Compressed Representations of Permutations, and Applications

We explore various techniques to compress a permutation $\pi$ over n integers, taking advantage of ordered subsequences in $\pi$, while supporting its application $\pi$(i) and the application of its inverse $\pi^{-1}(i)$ in small time. Our compression schemes yield several interesting byproducts, in many cases matching, improving or extending the best existing results on applications such as the encoding of a permutation in order to support iterated applications $\pi^k(i)$ of it, of integer functions, and of inverted lists and suffix arrays

A Frobenius formula for the structure coefficients of double-class algebras of Gelfand pairs

We generalise some well known properties of irreducible characters of finite groups to zonal spherical functions of Gelfand pairs. This leads to a Frobenius formula for Gelfand pairs. For a given Gelfand pair, the structure coefficients of its associated double-class algebra can be written in terms of zonal spherical functions. This is a generalisation of the Frobenius formula which writes the structure coefficients of the center of a finite group algebra in terms of irreducible characters

Evidence for 9 planets in the HD 10180 system

We re-analyse the HARPS radial velocities of HD 10180 and calculate the probabilities of models with differing numbers of periodic signals in the data. We test the significance of the seven signals, corresponding to seven exoplanets orbiting the star, in the Bayesian framework and perform comparisons of models with up to nine periodicities. We use posterior samplings and Bayesian model probabilities in our analyses together with suitable prior probability densities and prior model probabilities to extract all the significant signals from the data and to receive reliable uncertainties for the orbital parameters of the six, possibly seven, known exoplanets in the system. According to our results, there is evidence for up to nine planets orbiting HD 10180, which would make this this star a record holder in having more planets in its orbits than there are in the Solar system. We revise the uncertainties of the previously reported six planets in the system, verify the existence of the seventh signal, and announce the detection of two additional statistically significant signals in the data. If of planetary origin, these two additional signals would correspond to planets with minimum masses of 5.1$^{+3.1}_{-3.2}$ and 1.9$^{+1.6}_{-1.8}$ M$_{\oplus}$ on orbits with 67.55$^{+0.68}_{-0.88}$ and 9.655$^{+0.022}_{-0.072}$ days periods (denoted using the 99% credibility intervals), respectively.Comment: 12 pages, 7 figures, accepted for publication in the Astronomy and Astrophysic

Asymptotic theory of characters of the symmetric groups

Ankara : Department of Mathematics and Institute of Engineering and Science, Bilkent University, 1996.Thesis (Master's) -- Bilkent University, 1996.Includes bibliographical references leaves 70-71.In this work, we studied the connection between ramified coverings of Riemann surfaces tt : X V oi degree n and characters of symmetric group Sn- We considered asymptotics of characters of as n —> oo and normalized characters of Sn under some restrictions.Kurtaran, ElifM.S

Off-diagonal long-range order for the free Bose gas via the Feynman--Kac formula

We consider the path-integral representation of the ideal Bose gas under various boundary conditions. We show that Bose--Einstein condensation occurs at the famous critical density threshold, by proving that its $1$-particle-reduced density matrix exhibits off-diagonal long-range order above that threshold, but not below. Our proofs are based on the well-known Feynman--Kac formula and a representation in terms of a crucial Poisson point process. Furthermore, in the condensation regime, we derive a law of large numbers with strong concentration for the number of particles in short loops. In contrast to the situation for free boundary conditions, where the entire condensate sits in just one loop, for all other boundary conditions we obtain the limiting Poisson--Dirichlet distribution for the collection of the lengths of all long loops. Our proofs are new and purely probabilistic (apart from a standard eigenvalue expansion), using elementary tools like Markov's inequality, Poisson point processes, combinatorial formulas for cardinalities of particular partition sets, and asymptotics for random walks with Pareto-distributed steps.Comment: 34 page

Population connectivity of an overexploited coastal fish, Argyrosomus coronus (Sciaenidae), in an ocean-warming hotspot

The West Coast dusky kob Argyrosomus coronus is a commercially exploited fish with a distribution confined to the Angola–Benguela Frontal Zone (ABFZ) of the southeastern Atlantic Ocean. A previous study revealed that during a recent period of local warming the species extended its distribution into Namibian waters, where it hybridised with the resident and congeneric Argyrosomus inodorus. Environmental changes are a major threat to marine biodiversity and when combined with overfishing have the potential to accelerate the decline of species. However, little is known regarding the evolutionary history and population structure of A. coronus across the ABFZ. We investigated genetic diversity, population structure and historical demographic changes using mtDNA control region sequences and genotypes at six nuclear microsatellite loci, from 180 individuals. A single, genetically homogeneous population was indicated across the distributional range of A. coronus (ϕST = 0.041, FST = 0.000, D = 0.000; p > 0.05). These findings imply that the oceanographic features within the ABFZ do not appear to significantly influence population connectivity in A. coronus, which simplifies management of the species. However, reconstruction of the demographic history points to a close link between the evolutionary history of A. coronus and the environmental characteristics of the ABFZ. This outcome suggests the species’ vulnerability to the rapid environmental changes being observed across this region, and highlights a pressing need for transboundary management to mitigate the impacts of climate change in this global hotspot of seawater temperature changes.Keywords: Angola–Benguela Frontal Zone, climate change, demographic history, marine fisheries, molecular ecology, population structur

Beyond orientability and compactness: new results on the dynamics of flat surfaces

In the first part, we prove the non-uniform hyperbolicity of the Kontsevich-Zorich cocycle for a measure supported on abelian differentials which come from non-orientable quadratic differentials. The proof uses Forni's criterion for non-uniform hyperbolicity of the cocycle for SL(2;R)-invariant measures. We apply these results to the study of deviations in homology of typical leaves of the vertical and horizontal (non-orientable) foliations and deviations of ergodic averages. In the second part, we prove an ergodic theorem for flat surfaces of finite area whose Teichmuller orbits are recurrent to a compact set of SL(2;R)/SL(S), where SL(S) is the Veech group of the surface. In this setting, this means that the translation flow on a flat surface can be renormalized through its Veech group. This result applies in particular to flat surfaces of infinite genus and finite area, and we apply our result to existing surfaces in the literature to prove that the corresponding foliations of the surface corresponding to a periodic or recurrent Teichmuller orbit are ergodic

Resilient gossip-inspired all-reduce algorithms for high-performance computing - Potential, limitations, and open questions

We investigate the usefulness of gossip-based reduction algorithms in a high-performance computing (HPC) context. We compare them to state-of-the-art deterministic parallel reduction algorithms in terms of fault tolerance and resilience against silent data corruption (SDC) as well as in terms of performance and scalability. New gossip-based reduction algorithms are proposed, which significantly improve the state-of-the-art in terms of resilience against SDC. Moreover, a new gossip-inspired reduction algorithm is proposed, which promises a much more competitive runtime performance in an HPC context than classical gossip-based algorithms, in particular for low accuracy requirements.This work has been partially funded by the Spanish Ministry of Science and Innovation [contract TIN2015-65316]; by the Government of Catalonia [contracts 2014-SGR-1051, 2014-SGR-1272]; by the RoMoL ERC Advanced Grant [grant number GA 321253] and by the Vienna Science and Technology Fund (WWTF) through project ICT15-113.Peer ReviewedPostprint (author's final draft