Causal Fermion Systems: A Quantum Space-Time Emerging from an Action Principle

Causal fermion systems are introduced as a general mathematical framework for formulating relativistic quantum theory. By specializing, we recover earlier notions like fermion systems in discrete space-time, the fermionic projector and causal variational principles. We review how an effect of spontaneous structure formation gives rise to a topology and a causal structure in space-time. Moreover, we outline how to construct a spin connection and curvature, leading to a proposal for a "quantum geometry" in the Lorentzian setting. We review recent numerical and analytical results on the support of minimizers of causal variational principles which reveal a "quantization effect" resulting in a discreteness of space-time. A brief survey is given on the correspondence to quantum field theory and gauge theories.Comment: 23 pages, LaTeX, 2 figures, footnote added on page

Parameter estimation in pair hidden Markov models

This paper deals with parameter estimation in pair hidden Markov models (pair-HMMs). We first provide a rigorous formalism for these models and discuss possible definitions of likelihoods. The model being biologically motivated, some restrictions with respect to the full parameter space naturally occur. Existence of two different Information divergence rates is established and divergence property (namely positivity at values different from the true one) is shown under additional assumptions. This yields consistency for the parameter in parametrization schemes for which the divergence property holds. Simulations illustrate different cases which are not covered by our results.Comment: corrected typo

Stormy weather in 3C 196.1: nuclear outbursts and merger events shape the environment of the hybrid radio galaxy 3C 196.1

We present a multi-wavelength analysis based on archival radio, optical and X-ray data of the complex radio source 3C 196.1, whose host is the brightest cluster galaxy of a $z=0.198$ cluster. HST data show H$\alpha$+[N II] emission aligned with the jet 8.4 GHz radio emission. An H$\alpha$+[N II] filament coincides with the brightest X-ray emission, the northern hotspot. Analysis of the X-ray and radio images reveals cavities located at galactic- and cluster- scales. The galactic-scale cavity is almost devoid of 8.4 GHz radio emission and the south-western H$\alpha$+[N II] emission is bounded (in projection) by this cavity. The outer cavity is co-spatial with the peak of 147 MHz radio emission, and hence we interpret this depression in X-ray surface brightness as being caused by a buoyantly rising bubble originating from an AGN outburst $\sim$280 Myrs ago. A \textit{Chandra} snapshot observation allowed us to constrain the physical parameters of the cluster, which has a cool core with a low central temperature $\sim$2.8 keV, low central entropy index $\sim$13 keV cm$^2$ and a short cooling time of $\sim$500 Myr, which is $<0.05$ of the age of the Universe at this redshift. By fitting jumps in the X-ray density we found Mach numbers between 1.4 and 1.6, consistent with a shock origin. We also found compelling evidence of a past merger, indicated by a morphology reminiscent of gas sloshing in the X-ray residual image. Finally, we computed the pressures, enthalpies $E_{cav}$ and jet powers $P_{jet}$ associated with the cavities: $E_{cav}\sim7\times10^{58}$ erg, $P_{jet}\sim1.9\times10^{44}$ erg s$^{-1}$ for the inner cavity and $E_{cav}\sim3\times10^{60}$ erg, $P_{jet}\sim3.4\times10^{44}$ erg s$^{-1}$ for the outer cavity.Comment: 14 pages, 4 figures, ApJ accepte

Infrared Diagnostics for the Extended 12 micron Sample of Seyferts

We present an analysis of Spitzer IRS spectroscopy of 83 active galaxies from the extended 12 micron sample. We find rank correlations between several tracers of star formation which suggest that (1) the PAH feature is a reliable tracer of star formation, (2) there is a significant contribution to the heating of the cool dust by stars, (3) the H$_2$ emission is also primarily excited by star formation. The 55-90 vs. 20-30 spectral index plot is also a diagnostic of the relative contribution of Starburst to AGN. We see there is a large change in spectral index across the sample. Thus, the contribution to the IR spectrum from the AGN and starburst components can be comparable in magnitude but the relative contribution also varies widely across the sample. We find rank correlations between several AGN tracers. We search for correlations between AGN and Starburst tracers and we conclude that the AGN and Starburst tracers are not correlated. This is consistent with our conclusion that the relative strength of the AGN and Starburst components varies widely across the sample. Thus, there is no simple link between AGN fueling and Black Hole Growth and star formation in these galaxies. The distribution of Sil 10 micron and 18 micron strengths is consistent with the clumpy torus models of Sirocky et al. We find a rank correlation between the [NeV] 14 micron line and the 6.7 micron continuum which may be due to an extended component of hot dust. The Sy 2s with a Hidden Broad Line Region (HBLR) have a higher ratio of AGN to Starburst contribution to the SED than Sy 2s without an HBLR. This may contribute to the detection of the HBLR in polarized light. The Sy 2s with an HBLR are more similar to the Sy 1s than they are to the Sy 2s without an HBLR

Inducing Probabilistic Grammars by Bayesian Model Merging

We describe a framework for inducing probabilistic grammars from corpora of positive samples. First, samples are {\em incorporated} by adding ad-hoc rules to a working grammar; subsequently, elements of the model (such as states or nonterminals) are {\em merged} to achieve generalization and a more compact representation. The choice of what to merge and when to stop is governed by the Bayesian posterior probability of the grammar given the data, which formalizes a trade-off between a close fit to the data and a default preference for simpler models (`Occam's Razor'). The general scheme is illustrated using three types of probabilistic grammars: Hidden Markov models, class-based $n$-grams, and stochastic context-free grammars.Comment: To appear in Grammatical Inference and Applications, Second International Colloquium on Grammatical Inference; Springer Verlag, 1994. 13 page

Rigidity of compact Riemannian spin Manifolds with Boundary

In this article, we prove new rigidity results for compact Riemannian spin manifolds with boundary whose scalar curvature is bounded from below by a non-positive constant. In particular, we obtain generalizations of a result of Hang-Wang \cite{hangwang1} based on a conjecture of Schroeder and Strake \cite{schroeder}.Comment: English version of "G\'eom\'etrie spinorielle extrins\`eque et rigidit\'es", Corollary 6 in Section 3 added, to appear in Letters Math. Phy