Efficient Monitoring of ??-languages

We present a technique for generating efficient monitors for Omega-regular-languages. We show how Buchi automata can be reduced in size and transformed into special, statistically optimal nondeterministic finite state machines, called binary transition tree finite state machines (BTT-FSMs), which recognize precisely the minimal bad prefixes of the original omega-regular-language. The presented technique is implemented as part of a larger monitoring framework and is available for download

Quantum group covariant (anti)symmetrizers, epsilon-tensors, vielbein, Hodge map and Laplacian

GL_q(N)- and SO_q(N)-covariant deformations of the completely symmetric/antisymmetric projectors with an arbitrary number of indices are explicitly constructed as polynomials in the braid matrices. The precise relation between the completely antisymmetric projectors and the completely antisymmetric tensor is determined. Adopting the GL_q(N)- and SO_q(N)-covariant differential calculi on the corresponding quantum group covariant noncommutative spaces C_q^N, R_q^N, we introduce a generalized notion of vielbein basis (or "frame"), based on differential-operator-valued 1-forms. We then give a thorough definition of a SO_q(N)-covariant R_q^N-bilinear Hodge map acting on the bimodule of differential forms on R_q^N, introduce the exterior coderivative and show that the Laplacian acts on differential forms exactly as in the undeformed case, namely it acts on each component as it does on functions.Comment: latex file, 24 pages. Some citations added and misprints corrected. Final version to appear in J. Phys. A Math. and Ge

Fisher information matrix for single molecules with stochastic trajectories

Tracking of objects in cellular environments has become a vital tool in molecular cell biology. A particularly important example is single molecule tracking which enables the study of the motion of a molecule in cellular environments and provides quantitative information on the behavior of individual molecules in cellular environments, which were not available before through bulk studies. Here, we consider a dynamical system where the motion of an object is modeled by stochastic differential equations (SDEs), and measurements are the detected photons emitted by the moving fluorescently labeled object, which occur at discrete time points, corresponding to the arrival times of a Poisson process, in contrast to uniform time points which have been commonly used in similar dynamical systems. The measurements are distributed according to optical diffraction theory, and therefore, they would be modeled by different distributions, e.g., a Born and Wolf profile for an out-of-focus molecule. For some special circumstances, Gaussian image models have been proposed. In this paper, we introduce a stochastic framework in which we calculate the maximum likelihood estimates of the biophysical parameters of the molecular interactions, e.g., diffusion and drift coefficients. More importantly, we develop a general framework to calculate the Cram\'er-Rao lower bound (CRLB), given by the inverse of the Fisher information matrix, for the estimation of unknown parameters and use it as a benchmark in the evaluation of the standard deviation of the estimates. There exists no established method, even for Gaussian measurements, to systematically calculate the CRLB for the general motion model that we consider in this paper. We apply the developed methodology to simulated data of a molecule with linear trajectories and show that the standard deviation of the estimates matches well with the square root of the CRLB

Petrology and Geochemistry of the Enriched Poikilitic Shergottite Northwest Africa 10169: Insight into the Martian Interior

The martian meteorite Northwest Africa (NWA) 10169 is classified as a new member of the geochemically enriched poikilitic shergottites, based on mineral composition, Lu-Hf isotope systematics, and rare earth element (REE) composition. Akin to other poikilitic shergottites, it shows a similar bimodal texture to other enriched and intermediate poikilitic shergottites. In addition, olivine and pyroxene in the poikilitic zone have higher Mg#’s (Mg/Mg+Fe) than those in the interstitial areas, suggesting that the poikilitic texture represents early-stage crystallization, opposed to late-stage non-poikilitic crystallization. Calculated fO2 values are reduced (FMQ -2.3 ± 0.23) within the poikilitic texture, and more oxidized (FMQ -1.07 ± 0.14) within the interstitial areas likely representing auto-oxidation and degassing during magma crystallization. Melt inclusions within olivine crystals provide snapshots of magma composition throughout parent melt evolution. The calculated parental melt compositions share evolution trends with the enriched olivine-phyric shergottite Larkman Nunatuk (LAR) 06319, and suggest that two melts (K-poor and K-rich) were involved in the formation of NWA 10169, likely representing interaction with a metasomatized melt during the entrapment of the K-rich melt inclusions. The Lu-Hf crystallization age for NWA 10169 is 167 ± 31 Ma, consistent with the other enriched shergottites. Based on the isochron initial 176Hf/177Hf value, the modeled the source 176Lu/177Hf composition for NWA 10169 is 0.02748 ± 0.00037, identical within error to the source compositions of the enriched shergottites Shergotty, Zagami, LAR 06319, NWA 4468, and Roberts Massif (RBT) 04262, suggesting a shared, long-lived geochemical source, distinct from the source tapped by Los Angeles, NWA 856, and NWA 7320. This study reveals that at least two sources are responsible for the enriched shergottites, and a more heterogeneous martian mantle than previously thought. Additionally, the shared source with NWA 10169, coupled with consistent crystallization ages and magmatic histories indicates that a common magmatic system on Mars is likely responsible for the formation of this group of shergottites

Representations of specific acoustic patterns in the auditory cortex and hippocampus

Previous behavioural studies have shown that repeated presentation of a randomly chosen acoustic pattern leads to the unsupervised learning of some of its specific acoustic features. The objective of our study was to determine the neural substrate for the representation of freshly learnt acoustic patterns. Subjects first performed a behavioural task that resulted in the incidental learning of three different noise-like acoustic patterns. During subsequent high-resolution functional magnetic resonance imaging scanning, subjects were then exposed again to these three learnt patterns and to others that had not been learned. Multi-voxel pattern analysis was used to test if the learnt acoustic patterns could be 'decoded' from the patterns of activity in the auditory cortex and medial temporal lobe. We found that activity in planum temporale and the hippocampus reliably distinguished between the learnt acoustic patterns. Our results demonstrate that these structures are involved in the neural representation of specific acoustic patterns after they have been learnt

Optimization of stochastic lossy transport networks and applications to power grids

Motivated by developments in renewable energy and smart grids, we formulate a stylized mathematical model of a transport network with stochastic load fluctuations. Using an affine control rule, we explore the trade-off between the number of controllable resources in a lossy transport network and the performance gain they yield in terms of expected power losses. Our results are explicit and reveal the interaction between the level of flexibility, the intrinsic load uncertainty and the network structure.Comment: 30 pages, 10 figure