On pattern classification algorithms - Introduction and survey

Pattern recognition algorithms, and mathematical techniques of estimation, decision making, and optimization theor

Condition for tripartite entanglement

We propose a scheme for classifying the entanglement of a tripartite pure qubit state. This classification scheme consists of an ordered list of seven elements. These elements are the Cayley hyper-determinant, and its six associated $2 \times 2$ subdeterminants. In particular we show that this classification provides a necessary and sufficient condition for separability.Comment: 8 pages, to appear in the Proceedings of "Quantum Theory and Symmetries 7", Prague, Aug 7-13, 201

Generalized Rayleigh and Jacobi processes and exceptional orthogonal polynomials

We present four types of infinitely many exactly solvable Fokker-Planck equations, which are related to the newly discovered exceptional orthogonal polynomials. They represent the deformed versions of the Rayleigh process and the Jacobi process.Comment: 17 pages, 4 figure

An Automated Social Graph De-anonymization Technique

We present a generic and automated approach to re-identifying nodes in anonymized social networks which enables novel anonymization techniques to be quickly evaluated. It uses machine learning (decision forests) to matching pairs of nodes in disparate anonymized sub-graphs. The technique uncovers artefacts and invariants of any black-box anonymization scheme from a small set of examples. Despite a high degree of automation, classification succeeds with significant true positive rates even when small false positive rates are sought. Our evaluation uses publicly available real world datasets to study the performance of our approach against real-world anonymization strategies, namely the schemes used to protect datasets of The Data for Development (D4D) Challenge. We show that the technique is effective even when only small numbers of samples are used for training. Further, since it detects weaknesses in the black-box anonymization scheme it can re-identify nodes in one social network when trained on another.Comment: 12 page

On some further properties of nonzero-sum diffential games

Optimality principle and open loop-closed loop control relations in nonzero-sum differential game

Buoyancy and g-modes in young superfluid neutron stars

We consider the local dynamics of a realistic neutron star core, including composition gradients, superfluidity and thermal effects. The main focus is on the gravity g-modes, which are supported by composition stratification and thermal gradients. We derive the equations that govern this problem in full detail, paying particular attention to the input that needs to be provided through the equation of state and distinguishing between normal and superfluid regions. The analysis highlights a number of key issues that should be kept in mind whenever equation of state data is compiled from nuclear physics for use in neutron star calculations. We provide explicit results for a particular stellar model and a specific nucleonic equation of state, making use of cooling simulations to show how the local wave spectrum evolves as the star ages. Our results show that the composition gradient is effectively dominated by the muons whenever they are present. When the star cools below the superfluid transition, the support for g-modes at lower densities (where there are no muons) is entirely thermal. We confirm the recent suggestion that the g-modes in this region may be unstable, but our results indicate that this instability will be weak and would only be present for a brief period of the star's life. Our analysis accounts for the presence of thermal excitations encoded in entrainment between the entropy and the superfluid component. Finally, we discuss the complete spectrum, including the normal sound waves and, in superfluid regions, the second sound.Comment: 29 pages, 9 figures, submitted to MNRA

Iron Emission in the z=6.4 Quasar SDSS J114816.64+525150.3

We present near-infrared J and K-band spectra of the z = 6.4 quasar SDSS J114816.64+525150.3 obtained with the NIRSPEC spectrograph at the Keck-II telescope, covering the rest-frame spectral regions surrounding the C IV 1549 and Mg II 2800 emission lines. The iron emission blend at rest wavelength 2900-3000 A is clearly detected and its strength appears nearly indistinguishable from that of typical quasars at lower redshifts. The Fe II / Mg II ratio is also similar to values found for lower-redshift quasars, demonstrating that there is no strong evolution in Fe/alpha broad-line emission ratios even out to z=6.4. In the context of current models for iron enrichment from Type Ia supernovae, this implies that the SN Ia progenitor stars formed at z > 10. We apply the scaling relations of Vestergaard and of McLure & Jarvis to estimate the black hole mass from the widths of the C IV and Mg II emission lines and the ultraviolet continuum luminosity. The derived mass is in the range (2-6)x10^9 solar masses, with an additional uncertainty of a factor of 3 due to the intrinsic scatter in the scaling relations. This result is in agreement with the previous mass estimate of 3x10^9 solar masses by Willott, McLure, & Jarvis, and supports their conclusion that the quasar is radiating close to its Eddington luminosity.Comment: To appear in ApJ Letter

Intermediate-mass Black Holes in Galactic Nuclei

We present the first homogeneous sample of intermediate-mass black hole candidates in active galactic nuclei. Starting with broad-line active nuclei from the Sloan Digital Sky Survey, we use the linewidth-luminosity-mass scaling relation to select a sample of 19 galaxies in the mass range M_BH ~ 8 x 10^4 - 10^6 solar masses. In contrast to the local active galaxy population, the host galaxies are ~1 mag fainter than M* and thus are probably late-type systems. The active nuclei are also faint, with M_g ~ -15 to -18 mag, while the bolometric luminosities are close to the Eddington limit. The spectral properties of the sample are compared to the related class of objects known as narrow-line Seyfert 1 galaxies. We discuss the importance of our sample as observational analogues of primordial black holes, contributors to the integrated signal for future gravitational wave experiments, and as a valuable tool in the calibration of the M-sigma relation.Comment: 4 pages, 4 figures. To appear in "The Interplay among Black Holes, Stars and ISM in Galactic Nuclei," Proc. IAU 222 (Gramado, Brazil), eds Th. Storchi Bergmann, L.C. Ho, H.R. Schmit

Atmospheres and radiating surfaces of neutron stars with strong magnetic fields

We review the current status of the theory of thermal emission from the surface layers of neutron stars with strong magnetic fields $B\sim 10^{10}-10^{15}$ G, including formation of the spectrum in a partially ionized atmosphere and at a condensed surface. In particular, we describe recent progress in modeling partially ionized atmospheres of central compact objects in supernova remnants, which may have moderately strong fields $B\sim 10^{10}-10^{11}$ G. Special attention is given to polarization of thermal radiation emitted by a neutron star surface. Finally, we briefly describe applications of the theory to observations of thermally emitting isolated neutron stars.Comment: 27 pages, 5 figures, invited review at the conference "The Modern Physics of Compact Stars 2015" (Yerevan, Armenia, Sept. 30 - Oct. 3, 2015), edited by R. Avagyan, A. Saharian, and A. Sedrakian. In v.2, a citation (Ref.114) is correcte