Distribution of Eigenvalues for the Modular Group

The two-point correlation function of energy levels for free motion on the modular domain, both with periodic and Dirichlet boundary conditions, are explicitly computed using a generalization of the Hardy-Littlewood method. It is shown that ion the limit of small separations they show an uncorrelated behaviour and agree with the Poisson distribution but they have prominent number-theoretical oscillations at larger scale. The results agree well with numerical simulations.Comment: 72 pages, Latex, the fiogures mentioned in the text are not vital, but can be obtained upon request from the first Autho

A new proof of the Vorono\"i summation formula

We present a short alternative proof of the Vorono\"i summation formula which plays an important role in Dirichlet's divisor problem and has recently found an application in physics as a trace formula for a Schr\"odinger operator on a non-compact quantum graph \mathfrak{G} [S. Egger n\'e Endres and F. Steiner, J. Phys. A: Math. Theor. 44 (2011) 185202 (44pp)]. As a byproduct we give a new proof of a non-trivial identity for a particular Lambert series which involves the divisor function d(n) and is identical with the trace of the Euclidean wave group of the Laplacian on the infinite graph \mathfrak{G}.Comment: Enlarged version of the published article J. Phys. A: Math. Theor. 44 (2011) 225302 (11pp

Operator renewal theory and mixing rates for dynamical systems with infinite measure

We develop a theory of operator renewal sequences in the context of infinite ergodic theory. For large classes of dynamical systems preserving an infinite measure, we determine the asymptotic behaviour of iterates $L^n$ of the transfer operator. This was previously an intractable problem. Examples of systems covered by our results include (i) parabolic rational maps of the complex plane and (ii) (not necessarily Markovian) nonuniformly expanding interval maps with indifferent fixed points. In addition, we give a particularly simple proof of pointwise dual ergodicity (asymptotic behaviour of $\sum_{j=1}^nL^j$) for the class of systems under consideration. In certain situations, including Pomeau-Manneville intermittency maps, we obtain higher order expansions for $L^n$ and rates of mixing. Also, we obtain error estimates in the associated Dynkin-Lamperti arcsine laws.Comment: Preprint, August 2010. Revised August 2011. After publication, a minor error was pointed out by Kautzsch et al, arXiv:1404.5857. The updated version includes minor corrections in Sections 10 and 11, and corresponding modifications of certain statements in Section 1. All main results are unaffected. In particular, Sections 2-9 are unchanged from the published versio

Axiomatic relation between thermodynamic and information-theoretic entropies

Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a measure of uncertainty. In this Letter, we connect these two notions of entropy, using an axiomatic framework for thermodynamics [Lieb, Yngvason, Proc. Roy. Soc.(2013)]. In particular, we obtain a direct relation between the Clausius entropy and the Shannon entropy, or its generalisation to quantum systems, the von Neumann entropy. More generally, we find that entropy measures relevant in non-equilibrium thermodynamics correspond to entropies used in one-shot information theory

Why Has Human–Carnivore Conflict Not Been Resolved in Namibia?

Human–wildlife conflict has historically been portrayed as a management problem where solutions lie in technical changes or financial incentives. However, recent research shows many conflicts stem from social, economic, and political drivers. We undertook qualitative data collection on livestock farms to determine whether relationships between farmers and their workers affected frequency of reported livestock depredation in Namibia. We found that the conflict was affected by social and economic inequalities embedded in the previous apartheid regime. Macro- and microlevel socioeconomic problems created an environment where livestock depredation was exacerbated by unmotivated farm workers. Poor treatment of workers by farmers resulted in vengeful behaviors, such as livestock theft and wildlife poaching. Successfully addressing this situation therefore requires recognition and understanding of its complexity, rather than reducing it to its most simplistic part

When simple sequence comparison fails: the cryptic case of the shared domains of the bacterial replication initiation proteins DnaB and DnaD

DnaD and DnaB are essential DNA-replication-initiation proteins in low-G+C content Gram-positive bacteria. Here we use sensitive Hidden Markov Model-based techniques to show that the DnaB and DnaD proteins share a common structure that is evident across all their structural domains, termed DDBH1 and DDBH2 (DnaD DnaB Homology 1 and 2). Despite strong sequence divergence, many of the DNA-binding and oligomerization properties of these domains have been conserved. Although eluding simple sequence comparisons, the DDBH2 domains share the only strong sequence motif; an extremely highly conserved YxxxIxxxW sequence that contributes to DNA binding. Sequence alignments of DnaD alone fail to identify another key part of the DNA-binding module, since it includes a poorly conserved sequence, a solvent-exposed and somewhat unstable helix and a mobile segment. We show by NMR, in vitro mutagenesis and in vivo complementation experiments that the DNA-binding module of Bacillus subtilis DnaD comprises the YxxxIxxxW motif, the unstable helix and a portion of the mobile region, the latter two being essential for viability. These structural insights lead us to a re-evaluation of the oligomerization and DNA-binding properties of the DnaD and DnaB proteins

c-di-AMP Is a New Second Messenger in Staphylococcus aureus with a Role in Controlling Cell Size and Envelope Stress.

Published versio

Co-Orientation of Replication and Transcription Preserves Genome Integrity

In many bacteria, there is a genome-wide bias towards co-orientation of replication and transcription, with essential and/or highly-expressed genes further enriched co-directionally. We previously found that reversing this bias in the bacterium Bacillus subtilis slows replication elongation, and we proposed that this effect contributes to the evolutionary pressure selecting the transcription-replication co-orientation bias. This selection might have been based purely on selection for speedy replication; alternatively, the slowed replication might actually represent an average of individual replication-disruption events, each of which is counter-selected independently because genome integrity is selected. To differentiate these possibilities and define the precise forces driving this aspect of genome organization, we generated new strains with inversions either over ∼1/4 of the chromosome or at ribosomal RNA (rRNA) operons. Applying mathematical analysis to genomic microarray snapshots, we found that replication rates vary dramatically within the inverted genome. Replication is moderately impeded throughout the inverted region, which results in a small but significant competitive disadvantage in minimal medium. Importantly, replication is strongly obstructed at inverted rRNA loci in rich medium. This obstruction results in disruption of DNA replication, activation of DNA damage responses, loss of genome integrity, and cell death. Our results strongly suggest that preservation of genome integrity drives the evolution of co-orientation of replication and transcription, a conserved feature of genome organization