetrical representation and the spherically symmetrical representation, respectively. These other two representations are relevant to some current photon experiments in quantum optics. In addition, the latter is useful for us to extract the information on the quantized black holes. The framework and approach presented here are also applicable to other particles with arbitrary mass and spin, such as the particle with spin 1/2.Comment: 15 pages, typos corrected, references added, corrections and improvements made owing to the anonymous referee's responsible and helpful remarks, accepted for publication in Journal of Mathematical Physics:

Influence of the fiber direction on the tribological behavior of carbon-fiber reinforced epoxy composites manufactured by prepeg laminates

In this work, friction behavior of different carbon fiber-epoxy composites is evaluated. Linear friction tests are carried out and wear behaviour has been established from several parameters as wear depth, wear band width and macrostructural observation. The experimental variables considered were load (10-40N) and the fiber orientation with respect to the sliding direction (0°, 90° and multidirectional). Layers with the fiber oriented in the sliding direction showed larger wear due to cracks existing in the fibermatrix interface once the wear depth reached the fibers. The best results were obtained in those cases in which no influence of the resin matrix existed

Correlator Bank Detection of GW chirps. False-Alarm Probability, Template Density and Thresholds: Behind and Beyond the Minimal-Match Issue

The general problem of computing the false-alarm rate vs. detection-threshold relationship for a bank of correlators is addressed, in the context of maximum-likelihood detection of gravitational waves, with specific reference to chirps from coalescing binary systems. Accurate (lower-bound) approximants for the cumulative distribution of the whole-bank supremum are deduced from a class of Bonferroni-type inequalities. The asymptotic properties of the cumulative distribution are obtained, in the limit where the number of correlators goes to infinity. The validity of numerical simulations made on small-size banks is extended to banks of any size, via a gaussian-correlation inequality. The result is used to estimate the optimum template density, yielding the best tradeoff between computational cost and detection efficiency, in terms of undetected potentially observable sources at a prescribed false-alarm level, for the simplest case of Newtonian chirps.Comment: submitted to Phys. Rev.