Confluence reduction for Markov automata

Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. Recently, the process algebra MAPA was introduced to efficiently model such systems. As always, the state space explosion threatens the analysability of the models generated by such specifications. We therefore introduce confluence reduction for Markov automata, a powerful reduction technique to keep these models small. We define the notion of confluence directly on Markov automata, and discuss how to syntactically detect confluence on the MAPA language as well. That way, Markov automata generated by MAPA specifications can be reduced on-the-fly while preserving divergence-sensitive branching bisimulation. Three case studies demonstrate the significance of our approach, with reductions in analysis time up to an order of magnitude

Mathematical modeling of drug-induced receptor internalization in the HER2-positive SKBR3 breast cancer cell-line

About 20% of breast cancer tumors over-express the HER2 receptor. Trastuzumab, an approved drug to treat this type of breast cancer, is a monoclonal antibody directly binding at the HER2 receptor and ultimately inhibiting cancer cell growth. The goal of our study was to understand the early impact of trastuzumab on HER2 internalization and recycling in the HER2-overexpressing breast cancer cell line SKBR3. To this end, fluorescence microscopy, monitoring the amount of HER2 expression in the plasma membrane, was combined with mathematical modeling to derive the flux of HER2 receptors from and to the membrane. We constructed a dynamic multi-compartment model based on ordinary differential equations. To account for cancer cell heterogeneity, a first, dynamic model was expanded to a second model including two distinct cell phenotypes, with implications for different conformational states of HER2, i.e. monomeric or homodimeric. Our mathematical model shows that the hypothesis of fast constitutive HER2 recycling back to the plasma membrane does not match the experimental data. It conclusively describes the experimental observation that trastuzumab induces sustained receptor internalization in cells with membrane ruffles. It is also concluded that for rare, non-ruffled (flat) cells, HER2 internalization occurs three orders of magnitude slower than for the bulk, ruffled cell population. © 2019, The Author(s)

A Multi-Wavelength Study of Sgr A*: The Role of Near-IR Flares in Production of X-ray, Soft γ\gamma-ray and Sub-millimeter Emission

(abridged) We describe highlights of the results of two observing campaigns in 2004 to investigate the correlation of flare activity in Sgr A* in different wavelength regimes, using a total of nine ground and space-based telescopes. We report the detection of several new near-IR flares during the campaign based on {\it HST} observations. The level of near-IR flare activity can be as low as $\sim0.15$ mJy at 1.6 $\mu$m and continuous up to about 40% of the total observing time. Using the NICMOS instrument on the {\it HST}, the {\it XMM-Newton} and CSO observatories, we also detect simultaneous bright X-ray and near-IR flare in which we observe for the first time correlated substructures as well as simultaneous submillimeter and near-IR flaring. X-ray emission is arising from the population of near-IR-synchrotron-emitting relativistic particles which scatter submillimeter seed photons within the inner 10 Schwarzschild radii of Sgr A* up to X-ray energies. In addition, using the inverse Compton scattering picture, we explain the high energy 20-120 keV emission from the direction toward Sgr A*, and the lack of one-to-one X-ray counterparts to near-IR flares, by the variation of the magnetic field and the spectral index distributions of this population of nonthermal particles. In this picture, the evidence for the variability of submillimeter emission during a near-IR flare is produced by the low-energy component of the population of particles emitting synchrotron near-IR emission. Based on the measurements of the duration of flares in near-IR and submillimeter wavelengths, we argue that the cooling could be due to adiabatic expansion with the implication that flare activity may drive an outflow.Comment: 48 pages, 12 figures, ApJ (in press

Modelling and analysis of Markov reward automata

Costs and rewards are important ingredients for many types of systems, modelling critical aspects like energy consumption, task completion, repair costs, and memory usage. This paper introduces Markov reward automata, an extension of Markov automata that allows the modelling of systems incorporating rewards (or costs) in addition to nondeterminism, discrete probabilistic choice and continuous stochastic timing. Rewards come in two flavours: action rewards, acquired instantaneously when taking a transition; and state rewards, acquired while residing in a state. We present algorithms to optimise three reward functions: the expected cumulative reward until a goal is reached, the expected cumulative reward until a certain time bound, and the long-run average reward. We have implemented these algorithms in the SCOOP/IMCA tool chain and show their feasibility via several case studies

Characterization of the Crab Pulsar's Timing Noise

We present a power spectral analysis of the Crab pulsar's timing noise, mainly using radio measurements from Jodrell Bank taken over the period 1982-1989. The power spectral analysis is complicated by nonuniform data sampling and the presence of a steep red power spectrum that can distort power spectra measurement by causing severe power ``leakage''. We develop a simple windowing method for computing red noise power spectra of uniformly sampled data sets and test it on Monte Carlo generated sample realizations of red power-law noise. We generalize time-domain methods of generating power-law red noise with even integer spectral indices to the case of noninteger spectral indices. The Jodrell Bank pulse phase residuals are dense and smooth enough that an interpolation onto a uniform time series is possible. A windowed power spectrum is computed revealing a periodic or nearly periodic component with a period of about 568 days and a 1/f^3 power-law noise component with a noise strength of 1.24 +/- 0.067 10^{-16} cycles^2/sec^2 over the analysis frequency range 0.003 - 0.1 cycles/day. This result deviates from past analyses which characterized the pulse phase timing residuals as either 1/f^4 power-law noise or a quasiperiodic process. The analysis was checked using the Deeter polynomial method of power spectrum estimation that was developed for the case of nonuniform sampling, but has lower spectral resolution. The timing noise is consistent with a torque noise spectrum rising with analysis frequency as f implying blue torque noise, a result not predicted by current models of pulsar timing noise. If the periodic or nearly periodic component is due to a binary companion, we find a companion mass > 3.2 Earth masses.Comment: 53 pages, 9 figures, submitted to MNRAS, abstract condense

