Separation of trajectories and its Relation to Entropy for Intermittent Systems with a Zero Lyapunov exponent

One dimensional intermittent maps with stretched exponential separation of nearby trajectories are considered. When time goes infinity the standard Lyapunov exponent is zero. We investigate the distribution of $\lambda_{\alpha}= \sum_{i=0}^{t-1} \ln \left| M'(x_i) \right|/t^{\alpha}$, where $\alpha$ is determined by the nonlinearity of the map in the vicinity of marginally unstable fixed points. The mean of $\lambda_{\alpha}$ is determined by the infinite invariant density. Using semi analytical arguments we calculate the infinite invariant density for the Pomeau-Manneville map, and with it obtain excellent agreement between numerical simulation and theory. We show that \alpha \left is equal to Krengel's entropy and to the complexity calculated by the Lempel-Ziv compression algorithm. This generalized Pesin's identity shows that \left and Krengel's entropy are the natural generalizations of usual Lyapunov exponent and entropy for these systems.Comment: 12 pages, 10 figure

Pesin-type relation for subexponential instability

We address here the problem of extending the Pesin relation among positive Lyapunov exponents and the Kolmogorov-Sinai entropy to the case of dynamical systems exhibiting subexponential instabilities. By using a recent rigorous result due to Zweim\"uller, we show that the usual Pesin relation can be extended straightforwardly for weakly chaotic one-dimensional systems of the Pomeau-Manneville type, provided one introduces a convenient subexponential generalization of the Kolmogorov-Sinai entropy. We show, furthermore, that Zweim\"uller's result provides an efficient prescription for the evaluation of the algorithm complexity for such systems. Our results are confirmed by exhaustive numerical simulations. We also point out and correct a misleading extension of the Pesin relation based on the Krengel entropy that has appeared recently in the literature.Comment: 10 pages, 4 figures. Final version to appear in Journal of Statistical Mechanics (JSTAT

Complete genome sequence of Syntrophobacter fumaroxidans strain (MPOB(T)).

Syntrophobacter fumaroxidans strain MPOB(T) is the best-studied species of the genus Syntrophobacter. The species is of interest because of its anaerobic syntrophic lifestyle, its involvement in the conversion of propionate to acetate, H2 and CO2 during the overall degradation of organic matter, and its release of products that serve as substrates for other microorganisms. The strain is able to ferment fumarate in pure culture to CO2 and succinate, and is also able to grow as a sulfate reducer with propionate as an electron donor. This is the first complete genome sequence of a member of the genus Syntrophobacter and a member genus in the family Syntrophobacteraceae. Here we describe the features of this organism, together with the complete genome sequence and annotation. The 4,990,251 bp long genome with its 4,098 protein-coding and 81 RNA genes is a part of the Microbial Genome Program (MGP) and the Genomes to Life (GTL) Program project

Proteomic analysis reveals metabolic and regulatory systems involved in the syntrophic and axenic lifestyle of Syntrophomonas wolfei

Microbial syntrophy is a vital metabolic interaction necessary for the complete oxidation of organic biomass to methane in all-anaerobic ecosystems. However, this process is thermodynamically constrained and represents an ecosystem-level metabolic bottleneck. To gain insight into the physiology of this process, a shotgun proteomics approach was used to quantify the protein landscape of the model syntrophic metabolizer, Syntrophomonas wolfei, grown axenically and syntrophically with Methanospirillum hungatei. Remarkably, the abundance of most proteins as represented by normalized spectral abundance factor (NSAF) value changed very little between the pure and coculture growth conditions. Among the most abundant proteins detected were GroEL and GroES chaperonins, a small heat shock protein, and proteins involved in electron transfer, beta-oxidation, and ATP synthesis. Several putative energy conservation enzyme systems that utilize NADH and ferredoxin were present. The abundance of an EtfAB2 and the membrane-bound iron-sulfur oxidoreductase (Swol_0698 gene product) delineated a potential conduit for electron transfer between acyl-CoA dehydrogenases and membrane redox carriers. Proteins detected only when S. wolfei was grown with M. hungatei included a zinc-dependent dehydrogenase with a GroES domain, whose gene is present in genomes in many organisms capable of syntrophy, and transcriptional regulators responsive to environmental stimuli or the physiological status of the cell. The proteomic analysis revealed an emphasis on macromolecular stability and energy metabolism by S. wolfei and presence of regulatory mechanisms responsive to external stimuli and cellular physiological status

