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# Posts Tagged correlation

## Recent Postings from correlation

### CO luminosity - line width correlation of sub-millimeter galaxies and a possible cosmological application

Context. A possible correlation between CO luminosity (L_CO ) and its line width (FWHM) has been suggested and denied in the literature. Such claims were often based on a small, or heterogeneous sample of galaxies, and thus inconclusive. Aims. We aim to prove or dis-prove the L_CO -FWHM correlation. Methods. We compile a large sample of submm galaxies at z>2 from the literature, and investigate the L_CO-FWHM relation. Results. After carefully evaluating the selection effects and uncertainties such as inclination and magnification via gravitational lensing, we show that there exist a weak but significant correlation between L_CO and FWHM. We also discuss a feasibility to measure the cosmological distance using the correlation.

### The observed radio/gamma-ray emission correlation for blazars with the Fermi-LAT and the RATAN-600 data

We study the correlation between gamma-ray and radio band radiation for 123 blazars, using the Fermi-LAT first source catalog (1FGL) and the RATAN-600 data obtained at the same period of time (within a few months). We found an apparent positive correlation for BL Lac and flat-spectrum radio quasar (FSRQ) sources from our sample through testing the value of the Pearson product-moment correlation coefficient. The BL Lac objects show higher values of the correlation coefficient than FSRQs at all frequencies, except 21.7 GHz, and at all bands, except $10-100$ GeV, typically at high confidence level (> 99%). At higher gamma-ray energies the correlation weakens and even becomes negative for BL Lacs and FSRQs. For BL Lac blazars, the correlation of the fluxes appeared to be more sensitive to the considered gamma-ray energy band, than to the frequency, while for FSRQ sources the correlation changed notably both with the considered radio frequency and gamma-ray energy band. We used a data randomization method to quantify the significance of the computed correlation coefficients. We find that the statistical significance of the correlations we obtained between the flux densities at all frequencies and the photon flux in all gamma-ray bands below 3 GeV is high for BL Lacs (chance probability $\sim 10^{-3} – 10^{-7}$). The correlation coefficient is high and significant for the $0.1-0.3$ GeV band and low and insignificant for the $10-100$ GeV band for both types of blazars for all considered frequencies.

### On the Physical Origin of Galactic Conformity

Correlations between the star formation rates (SFRs) of nearby galaxies (so-called galactic conformity) have been observed for projected separations up to 4 Mpc, an effect not predicted by current semi-analytic models. We investigate correlations between the mass accretion rates (dMvir/dt) of nearby halos as a potential physical origin for this effect. We find that pairs of host halos "know about" each others’ assembly histories even when their present-day separation is greater than thirty times the virial radius of either halo. These distances are far too large for direct interaction between the halos to explain the correlation in their dMvir/dt. Instead, halo pairs at these distances reside in the same large-scale tidal environment, which regulates dMvir/dt for both halos. Larger halos are less affected by external forces, which naturally gives rise to a mass dependence of the halo conformity signal. SDSS measurements of galactic conformity exhibit a qualitatively similar dependence on stellar mass, including how the signal varies with distance. Based on the expectation that halo accretion and galaxy SFR are correlated, we predict the scale-, mass- and redshift-dependence of large-scale galactic conformity, finding that the signal should drop to undetectable levels by z > 1. These predictions are testable with current surveys to z ~ 1; confirmation would establish a strong correlation between dark matter halo accretion rate and central galaxy SFR.

### Time-reversal symmetry violation in several Lepton-Flavor-Violating processes

We compute a T-odd triple vector correlation for the $\mu\rightarrow e\gamma$ decay and the $\mu\rightarrow e$ conversion process. We find simple results in terms of the CP violating phases of the effective Hamiltonians. Then we focus on the minimal Left-Right symmetric extension of the Standard Model, which can lead to an appreciable correlation. We show that under rather general assumptions, this correlation can be used to discriminate between Parity or Charge-conjugation as the discrete Left-Right symmetry.

### Time-reversal symmetry violation in several Lepton-Flavor-Violating processes [Replacement]

We compute a T-odd triple vector correlation for the $\mu\rightarrow e\gamma$ decay and the $\mu\rightarrow e$ conversion process. We find simple results in terms of the CP violating phases of the effective Hamiltonians. Then we focus on the minimal Left-Right symmetric extension of the Standard Model, which can lead to an appreciable correlation. We show that under rather general assumptions, this correlation can be used to discriminate between Parity or Charge-conjugation as the discrete Left-Right symmetry.

### Time-reversal symmetry violation in several Lepton-Flavor-Violating processes [Replacement]

We compute a T-odd triple vector correlation for the $\mu\rightarrow e\gamma$ decay and the $\mu\rightarrow e$ conversion process. We find simple results in terms of the CP violating phases of the effective Hamiltonians. Then we focus on the minimal Left-Right symmetric extension of the Standard Model, which can lead to an appreciable correlation. We show that under rather general assumptions, this correlation can be used to discriminate between Parity or Charge-conjugation as the discrete Left-Right symmetry.

### The imprint of massive black-hole mergers on the correlation between nuclear clusters and their host galaxies [Cross-Listing]

A literature compilation of nuclear cluster (NSC) masses is used to study the correlation between global and NSC properties. A comparison of observational data to the predictions of semi-analytical galaxy formation models places constraints on the co-evolution of NSCs, massive black holes (MBHs) and host galaxies. Both data and theoretical predictions show an increased scatter in the NSC scaling correlations at high galaxy masses, and we show that this is due to the progressively more efficient ejection of stars from NSCs caused by MBH binaries in more massive stellar spheroids. Our results provide a natural explanation of why in nucleated galaxies hosting a MBH, the ratio (M_NSC+M_MBH)/M_bulge (with M_bulge the host spheroid’s mass) shows significantly less scatter than M_NSC/M_bulge, and suggest that the formation of MBHs and NSCs are not mutually exclusive, as also supported by observations of co-existing systems. Both MBHs and NSCs represent generic products of galaxy formation, with NSCs being destroyed or modified by the merger evolution of their companion MBHs.

### The imprint of massive black-hole mergers on the correlation between nuclear clusters and their host galaxies

A literature compilation of nuclear cluster (NSC) masses is used to study the correlation between global and NSC properties. A comparison of observational data to the predictions of semi-analytical galaxy formation models places constraints on the co-evolution of NSCs, massive black holes (MBHs) and host galaxies. Both data and theoretical predictions show an increased scatter in the NSC scaling correlations at high galaxy masses, and we show that this is due to the progressively more efficient ejection of stars from NSCs caused by MBH binaries in more massive stellar spheroids. Our results provide a natural explanation of why in nucleated galaxies hosting a MBH, the ratio (M_NSC+M_MBH)/M_bulge (with M_bulge the host spheroid’s mass) shows significantly less scatter than M_NSC/M_bulge, and suggest that the formation of MBHs and NSCs are not mutually exclusive, as also supported by observations of co-existing systems. Both MBHs and NSCs represent generic products of galaxy formation, with NSCs being destroyed or modified by the merger evolution of their companion MBHs.

### Time variation of Kepler transits induced by stellar rotating spots - a way to distinguish between prograde and retrograde motion. II. Application to KOIs

Mazeh, Holczer, and Shporer (2015) have presented an approach that can, in principle, use the derived transit timing variation (TTV) of some transiting planets observed by the Kepler mission to distinguish between prograde and retrograde motion of their orbits with respect to the rotation of their parent stars. The approach utilizes TTVs induced by spot-crossing events that occur when the transiting planet moves across a spot on the stellar surface, by looking for a correlation between the derived TTVs and the stellar brightness derivatives at the corresponding transits, even in data that can not resolve the spot-crossing events themselves. We present here the application of this approach to the Kepler KOIs, identifying nine systems where the photometric spot modulation is large enough and the transit timing accurate enough to allow detection of a TTV-brightness-slope correlation. Excluding KOI-1546, which has been found recently to be a stellar binary, we are left with eight hot-Jupiter systems with high sensitivity to the correlation detection. Five of those eight systems show highly significant prograde motion, including two confirmed planets (KOI-203.01 = Kepler-17b and KOI-217.01 = Kepler-71b) and three planetary candidates (KOI-883.01, KOI-895.01, and KOI-1074.01), while no system displays retrograde motion, consistent with the suggestion that planets orbiting cool stars have prograde motion. All five systems have derived impact parameter $\lesssim$0.5, and all systems with an impact parameter in that range show significant correlation, except KOI-3.01 (= Kepler-3b = HAT-P-11b) where the lack of a correlation is explained by its large stellar obliquity. Although our sample is small, these findings hint that stellar spots, or at least the larger ones, have a tendency to be located at a low latitude on the stellar disc, similar to the Sun.