Electronic Structure and Lattice Relaxation Related to Fe in Mgo

The electronic structure of Fe impurity in MgO was calculated by the linear muffin-tin orbital--full-potential method within the conventional local-density approximation (LDA) and making use of the LDA+$U$ formalism. The importance of introducing different potentials, depending on the screened Coulomb integral $U$, is emphasized for obtaining a physically reasonable ground state of the Fe$^{2+}$ ion configuration. The symmetry lowering of the ion electrostatic field leads to the observed Jahn--Teller effect; related ligand relaxation confined to tetragonal symmetry has been optimized based on the full-potential total energy results. The electronic structure of the Fe$^{3+}$ ion is also calculated and compared with that of Fe$^{2+}$.Comment: 13 pages + 4 PostScript figures, Revtex 3.0, SISSA-CM-94-00

Parameter estimation in spatially extended systems: The Karhunen-Loeve and Galerkin multiple shooting approach

Parameter estimation for spatiotemporal dynamics for coupled map lattices and continuous time domain systems is shown using a combination of multiple shooting, Karhunen-Loeve decomposition and Galerkin's projection methodologies. The resulting advantages in estimating parameters have been studied and discussed for chaotic and turbulent dynamics using small amounts of data from subsystems, availability of only scalar and noisy time series data, effects of space-time parameter variations, and in the presence of multiple time-scales.Comment: 11 pages, 5 figures, 4 Tables Corresponding Author - V. Ravi Kumar, e-mail address: [email protected]

A near-IR variability study of the Galactic black hole: a red noise source with no detected periodicity

We present the results of near-infrared (2 and 3 microns) monitoring of Sgr A*-IR with 1 min time sampling using the natural and laser guide star adaptive optics (LGS AO) system at the Keck II telescope. Sgr A*-IR was observed continuously for up to three hours on each of seven nights, between 2005 July and 2007 August. Sgr A*-IR is detected at all times and is continuously variable, with a median observed 2 micron flux density of 0.192 mJy, corresponding to 16.3 magnitude at K'. These observations allow us to investigate Nyquist sampled periods ranging from about 2 minutes to an hour. Using Monte Carlo simulations, we find that the variability of Sgr A* in this data set is consistent with models based on correlated noise with power spectra having frequency dependent power law slopes between 2.0 to 3.0, consistent with those reported for AGN light curves. Of particular interest are periods of ~20 min, corresponding to a quasi-periodic signal claimed based upon previous near-infrared observations and interpreted as the orbit of a 'hot spot' at or near the last stable orbit of a spinning black hole. We find no significant periodicity at any time scale probed in these new observations for periodic signals. This study is sensitive to periodic signals with amplitudes greater than 20% of the maximum amplitude of the underlying red noise component for light curves with duration greater than ~2 hours at a 98% confidence limit.Comment: 37 pages, 2 tables, 17 figures, accepted by Ap

Critical temperature of non-interacting Bose gases on disordered lattices

For a non-interacting Bose gas on a lattice we compute the shift of the critical temperature for condensation when random-bond and onsite disorder are present. We evidence that the shift depends on the space dimensionality D and the filling fraction f. For D -> infinity (infinite-range model), using results from the theory of random matrices, we show that the shift of the critical temperature is negative, depends on f, and vanishes only for large f. The connections with analogous results obtained for the spherical model are discussed. For D=3 we find that, for large f, the critical temperature Tc is enhanced by disorder and that the relative shift does not sensibly depend on f; at variance, for small f, Tc decreases in agreement with the results obtained for a Bose gas in the continuum. We also provide numerical estimates for the shift of the critical temperature due to disorder induced on a non-interacting Bose gas by a bichromatic incommensurate potential.Comment: 18 pages, 8 figures; Fig. 8 improved adding results for another value of q (q=830/1076

Long-term optical variability of PKS 2155-304

Aims: The optical variability of the blazar PKS 2155-304 is investigated to characterise the red noise behaviour at largely different time scales from 20 days to O(>10 yrs). Methods: The long-term optical light curve of PKS 2155-304 is assembled from archival data as well as from so-far unpublished observations mostly carried out with the ROTSE-III and the ASAS robotic telescopes. A forward folding technique is used to determine the best-fit parameters for a model of a power law with a break in the power spectral density function (PSD). The best-fit parameters are estimated using a maximum-likelihood method with simulated light curves in conjunction with the Lomb Scargle Periodogram (LSP) and the first-order Structure Function (SF). In addition, a new approach based upon the so-called Multiple Fragments Variance Function (MFVF) is introduced and compared to the other methods. Simulated light curves have been used to confirm the reliability of these methods as well as to estimate the uncertainties of the best-fit parameters. Results: The light curve is consistent with the assumed broken power-law PSD. All three methods agree within the estimated uncertainties with the MFVF providing the most accurate results. The red-noise behaviour of the PSD in frequency f follows a power law with f^-{\beta}, {\beta}=1.8 +0.1/-0.2 and a break towards f^0 at frequencies lower than f_min=(2.7 +2.2/-1.6 yrs)^-1.Comment: 10 pages, 8 figures, the ROTSE-light curve can be downloaded from http://vizier.cfa.harvard.edu/viz-bin/VizieR?-source=J/A+A/531/A12