Rota-Baxter algebras and new combinatorial identities

The word problem for an arbitrary associative Rota-Baxter algebra is solved. This leads to a noncommutative generalization of the classical Spitzer identities. Links to other combinatorial aspects, particularly of interest in physics, are indicated.Comment: 8 pages, improved versio

Cumulant-cumulant relations in free probability theory from Magnus' expansion

Relations between moments and cumulants play a central role in both classical and non-commutative probability theory. The latter allows for several distinct families of cumulants corresponding to different types of independences: free, Boolean and monotone. Relations among those cumulants have been studied recently. In this work we focus on the problem of expressing with a closed formula multivariate monotone cumulants in terms of free and Boolean cumulants. In the process we introduce various constructions and statistics on non-crossing partitions. Our approach is based on a pre-Lie algebra structure on cumulant functionals. Relations among cumulants are described in terms of the pre-Lie Magnus expansion combined with results on the continuous Baker-Campbell-Hausdorff formula due to A. Murua

Renormalization: a quasi-shuffle approach

In recent years, the usual BPHZ algorithm for renormalization in perturbative quantum field theory has been interpreted, after dimensional regularization, as a Birkhoff decomposition of characters on the Hopf algebra of Feynman graphs, with values in a Rota-Baxter algebra of amplitudes. We associate in this paper to any such algebra a universal semi-group (different in nature from the Connes-Marcolli "cosmical Galois group"). Its action on the physical amplitudes associated to Feynman graphs produces the expected operations: Bogoliubov's preparation map, extraction of divergences, renormalization. In this process a key role is played by commutative and noncommutative quasi-shuffle bialgebras whose universal properties are instrumental in encoding the renormalization process

Exponential renormalization

Moving beyond the classical additive and multiplicative approaches, we present an "exponential" method for perturbative renormalization. Using Dyson's identity for Green's functions as well as the link between the Faa di Bruno Hopf algebra and the Hopf algebras of Feynman graphs, its relation to the composition of formal power series is analyzed. Eventually, we argue that the new method has several attractive features and encompasses the BPHZ method. The latter can be seen as a special case of the new procedure for renormalization scheme maps with the Rota-Baxter property. To our best knowledge, although very natural from group-theoretical and physical points of view, several ideas introduced in the present paper seem to be new (besides the exponential method, let us mention the notions of counterfactors and of order n bare coupling constants).Comment: revised version; accepted for publication in Annales Henri Poincar

Time-ordering and a generalized Magnus expansion

Both the classical time-ordering and the Magnus expansion are well-known in the context of linear initial value problems. Motivated by the noncommutativity between time-ordering and time derivation, and related problems raised recently in statistical physics, we introduce a generalization of the Magnus expansion. Whereas the classical expansion computes the logarithm of the evolution operator of a linear differential equation, our generalization addresses the same problem, including however directly a non-trivial initial condition. As a by-product we recover a variant of the time ordering operation, known as T*-ordering. Eventually, placing our results in the general context of Rota-Baxter algebras permits us to present them in a more natural algebraic setting. It encompasses, for example, the case where one considers linear difference equations instead of linear differential equations

Commissioning of the CMS High Level Trigger

The CMS experiment will collect data from the proton-proton collisions delivered by the Large Hadron Collider (LHC) at a centre-of-mass energy up to 14 TeV. The CMS trigger system is designed to cope with unprecedented luminosities and LHC bunch-crossing rates up to 40 MHz. The unique CMS trigger architecture only employs two trigger levels. The Level-1 trigger is implemented using custom electronics, while the High Level Trigger (HLT) is based on software algorithms running on a large cluster of commercial processors, the Event Filter Farm. We present the major functionalities of the CMS High Level Trigger system as of the starting of LHC beams operations in September 2008. The validation of the HLT system in the online environment with Monte Carlo simulated data and its commissioning during cosmic rays data taking campaigns are discussed in detail. We conclude with the description of the HLT operations with the first circulating LHC beams before the incident occurred the 19th September 2008

VERGE: A Multimodal Interactive Search Engine for Video Browsing and Retrieval.

This paper presents VERGE interactive search engine, which is capable of browsing and searching into video content. The system integrates content-based analysis and retrieval modules such as video shot segmentation, concept detection, clustering, as well as visual similarity and object-based search

Anthocyanins, phenols, and antioxidant activity in blackberry juice with plant extracts addition during heating

In this work the influence of addition of different plant extracts (olive leaf, green tea, pine bark PE 95%, pine bark PE 5:1, red wine PE 30%, red wine PE 4:1, and bioflavonoids) to blackberry juice during heating (at 30, 50, 70 and 90 °C) on the anthocyanin and phenol contents, polymeric colour, and antioxidant activity was investigated. Also, reaction rate constant, half-lives of degradation, and activation energy were calculated. Control sample was juice without addition of extracts. The highest anthocyanin content at 30 °C was in samples with the addition of olive leaf and green tea. At 90 °C the highest anthocyanin content was measured in samples with the addition of extract of red wine and bioflavonoides. Samples supplemented with the extracts had much higher antioxidant activity in comparison to the control sample. Results showed that at 90 °C the sample with green tea supplementation had the lowest reaction rate constant and the highest half-life. Activation energy ranged from 29 to 44 kJ mol−1

Measurements of branching fraction ratios and CP-asymmetries in suppressed B^- -> D(-> K^+ pi^-)K^- and B^- -> D(-> K^+ pi^-)pi^- decays

We report the first reconstruction in hadron collisions of the suppressed decays B^- -> D(-> K^+ pi^-)K^- and B^- -> D(-> K^+ pi^-)pi^-, sensitive to the CKM phase gamma, using data from 7 fb^-1 of integrated luminosity collected by the CDF II detector at the Tevatron collider. We reconstruct a signal for the B^- -> D(-> K^+ pi^-)K^- suppressed mode with a significance of 3.2 standard deviations, and measure the ratios of the suppressed to favored branching fractions R(K) = [22.0 \pm 8.6(stat)\pm 2.6(syst)]\times 10^-3, R^+(K) = [42.6\pm 13.7(stat)\pm 2.8(syst)]\times 10^-3, R^-(K)= [3.8\pm 10.3(stat)\pm 2.7(syst]\times 10^-3, as well as the direct CP-violating asymmetry A(K) = -0.82\pm 0.44(stat)\pm 0.09(syst) of this mode. Corresponding quantities for B^- -> D(-> K^+ pi^-)pi^- decay are also reported.Comment: 8 pages, 1 figure, accepted by Phys.Rev.D Rapid Communications for Publicatio