### Image patch analysis of sunspots and active regions. I. Intrinsic dimension and correlation analysis

Complexity of an active region is related to its flare-productivity. Mount Wilson or McIntosh sunspot classifications measure such complexity but in a categorical way, and may therefore not use all the information present in the observations. Moreover, such categorical schemes hinder a systematic study of an active region’s evolution for example. We propose fine-scale quantitative descriptors for an active region’s complexity and relate them to the Mount Wilson classification. We analyze the local correlation structure within continuum and magnetogram data, as well as the cross-correlation between continuum and magnetogram data. We compute the intrinsic dimension, partial correlation, and canonical correlation analysis (CCA) of image patches of continuum and magnetogram active region images taken from the SOHO-MDI instrument. We use masks of sunspots derived from continuum as well as larger masks of magnetic active regions derived from the magnetogram to analyze separately the core part of an active region from its surrounding part. We find the relationship between complexity of an active region as measured by Mount Wilson and the intrinsic dimension of its image patches. Partial correlation patterns exhibit approximately a third-order Markov structure. CCA reveals different patterns of correlation between continuum and magnetogram within the sunspots and in the region surrounding the sunspots. These results also pave the way for patch-based dictionary learning with a view towards automatic clustering of active regions.

### A statistical correlation of sunquakes based on their seismic, white light, and X-ray emission

Several mechanisms have been proposed to explain the transient seis- mic emission, i.e., sunquakes, from some solar flares. Some theories associate high-energy electrons and/or white-light emission with sunquakes. High-energy charged particles and their subsequent heating of the photosphere and/or chro- mosphere could induce acoustic waves in the solar interior. We carried out a correlative study of solar flares with emission in hard-X rays (HXRs), enhanced continuum emission at 6173{\AA}, and transient seismic emission. We selected those flares observed by RHESSI (Reuven Ramaty High Energy Solar Spectroscopic Imager) with a considerable flux above 50 keV between January 1, 2010 and June 26, 2014. We then used data from the Helioseismic and Magnetic Imager onboard the Solar Dynamic Observatory (SDO/HMI) to search for excess visible continuum emission and new sunquakes not previously reported. We found a total of 18 sunquakes out of 75 investigated. All of the sunquakes were associated with a enhancement of the visible continuum during the flare time. Finally, we calculated a coefficient of correlation for a set of dichotomic variables related to these observations. We found a strong correlation between two of the standard helioseismic detection techniques, and between sunquakes and visible continuum enhancements. We discuss the phenomenological connectivity between these physical quantities and the observational difficulties of detecting seismic signals and excess continuum radiation.

### Searching for signatures of planet formation in stars with circumstellar debris discs

(Abridged) Tentative correlations between the presence of dusty debris discs and low-mass planets have been presented. In parallel, detailed chemical abundance studies have reported different trends between samples of planet and non-planet hosts. We determine in a homogeneous way the metallicity, and abundances of a sample of 251 stars including stars with known debris discs, with debris discs and planets, and only with planets. Stars with debris discs and planets have the same [Fe/H] behaviour as stars hosting planets, and they also show a similar <[X/Fe]>-Tc trend. Different behaviour in the <[X/Fe]>-Tc trend is found between the samples of stars without planets and the samples of planet hosts. In particular, when considering only refractory elements, negative slopes are shown in cool giant planet hosts, whilst positive ones are shown in stars hosting low-mass planets. Stars hosting exclusively close-in giant planets show higher metallicities and positive <[X/Fe]>-Tc slope. A search for correlations between the <[X/Fe]>-Tc slopes and the stellar properties reveals a moderate but significant correlation with the stellar radius and as well as a weak correlation with the stellar age. The fact that stars with debris discs and stars with low-mass planets do not show neither metal enhancement nor a different <[X/Fe]>-Tc trend might indicate a correlation between the presence of debris discs and the presence of low-mass planets. We extend results from previous works which reported differences in the <[X/Fe]>-Tc trends between planet hosts and non hosts. However, these differences tend to be present only when the star hosts a cool distant planet and not in stars hosting exclusively low-mass planets.

### T violation in radiative $β$ decay and electric dipole moments

In radiative $\beta$ decay, $T$ violation can be studied through a spin-independent $T$-odd correlation. We consider contributions to this correlation by beyond the standard model (BSM) sources of $T$-violation, arising above the electroweak scale. At the same time such sources, parametrized by dimension-6 operators, can induce electric dipole moments (EDMs). As a consequence, the manifestations of the $T$-odd BSM physics in radiative $\beta$ decay and EDMs are not independent. Here we exploit this connection to show that current EDM bounds already strongly constrain the spin-independent $T$-odd correlation in radiative $\beta$ decay.

### Reanalyzing the visible colors of Centaurs and KBOs: what is there and what we might be missing

Visible colors (BVRI) are a reasonable proxy for real spectra of Centaurs and Kuiper Belt Objects, which are rather linear in this range. Colors provide limited information but remain the best tool to study the bulk surface properties. We explore recurrent effects in the study of visible colors: i) how a correlation could be missed or weakened as a result of the data error bars, ii) the "risk" of missing an existing trend because of low sampling, and the possibility of making quantified predictions on the sample size needed to detect a trend at a given significance level, iii) the use of partial correlations to distinguish the mutual effect of two or more parameters, and iv) the sensitivity of the "reddening line" tool to the central wavelength of the filters used. We have compiled the visible colors of about 370 objects available in the literature and carried out an analysis per dynamical family. Our results show how a) data error bars impose a limit on the detectable correlations regardless of sample size and that therefore, once that limit is achieved, it is important to diminish the error bars, but it is pointless to enlarge the sampling with the same or larger errors; b) almost all dynamical families still require larger samplings to ensure the detection of correlations stronger than 0.5; c) the correlation strength between (V-R) vs. (R-I) is systematically lower than the one between (B-V) vs. (V-R) and is not related with error-bar differences between these colors; d) it is statistically equivalent to use any of the different flavors of orbital excitation or collisional velocity parameters regarding the color-inclination correlation of classical KBOs whereas the inclination and Tisserand parameter relative to Neptune cannot be separated from one another; and e) classical KBOs are the only dynamical family that shows neither (B-V) vs. (V-R) nor (V-R) vs. (R-I) correlations.

### Discovery of the correlation between peak episodic jet power and X-ray peak luminosity of the soft state in black hole transients

Episodic jets are usually observed in the intermediate state of black hole transients during their X-ray outbursts. Here we report the discovery of a strong positive correlation between the peak radio power of the episodic jet $P_{\rm jet}$ and the corresponding peak X-ray luminosity $L_{\rm x}$ of the soft state (in Eddington units) in a complete sample of the outbursts of black hole transients observed during the RXTE era of which data are available, which follows the relation $\log P_{\rm jet}=(2.17\pm{0.32})+(1.63\pm0.24)\times \log {L_{\rm x}}$. The transient ultra-luminous X-ray source in M31 and HLX-1 in EXO 243-49 fall on the relation if they contain stellar mass black hole and either stellar mass black hole or intermediate mass black hole, respectively. Besides, a significant correlation between the peak power of the episodic jet and the rate-of-increase of the X-ray luminosity $\rm dL_{x}/dt$ during the rising phase of those outbursts is also found, following $\log P_{\rm jet}=(1.97\pm{0.42})+(0.69\pm0.15)\times \log {\rm d}L_{\rm x}/{\rm d}t$. In GX 339$-$4 and H 1743$-$322 in which data for two outbursts are available, measurements of the peak radio power of the episodic jet and the X-ray peak luminosity (and its rate-of-change) shows similar positive correlations between outbursts, which demonstrate the dominant role of accretion over black hole spin in generating episodic jet power. On the other hand, no significant difference is seen among the systems with different measured black hole spin in current sample. This implies that the power of the episodic jet is strongly affected by non-stationary accretion characterised primarily by the rate-of-change of the mass accretion rate.

### Analysing the effects of apodizing windows on local correlation tracking using Nirvana simulations of convection

We employ different shapes of apodizing windows in the local correlation tracking (LCT) routine to retrieve horizontal velocities using numerical simulations of convection. LCT was applied on a time sequence of temperature maps generated by the Nirvana code with four different apodizing windows, namely–Gaussian, Lorentzian, trapezoidal and triangular, with varying widths. In terms of correlations (between the LCT-retrieved and simulated flow field), the triangular and the trapezoidal perform the best and worst, respectively. On segregating the intrinsic velocities in the simulations on the basis of their magnitudes, we find that for all windows, a significantly higher correlation is obtained for the intermediate and high-velocity bins and only modest or weak values in the low-velocity bins. The differences between the LCT-retrieved and simulated flow fields were determined spatially which show large residuals at or close to the boundary of granules. The extent to which the horizontal flow vectors retrieved by LCT compare with the simulated values, depends entirely on the width of the central peak of the apodizing window for a given $\sigma$. Even though LCT suffers from a lack of spatial content as seen in simulations, its simplicity and speed could serve as a viable first-order tool to probe horizontal flows–one that is ideal for large data sets.

