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

Speckle-free laser imaging

Many imaging applications require increasingly bright illumination sources, motivating the replacement of conventional thermal light sources with light emitting diodes (LEDs), superluminescent diodes (SLDs) and lasers. Despite their brightness, lasers and SLDs are poorly suited for full-field imaging applications because their high spatial coherence leads to coherent artifacts known as speckle that corrupt image formation. We recently demonstrated that random lasers can be engineered to provide low spatial coherence. Here, we exploit the low spatial coherence of specifically-designed random lasers to perform speckle-free full-field imaging in the setting of significant optical scattering. We quantitatively demonstrate that images generated with random laser illumination exhibit higher resolution than images generated with spatially coherent illumination. By providing intense laser illumination without the drawback of coherent artifacts, random lasers are well suited for a host of full-field imaging applications from full-field microscopy to digital light projector systems.Comment: 5 pages, 4 figure

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

Dwarf Copper-Gold Porphyry Deposits of the Buchim-Damjan-Borov Dol Ore District, Republic of Macedonia (FYROM)

The metallogenic aspects, tectonic setting, magmatism, structure, and composition of Au-and Ag-bearing porphyry copper deposits in the Buchim-Damjan-Borov Dol ore district and their genetic features are considered and compared with earlier published data. Special attention is paid to supergene gold in heavy concentrate halos of the Borov Dol deposit. The total Cu reserves of the deposits discussed in this paper do not exceed 150 kt. The Buchim deposit likely is the world's smallest deposit of this type currently involved in mining. A comprehensive study of these dwarf porphyry copper deposits is undertaken to answer questions on the conditions of their formation. How do they differ from formation conditions of giant deposits

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

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