Random walks in compact groups

Let X_1,X_2,... be independent identically distributed random elements of a compact group G. We discuss the speed of convergence of the law of the product X_l*...*X_1 to the Haar measure. We give poly-log estimates for certain finite groups and for compact semi-simple Lie groups. We improve earlier results of Solovay, Kitaev, Gamburd, Shahshahani and Dinai.Comment: 35 pages, no figures, revision based on referee's report, results and proofs unchange

Analysis of radial velocity variations in multiple planetary systems

The study of multiple extrasolar planetary systems has the opportunity to obtain constraints for the planetary masses and orbital inclinations via the detection of mutual perturbations. The analysis of precise radial velocity measurements might reveal these planet-planet interactions and yields a more accurate view of such planetary systems. Like in the generic data modelling problems, a fit to radial velocity data series has a set of unknown parameters of which parametric derivatives have to be known by both the regression methods and the estimations for the uncertainties. In this paper an algorithm is described that aids the computation of such derivatives in case of when planetary perturbations are not neglected. The application of the algorithm is demonstrated on the planetary systems of HD 73526, HD 128311 and HD 155358. In addition to the functions related to radial velocity analysis, the actual implementation of the algorithm contains functions that computes spatial coordinates, velocities and barycentric coordinates for each planet. These functions aid the joint analysis of multiple transiting planetary systems, transit timing and/or duration variations or systems where the proper motion of the host star is also measured involving high precision astrometry. The practical implementation related to the above mentioned problems features functions that makethese kind of investigations rather simple and effective.Comment: Accepted for publication in MNRAS, 11 pages, 1 figure, 3 table

Kulcsfontosságú gének genomikai előrejelzése: In Silico megközelítés = Genomic prediction of essential genes: in silico approach

Kulcsfontosságú gének bioinformatikai elemzése: Csoportunk számos számos olyan sajátságot ismertek fel, melyek segítségével jellemezni lehet az esszenciális vagy a géndózis változására érzékeny géneket. Ezek közül a génduplikációt, az alternatív anyagcsereútvonalak jelenlétét, a génkifejeződés mértékét és a gén genomon belüli pozícióját érdemes megemlíteni. Rendszerbiológiai modellek alapján kulcsfontosságú metabolikus gének előrejelzése: Előzetesen leírt módszerekre alapozva, részletes vizsgálatnak vetettük alá a sörélesztő rekonstruált metabolikus hálózatát, majd megvizsgáltuk, hogyan viselkedik a rendszer ha egy-egy enzim működésképtelen. Módszerünk sikeresen jelzi előre az esszenciális gének 85%-át. Ez a siker lehetővé tette, hogy a biológia olyan kulcskérdéseire keressünk választ, mint a mutációkkal szembeni robusztusság háttere, a biológiai hálózatok evolúciós változása vagy a minimál genomok természete. Genetikai interakciók rendszerbiológiai és kísérleti vizsgálata: Anyagcserehálózat rendszerbiológiai modellünk komoly lehetőséget biztosít a genetikai interakciók mélyebb megértéséhez. A modell sikeresen képes előrejelezni speciális genetikai interakciók jelenlétét. Számos érvünk szól amelett, hogy a mutációkkal szembeni robusztusság a különböző környezeti feltételekhez való alkalmazkodás mellékterméke. | Bioinformatics analyses of essential genes: We identified several cellular and genomic features that enable reliable characterization of essential and dosage sensitive genes: Gene duplication, alternative metabolic pathways, gene expression level and genomic position all have some effect on gene dispensability. In silico prediction of essential metabolic genes using systems biological models: We have employed and further developed a previously elaborated metabolic network model of yeast. Our method predicts gene essentiality with about 85% accuracy. These methods have enabled us to study several key issues in evolutionary biology, such as the nature of mutational robustness and minimal genomes or the driving forces in the evolution of metabolic networks. Computational and experimental analyses of genetic interactions: The computational model described above paves the way for gaining novel insights into the nature of genetic interactions. The current model is able to predict the presence of genetic interactions in the metabolic networks of yeast with nearly 50% accuracy, while only approximately 0.5% would be expected by chance. Along with other arguments, our findings suggest that apparent robustness against harmful mutations is not a directly selected trait, but it's rather a by-product of organismal adaptation to varying environments

Hysteretic optimization for the Sherrington-Kirkpatrick spin glass

Hysteretic optimization is a heuristic optimization method based on the observation that magnetic samples are driven into a low energy state when demagnetized by an oscillating magnetic field of decreasing amplitude. We show that hysteretic optimization is very good for finding ground states of Sherrington-Kirkpatrick spin glass systems. With this method it is possible to get good statistics for ground state energies for large samples of systems consisting of up to about 2000 spins. The way we estimate error rates may be useful for some other optimization methods as well. Our results show that both the average and the width of the ground state energy distribution converges faster with increasing size than expected from earlier studies.Comment: Physica A, accepte

Maps on classes of Hilbert space operators preserving measure of commutativity

In this paper first we give a partial answer to a question of L. Moln\'ar and W. Timmermann. Namely, we will describe those linear (not necessarily bijective) transformations on the set of self-adjoint matrices which preserve a unitarily invariant norm of the commutator. After that we will characterize those (not necessarily linear or bijective) maps on the set of self-adjoint rank-one projections acting on a two-dimensional complex Hilbert space which leave the latter quantity invariant. Finally, this result will be applied in order to obtain a description of such bijective preservers on the unitary group and on the set of density operators.Comment: 16 pages, submitted to a journa