### Extending the Correlation of $L_R - L_X$ to Gamma Ray Bursts

The well-known correlation between the radio luminosity ($L_R$) and the X-ray luminosity ($L_X$) $L_R / L_X \simeq 10^{-5}$ holds for a variety of objects like active galactic nuclei, galactic black holes, solar flares and cool stars. Here we extend the relation to gamma-ray bursts (GRBs), and find the GRBs also lay on the same $L_R-L_X$ relation, with a slightly different slope as $L_R \propto L_X^{1.1}$. This relation implies the explosions in different scales may have a common underlying origin.

### Radio--Far infrared correlation in "blue cloud" galaxies with 0<z<1.2

We study the radio–far infrared (FIR) correlation in "blue cloud" galaxies chosen from the PRism MUltiobject Survey (PRIMUS) up to redshift ($z$) of 1.2 in the XMM-LSS field. We use rest-frame emission at 1.4 GHz in the radio and both monochromatic (at 70$\mu$m) and bolometric (between $8-1000~\mu$m) emission in the FIR. To probe the nature of the correlation up to $z\sim1.2$, where direct detection of blue star-forming galaxies is impossible with current technology, we employ the technique of image stacking at 0.325 and 1.4 GHz in the radio and in six infrared bands, viz. 24, 70, 160, 250, 350 and $500~\mu$m. For comparison, we also study the correlation for more luminous galaxies that are directly detected. The stacking analysis allows us to probe the radio–FIR correlation for galaxies that are up to 2 orders of magnitude fainter than the ones detected directly. The $k-$correction in the infrared wavebands is obtained by fitting the observed spectral energy distribution (SED) with a composite mid-IR power law and a single temperature greybody model. We find that the radio luminosity at 1.4 GHz ($L_{\rm 1.4GHz}$) is strongly correlated with monochromatic FIR luminosity at 70 $\mu$m ($L_{\rm 70\mu m}$) having slope $1.09\pm0.05$ and with bolometric luminosity ($L_{\rm TIR}$) having slope $1.11\pm0.04$. The quantity $q_{\rm TIR} (=\log_{10}[L_{\rm TIR}/(3.75\times 10^{12} L_{\rm 1.4 GHz})])$ is observed to decrease with redshift as $q_{\rm TIR} \propto (1+z)^{-0.16\pm0.03}$ probably caused due to the non-linear slope of the radio–FIR correlation. Within the uncertainties of our measurement and the limitations of our flux-limited and color-selected sample, we do not find any evolution of the radio–FIR correlation with redshift.

### Breaking FIR-Radio Correlation: The Case of Interacting Galaxies

Far-infrared (FIR)–radio correlation is a well-established empirical connection between continuum radio and dust emission of star-forming galaxies, used as a tool in determining star-formation rates. Here we point out that in the case of interacting star-forming galaxies this tool might break. Galactic interactions and mergers have been known to give rise to tidal shocks and disrupt morphologies especially in the smaller of the interacting components. Moreover, these shocks can also heat the gas and dust and accelerate particles leading to tidal cosmic-ray population in addition to standard galactic cosmic rays. Both heating and additional non-thermal radiation will obviously affect the FIR-radio correlation of these systems. To test this hypothesis we have analyzed a sample of 43 infrared bright star-forming interacting galaxies at different merger stages. We have found that their FIR-radio correlation parameter and radio emission spectral index vary over different merger stages and behave as it would be expected from our tidal-shock scenario. Important implications of breaking the FIR-radio correlation are discussed.

### Using machine learning to classify the diffuse interstellar bands

Using over a million and a half extragalactic spectra we study the correlations of the Diffuse Interstellar Bands (DIBs) in the Milky Way. We measure the correlation between DIB strength and dust extinction for 142 DIBs using 24 stacked spectra in the reddening range E(B-V) < 0.2, many more lines than ever studied before. Most of the DIBs do not correlate with dust extinction. However, we find 10 weak and barely studied DIBs with correlations that are higher than 0.7 with dust extinction and confirm the high correlation of additional 5 strong DIBs. Furthermore, we find a pair of DIBs, 5925.9A and 5927.5A which exhibits significant negative correlation with dust extinction, indicating that their carrier may be depleted on dust. We use Machine Learning algorithms to divide the DIBs to spectroscopic families based on 250 stacked spectra. By removing the dust dependency we study how DIBs follow their local environment. We thus obtain 6 groups of weak DIBs, 4 of which are tightly associated with C2 or CN absorption lines.

### Does the presence of planets affect the frequency and properties of extrasolar Kuiper Belts? Results from the Herschel DEBRIS and DUNES surveys [Replacement]

The study of the planet-debris disk connection can shed light on the formation and evolution of planetary systems, and may help predict the presence of planets around stars with certain disk characteristics. In preliminary analyses of the Herschel DEBRIS and DUNES surveys, Wyatt et al. (2012) and Marshall et al. (2014) identified a tentative correlation between debris and low-mass planets. Here we use the cleanest possible sample out these surveys to assess the presence of such a correlation, discarding stars without known ages, with ages < 1 Gyr and with binary companions <100 AU, to rule out possible correlations due to effects other than planet presence. In our sample of 204 FGK stars, we do not find evidence that debris disks are more common or more dusty around stars harboring high-mass or low-mass planets compared to a control sample without identified planets, nor that debris disks are more or less common (or more or less dusty) around stars harboring multiple planets compared to single-planet systems. Diverse dynamical histories may account for the lack of correlations. The data show the correlation between the presence of high-mass planets and stellar metallicity, but no correlation between the presence of low-mass planets or debris and stellar metallicity. Comparing the observed cumulative distribution of fractional luminosity to those expected from a Gaussian distribution, we find that a distribution centered on the Solar system’s value fits well the data, while one centered at 10 times this value can be rejected. This is of interest in the context of future terrestrial planet characterization because it indicates that there are good prospects for finding a large number of debris disk systems (i.e. with evidence of harboring the building blocks of planets) with exozodiacal emission low enough to be appropriate targets for an ATLAST-type mission to search for biosignatures.

### Does the presence of planets affect the frequency and properties of extrasolar Kuiper Belts? Results from the Herschel DEBRIS and DUNES surveys

The study of the planet-debris disk connection can shed light on the formation and evolution of planetary systems, and may help predict the presence of planets around stars with certain disk characteristics. In preliminary analyses of the Herschel DEBRIS and DUNES surveys, Wyatt et al. (2012) and Marshall et al. (2014) identified a tentative correlation between debris and low-mass planets. Here we use the cleanest possible sample out these surveys to assess the presence of such a correlation, discarding stars without known ages, with ages < 1 Gyr and with binary companions <100 AU, to rule out possible correlations due to effects other than planet presence. In our sample of 204 FGK stars, we do not find evidence that debris disks are more common or more dusty around stars harboring high-mass or low-mass planets compared to a control sample without identified planets, nor that debris disks are more or less common (or more or less dusty) around stars harboring multiple planets compared to single-planet systems. Diverse dynamical histories may account for the lack of correlations. The data show the correlation between the presence of high-mass planets and stellar metallicity, but no correlation between the presence of low-mass planets or debris and stellar metallicity. Comparing the observed cumulative distribution of fractional luminosity to those expected from a Gaussian distribution, we find that a distribution centered on the Solar system’s value fits well the data, while one centered at 10 times this value can be rejected. This is of interest in the context of future terrestrial planet characterization because it indicates that there are good prospects for finding a large number of debris disk systems (i.e. with evidence of harboring the building blocks of planets) with exozodiacal emission low enough to be appropriate targets for an ATLAST-type mission to search for biosignatures.

### A disc corona-jet model for the radio/X-ray correlation in black hole X-ray binaries

The observed tight radio/X-ray correlation in the low spectral state of some black hole X-ray binaries implies the strong coupling of the accretion and jet. The correlation of $L_{\rm R} \propto L_{\rm X}^{\sim 0.5-0.7}$ was well explained by the coupling of a radiatively inefficient accretion flow and a jet. Recently, however, a growing number of sources show more complicated radio/X-ray correlations, e.g., $L_{\rm R} \propto L_{\rm X}^{\sim 1.4}$ for $L_{\rm X}/L_{\rm Edd} \gtrsim 10^{-3}$, which is suggested to be explained by the coupling of a radiatively efficient accretion flow and a jet. In this work, we interpret the deviation from the initial radio/X-ray correlation for $L_{\rm X}/L_{\rm Edd} \gtrsim 10^{-3}$ with a detailed disc corona-jet model. In this model, the disc and corona are radiatively and dynamically coupled. Assuming a fraction of the matter in the accretion flow, $\eta\equiv \dot M_{\rm jet}/\dot M$, is ejected to form the jet, we can calculate the emergent spectrum of the disc corona-jet system. We calculate $L_{\rm R}$ and $L_{\rm X}$ at different $\dot M$, adjusting $\eta$ to fit the observed radio/X-ray correlation of the black hole X-ray transient H1743-322 for $L_{\rm X}/L_{\rm Edd}> 10^{-3}$. It is found that always the X-ray emission is dominated by the disc corona and the radio emission is dominated by the jet. We noted that the value of $\eta$ for the deviated radio/X-ray correlation for $L_{\rm X}/L_{\rm Edd} > 10^{-3}$, is systematically less than that of the case for $L_{\rm X}/L_{\rm Edd} < 10^{-3}$, which is consistent with the general idea that the jet is often relatively suppressed at the high luminosity phase in black hole X-ray binaries.

