Emergence of order in selection-mutation dynamics

We characterize the time evolution of a d-dimensional probability distribution by the value of its final entropy. If it is near the maximally-possible value we call the evolution mixing, if it is near zero we say it is purifying. The evolution is determined by the simplest non-linear equation and contains a d times d matrix as input. Since we are not interested in a particular evolution but in the general features of evolutions of this type, we take the matrix elements as uniformly-distributed random numbers between zero and some specified upper bound. Computer simulations show how the final entropies are distributed over this field of random numbers. The result is that the distribution crowds at the maximum entropy, if the upper bound is unity. If we restrict the dynamical matrices to certain regions in matrix space, for instance to diagonal or triangular matrices, then the entropy distribution is maximal near zero, and the dynamics typically becomes purifying.Comment: 8 pages, 8 figure

Asymptotic boundary forms for tight Gabor frames and lattice localization domains

We consider Gabor localization operators $G_{\phi,\Omega}$ defined by two parameters, the generating function $\phi$ of a tight Gabor frame $\{\phi_\lambda\}_{\lambda \in \Lambda}$, parametrized by the elements of a given lattice $\Lambda \subset \Bbb{R}^2$, i.e. a discrete cocompact subgroup of $\Bbb{R}^2$, and a lattice localization domain $\Omega \subset \Bbb{R}^2$ with its boundary consisting of line segments connecting points of $\Lambda$. We find an explicit formula for the boundary form $BF(\phi,\Omega)=\text{A}_\Lambda \lim_{R\rightarrow \infty}\frac{PF(G_{\phi,R\Omega})}{R}$, the normalized limit of the projection functional $PF(G_{\phi,\Omega})=\sum_{i=0}^{\infty}\lambda_i(G_{\phi,\Omega})(1-\lambda_i(G_{\phi,\Omega}))$, where $\lambda_i(G_{\phi,\Omega})$ are the eigenvalues of the localization operators $G_{\phi,\Omega}$ applied to dilated domains $R\Omega$, $R$ is an integer and $\text{A}_\Lambda$ is the area of the fundamental domain of the lattice $\Lambda$.Comment: 35 page

The Penn State - Toru\'n Centre for Astronomy Planet Search stars IV. Dwarfs and the complete sample

Our knowledge of the intrinsic parameters of exoplanets is as precise as our determinations of their stellar hosts parameters. In the case of radial velocity searches for planets, stellar masses appear to be crucial. But before estimating stellar masses properly, detailed spectroscopic analysis is essential. With this paper we conclude a general spectroscopic description of the Pennsylvania-Torun Planet Search (PTPS) sample of stars. We aim at a detailed description of basic parameters of stars representing the complete PTPS sample. We present atmospheric and physical parameters for dwarf stars observed within the PTPS along with updated physical parameters for the remaining stars from this sample after the first Gaia data release. We used high resolution (R=60 000) and high signal-to-noise-ratio (S/N=150-250) spectra from the Hobby-Eberly Telescope and its High Resolution Spectrograph. Stellar atmospheric parameters were determined through a strictly spectroscopic local thermodynamic equilibrium analysis (LTE) of the equivalent widths of FeI and FeII lines. Stellar masses, ages, and luminosities were estimated through a Bayesian analysis of theoretical isochrones. We present $T_{eff}$, log$g$ , [Fe/H], micrturbulence velocities, absolute radial velocities, and rotational velocities for 156 stars from the dwarf sample of PTPS. For most of these stars these are the first determinations. We refine the definition of PTPS subsamples of stars (giants, subgiants, and dwarfs) and update the luminosity classes for all PTPS stars. Using available Gaia and Hipparcos parallaxes, we redetermine the stellar parameters (masses, radii, luminosities, and ages) for 451 PTPS stars. The complete PTPS sample of 885 stars is composed of 132 dwarfs, 238 subgiants, and 515 giants, of which the vast majority are of roughly solar mass.Comment: 11 pages, 10 figures, Accepted for publication in Astronomy & Astrophysic

Eigenvalues and Singular Values of Products of Rectangular Gaussian Random Matrices (The Extended Version)

