A Study of an Unusually Heat Resistant Variant of Bacilius Circulans

The problem herein described was initiated while following the growth rate of a culture over a ten-hour period. A flask of polypeptone agar had been held in a 47-degree Celsius water bath to maintain it melted so that the plates could be poured periodically

The L1-Potts functional for robust jump-sparse reconstruction

We investigate the non-smooth and non-convex $L^1$-Potts functional in discrete and continuous time. We show $\Gamma$-convergence of discrete $L^1$-Potts functionals towards their continuous counterpart and obtain a convergence statement for the corresponding minimizers as the discretization gets finer. For the discrete $L^1$-Potts problem, we introduce an $O(n^2)$ time and $O(n)$ space algorithm to compute an exact minimizer. We apply $L^1$-Potts minimization to the problem of recovering piecewise constant signals from noisy measurements $f.$ It turns out that the $L^1$-Potts functional has a quite interesting blind deconvolution property. In fact, we show that mildly blurred jump-sparse signals are reconstructed by minimizing the $L^1$-Potts functional. Furthermore, for strongly blurred signals and known blurring operator, we derive an iterative reconstruction algorithm

Towards a Computational Model of Frame of Reference Alignment in Swedish Dialogue

In this paper we examine how people negotiate, interpret and repair the frame of reference (FoR) in online text based dialogues discussing spatial scenes in Swedish. We describe work-in-progress in which participants are given different perspectives of the same scene and asked to locate several objects that are only shown on one of their pictures. This task requires participants to coordinate on FoR in order to identify the missing objects. This study has implications for situated dialogue systems

Solutions of Higher Dimensional Gauss-Bonnet FRW Cosmology

We examine the effect on cosmological evolution of adding a Gauss-Bonnet term to the standard Einstein-Hilbert action for a (1 + 3)+ d dimensional Friedman-Robertson-Walker (FRW) metric. By assuming that the additional dimensions compactify as a power law as the usual 3 spatial dimensions expand, we solve the resulting dynamical equations and find that the solution may be of either de Sitter or Kasner form depending upon whether the Gauss-Bonnet term or the Einstein term dominates.Comment: 10 pages, references added/corrected, accepted for publication in General Relativity and Gravitatio

Billiard Representation for Multidimensional Cosmology with Intersecting p-branes near the Singularity

Multidimensional model describing the cosmological evolution of n Einstein spaces in the theory with l scalar fields and forms is considered. When electro-magnetic composite p-brane ansatz is adopted, and certain restrictions on the parameters of the model are imposed, the dynamics of the model near the singularity is reduced to a billiard on the (N-1)-dimensional Lobachevsky space, N = n+l. The geometrical criterion for the finiteness of the billiard volume and its compactness is used. This criterion reduces the problem to the problem of illumination of (N-2)-dimensional sphere by point-like sources. Some examples with billiards of finite volume and hence oscillating behaviour near the singularity are considered. Among them examples with square and triangle 2-dimensional billiards (e.g. that of the Bianchi-IX model) and a 4-dimensional billiard in ``truncated'' D = 11 supergravity model (without the Chern-Simons term) are considered. It is shown that the inclusion of the Chern-Simons term destroys the confining of a billiard.Comment: 27 pages Latex, 3 figs., submit. to Class. Quantum Gra

Kovalevski exponents and integrability properties in class A homogeneous cosmological models

Qualitative approach to homogeneous anisotropic Bianchi class A models in terms of dynamical systems reveals a hierarchy of invariant manifolds. By calculating the Kovalevski Exponents according to Adler - van Moerbecke method we discuss how algebraic integrability property is distributed in this class of models. In particular we find that algebraic nonintegrability of vacuum Bianchi VII_0 model is inherited by more general Bianchi VIII and Bianchi IX vacuum types. Matter terms (cosmological constant, dust and radiation) in the Einstein equations typically generate irrational or complex Kovalevski exponents in class A homogeneous models thus introducing an element of nonintegrability even though the respective vacuum models are integrable.Comment: arxiv version is already officia

Supergravity Black Holes and Billiards and Liouville integrable structure of dual Borel algebras

In this paper we show that the supergravity equations describing both cosmic billiards and a large class of black-holes are, generically, both Liouville integrable as a consequence of the same universal mechanism. This latter is provided by the Liouville integrable Poissonian structure existing on the dual Borel algebra B_N of the simple Lie algebra A_{N-1}. As a by product we derive the explicit integration algorithm associated with all symmetric spaces U/H^{*} relevant to the description of time-like and space-like p-branes. The most important consequence of our approach is the explicit construction of a complete set of conserved involutive hamiltonians h_{\alpha} that are responsible for integrability and provide a new tool to classify flows and orbits. We believe that these will prove a very important new tool in the analysis of supergravity black holes and billiards.Comment: 48 pages, 7 figures, LaTex; V1: misprints corrected, two references adde

Cosmological dynamics of exponential gravity

We present a detailed investigation of the cosmological dynamics based on $\exp (-R/{\Lambda})$ gravity. We apply the dynamical system approach to both the vacuum and matter cases and obtain exact solutions and their stability in the finite and asymptotic regimes. The results show that cosmic histories exist which admit a double de-Sitter phase which could be useful for describing the early and the late-time accelerating universe.Comment: 17 pages LaTeX, 3 figure

O(d,d)-invariance in inhomogeneous string cosmologies with perfect fluid

In the first part of the present paper, we show that O(d,d)-invariance usually known in a homogeneous cosmological background written in terms of proper time can be extended to backgrounds depending on one or several coordinates (which may be any space-like or time-like coordinate(s)). In all cases, the presence of a perfect fluid is taken into account and the equivalent duality transformation in Einstein frame is explicitly given. In the second part, we present several concrete applications to some four-dimensional metrics, including inhomogeneous ones, which illustrate the different duality transformations discussed in the first part. Note that most of the dual solutions given here do not seem to be known in the literature.Comment: 25 pages, no figures, Latex. Accepted for publication in General Relativity and Gravitatio