### Optical Flickering of the recurrent nova RS Ophiuchi: amplitude - flux relation

We report observations of the flickering variability of the symbiotic recurrent nova RS Oph at quiescence in five bands (UBVRI). We find evidence of correlation between the peak-to-peak flickering amplitude (\Delta F) and the average flux of the hot component ($F_{av}$). The correlation is highly significant with correlation coefficient 0.85 and p-value $\sim 10^{-15}$. Combining the data from all wavebands, we find a dependence of the type $\Delta F \propto F_{av}^k$, with power-law index $k = 1.02 \pm 0.04$ for the UBVRI flickering of RS Oph. Thus, the rms amplitude of variability scale almost linearly with the average flux of the hot component, $< \sigma_{rms} / F_{av} > = 0.08 \pm 0.02$. The detected correlation is similar to that found in some X-ray binaries. The possible reasons are briefly discussed. The data are available upon request from the authors.

### The $E_{\rm p}$ - $E_{\rm iso}$ relation and the internal shock model

The validity of the $E_{\rm p}$ – $E_{\rm iso}$ correlation in gamma-ray bursts and the possibility of explaining the prompt emission with internal shocks are highly debated questions. We study whether the $E_{\rm p}$ – $E_{\rm iso}$ correlation can be reproduced if internal shocks are indeed responsible for the prompt emission, or conversely, if the correlation can be used to constrain the internal shock scenario. We developed a toy model where internal shocks are limited to the collision of only two shells. Synthetic burst populations were constructed for various distributions of the model parameters, such as the injected power in the relativistic outflow, the average Lorentz factor, and its typical contrast between the shells. These parameters can be independent or linked by various relations. Synthetic $E_{\rm p}$ – $E_{\rm iso}$ diagrams are obtained in the different cases and compared with the observed correlation. The reference observed correlation is the one defined by the BAT6 sample, a sample of Swift bursts almost complete in redshift and affected by well-known and reproducible instrumental selection effects. The comparison is then performed with a subsample of synthetic bursts that satisfy the same selection criteria as were imposed on the BAT6 sample. A satisfactory agreement between model and data can often be achieved, but only if several strong constraints are satisfied on both the dynamics of the flow and the microphysics that governs the redistribution of the shock-dissipated energy.

### On The Relation Between the AGN Jet and Accretion Disk Emissions

Active galactic nuclei jets are detected via their radio and/or gamma-ray emissions while the accretion disks are detected by their optical and UV radiation. Observations of the radio and optical luminosities show a strong correlation between the two luminosities. However, part of this correlation is due to the redshift or distances of the sources that enter in calculating the luminosities from the observed fluxes and part of it could be due to the differences in the cosmological evolution of luminosities. Thus, the determination of the intrinsic correlations between the luminosities is not straightforward. It is affected by the observational selection effects and other factors that truncate the data, sometimes in a complex manner (e.g. Antonucci (2011) and Pavildou et al. (2010)). In this paper we describe methods that allow us to determine the evolution of the radio and optical luminosities, and determine the true intrinsic correlation between the two luminosities. We find a much weaker correlation than observed and sub-linear relations between the luminosities. This has a significant implication for jet and accretion disk physics.

### Selection effects in Gamma Ray Bursts correlations: consequences on the ratio between GRB and star formation rates [Replacement]

Gamma Ray Bursts (GRBs) visible up to very high redshift have become attractive targets as potential new distance indicators. It is still not clear whether the relations proposed so far originate from an unknown GRB physics or result from selection effects. We investigate this issue in the case of the $L_X-T^*_a$ correlation (hereafter LT) between the X-ray luminosity $L_X (T_a)$ at the end of the plateau phase, $T_a$, and the rest frame time $T^{*}_a$. We devise a general method to build mock data sets starting from a GRB world model and taking into account selection effects on both time and luminosity. This method shows how not knowing the efficiency function could influence the evaluation of the intrinsic slope of any correlation and the GRB density rate. We investigate biases (small offsets in slope or normalization) that would occur in the LT relation as a result of truncations, possibly present in the intrinsic distributions of $L_X$ and $T^*_a$. We compare these results with the ones in Dainotti et al. (2013) showing that in both cases the intrinsic slope of the LT correlation is $\approx -1.0$. This method is general, therefore relevant to investigate if any other GRB correlation is generated by the biases themselves. Moreover, because the farthest GRBs and star-forming galaxies probe the reionization epoch, we evaluate the redshift-dependent ratio $\Psi(z)=(1+z)^{\alpha}$ of the GRB rate to star formation rate (SFR). We found a modest evolution $-0.2\leq \alpha \leq 0.5$ consistent with Swift GRB afterglow plateau in the redshift range $0.99<z<9.4$.

### Selection effects in Gamma Ray Bursts correlations: consequences on the ratio between GRB and star formation rates [Replacement]

Gamma Ray Bursts (GRBs) visible up to very high redshift have become attractive targets as potential new distance indicators. It is still not clear whether the relations proposed so far originate from an unknown GRB physics or result from selection effects. We investigate this issue in the case of the $L_X-T^*_a$ correlation (hereafter LT) between the X-ray luminosity $L_X (T_a)$ at the end of the plateau phase, $T_a$, and the rest frame time $T^{*}_a$. We devise a general method to build mock data sets starting from a GRB world model and taking into account selection effects on both time and luminosity. This method shows how not knowing the efficiency function could influence the evaluation of the intrinsic slope of any correlation and the GRB density rate. We investigate biases (small offsets in slope or normalization) that would occur in the LT relation as a result of truncations, possibly present in the intrinsic distributions of $L_X$ and $T^*_a$. We compare these results with the ones in Dainotti et al. (2013) showing that in both cases the intrinsic slope of the LT correlation is $\approx -1.0$. This method is general, therefore relevant to investigate if any other GRB correlation is generated by the biases themselves. Moreover, because the farthest GRBs and star-forming galaxies probe the reionization epoch, we evaluate the redshift-dependent ratio $\Psi(z)=(1+z)^{\alpha}$ of the GRB rate to star formation rate (SFR). We found a modest evolution $-0.2\leq \alpha \leq 0.5$ consistent with Swift GRB afterglow plateau in the redshift range $0.99<z<9.4$.

### Selection effects in Gamma Ray Bursts correlations: consequences on the ratio between GRB and star formation rates

Gamma Ray Bursts (GRBs) visible up to very high redshift have become attractive targets as potential new distance indicators. It is still not clear whether the relations proposed so far originate from an unknown GRB physics or result from selection effects. We investigate this issue in the case of the $L_X-T^*_a$ correlation (hereafter LT) between the X-ray luminosity $L_X (T_a)$ at the end of the plateau phase, $T_a$, and the rest frame time $T^{*}_a$. We devise a general method to build mock data sets starting from a GRB world model and taking into account selection effects on both time and luminosity. This method shows how not knowing the efficiency function could influence the evaluation of the intrinsic slope of any correlation and the GRB density rate. We investigate biases (small offsets in slope or normalization) that would occur in the LT relation as a result of truncations, possibly present in the intrinsic distributions of $L_X$ and $T^*_a$. We compare these results with the ones in Dainotti et al. (2013) showing that in both cases the intrinsic slope of the LT correlation is $\approx -1.0$. This method is general, therefore relevant to investigate if any other GRB correlation is generated by the biases themselves. Moreover, because the farthest GRBs and star-forming galaxies probe the reionization epoch, we evaluate the redshift-dependent ratio $\Psi(z)=(1+z)^{\alpha}$ of the GRB rate to star formation rate (SFR). We found a modest evolution $-0.2\leq \alpha \leq 0.5$ consistent with Swift GRB afterglow plateau in the redshift range $0.99<z<9.4$.