We consider a product of an arbitrary number of independent rectangular Gaussian random matrices. We derive the mean densities of its eigenvalues and singular values in the thermodynamic limit, eventually verified numerically. These densities are encoded in the form of the so called M-transforms, for which polynomial equations are found. We exploit the methods of planar diagrammatics, enhanced to the non-Hermitian case, and free random variables, respectively; both are described in the appendices. As particular results of these two main equations, we find the singular behavior of the spectral densities near zero. Moreover, we propose a finite-size form of the spectral density of the product close to the border of its eigenvalues' domain. Also, led by the striking similarity between the two main equations, we put forward a conjecture about a simple relationship between the eigenvalues and singular values of any non-Hermitian random matrix whose spectrum exhibits rotational symmetry around zero.Comment: 50 pages, 8 figures, to appear in the Proceedings of the 23rd Marian Smoluchowski Symposium on Statistical Physics: "Random Matrices, Statistical Physics and Information Theory," September 26-30, 2010, Krakow, Polan

Relativistic Iron Lines in Galactic Black Holes: Recent Results and Lines in the ASCA Archive

Recent observations with Chandra and XMM-Newton, aided by broad-band spectral coverage from RXTE, have revealed skewed relativistic iron emission lines in stellar-mass Galactic black hole systems. Such systems are excellent laboratories for testing General Relativity, and relativistic iron lines provide an important tool for making such tests. In this contribution to the Proceedings of the 10th Annual Marcel Grossmann Meeting on General Relativity, we briefly review recent developments and present initial results from fits to archival ASCA observations of Galactic black holes. It stands to reason that relativistic effects, if real, should be revealed in many systems (rather than just one or two); the results of our archival work have borne-out this expectation. The ASCA spectra reveal skewed, relativistic lines in XTE J1550-564, GRO J1655-40, GRS 1915+105, and Cygnus X-1.Comment: to appear in the proc. of the 10th Annual Marcel Grossmann Meeting on General Relativity, 5 pages, 1 figure, uses specific .cls and .sty file

Different kinds of long-term variability from Cygnus X-1

We present a study of the long-term variability of Cyg X-1 using data from the RXTE/ASM and the RXTE/PCA during the time between the two soft states of 1996 and 2001/2002. This period has been characterized by many short ASM flaring episodes which we have identified as "failed state transitions". The 150 d period which has been seen before and shortly after the 1996 soft state is not obviously present in the ASM rate during most of this time. Applying selection criteria from our pointed RXTE/PCA observations to exclude the flaring episodes we show that the 150 d period can indeed still be significantly detected in the hard state. Furthermore, while the ~420 d timescale associated with the flaring is reduced in the selected hard state count rate, it is still pronounced in the temporal evolution of the corresponding hardness ratios. The Ryle radio flux is also consistent with the 150 d period being present but distorted during this time.Comment: 4 pages, 6 figures, to appear in Proceedings of "X-ray Timing 2003: Rossi and Beyond", ed. P. Kaaret, F.K. Lamb, & J.H. Swan

Planets Around the K-Giants BD+20 274 and HD 219415

We present the discovery of planet-mass companions to two giant stars by the ongoing Penn State- Toru\'n Planet Search (PTPS) conducted with the 9.2 m Hobby-Eberly Telescope. The less massive of these stars, K5-giant BD+20 274, has a 4.2 MJ minimum mass planet orbiting the star at a 578-day period and a more distant, likely stellar-mass companion. The best currently available model of the planet orbiting the K0-giant HD 219415 points to a Jupiter-mass companion in a 5.7-year, eccentric orbit around the star, making it the longest period planet yet detected by our survey. This planet has an amplitude of \sim18 m/s, comparable to the median radial velocity (RV) "jitter", typical of giant stars.Comment: 5 figures, 13 pages, accepted by the Astrophysical Journal. arXiv admin note: substantial text overlap with arXiv:1110.164

Anomalous Chiral Fermi Surface

We provide a geometrical argument for the emergence of a Wess-Zumino-Witten (WZW) term for a Fermi surface threaded by a Berry curvature. In the presence of external fields, the gauged WZW term yields a chiral (triangle) anomaly for the fermionic current at the edge of the Fermi surface. Fermion number is conserved though since the Berry curvatures occur always in pairs with opposite (monopole) charge. The anomalous vector and axial currents for a a fermionic fluid at low temperature threaded by pairs of Berry curvatures are discussed. The leading temperature correction to the chiral vortical effect in a slowly rotating Fermi surface threaded by a Berry curvature maybe tied to the gravitational anomaly.Comment: 4 pages; version to appear in PR