Adaptive Gaussian inverse regression with partially unknown operator

This work deals with the ill-posed inverse problem of reconstructing a function $f$ given implicitly as the solution of $g = Af$, where $A$ is a compact linear operator with unknown singular values and known eigenfunctions. We observe the function $g$ and the singular values of the operator subject to Gaussian white noise with respective noise levels $\varepsilon$ and $\sigma$. We develop a minimax theory in terms of both noise levels and propose an orthogonal series estimator attaining the minimax rates. This estimator requires the optimal choice of a dimension parameter depending on certain characteristics of $f$ and $A$. This work addresses the fully data-driven choice of the dimension parameter combining model selection with Lepski's method. We show that the fully data-driven estimator preserves minimax optimality over a wide range of classes for $f$ and $A$ and noise levels $\varepsilon$ and $\sigma$. The results are illustrated considering Sobolev spaces and mildly and severely ill-posed inverse problems

Generalized Chern-Simons action and maximally supersymmetric gauge theories

We study observables and deformations of generalized Chern-Simons action and show how to apply these results to maximally supersymmetric gauge theories. We describe a construction of large class of deformations based on some results on the cohomology of super Lie algebras proved in the Appendix.Comment: The talk for the workshop String-Math 2012, Bonn. 22 page

On the Nature of the Binary Components of RX J0806.3+1527

We present imaging circular polarimetry and near-infrared photometry of the suspected ultra-short period white-dwarf binary RX J0806.3+1527 obtained with the ESO VLT and discuss the implications for a possible magnetic nature of the white dwarf accretor and the constraints derived for the nature of the donor star. Our V-filter data show marginally significant circular polarization with a modulation amplitude of ~0.5% typical for cyclotron emission from an accretion column in a magnetic field of order 10 MG and not compatible with a direct-impact accretor model. The optical to near-infrared flux distribution is well described by a single blackbody with temperature kT_bb = 35000 K and excludes a main-sequence stellar donor unless the binary is located several scale heights above the galactic disk population.Comment: 2 pages including 2 figures. To appear in RevMexAA(SC) Conference Series, Proc. of IAU Colloquium 194 `Compact Binaries in the Galaxy and Beyond', La Paz (Mexico), eds. G. Tovmassian & E. Sio

Homology of Lie algebra of supersymmetries and of super Poincare Lie algebra

We study the homology and cohomology groups of super Lie algebra of supersymmetries and of super Poincare Lie algebra in various dimensions. We give complete answers for (non-extended) supersymmetry in all dimensions $\leq 11$. For dimensions $D=10,11$ we describe also the cohomology of reduction of supersymmetry Lie algebra to lower dimensions. Our methods can be applied to extended supersymmetry algebra.Comment: New version with some additions and correction

Decomposition of multicomponent mass spectra using Bayesian probability theory

We present a method for the decomposition of mass spectra of mixture gases using Bayesian probability theory. The method works without any calibration measurement and therefore applies also to the analysis of spectra containing unstable species. For the example of mixtures of three different hydrocarbon gases the algorithm provides concentrations and cracking coefficients of each mixture component as well as their confidence intervals. The amount of information needed to obtain reliable results and its relation to the accuracy of our analysis are discussed

1RXSJ062518.2+733433: A bright, soft intermediate polar

We present the results of 50 hours time-resolved R-band photometry of the ROSAT all-sky survey source 1RXSJ062518.2+733433. The source was identified by Wei et al. (1999) as a cataclysmic variable. Our photometry, performed in 10 nights between February 11, 2003, and March 21, 2003, reveals two stable periodicities at 19.7874 and 283.118 min, which are identified as probable spin and orbital periods of the binary. We therefore classify 1RXSJ062518.2+733433 as an intermediate polar. Analysis of the RASS X-ray observations reveal a variability of 100% in the X-ray flux and a likely soft X-ray excess. The new IP thus joins the rare group of soft IPs with only four members so far.Comment: submitted to A&A, 5 pages, 6 figures of reduced qualit

Sp(4,R)/GL(2,R) Matrix Structure of Geodesic Solutions for Einstein--Maxwell--Dilaton--Axion Theory

The constructed $Sp(4,R)/GL(2,R)$ matrix operator defines the family of isotropic geodesic containing vacuum point lines in the target space of the stationary D=4 Einstein--Maxwell--dilaton--axion theory. This operator is used to derive a class of solutions which describes a point center system with nontrivial values of mass, parameter NUT, as well as electric, magnetic, dilaton and axion charges. It is shown that this class contains both particular solutions Majumdar--Papapetrou--like black holes and massless asymptotically nonflat naked singularities.Comment: 20 pages, RevTex, no figures, Submitted to Phys.Rev.

Generalized Green-Schwarz mechanism in F theory

We derive the anomaly 8-form of 6-dimensional gauge theories arising in F theory compactifications on elliptic Calabi-Yau threefolds. The result allows to determine the matter content of certain such theories in terms of intersection numbers on the base of elliptic fibration. We also discuss gauge theories on 7-branes with double point singularities on the worldvolume. Applications to Type II compactifications on Hirzebruch surfaces and $P^2$ are outlined.Comment: 11 pages, harvmac. Normalization of (tr R^2)^2 term correcte