Aspects of the Modular Symmetry Approach to Lepton Flavour

A new bottom-up approach to the flavour problem based on modular invariance has been recently proposed and has gained considerable attention in the literature. In the present thesis we develop basic aspects of the requisite modular symmetry formalism and explore its application to the lepton flavour problem. After introducing the relevant notions (the modular group, the modulus field and modular forms), we concentrate on the theoretical tools required for model-building such as explicit construction of the modular forms, the interplay of modular and CP transformations and of the related symmetries, classification of residual symmetries and their possible relation to the observed hierarchical flavour patterns. Armed with these tools, we construct and discuss three examples of viable models of lepton flavour: a simple predictive model depending on a small number of parameters, a model with an unbroken residual symmetry which leads to trimaximal neutrino mixing, and a model with a slightly broken residual symmetry which explains the observed pattern of charged-lepton masses without fine-tuning

Spinning waveforms from KMOC at leading order

We provide the analytic waveform in time domain for the scattering of two Kerr black holes at leading order in the post-Minkowskian expansion and up to fourth order in both spins. The result is obtained by the generalization of the KMOC formalism to radiative observables, combined with the analytic continuation of the five-point scattering amplitude to complex kinematics. We use analyticity arguments to express the waveform directly in terms of the three-point coupling of the graviton to the spinning particles and the gravitational Compton amplitudes, completely bypassing the need to compute and integrate the five-point amplitude. In particular, this allows to easily include higher-order spin contributions for any spinning compact body. Finally, in the spinless case we find a new compact and gauge-invariant representation of the Kovacs-Thorne waveform.Comment: 7 pages, 1 figure; v2: minor improvements, references adde

Statistical Approach to Estimated Uncertainty of Nuclear Concentration in Problems of Isotope Kinetics

The minority of papers only is devoted to the study of impact of the uncertainties in nuclear data on the nuclear concentration received during the solution of the problem of fuel burn-up in the reactor facility. On the other hand, uncertainties of known reaction rates, neutron fluxes, etc. can lead to considerable distortions of the results obtained therefore it is important to be able to assess the impact of such uncertainties on nuclear concentration of nuclides. In this paper we consider the problem of the impact assessment of uncertainties in nuclear data on reactor functionalities as applied to isotope kinetics which represents the well-known Cauchy linear problem. The most exact approach is the statistical approach of the randomized selection of input parameters in  using different distribution laws. But the simplest method of the analysis of sensitivity of model to perturbation parameters is the following (it has several names in the literature: one-at-a-time sensitivity measures, 1% sensitivity method): by varying one of the input parameters of the task for the small amount (for example, for 1%) when other parameters are constant, the corresponding response of output parameters is defined (variation approach). Our results show that in burn-up calculations the mean square deviations of nuclear concentrations obtained using statistical approach coincide with the variations of nuclear concentrations obtained in the variation approach

RegPrecise web services interface: programmatic access to the transcriptional regulatory interactions in bacteria reconstructed by comparative genomics.

Web services application programming interface (API) was developed to provide a programmatic access to the regulatory interactions accumulated in the RegPrecise database (http://regprecise.lbl.gov), a core resource on transcriptional regulation for the microbial domain of the Department of Energy (DOE) Systems Biology Knowledgebase. RegPrecise captures and visualize regulogs, sets of genes controlled by orthologous regulators in several closely related bacterial genomes, that were reconstructed by comparative genomics. The current release of RegPrecise 2.0 includes >1400 regulogs controlled either by protein transcription factors or by conserved ribonucleic acid regulatory motifs in >250 genomes from 24 taxonomic groups of bacteria. The reference regulons accumulated in RegPrecise can serve as a basis for automatic annotation of regulatory interactions in newly sequenced genomes. The developed API provides an efficient access to the RegPrecise data by a comprehensive set of 14 web service resources. The RegPrecise web services API is freely accessible at http://regprecise.lbl.gov/RegPrecise/services.jsp with no login requirements

PHOG: a database of supergenomes built from proteome complements

BACKGROUND: Orthologs and paralogs are widely used terms in modern comparative genomics. Existing procedures for resolving orthologous/paralogous relationships are often based on manual revision of clusters of orthologous groups and/or lack any rigorous evolutionary base. DESCRIPTION: We developed a completely automated procedure that creates clusters of orthologous groups at each node of the taxonomy tree (PHOGs – Phylogenetic Orthologous Groups). As a result of this procedure, a tree of orthologous groups was obtained. Each cluster is a "supergene" and it is represented by an "ancestral" sequence obtained from the multiple alignment of orthologous and paralogous genes. The procedure has been applied to the taxonomy tree of organisms from all three domains of life. Protein complements from 50 bacterial, archaeal and eukaryotic species were used to create PHOGs at all tree nodes. 51367 PHOGs were obtained at the root node. CONCLUSION: The PHOG database demonstrates that it is possible to automatically process any number of sequenced genomes and to reconstruct orthologous and paralogous relationships between genomes using a rigorous evolutionary approach. This database can become a very useful tool in various areas of comparative genomics

Modular S 4 models of lepton masses and mixing

We investigate models of charged lepton and neutrino masses and lepton mixing based on broken modular symmetry. The matter fields in these models are assumed to transform in irreducible representations of the finite modular group \u393 4 43 S 4 . We analyse the minimal scenario in which the only source of symmetry breaking is the vacuum expectation value of the modulus field. In this scenario there is no need to introduce flavon fields. Using the basis for the lowest weight modular forms found earlier, we build minimal phenomenologically viable models in which the neutrino masses are generated via the type I seesaw mechanism. While successfully accommodating charged lepton masses, neutrino mixing angles and mass-squared differences, these models predict the values of the lightest neutrino mass (i.e., the absolute neutrino mass scale), of the Dirac and Majorana CP violation (CPV) phases, as well as specific correlations between the values of the atmospheric neutrino mixing parameter sin 2 \u3b8 23 and i) the Dirac CPV phase \u3b4, ii) the sum of the neutrino masses, and iii) the effective Majorana mass in neutrinoless double beta decay. We consider also the case of residual symmetries \u2124 3ST and \u2124 2S respectively in the charged lepton and neutrino sectors, corresponding to specific vacuum expectation values of the modulus