### Selection effects in Gamma Ray Bursts correlations: consequences on the ratio between GRB and star formation rates [Replacement]

Gamma Ray Bursts (GRBs) visible up to very high redshift have become attractive targets as potential new distance indicators. It is still not clear whether the relations proposed so far originate from an unknown GRB physics or result from selection effects. We investigate this issue in the case of the $L_X-T^*_a$ correlation (hereafter LT) between the X-ray luminosity $L_X (T_a)$ at the end of the plateau phase, $T_a$, and the rest frame time $T^{*}_a$. We devise a general method to build mock data sets starting from a GRB world model and taking into account selection effects on both time and luminosity. This method shows how not knowing the efficiency function could influence the evaluation of the intrinsic slope of any correlation and the GRB density rate. We investigate biases (small offsets in slope or normalization) that would occur in the LT relation as a result of truncations, possibly present in the intrinsic distributions of $L_X$ and $T^*_a$. We compare these results with the ones in Dainotti et al. (2013) showing that in both cases the intrinsic slope of the LT correlation is $\approx -1.0$. This method is general, therefore relevant to investigate if any other GRB correlation is generated by the biases themselves. Moreover, because the farthest GRBs and star-forming galaxies probe the reionization epoch, we evaluate the redshift-dependent ratio $\Psi(z)=(1+z)^{\alpha}$ of the GRB rate to star formation rate (SFR). We found a modest evolution $-0.2\leq \alpha \leq 0.5$ consistent with Swift GRB afterglow plateau in the redshift range $0.99<z<9.4$.

### Correlation between the photon index and X-ray luminosity of black hole X-ray binaries and active galactic nuclei: observations and interpretation

We investigate the observed correlation between the 2–10 keV X-ray luminosity (in unit of the Eddington luminosity; $l_X \equiv L_X/L_{Edd}$) and the photon index ($\Gamma$) of the X-ray spectrum for both black hole X-ray binaries (BHBs) and active galactic nuclei (AGNs). We construct a large sample, with $10^{-9} < l_X < 10^{-1}$. We find that $\Gamma$ is positively and negatively correlated with $l_X$ when $l_X > 10^{-3}$ and $10^{-6.5} < l_X < 10^{-3}$ respectively, while $\Gamma$ is nearly a constant when $l_X < 10^{-6.5}$. We explain the above correlation in the framework of a coupled hot accretion flow — jet model. The radio emission always come from the jet while the X-ray emission comes from the accretion flow and jet when $l_X$ is above and below $10^{-6.5}$, respectively. More specifically, we assume that with the increase of mass accretion rate, the hot accretion flow develops into a clumpy and further a disc — corona two-phase structure because of thermal instability. We argue that such kind of two-phase accretion flow can explain the observed positive correlation.

### n-partite information in Hawking radiation [Cross-Listing]

We study the entanglement among sequential Hawking radiations in the Parikh-Wilczek tunneling model of Schwarzschild black hole. We identify the part of classical correlation and that of quantum entanglement in bipartite information and point out its imitated relation to quantum gravity correction. Explicit computation of n-partite information shows that it is positive (negative) for even (odd) $n$, which happens to agree with the holographic computation. The fact that entanglement in the mutual information grows with time mimics the second law of thermodynamics. Later we extend our study to the AdS black hole and find the total mutual information which includes the classical correlation is sensible to the Hawking-Page phase transition.

### n-partite information in Hawking radiation

We study the entanglement among sequential Hawking radiations in the Parikh-Wilczek tunneling model of Schwarzschild black hole. We identify the part of classical correlation and that of quantum entanglement in bipartite information and point out its imitated relation to quantum gravity correction. Explicit computation of n-partite information shows that it is positive (negative) for even (odd) $n$, which happens to agree with the holographic computation. The fact that entanglement in the mutual information grows with time mimics the second law of thermodynamics. Later we extend our study to the AdS black hole and find the total mutual information which includes the classical correlation is sensible to the Hawking-Page phase transition.

### Selection biases in the gamma ray burst E$_{\rm iso}$ -- L$_{\rm opt,X}$ correlation

Gamma ray burst (GRB) optical and X-ray afterglow luminosity is expected to correlate with the GRB isotropic equivalent kinetic energy of the outflow in the standard synchrotron model for GRB afterglows. Previous studies, using prompt GRB isotropic equivalent energy ($E_{\rm iso}$) as a proxy for isotropic equivalent kinetic energy, have generally confirmed a correlation between X-ray and optical afterglow luminosities. Assuming that GRB afterglow luminosity does not evolve strongly with redshift, we identify a strong Malmquist bias in GRB optical and X-ray afterglow luminosity data. We show that selection effects dominate the observed E$_{\rm iso}$ — L$_{\rm opt,X}$ correlations, and have likely been underestimated in other studies. The bias is strongest for a subset of optically faint bursts $m>24$ at 24 hr with $z>2$. After removing this optical selection bias, the E$_{\rm iso}$ — L$_{\rm opt,X}$ correlation for long GRBs is not statistically significant, but combining both long and short GRB luminosity data the correlation is significant. Using the median of the $E_{\rm iso}$ and $L_{\rm opt,X}$ distributions, we apply the synchrotron model assuming the same power law index for short and long GRBs, but different microphysical parameter distributions. Comparing the ratio of optical and X-ray luminosities, we find tentative evidence that the fraction of post-shock energy in magnetic fields, $\epsilon_B$, could be systematically higher in SGRBs compared to LGRBs.

### The power of relativistic jets is larger than the luminosity of their accretion disks

Theoretical models for the production of relativistic jets from active galactic nuclei predict that jet power arises from the spin and mass of the central black hole, as well as the magnetic field near the event horizon. The physical mechanism mechanism underlying the contribution from the magnetic field is the torque exerted on the rotating black hole by the field amplified by the accreting material. If the squared magnetic field is proportional to the accretion rate, then there will be a correlation between jet power and accretion luminosity. There is evidence for such a correlation, but inadequate knowledge of the accretion luminosity of the limited and inhomogeneous used samples prevented a firm conclusion. Here we report an analysis of archival observations of a sample of blazars (quasars whose jets point towards Earth) that overcomes previous limitations. We find a clear correlation between jet power as measured through the gamma-ray luminosity, and accretion luminosity as measured by the broad emission lines, with the jet power dominating over the disk luminosity, in agreement with numerical simulations. This implies that the magnetic field threading the black hole horizon reaches the maximum value sustainable by the accreting matter.

### Positive metallicity correlation for coreless giant planets

Frequency of detected giant planets is observed to increase rapidly with metallicity of the host star. This is usually interpreted as evidence in support of the Core Accretion (CA) theory, which assembles giant planets as a result of formation of a massive solid core. A strong positive planet-metallicity correlation for giant planets formed in the framework of Gravitational disc Instability (GI) model is found here. The key novelty of this work is "pebble accretion" onto GI fragments which has been recently demonstrated to accelerate contraction of GI fragments. Driven closer to the star by the inward migration, only the fragments that accrete metals rapidly enough collapse and survive the otherwise imminent tidal disruption. The survival fraction of simulated planets correlates strongly with the metallicity of the host star, as observed.

### Revisiting the correlation between stellar activity and planetary surface gravity

Aims: We re-evaluate the correlation between planetary surface gravity and stellar host activity as measured by the index log($R’_{HK}$). This correlation, previously identified by Hartman (2010), is now analyzed in light of an extended measurements dataset, roughly 3 times larger than the original one. Methods: We calculated the Spearman’s rank correlation coefficient between the two quantities and its associated p-value. The correlation coefficient was calculated for both the full dataset and the star-planet pairs that follow the conditions proposed by Hartman (2010). In order to do so, we considered effective temperatures both as collected from the literature and from the SWEET-Cat catalog, which provides a more homogeneous and accurate effective temperature determination. Results: The analysis delivers significant correlation coefficients, but with a lower value than those obtained by Hartman (2010). Yet, the two datasets are compatible, and we show that a correlation coefficient as large as previously published can arise naturally from a small-number statistics analysis of the current dataset. The correlation is recovered for star-planet pairs selected using the different conditions proposed by Hartman (2010). Remarkably, the usage of SWEET-Cat temperatures leads to larger correlation coefficient values. We highlight and discuss the role of the correlation betwen different parameters such as effective temperature and activity index. Several additional effects on top of those discussed previously were considered, but none fully explains the detected correlation. In light of the complex issue discussed here, we encourage the different follow-up teams to publish their activity index values in the form of log($R’_{HK}$) index so that a comparison across stars and instruments can be pursued.

### Fluctuation dynamo at finite correlation times using renewing flows

Fluctuation dynamos are generic to turbulent astrophysical systems. The only analytical model of the fluctuation dynamo, due to Kazantsev, assumes the velocity to be delta-correlated in time. This assumption breaks down for any realistic turbulent flow. We generalize the analytic model of fluctuation dynamo to include the effects of a finite correlation time, $\tau$, using renewing flows. The generalized evolution equation for the longitudinal correlation function $M_L$ leads to the standard Kazantsev equation in the $\tau \to 0$ limit, and extends it to the next order in $\tau$. We find that this evolution equation involves also third and fourth spatial derivatives of $M_L$, indicating that the evolution for finite $\tau$ will be non-local in general. In the perturbative case of small-$\tau$ (or small Strouhl number), it can be recast using the Landau-Lifschitz approach, to one with at most second derivatives of $M_L$. Using both a scaling solution and the WKBJ approximation, we show that the dynamo growth rate is reduced when the correlation time is finite. Interestingly, to leading order in $\tau$, we show that the magnetic power spectrum, preserves the Kazantsev form, $M(k) \propto k^{3/2}$, in the large $k$ limit, independent of $\tau$.

