Enumeration of Hamiltonian Cycles on a Complete Graph using ECO method

ECO is a method for enumerating classes of combinatorial objects based on recursive constructions of such classes. A construction for a class of Hamiltonian cycles in a complete graph consisting of n nodes is constructed based on ECO method. Here, a Hamiltonian cycle is represented as a permutation cycle of length n whose permutation and its corresponding inverse permutation are not distinguished. Later, this construction is translated into a succession rule. The final goal of this paper is to determine the generating function of Hamiltonian cycles and it is achieved by making use of the ordinary generating function of a permutation class and the exponential generating function of the infinite sequences of 1s. Keywords: ECO method, Hamiltonian cycle, cycle permutation, generating function, succession rule

Pacifying the Fermi-liquid: battling the devious fermion signs

The fermion sign problem is studied in the path integral formalism. The standard picture of Fermi liquids is first critically analyzed, pointing out some of its rather peculiar properties. The insightful work of Ceperley in constructing fermionic path integrals in terms of constrained world-lines is then reviewed. In this representation, the minus signs associated with Fermi-Dirac statistics are self consistently translated into a geometrical constraint structure (the {\em nodal hypersurface}) acting on an effective bosonic dynamics. As an illustrative example we use this formalism to study 1+1-dimensional systems, where statistics are irrelevant, and hence the sign problem can be circumvented. In this low-dimensional example, the structure of the nodal constraints leads to a lucid picture of the entropic interaction essential to one-dimensional physics. Working with the path integral in momentum space, we then show that the Fermi gas can be understood by analogy to a Mott insulator in a harmonic trap. Going back to real space, we discuss the topological properties of the nodal cells, and suggest a new holographic conjecture relating Fermi liquids in higher dimensions to soft-core bosons in one dimension. We also discuss some possible connections between mixed Bose/Fermi systems and supersymmetry.Comment: 28 pages, 5 figure

Middle to upper Devonian (givetian and frasnian) shallow-water carbonates of Western Europe: fades analysis and cyclicity

The Middle and Upper Devonian (Givetian-Frasnian) shallow-water carbonate facies of western Europe were deposited as a large-scale transgressive succession over continental facies of the Old Red Continent. The transgression was in a northerly direction, reaching the southern Ardennes by the lower Eifelian and the Aachen area of Germany by the middle Givetian. Carbonate sedimentation continued through to the middle Frasnian, when a major pulse m relative sea-level rise drowned the platform. The carbonate platform had a complex internal structure, with three major palaeosettings. During the Eifelian, a storm-influenced homoclinal ramp existed over much of the Ardennes. Sedimentation was mostly open-marine in nature, with a protected back-ramp and tidal-Oats. The Givetian saw a transition from a ramp to shelf setting, with stromatoporoid reefs at the shelf edge providing protection for abroad shelf lagoon. The shelf had an ESE-WNW trend and extended from Boulogne (northern France) in the west to Aachen (western Germany) in the east. East of the river Rhine in the Rheinisches Schiefergebirge area of Germany, and in Southwest England, isolated carbonate complexes developed. These were positioned either on the shelf-edge, within the shelf or upon topographic highs within the basin. Synsedimentary tectonism and volcanism strongly influenced their development. As a result of their areal extent, lagoonal environments were studied extensively in shelf and isolated complexes. Palaeontology and sedimentology were used to identify 14 major microfacies within the lagoonal successions, which could be broadly categorised into four major groups. The semi-restricted subtidal microfacies group has a rich faunal assemblage which, although diverse, did not represent fully open-marine deposition. Sedimentation was entirely subtidal in nature. The restricted subtidal microfacies group is either characterised by monospecific fossil assemblages (chiefly molluscs or amphiporoids), or by macrofossil-poor facies. These facies represent poorly-circulated, subtidal environments which may have been subjected to flucmating salinities The intertidal microfacies group is characterised by fenestral limestones, which are commonly poorly-fossiliferous. Finally the supratidal microfacies group is typified by dolomudstones, microbial laminites and calcretes. A metre-scale cyclicity is prevelant in these lagoonal facies and two major types of cycle have been identified. Subtidal cycles show a decrease in circulation, decrease in diversity of organisms and increase in fluctuation of salinity upwards through the cycle. Peritidal cycles shallow upwards from a subtidal base through to an intertidal or supratidal cap. Subtidal cycles seem particularly common within the isolated carbonate complexes, yet both peritidal and subtidal cycles are identified in the shelf lagoon. The distribution of facies and cycles was controlled by a complex interaction of eustasy and differential subsidence. The setting (i.e., whether it was the shelf lagoon, or isolated carbonate complex) also influenced this distribution. Fischer plots were used successfully to correlate successions across the carbonate platform, and to identify areas of condensed or expanded sedimentation. Cycles were calculated to have a duration of approximately 42,000 years for the Upper Givetian. The magnitude of relative sea- level change was in the order of l-3m. The development of the metre-scale cyclicity is best explained by orbital forcing, yet this signature has been overprinted by autocyclic and tectonic noise. Third-order eustatic sea-level fluctuations were delineated by major marine transgressions, and a eustatic sea-level curve was established for the study area

