Probabilistic Reachability for Parametric Markov Models

Abstract. Given a parametric Markov model, we consider the problem of computing the formula expressing the probability of reaching a given set of states. To attack this principal problem, Daws has suggested to first convert the Markov chain into a finite automaton, from which a regular expression is computed. Afterwards, this expression is evaluated to a closed form expression representing the reachability probability. This paper investigates how this idea can be turned into an effective procedure. It turns out that the bottleneck lies in an exponential growth of the regular expression relative to the number of states. We therefore proceed differently, by tightly intertwining the regular expression computation with its evaluation. This allows us to arrive at an effective method that avoids the exponential blow up in most practical cases. We give a detailed account of the approach, also extending to parametric models with rewards and with non-determinism. Experimental evidence is provided, illustrating that our implementation provides meaningful insights on non-trivial models.

Mice Lacking the Circadian Modulators SHARP1 and SHARP2 Display Altered Sleep and Mixed State Endophenotypes of Psychiatric Disorders

Increasing evidence suggests that clock genes may be implicated in a spectrum of psychiatric diseases, including sleep and mood related disorders as well as schizophrenia. The bHLH transcription factors SHARP1/DEC2/BHLHE41 and SHARP2/DEC1/ BHLHE40 are modulators of the circadian system and SHARP1/DEC2/BHLHE40 has been shown to regulate homeostatic sleep drive in humans. In this study, we characterized Sharp1 and Sharp2 double mutant mice (S1/2(-/-)) using online EEG recordings in living animals, behavioral assays and global gene expression profiling. EEG recordings revealed attenuated sleep/wake amplitudes and alterations of theta oscillations. Increased sleep in the dark phase is paralleled by reduced voluntary activity and cortical gene expression signatures reveal associations with psychiatric diseases. S1/2(-/-) mice display alterations in novelty induced activity, anxiety and curiosity. Moreover, mutant mice exhibit impaired working memory and deficits in prepulse inhibition resembling symptoms of psychiatric diseases. Network modeling indicates a connection between neural plasticity and clock genes, particularly for SHARP1 and PER1. Our findings support the hypothesis that abnormal sleep and certain (endo) phenotypes of psychiatric diseases may be caused by common mechanisms involving components of the molecular clock including SHARP1 and SHARP2

Investigating human audio-visual object perception with a combination of hypothesis-generating and hypothesis-testing fMRI analysis tools

Primate multisensory object perception involves distributed brain regions. To investigate the network character of these regions of the human brain, we applied data-driven group spatial independent component analysis (ICA) to a functional magnetic resonance imaging (fMRI) data set acquired during a passive audio-visual (AV) experiment with common object stimuli. We labeled three group-level independent component (IC) maps as auditory (A), visual (V), and AV, based on their spatial layouts and activation time courses. The overlap between these IC maps served as definition of a distributed network of multisensory candidate regions including superior temporal, ventral occipito-temporal, posterior parietal and prefrontal regions. During an independent second fMRI experiment, we explicitly tested their involvement in AV integration. Activations in nine out of these twelve regions met the max-criterion (A < AV > V) for multisensory integration. Comparison of this approach with a general linear model-based region-of-interest definition revealed its complementary value for multisensory neuroimaging. In conclusion, we estimated functional networks of uni- and multisensory functional connectivity from one dataset and validated their functional roles in an independent dataset. These findings demonstrate the particular value of ICA for multisensory neuroimaging research and using independent datasets to test hypotheses generated from a data-driven analysis

Measurement of χ c1 and χ c2 production with s√ = 7 TeV pp collisions at ATLAS

The prompt and non-prompt production cross-sections for the χ c1 and χ c2 charmonium states are measured in pp collisions at s√ = 7 TeV with the ATLAS detector at the LHC using 4.5 fb−1 of integrated luminosity. The χ c states are reconstructed through the radiative decay χ c → J/ψγ (with J/ψ → μ + μ −) where photons are reconstructed from γ → e + e − conversions. The production rate of the χ c2 state relative to the χ c1 state is measured for prompt and non-prompt χ c as a function of J/ψ transverse momentum. The prompt χ c cross-sections are combined with existing measurements of prompt J/ψ production to derive the fraction of prompt J/ψ produced in feed-down from χ c decays. The fractions of χ c1 and χ c2 produced in b-hadron decays are also measured

Search for gravitational-lensing signatures in the full third observing run of the LIGO-Virgo network

Gravitational lensing by massive objects along the line of sight to the source causes distortions of gravitational wave-signals; such distortions may reveal information about fundamental physics, cosmology and astrophysics. In this work, we have extended the search for lensing signatures to all binary black hole events from the third observing run of the LIGO--Virgo network. We search for repeated signals from strong lensing by 1) performing targeted searches for subthreshold signals, 2) calculating the degree of overlap amongst the intrinsic parameters and sky location of pairs of signals, 3) comparing the similarities of the spectrograms amongst pairs of signals, and 4) performing dual-signal Bayesian analysis that takes into account selection effects and astrophysical knowledge. We also search for distortions to the gravitational waveform caused by 1) frequency-independent phase shifts in strongly lensed images, and 2) frequency-dependent modulation of the amplitude and phase due to point masses. None of these searches yields significant evidence for lensing. Finally, we use the non-detection of gravitational-wave lensing to constrain the lensing rate based on the latest merger-rate estimates and the fraction of dark matter composed of compact objects

Search for eccentric black hole coalescences during the third observing run of LIGO and Virgo

Despite the growing number of confident binary black hole coalescences observed through gravitational waves so far, the astrophysical origin of these binaries remains uncertain. Orbital eccentricity is one of the clearest tracers of binary formation channels. Identifying binary eccentricity, however, remains challenging due to the limited availability of gravitational waveforms that include effects of eccentricity. Here, we present observational results for a waveform-independent search sensitive to eccentric black hole coalescences, covering the third observing run (O3) of the LIGO and Virgo detectors. We identified no new high-significance candidates beyond those that were already identified with searches focusing on quasi-circular binaries. We determine the sensitivity of our search to high-mass (total mass M>70 M⊙) binaries covering eccentricities up to 0.3 at 15 Hz orbital frequency, and use this to compare model predictions to search results. Assuming all detections are indeed quasi-circular, for our fiducial population model, we place an upper limit for the merger rate density of high-mass binaries with eccentricities 0<e≤0.3 at 0.33 Gpc−3 yr−1 at 90\% confidence level

Living Polymerization to Ultra-High Molecular Weight and Dye-Labeled Polyethylene for Single-Molecule Fluorescence Microscopy and Reactor Blends

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Post-Metallocenes in the Industrial Production of Polyolefins

Research on “post-metallocene” polymerization catalysis ranges methodologically from fundamental mechanistic studies of polymerization reactions over catalyst design to material properties of the polyolefins prepared. A common goal of these studies is the creation of practically useful new polyolefin materials or polymerization processes. This Review gives a comprehensive overview of post-metallocene polymerization catalysts that have been put into practice. The decisive properties for this success of a given catalyst structure are delineated

Enhanced accuracy of single-molecule diffusion measurements with a photocleavable energy-transfer dyad

A photocleavable energy-transfer dyad was synthesized, characterized, and applied to single-molecule fluorescence microscopy. After photocleavage, a combination of independent two-color single-molecule tracking and analysis of single-molecule energy-transfer efficiencies allows the determination of the temporal evolution of the relative distances between both fragments from the nm to the μm scale. This gives access to a broad range of diffusion coefficients