### Initial fluctuations and correlation of finite distributions of secondary particles in interaction of heavy ions with photoemulsion nuclei [Cross-Listing]

The study of the peculiarities of the distribution of secondary particles depending on the degree centrality and the degree of asymmetry of the interacting nuclei, is performed. The number of multicharged fragments of the projectile nucleus $N_f$ in interactions sharply asymmetric nuclei depends on the centrality degree of interaction. At that, the events with $N_f$ =1 are separated clearly in the distribution of the total charge of the fragments of a projectile nucleus $Q$ depending on the nature of the correlation of the number of fragments of the target nucleus and the multiplicity of secondary particles.

### Possible signature of distant foreground in the Planck data

By using the Planck map of the cosmic microwave background (CMB) radiation we have checked and confirmed the existence of a correlation between supernova (SN) redshifts, $z_{\rm SN}$, and CMB temperature fluctuations at the SNe locations, $T_{\rm SN}$, which we previously reported for the Wilkinson Microwave Anisotropy Probe data. The Pearson correlation coefficient for the Planck data is $r=+0.38\pm 0.08$ which indicates that the correlation is statistically significant (the signal is about $5\sigma$ above the noise level). The correlation becomes even stronger for the type Ia subsample of SNe, $r_{\rm Ia}=+0.45\pm 0.09$, whereas for the rest of the SNe it is vanishing. By checking the slopes of the regression lines $T_{\rm SN} / z_{\rm SN}$ for Planck’s different frequency bands we have also excluded the possibility of this anomaly being caused by the Sunyaev-Zeldovich effect. The remaining possibility is some, unaccounted for, contribution to the CMB from distant ($z>0.3$) foreground through either the integrated Sachs-Wolfe effect or thermal emission from intergalactic matter.

### A comprehensive X-ray and multiwavelength study of the Colliding Galaxy Pair NGC2207/IC2163

We present a comprehensive study of the total X-ray emission from the colliding galaxy pair NGC2207/IC2163, based on Chandra, Spitzer, and GALEX data. We repeat our correlation study between the local SFR and the number and luminosity of ULXs with improved significance, due to a fivefold increase in Chandra exposure. Thanks to ULX variability we now detect 28 ULXs, 7 of which were not visible previously. We confirm that global relations between N(ULXs), L(ULXs) and the integrated SFR of the host galaxy also hold on local scales. We investigate the long-term flux and spectral variability of the ULX population: 12 sources show significant long-term variability, 7 of these are transient candidates. No spectral changes are correlated with flux variability. The average XLF of NGC2207/IC2163 is consistent with that typical for HMXBs and appears unaffected by variability. We study the possible correlation of dust extinction with the bright XRB population on sub-galactic scales using the same technique as that applied to the correlation with SFR. We find that the distributions of Nx and Lx are peaked at L(IR)/L(NUV)~1, and speculate that this is an effect of the different star formation timescales traced by the IR and NUV, associating the observed peak with an age of ~10Myr for the underlying stellar population. We disentangle and compare the X-ray spectrum of the hot ISM with that of the of the bright XRBs. We find that the hot ISM has a temperature kT~0.28keV and dominates the overall X-ray output at E<1keV, while unresolved accreting compact objects dominate the diffuse X-ray emission at E>1keV. The intrinsic 0.5-2keV luminosity of the thermal plasma is 7.9e+40erg/s, a factor of ~2 larger than the average thermal luminosity produced per unit SFR in local star-forming galaxies. The total X-ray output of NGC2207/IC2163 is 1.5e+41erg/s, and the corresponding total integrated SFR is 23.7 Msol/yr

### Galactic rotation curves, the baryon-to-dark-halo-mass relation and space-time scale invariance

Low-acceleration space-time scale invariant dynamics (SID, Milgrom 2009a) predicts two fundamental correlations known from observational galactic dynamics: the baryonic Tully-Fisher relation (BTFR) and a correlation between the observed mass discrepancy and acceleration (MDA) in the low acceleration regime for disc galaxies. SID corresponds to the deep MOND limit (Milgrom 1983c). The MDA data emerging in cold/warm dark matter (C/WDM) cosmological simulations disagree significantly with the tight MDA correlation of the observed galaxies. Therefore, the most modern simulated disc galaxies, which are delicately selected to have a quiet merging history in a standard dark-matter-cosmological model, still do not represent the correct rotation curves. Also, the observed tight correlation contradicts the postulated stochastic formation of galaxies in low-mass DM halos. Moreover, we find that SID predicts a baryonic to apparent virial halo (dark matter) mass relation which agrees well with the correlation deduced observationally assuming Newtonian dynamics to be valid, while the baryonic to halo mass relation predicted from CDM models does not. The distribution of the observed ratios of dark-matter halo masses to baryonic masses may be empirical evidence for the external field effect, which is predicted in SID as a consequence of the forces acting between two galaxies depending on the position and mass of a third galaxy. Applying the external field effect, we predict the masses of galaxies in the proximity of the dwarf galaxies in the Miller et al. (2014) sample. Classical non-relativistic gravitational dynamics is thus best described as being Milgromian, rather than Newtonian.

### Galactic rotation curves, the baryon-to-dark-halo-mass relation and space-time scale invariance [Replacement]

Low-acceleration space-time scale invariant dynamics (SID, Milgrom 2009a) predicts two fundamental correlations known from observational galactic dynamics: the baryonic Tully-Fisher relation (BTFR) and a correlation between the observed mass discrepancy and acceleration (MDA) in the low acceleration regime for disc galaxies. SID corresponds to the deep MOdified Newtonian Dynamics (MOND) limit. The MDA data emerging in cold/warm dark matter (C/WDM) cosmological simulations disagree significantly with the tight MDA correlation of the observed galaxies. Therefore, the most modern simulated disc galaxies, which are delicately selected to have a quiet merging history in a standard dark-matter-cosmological model, still do not represent the correct rotation curves. Also, the observed tight correlation contradicts the postulated stochastic formation of galaxies in low-mass DM halos. Moreover, we find that SID predicts a baryonic to apparent virial halo (dark matter) mass relation which agrees well with the correlation deduced observationally assuming Newtonian dynamics to be valid, while the baryonic to halo mass relation predicted from CDM models does not. The distribution of the observed ratios of dark-matter halo masses to baryonic masses may be empirical evidence for the external field effect, which is predicted in SID as a consequence of the forces acting between two galaxies depending on the position and mass of a third galaxy. Applying the external field effect, we predict the masses of galaxies in the proximity of the dwarf galaxies in the Miller et al. sample. Classical non-relativistic gravitational dynamics is thus best described as being Milgromian, rather than Newtonian.

### Quark spin-orbit correlations

The proton spin puzzle issue focused the attention on the parton spin and orbital angular momentum contributions to the proton spin. However, a complete characterization of the proton spin structure requires also the knowledge of the parton spin-orbit correlation. We showed that this quantity can be expressed in terms of moments of measurable parton distributions. Using the available phenomenological information about the valence quarks, we concluded that this correlation is negative, meaning that the valence quark spin and kinetic orbital angular momentum are, in average, opposite. The quark spin-orbit correlation can also be expressed more intuitively in terms of relativistic phase-space distributions, which can be seen as the mother distributions of the standard generalized and transverse-momentum dependent parton distributions. We present here for the first time some examples of the general multipole decomposition of these phase-space distributions.

### Estimation of the Extragalactic Background Light using TeV Observations of BL~Lacs

The very high energy (VHE) gamma ray spectral index of high energy peaked blazars correlates strongly with its corresponding redshift whereas no such correlation is observed in the X-ray or the GeV bands. We attribute this correlation to a result of photon-photon absorption of TeV photons with the extragalactic background light (EBL) and utilizing this, we compute the allowed flux range for the EBL, which is independent of previous estimates. The observed VHE spectrum of the sources in our sample can be well approximated by a power-law, and if the de-absorbed spectrum is also assumed to be a power law, then we show that the spectral shape of EBL will be $\epsilon n(\epsilon) \sim k log(\frac{\epsilon}{\epsilon_p})$. We estimate the range of values for the parameters defining the EBL spectrum, $k$ and $\epsilon_p$, such that the correlation of the intrinsic VHE spectrum with redshift is nullified. The estimated EBL depends only on the observed correlation and the assumption of a power law source spectrum. Specifically, it does not depend on the spectral modeling or radiative mechanism of the sources, nor does it depend on any theoretical shape of the EBL spectrum obtained through cosmological calculations. The estimated EBL spectrum is consistent with the upper and lower limits imposed by different observations. Moreover, it also agrees closely with the theoretical estimates obtained through cosmological evolution models.