Consensus for quantum networks: from symmetry to gossip iterations

This paper extends the consensus framework, widely studied in the literature on distributed computing and control algorithms, to networks of quantum systems. We define consensus situations on the basis of invariance and symmetry properties, finding four different generalizations of classical consensus states. This new viewpoint can be directly used to study consensus for probability distributions, as these can be seen as a particular case of quantum statistical states: in this light, our analysis is also relevant for classical problems. We then extend the gossip consensus algorithm to the quantum setting and prove it converges to symmetric states while preserving the expectation of permutation-invariant global observables. Applications of the framework and the algorithms to estimation and control problems on quantum networks are discussed

Classification of the line-soliton solutions of KPII

In the previous papers (notably, Y. Kodama, J. Phys. A 37, 11169-11190 (2004), and G. Biondini and S. Chakravarty, J. Math. Phys. 47 033514 (2006)), we found a large variety of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation. The line-soliton solutions are solitary waves which decay exponentially in $(x,y)$-plane except along certain rays. In this paper, we show that those solutions are classified by asymptotic information of the solution as $|y| \to \infty$. Our study then unravels some interesting relations between the line-soliton classification scheme and classical results in the theory of permutations.Comment: 30 page

Seasonality of Planktonic Freshwater Ciliates: Are Analyses Based on V9 Regions of the 18S rRNA Gene Correlated With Morphospecies Counts?

Ciliates represent central nodes in freshwater planktonic food webs, and many species show pronounced seasonality, with short-lived maxima of a few dominant taxa while many being rare or ephemeral. These observations are primarily based on morphospecies counting methods, which, however, have limitations concerning the amount and volume of samples that can be processed. For high sampling frequencies at large scales, high throughput sequencing (HTS) of freshwater ciliates seems to be a promising tool. However, several studies reported large discrepancy between species abundance determinations by molecular compared to morphological means. Therefore, we compared ciliate DNA metabarcodes (V9 regions of the 18S rRNA gene) with morphospecies counts for a 3-year study (Lake Zurich, Switzerland; biweekly sampling, n = 74). In addition, we isolated, cultivated and sequenced the 18S rRNA gene of twelve selected ciliate species that served as seeds for HTS analyses. This workflow allowed for a detailed comparison of V9 data with microscopic analyses by quantitative protargol staining (QPS). The dynamics of V9 read abundances over the seasonal cycle corroborated well with morphospecies population patterns. Annual successions of rare and ephemeral species were more adequately characterized by V9 reads than by QPS. However, numbers of species specific sequence reads only partly reflected rank orders seen by counts. In contrast, biomass-based assemblage compositions showed higher similarity to V9 read numbers, probably indicating a relation between cell sizes and numbers / sizes of macronuclei (or 18S rRNA operons). Full-length 18S rRNA sequences of ciliates assigned to certain morphospecies are urgently needed for barcoding approaches as planktonic taxa are still poorly represented in public databases and the interpretation of HTS data depends on profound reference sequences. Through linking operational taxonomic units (OTUs) with known morphospecies, we can use the deep knowledge about the autecology of these species

ADAPTATION OF MICROBIAL COMMUNITIES AND THEIR FUNCTIONS TO ENVIRONMENTAL PRESSURES IN AN URBAN WATERWAYS SYSTEM

Ph.DDOCTOR OF PHILOSOPH