Approximation of ruin probability using phase-type distributions

The purpose of this master’s thesis is to find an approximation of ruin probabilities that is more accurate than well-known De Vylder’s method, but at the same time is mathematically simple enough. This new approximation method is based on the idea of De Vylder’s approximation, but instead of exponential distribution of claims some more complicated phase-type distributions are used. In theoretical part of the thesis an overview of main concepts of risk theory, the notion of phase-type distribution and De Vylder’s approximation is given. In practical part accuracy of six approximations of ruin probability based on phase-type distributions are compared with De Vylder’s method. The comparison is based on numerical examples of four different risk processes. According to the results, new methods are more accurate than De Vylder’s approximation

Two-loop planar master integrals for the production of off-shell vector bosons in hadron collisions

We describe the calculation of all planar master integrals that are needed for the computation of NNLO QCD corrections to the production of two off-shell vector bosons in hadron collisions. The most complicated representatives of integrals in this class are the two-loop four-point functions where two external lines are on the light-cone and two other external lines have different invariant masses. We compute these and other relevant integrals analytically using differential equations in external kinematic variables and express our results in terms of Goncharov polylogarithms. The case of two equal off-shellnesses, recently considered in Ref. [1], appears as a particular case of our general solution.Comment: 28 pages, many figures; ancillary files included with arXiv submissio

Rational Function Simplification for Integration-by-Parts Reduction and Beyond

We present FUEL (Fractional Universal Evaluation Library), a C++ library for performing rational function arithmetic with a flexible choice of third-party computer algebra systems as simplifiers. FUEL is an outgrowth of a C++ interface to Fermat which was originally part of the FIRE code for integration-by-parts (IBP) reduction for Feynman integrals, now promoted to be a standalone library and with access to simplifiers other than Fermat. We compare the performance of various simplifiers for standalone benchmark problems as well as IBP reduction runs with FIRE.Comment: 18 pages, 1 figure, 6 table

Eesti piimakarjas kasutatavate pullide geneetiline sugulus

Käesoleva bakalaureusetöö eesmärk on uurida tänapäeval Eestis piimakarjades kasutatavate pullide omavahelist geneetilist sugulust tuginedes kogu teadaolevale põlvnemisinfole. Töö teoreetilises osas antakse ülevaade inbriidingukoefitsiendi ja aditiivgeneetilise suguluse kordaja olemusest ning nende arvutamise meetoditest, tutvustatakse suguluskoefitsientide leidmist tarkvara R abil. Töö praktilises osas analüüsitakse kogu elektroonselt olemas olevat Eesti piimaveiste sugupuud. Andmestiku, mis on pärit Eesti Põllumajandusloomade Jõudluskontrolli AS- st ja sisaldab üle 1,7 miljoni looma, alusel hinnatakse R-i paketiga pedigreemm kõigi loomade inbriidingukoefitsiendid ning uuritakse täpsemalt Eestis viimastel aastatel enam kasutatud pullide omavahelist sugulust

Continuum methods in lattice perturbation theory

We show how methods of continuum perturbation theory can be used to simplify perturbative lattice calculations. We use the technique of asymptotic expansions to expand lattice loop integrals around the continuum limit. After the expansion, all nontrivial dependence on momenta and masses is encoded in continuum loop integrals and the only genuine lattice integrals left are tadpole integrals. Using integration-by-parts relations all of these can be expressed in terms of a small number of master integrals. Four master integrals are needed for bosonic one loop integrals, sixteen in QCD with Wilson or staggered fermions.Comment: 5 pages. Talk presented at RADCOR/Loops and Legs 2002, Kloster Banz, Germany, 8-13 Sep 200

Finding a Second Wind: Speeding Up Graph Traversal Queries in RDBMSs Using Column-Oriented Processing

Recursive queries and recursive derived tables constitute an important part of the SQL standard. Their efficient processing is important for many real-life applications that rely on graph or hierarchy traversal. Position-enabled column-stores offer a novel opportunity to improve run times for this type of queries. Such systems allow the engine to explicitly use data positions (row ids) inside its core and thus, enable novel efficient implementations of query plan operators. In this paper, we present an approach that significantly speeds up recursive query processing inside RDBMSes. Its core idea is to employ a particular aspect of column-store technology (late materialization) which enables the query engine to manipulate data positions during query execution. Based on it, we propose two sets of Volcano-style operators intended to process different query cases. In order validate our ideas, we have implemented the proposed approach in PosDB, an RDBMS column-store with SQL support. We experimentally demonstrate the viability of our approach by providing a comparison with PostgreSQL. Experiments show that for breadth-first search: 1) our position-based approach yields up to 6x better results than PostgreSQL, 2) our tuple-based one results in only 3x improvement when using a special rewriting technique, but it can work in a larger number of cases, and 3) both approaches can't be emulated in row-stores efficiently

On the QCD corrections to Vainshtein's theorem for VVA correlator

We point out that, contrary to existing claims of the opposite, Vainshtein's theorem on the non-renormalization of the correlator of an axial and two vector currents, is only valid in the chiral limit. When quarks, that contribute to the correlator, are massive, the QCD corrections do not vanish and the transversal and longitudinal functions are renormalized differently. We compute those corrections and study their implications for QCD effects in electroweak corrections to the muon anomalous magnetic moment.Comment: 6 pages, 4 figure

Threshold expansion for heavy-light systems and flavor off-diagonal current-current correlators

An expansion scheme is developed for Feynman diagrams describing the production of one massive and one massless particle near the threshold. As an example application, we compute the correlators of heavy-light quark currents, (\bar b gamma_mu u) and (\bar b gamma_5 u), through O(alpha_s^2).Comment: 4 pages, revtex

Hadronic light-by-light scattering contribution to the muon anomalous magnetic moment revisited

We discuss hadronic light-by-light scattering contribution to the muon anomalous magnetic moment a_\mu^{\rm lbl}, paying particular attention to the consistent matching between the short- and the long-distance behavior of the light-by-light scattering amplitude. We argue that the short-distance QCD imposes strong constraints on this amplitude overlooked in previous analyses. We find that accounting for these constraints leads to approximately 50 per cent increase in the central value of a_\mu^{\rm lbl}, compared to existing estimates. The hadronic light-by-light scattering contribution becomes a_\mu^{\rm lbl}=136(25) \times 10^{-11}, thereby shifting the Standard Model prediction closer to the experimental value.Comment: 16 pages, 2 figure

An estimate of the QCD corrections to the decay Z --> W u d

We present an estimate of perturbative QCD corrections to the decay $Z \to Wu\bar d$. A simple approximate approach is described in detail. The difference of masses of $M_Z$ and $M_W$ is used as an expansion parameter. A complete analytical formula for a part of the corrections is also presented.Comment: 9 pages, late