On conformal measures and harmonic functions for group extensions

We prove a Perron-Frobenius-Ruelle theorem for group extensions of topological Markov chains based on a construction of $\sigma$-finite conformal measures and give applications to the construction of harmonic functions.Comment: To appear in Proceedings of "New Trends in Onedimensional Dynamics, celebrating the 70th birthday of Welington de Melo

Pyrophosphate-Dependent ATP Formation from Acetyl Coenzyme A in Syntrophus aciditrophicus, a New Twist on ATP Formation.

UnlabelledSyntrophus aciditrophicus is a model syntrophic bacterium that degrades key intermediates in anaerobic decomposition, such as benzoate, cyclohexane-1-carboxylate, and certain fatty acids, to acetate when grown with hydrogen-/formate-consuming microorganisms. ATP formation coupled to acetate production is the main source for energy conservation by S. aciditrophicus However, the absence of homologs for phosphate acetyltransferase and acetate kinase in the genome of S. aciditrophicus leaves it unclear as to how ATP is formed, as most fermentative bacteria rely on these two enzymes to synthesize ATP from acetyl coenzyme A (CoA) and phosphate. Here, we combine transcriptomic, proteomic, metabolite, and enzymatic approaches to show that S. aciditrophicus uses AMP-forming, acetyl-CoA synthetase (Acs1) for ATP synthesis from acetyl-CoA. acs1 mRNA and Acs1 were abundant in transcriptomes and proteomes, respectively, of S. aciditrophicus grown in pure culture and coculture. Cell extracts of S. aciditrophicus had low or undetectable acetate kinase and phosphate acetyltransferase activities but had high acetyl-CoA synthetase activity under all growth conditions tested. Both Acs1 purified from S. aciditrophicus and recombinantly produced Acs1 catalyzed ATP and acetate formation from acetyl-CoA, AMP, and pyrophosphate. High pyrophosphate levels and a high AMP-to-ATP ratio (5.9 ± 1.4) in S. aciditrophicus cells support the operation of Acs1 in the acetate-forming direction. Thus, S. aciditrophicus has a unique approach to conserve energy involving pyrophosphate, AMP, acetyl-CoA, and an AMP-forming, acetyl-CoA synthetase.ImportanceBacteria use two enzymes, phosphate acetyltransferase and acetate kinase, to make ATP from acetyl-CoA, while acetate-forming archaea use a single enzyme, an ADP-forming, acetyl-CoA synthetase, to synthesize ATP and acetate from acetyl-CoA. Syntrophus aciditrophicus apparently relies on a different approach to conserve energy during acetyl-CoA metabolism, as its genome does not have homologs to the genes for phosphate acetyltransferase and acetate kinase. Here, we show that S. aciditrophicus uses an alternative approach, an AMP-forming, acetyl-CoA synthetase, to make ATP from acetyl-CoA. AMP-forming, acetyl-CoA synthetases were previously thought to function only in the activation of acetate to acetyl-CoA

Exotic Differentiable Structures and General Relativity

We review recent developments in differential topology with special concern for their possible significance to physical theories, especially general relativity. In particular we are concerned here with the discovery of the existence of non-standard (``fake'' or ``exotic'') differentiable structures on topologically simple manifolds such as $S^7$, \R and $S^3\times {\bf R^1}.$ Because of the technical difficulties involved in the smooth case, we begin with an easily understood toy example looking at the role which the choice of complex structures plays in the formulation of two-dimensional vacuum electrostatics. We then briefly review the mathematical formalisms involved with differentiable structures on topological manifolds, diffeomorphisms and their significance for physics. We summarize the important work of Milnor, Freedman, Donaldson, and others in developing exotic differentiable structures on well known topological manifolds. Finally, we discuss some of the geometric implications of these results and propose some conjectures on possible physical implications of these new manifolds which have never before been considered as physical models.Comment: 11 pages, LaTe

