Markov Control with Rare State Observation: Average Optimality

This paper investigates the criterion of long-term average costs for a Markov decision process (MDP) which is not permanently observable. Each observation of the process produces a fixed amount of information costs which enter the considered performance criterion and preclude from arbitrarily frequent state testing. Choosing the rare observation times is part of the control procedure. In contrast to the theory of partially observable Markov decision processes, we consider an arbitrary continuous-time Markov process on a finite state space without further restrictions on the dynamics or the type of interaction. Based on the original Markov control theory, we redefine the control model and the average cost criterion for the setting of information costs. We analyze the constant of average costs for the case of ergodic dynamics and present an optimality equation which characterizes the optimal choice of control actions and observation times. For this purpose, we construct an equivalent freely observable MDP and translate the well-known results from the original theory to the new setting

Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems

Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales, there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows expressing various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. Especially, we reveal the cause of error in the case of small volume approximations

Exploring transmission Kikuchi diffraction using a Timepix detector

Electron backscatter diffraction (EBSD) is a well-established scanning electron microscope (SEM)-based technique [1]. It allows the non-destructive mapping of the crystal structure, texture, crystal phase and strain with a spatial resolution of tens of nanometers. Conventionally this is performed by placing an electron sensitive screen, typically consisting of a phosphor screen combined with a charge coupled device (CCD) camera, in front of a specimen, usually tilted 70° to the normal of the exciting electron beam. Recently, a number of authors have shown that a significant increase in spatial resolution is achievable when Kikuchi diffraction patterns are acquired in transmission geometry; that is when diffraction patterns are generated by electrons transmitted through an electron-transparent, usually thinned, specimen. The resolution of this technique, called transmission Kikuchi diffraction (TKD), has been demonstrated to be better than 10 nm [2,3]. We have recently demonstrated the advantages of a direct electron detector, Timepix [4,5], for the acquisition of standard EBSD patterns [5]. In this article we will discuss the advantages of Timepix to perform TKD and for acquiring spot diffraction patterns and more generally for acquiring scanning transmission electron microscopy micrographs in the SEM. Particularly relevant for TKD, is its very compact size, which allows much more flexibility in the positioning of the detector in the SEM chamber. We will furthermore show recent results using Timepix as a virtual forward scatter detector, and will illustrate the information derivable on producing images through processing of data acquired from different areas of the detector. We will show results from samples ranging from gold nanoparticles to nitride semiconductor nanorods

Sedimentological and stratigraphic framework of the several hundred thousand years old lacustrine record from Lake Van, Turkey

Within the frame of the International Continental scientific Drilling Program (ICDP) project PALEOVAN, a long and continuous sediment record from Lake Van, a closed lake situated in a climatically sensitive semiarid and tectonically active region in Eastern Anatolia, has been drilled in summer 2010. At two sites, Ahlat Ridge and Northern Basin, sedimentary records of 220 and 140 m were recovered, respectively. With basal ages possibly around 500'000 years, these records span several glacial-interglacial cycles and reach back until the lake’s initial transgression in the Middle Pleistocene. First results from ongoing analysis of core-catcher samples and newly opened cores document the sedimentological and geochemical succession. Two composite profiles of the drill sites were defined. Core catcher-based geochemical data such as proxies of lake’s productivity and catchment alterations show large variations and reflect a rich paleoenvironmental history. Most of the 220 m thick succession consists of carbonate mud, mostly sub-mm-thick laminated and interbedded by either homogenous mud or pyroclastic cm-thick layers. The lowermost sediments from the Ahlat Ridge site represent the initial lake transition as the drilling could not penetrate further and the seismic data indicates coincidence with the ‘acoustic’ basement. Such an early transgressive state of the lake’s history is also supported by the lithology consisting of a gravel unit as an indicator of a beach-like environment, which is overlain by sand deposits containing fresh-water gastropods (Bithynia). Above 200 mblf, the laminated mud clearly indicates that the lake was already deep enough to form anoxic bottom water as the laminations were preserved. This unique paleoclimate archive indicates that great changes of the depositional conditions occurred that hint to a fascinating evolution of the environment and has ideal prerequisites for the investigation of the Quaternary climate evolution in the Near East

Neutrino-induced coherent pion production off nuclei reexamined

It is pointed out that so far all theoretical estimates of coherent pion production off nuclei induced by neutrinos rely on the 'local approximation' well known in photonuclear physics. The effects of dropping this approximation are discussed. It is found that in a plane wave approximation for the pion the local approximation overestimates the coherent neutrino-induced pion production on nuclei.Comment: v3: comments on pion FSI added, minor corrections; version as published in Phys. Rev.

Niobium-based superconducting nano-devices fabrication using all-metal suspended masks

We report a novel method for the fabrication of superconducting nanodevices based on niobium. The well-known difficulties of lithographic patterning of high-quality niobium are overcome by replacing the usual organic resist mask by a metallic one. The quality of the fabrication procedure is demonstrated by the realization and characterization of long and narrow superconducting lines and niobium-gold-niobium proximity SQUIDs

Optimal control of molecular dynamics using Markov state models

A numerical scheme for solving high-dimensional stochastic control problems on an infinite time horizon that appear relevant in the context of molecular dynamics is outlined. The scheme rests on the interpretation of the corresponding Hamilton-Jacobi-Bellman equation as a nonlinear eigenvalue problem that, using a logarithmic transformation, can be recast as a linear eigenvalue problem, for which the principal eigenvalue and its eigenfunction are sought. The latter can be computed efficiently by approximating the underlying stochastic process with a coarse-grained Markov state model for the dominant metastable sets. We illustrate our method with two numerical examples, one of which involves the task of maximizing the population of $\alpha$-helices in an ensemble of small biomolecules (Alanine dipeptide), and discuss the relation to the large deviation principle of Donsker and Varadhan

On the Lichnerowicz conjecture for CR manifolds with mixed signature

We construct examples of nondegenerate CR manifolds with Levi form of signature $(p,q)$, $2\leq p\leq q$, which are compact, not locally CR flat, and admit essential CR vector fields. We also construct an example of a noncompact nondegenerate CR manifold with signature $(1,n-1)$ which is not locally CR flat and admits an essential CR vector fields. These provide counterexamples to the analogue of the Lichnerowicz conjecture for CR manifolds with mixed signature.Comment: 7 page