### Correlation between the phase and the log-amplitude of a wave through the vertical atmospheric propagation

I present expressions of the correlation between the log-amplitude and the phase of a wavefront propagating through the atmospheric turbulence. The properties of the angular correlation functions are discussed using usual synthetic turbulence profiles. The theoretical study is completed by practical implementations that can be envisioned to determine and eventually compensate the effects of the fluctuations of the intensity during the astronomical observations. The close formulation between the phase and the log-amplitude allows an analytic formulation in the Rytov approximation. Equations contain the product of an arbitrary number of hypergeometric functions that are evaluated using the Mellin transforms integration method.

### Correlation between the phase and the log-amplitude of a wave through the vertical atmospheric propagation [Replacement]

Expressions of the correlation between the log-amplitude and the phase of a wavefront propagating through the atmospheric turbulence are presented. These expressions are useful to evaluate the feasibility of proposed methods to increase the confidence level of the detection of faint transient astronomical objects. The properties of the derived angular correlation functions are discussed using usual synthetic turbulence profiles. The close formulation between the phase and the log-amplitude allows an analytic formulation in the Rytov approximation. Equations contain the product of an arbitrary number of hypergeometric functions that are evaluated using the Mellin transforms integration method.

### Correlation between the phase and the log-amplitude of a wave through the vertical atmospheric propagation [Replacement]

Expressions of the correlation between the log-amplitude and the phase of a wavefront propagating through the atmospheric turbulence are presented. These expressions are useful to evaluate the feasibility of proposed methods to increase the confidence level of the detection of faint transient astronomical objects. The properties of the derived angular correlation functions are discussed using usual synthetic turbulence profiles. The close formulation between the phase and the log-amplitude allows an analytic formulation in the Rytov approximation. Equations contain the product of an arbitrary number of hypergeometric functions that are evaluated using the Mellin transforms integration method.

### Inflationary tensor fossils in large-scale structure

Inflation models make specific predictions for a tensor-scalar-scalar three-point correlation, or bispectrum, between one gravitational-wave (tensor) mode and two density-perturbation (scalar) modes. This tensor-scalar-scalar correlation leads to a local power quadrupole, an apparent departure from statistical isotropy in our Universe, as well as characteristic four-point correlations in the current mass distribution in the Universe. So far, the predictions for these observables have been worked out only for single-clock models in which certain consistency conditions between the tensor-scalar-scalar correlation and tensor and scalar power spectra are satisfied. Here we review the requirements on inflation models for these consistency conditions to be satisfied. We then consider several examples of inflation models, such as non-attractor and solid inflation models, in which these conditions are put to the test. In solid inflation the simplest consistency conditions are already violated whilst in the non-attractor model we find that, contrary to the standard scenario, the tensor-scalar-scalar correlator probes directly relevant model-dependent information. We work out the predictions for observables in these models. For non-attractor inflation we find an apparent local quadrupolar departure from statistical isotropy in large-scale structure but that this power quadrupole decreases very rapidly at smaller scales. The consistency of the CMB quadrupole with statistical isotropy then constrains the distance scale that corresponds to the transition from the non-attractor to attractor phase of inflation to be larger than the currently observable horizon. Solid inflation predicts clustering fossils signatures in the current galaxy distribution that may be large enough to be detectable with forthcoming, and possibly even current, galaxy surveys.

### Inflationary tensor fossils in large-scale structure [Cross-Listing]

Inflation models make specific predictions for a tensor-scalar-scalar three-point correlation, or bispectrum, between one gravitational-wave (tensor) mode and two density-perturbation (scalar) modes. This tensor-scalar-scalar correlation leads to a local power quadrupole, an apparent departure from statistical isotropy in our Universe, as well as characteristic four-point correlations in the current mass distribution in the Universe. So far, the predictions for these observables have been worked out only for single-clock models in which certain consistency conditions between the tensor-scalar-scalar correlation and tensor and scalar power spectra are satisfied. Here we review the requirements on inflation models for these consistency conditions to be satisfied. We then consider several examples of inflation models, such as non-attractor and solid inflation models, in which these conditions are put to the test. In solid inflation the simplest consistency conditions are already violated whilst in the non-attractor model we find that, contrary to the standard scenario, the tensor-scalar-scalar correlator probes directly relevant model-dependent information. We work out the predictions for observables in these models. For non-attractor inflation we find an apparent local quadrupolar departure from statistical isotropy in large-scale structure but that this power quadrupole decreases very rapidly at smaller scales. The consistency of the CMB quadrupole with statistical isotropy then constrains the distance scale that corresponds to the transition from the non-attractor to attractor phase of inflation to be larger than the currently observable horizon. Solid inflation predicts clustering fossils signatures in the current galaxy distribution that may be large enough to be detectable with forthcoming, and possibly even current, galaxy surveys.


text:
1

### AIPMT 2003

Which one of the following statements is not correct for sigma- and pi- bonds formed between two carbon atoms?
A
sigma-bond is stronger than a pi-bond.
B
Bond energies of sigma- and pi-bonds are of the order of 264 kJ/mol and 347 kJ/mol, respectively
C
Free rotation of atoms about a sigma-bond is allowed but not in case of a pi-bond.
D
Sigma-bond determines the direction between carbon atoms but a pi-bond has no primary effect in this regard.

## Explanation

As sigma bond is stronger than the $\pi$(pi) bond, so it must be having higher bond energy than $\pi$(pi) bond.
2

### AIPMT 2002

Which of the following is isoelectronic?
A
CO2, NO2
B
NO2$-$, CO2
C
CN$-$, CO
D
SO2, CO2

## Explanation

In CO, the number of electrons

$\Rightarrow$ 6 + 8 = 14 [ Z of C = 6 and O = 8]

Electronic configuration of molecular orbital of CO :

${\left( {\sigma 1s} \right)^2}{\left( {{\sigma ^*}1s} \right)^2}{\left( {\sigma 2s} \right)^2}{\left( {{\sigma ^*}2s} \right)^2}{\left( {\pi 2{p_x}} \right)^2}{\left( {\pi 2{p_y}} \right)^2}{\left( {\pi 2{p_z}} \right)^2}$

CN- also get (6 + 7 + 1) 14 electrons and the configuration is similar to that CO.

So, CN and CO is isoelectronic.
3

### AIPMT 2002

In NO3$-$ ion number of bond pair and lone pair of electrons on nitrogen atom are
A
2, 2
B
3, 1
C
1, 3
D
4, 0

## Explanation

${O^ - }\hbox{---}\mathop N\limits^{\mathop \uparrow \limits^O } = O$

In NO3- ion, nitrogen has 4 bond pair of electrons and no lone pair of electrons.
4

### AIPMT 2002

Which of the following has p$\pi$ $-$ d$\pi$ bonding?
A
NO3$-$
B
SO32$-$
C
BO33$-$
D
CO32$-$

## Explanation

Electronic structure of S atom in excited state

In 'S' unhybride d- orbital is present, which will involved in bond formation with oxygen atom.

In oxygen two unpaired p- orbital is present in these one is involved in $\sigma$ bond formation while other is used in $\pi$ bond formation.

So, in SO32$-$, p$\pi$ $-$ d$\pi$ bonding present.

format: plain


text:
0

What is the indefinite integral?

Wiki User

2011-02-07 06:13:09

An indefinite integral is a version of an integral that, unlike a definite integral, returns an expression instead of a number.

The general form of a definite integral is:

∫ba f(x) dx.

The general form of an indefinite integral is:

∫ f(x) dx.

An example of a definite integral is:

∫20 x2 dx.

An example of an indefinite integral is:

∫ x2 dx

In the definite case, the answer is 23/3 - 03/3 = 8/3.

In the indefinite case, the answer is x3/3 + C, where C is an arbitrary constant.

Wiki User

2011-02-07 06:13:09
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A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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Q: What is the indefinite integral?


text:
# GPA prediction of college student

I have a dataset consist of 8 columns and 15600 rows with the following columns:-

1.Entry_academic_year which have 5 discrete value (2558,2559,2560,2561,2562)

2.Faculty (It is the faculty that student has taken like engineering)

3.branch (It is the branch that student has taken like software engineering)

4.Admission type (how the student enter the college)

6.province_of_school

7.GPA_high_school(It is the GPA of student in high school)

8.GPA_college(It is the GPA of the student during college)

I am trying to predict the GPA of the student at the college by dividing the GPA into 4 quartiles with respect to percentile (25,50,75), The problem I faced is that the Graduated_high_school columns have around 1732 unique value with some school contain only one row which makes the prediction around 30-35 % accuracy

Any idea on how to fix it?