Limit theorems for von Mises statistics of a measure preserving transformation

For a measure preserving transformation $T$ of a probability space $(X,\mathcal F,\mu)$ we investigate almost sure and distributional convergence of random variables of the form $$x \to \frac{1}{C_n} \sum_{i_1<n,...,i_d<n} f(T^{i_1}x,...,T^{i_d}x),\, n=1,2,...,$$ where $f$ (called the \emph{kernel}) is a function from $X^d$ to $\R$ and $C_1, C_2,...$ are appropriate normalizing constants. We observe that the above random variables are well defined and belong to $L_r(\mu)$ provided that the kernel is chosen from the projective tensor product $$L_p(X_1,\mathcal F_1, \mu_1) \otimes_{\pi}...\otimes_{\pi} L_p(X_d,\mathcal F_d, \mu_d)\subset L_p(\mu^d)$$ with $p=d\,r,\, r\ \in [1, \infty).$ We establish a form of the individual ergodic theorem for such sequences. Next, we give a martingale approximation argument to derive a central limit theorem in the non-degenerate case (in the sense of the classical Hoeffding's decomposition). Furthermore, for $d=2$ and a wide class of canonical kernels $f$ we also show that the convergence holds in distribution towards a quadratic form $\sum_{m=1}^{\infty} \lambda_m\eta^2_m$ in independent standard Gaussian variables $\eta_1, \eta_2,...$. Our results on the distributional convergence use a $T$--\,invariant filtration as a prerequisite and are derived from uni- and multivariate martingale approximations

The Standard Model with gravity couplings

In this paper, we examine the coupling of matter fields to gravity within the framework of the Standard Model of particle physics. The coupling is described in terms of Weyl fermions of a definite chirality, and employs only (anti)self-dual or left-handed spin connection fields. It is known from the work of Ashtekar and others that such fields can furnish a complete description of gravity without matter. We show that conditions ensuring the cancellation of perturbative chiral gauge anomalies are not disturbed. We also explore a global anomaly associated with the theory, and argue that its removal requires that the number of fundamental fermions in the theory must be multiples of 16. In addition, we investigate the behavior of the theory under discrete transformations P, C and T; and discuss possible violations of these discrete symmetries, including CPT, in the presence of instantons and the Adler-Bell-Jackiw anomaly.Comment: Extended, and replaced with LaTex file. 25 Page

Problem-based learning in dental education: what's the evidence for and against... and is it worth the effort?

The document attached has been archived with permission from the Australian Dental Association. An external link to the publisher’s copy is included.All Australian dental schools have introduced problem-based learning (PBL) approaches to their programmes over the past decade, although the nature of the innovations has varied from school to school. Before one can ask whether PBL is better than the conventional style of education, one needs to consider three key issues. Firstly, we need to agree on what is meant by the term PBL; secondly, we need to decide what “better” means when comparing educational approaches; and thirdly, we must look carefully at how PBL is implemented in given situations. It is argued that PBL fulfils, at least in theory, some important principles relating to the development of new knowledge. It also represents a change in focus from teachers and teaching in conventional programmes to learners and learning. Generally, students enjoy PBL programmes more than conventional programmes and feel they are more nurturing. There is also some evidence of an improvement in clinical and diagnostic reasoning ability associated with PBL curricula. The main negative points raised about PBL are the costs involved and mixed reports of insufficient grounding of students in the basic sciences. Financial restraints will probably preclude the introduction of pure or fully integrated PBL programmes in Australian dental schools. However, our research and experience, as well as other published literature, indicate that well-planned hybrid PBL programmes, with matching methods of assessment, can foster development of the types of knowledge, skills and attributes that oral health professionals will need in the future.T Winning and G Townsen