Perhaps you can see if Graduated_high_school is correlated in any way to GPA_college? If there is no correlation, you can try to fit a model by dropping the Graduated_high_school column.
Else, you can try to drop rows belonging to under-represented high schools. However, one problem I foresee is that future predictions might have Graduated_high_school that are unseen in the training dataset, leading to problems (e.g. schools that weren't mentioned in the dataset, or if someone decides to use your model, on a dataset from another country). So, if the Graduated_high_school is not important, I would consider dropping it altogether.
Or, maybe you can change Graduated_high_school to something else that is related, such as number of teachers in high school, teacher-student ratio etc.


text:
# MATEMATIK 4 KOMPLEKS FUNKTIONSTEORI MM 1.2

## Presentation on theme: "MATEMATIK 4 KOMPLEKS FUNKTIONSTEORI MM 1.2"— Presentation transcript:

MATEMATIK 4 KOMPLEKS FUNKTIONSTEORI MM 1.2
MM 1.1: Singulariteter og residuer Emner: Singulære punkter og nulpunkter Hævelig singularitet, pol, væsentlig singularitet Isoleret singularitet Residuer Regler til bestemmelse af et residuum i en pol

What should we learn today?
How to classify singular points and zeros of a function and how singularities affect behavior of a function What is a residue? How with the help of residue to calculate complex integrals? Formulas for residues in case singularities are poles

Singularities and Zeros
Definition. Funktion f(z) is singular (has a singularity) at a point z0 if f(z) is not analytic at z0, but every neighbourhood of z0 contains points at which f(z) is analytic. Definition. z0 is an isolated singularity if there exists a neighbourhood of z0 without further singularities of f(z). Example: tan z and tan(1/z)

Classification of isolated singularities
Removable singularity. All bn =0. The function can be made analytic in z0 by assigning it a value Example f(z)=sin(z)/z, z0 =0. Pole of m-th order. Only finitely many terms; all bn =0, n>m. Example 1: pole of the second order. Remark: The first order pole = simple pole. Essential singularity. Infinetely many terms. Example 2.

Classification of isolated singularities
The classification of singularotoes is not just a formal matter The behavior of an analytic function in a neighborhood of an essential singularity and a pole is different.

Removable singularity
Theorem. If an analytical function f(z) is bounded within a circle with some radius R (but without the center z0), then z0 is a removable singularity.

Pole Theorem. If f(z) goes to infinity for z  z0 , then f(z) has a pole in z0 .

Essential singularity
Picard’s theorem If f(z) is analytic and has an isolated essential singularity at point z0, it takes on every value, with at most one exeprional value, in an arbitrararily small neighborhood of z0 .

Zeros of analytic function
Definition. A zero has order m, if The zeros of an analytical function are isolated. Poles and zeros: Let f(z) be analytic at z0 and have a zero of m-th order. Then 1/f(z) has a pole of m-th order at z0 .

Analytic or singular at Infinity
We work with extended complex plane and want to investigate the behavior of f(z) at infinity. Idea: study behavior of g(w)=f(1/w)=f(z) in a neighborhood of w=0. If g(w) has a pole at 0, the same has f(z) at infinity etc

Typeopgave Typical problem: Determine the location and kind of singularities and zeros in the extended complex plane. Examples:

L’hospital rule

Residue Integration Method
We are interested in evaluation of integrals taken around a simple closed path C If f(z) is analytic  =0 by Cauchy’s integral theorem If f(z) has a singularity at z0 : Consider Laurent series that converges in a domain

Residue Integration Method
The coefficient b1 is called the residue of f(z) at z0 and it is denoted by

Two formulas for residues at simple poles
For a simple pole Another way to calculate the residue without the need of developing Laurent series:

Formula for the residue at a pole of m-th order

Multiple singularities inside the contour
Theorem Let f(z) be analytic inside a simple closed path C and on C, except for finitely many singular points inside C. Then the integral of f(z) taken counterclockwise around C equals


text:
# Commodification of accelerations for the Karp and Miller Construction.

4 MEXICO - Modeling and Exploitation of Interaction and Concurrency
Inria Saclay - Ile de France, LMF - Laboratoire Méthodes Formelles
Abstract : Karp and Miller's algorithm is based on an exploration of the reachability tree of a Petri net where, the sequences of transitions with positive incidence are accelerated. The tree nodes of Karp and Miller are labeled with omega-markings representing (potentially infinite) coverability sets. This set of omega-markings allows us to decide several properties of the Petri net, such as whether a marking is coverable or whether the reachability set is finite. The edges of the Karp and Miller tree are labeled by transitions but the associated semantic is unclear which yields to a complex proof of the algorithm correctness. In this work we introduce three concepts: abstraction, acceleration and exploration sequence. In particular, we generalize the definition of transitions to omega-transitions in order to represent accelerations by such transitions. The notion of abstraction makes it possible to greatly simplify the proof of the correctness. On the other hand, for an additional cost in memory, which we theoretically evaluated, we propose an accelerated" variant of the Karp and Miller algorithm with an expected gain in execution time. Based on a similar idea we have accelerated (and made complete) the minimal coverability graph construction, implemented it in a tool and performed numerous promising benchmarks issued from realistic case studies and from a random generator of Petri nets.
Keywords :
Document type :
Journal articles
Domain :

https://hal.inria.fr/hal-03137054
Contributor : Igor Khmelnitsky Connect in order to contact the contributor
Submitted on : Wednesday, February 10, 2021 - 10:21:00 AM
Last modification on : Friday, January 21, 2022 - 3:11:24 AM
Long-term archiving on: : Tuesday, May 11, 2021 - 6:22:32 PM

### File

JDEDS.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-03137054, version 1

### Citation

Alain Finkel, Serge Haddad, Igor Khmelnitsky. Commodification of accelerations for the Karp and Miller Construction.. Discrete Event Dynamic Systems, Springer Verlag, In press. ⟨hal-03137054⟩

### Metrics

Les métriques sont temporairement indisponibles


text:
×

# Need help with quicksort

I know this is kind of stupid but I was trying to implement quicksort in Python and it runs into an infinite loop can anyone tell me what's wrong??The partition subroutine works perfectly....The error is in quicksort..Here's the code

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  def QuickSort(A,p,r): if p < r: q = Partition(A,p,r) QuickSort(A,0,q) QuickSort(A,q+1,r) def Partition(A, l, r): p = A[l] i = l+1 for j in range(l+1,r): if A[j] < p: A[j],A[i] = A[i],A[j] i += 1 A[l],A[i-1] = A[i-1],A[l] return A.index(p)

3 years ago

Sort by:

 1 2 3 4 5 6 def Quicksort(A,p,r): if p < r: q = Partition(A,p,r) Quicksort(A,p,q-1) #Mistake is here Quicksort(A,q+1,r) return A
I am reasonably sure that this is what would work. @josh silverman, can you confirm? · 3 years ago

to start, your Quicksort doesn't return anything Staff · 3 years ago

Fixed!!Thanks a lot.....It feels so frustrated to do stupid mistakes on a known problem............ · 3 years ago

@Thaddeus Abiy @Ammar Fathin Sabili @Trevor B. Please help!!CS is one of the subjects that I study the most but failing such a trivial and known question today is driving me mad! · 3 years ago


text:
# Homework 1. Which of two things is larger? (SOLUTIONS)

Due: Thursday, September 19, 11:59 PM

Useful libraries for this assignment

In [8]:
# special IPython command to prepare the notebook for matplotlib
%matplotlib inline

from fnmatch import fnmatch

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import requests
from pattern import web

# set some nicer defaults for matplotlib
from matplotlib import rcParams

#these colors come from colorbrewer2.org. Each is an RGB triplet
dark2_colors = [(0.10588235294117647, 0.6196078431372549, 0.4666666666666667),
(0.8509803921568627, 0.37254901960784315, 0.00784313725490196),
(0.4588235294117647, 0.4392156862745098, 0.7019607843137254),
(0.9058823529411765, 0.1607843137254902, 0.5411764705882353),
(0.4, 0.6509803921568628, 0.11764705882352941),
(0.9019607843137255, 0.6705882352941176, 0.00784313725490196),
(0.6509803921568628, 0.4627450980392157, 0.11372549019607843),
(0.4, 0.4, 0.4)]

rcParams['figure.figsize'] = (10, 6)
rcParams['figure.dpi'] = 150
rcParams['axes.color_cycle'] = dark2_colors
rcParams['lines.linewidth'] = 2
rcParams['axes.grid'] = True
rcParams['axes.facecolor'] = '#eeeeee'
rcParams['font.size'] = 14
rcParams['patch.edgecolor'] = 'none'

## Introduction

This was the XKCD comic after the 2012 Presidential election:

The comic refers to the fact that Nate Silver's statistical model (which is based mostly on combining information from pre-election polls) correctly predicted the outcome of the 2012 presidential race in all 50 states.

Polling data isn't a perfect predictor for the future, and some polls are more accurate than others. This means that election forecastors must consider prediction uncertainty when building models.

In this first assignment, you will perform a simple analysis of polling data about the upcoming Governor races. The assignment has three main parts:

First you will build some tools to download historical polling data from the web, and parse it into a more convenient format.

Next you will use these tools to aggregate and visualize several past Governor races

Finally you will run a bootstrap analysis to estimate the probable outcome of current Governor races, given the level of precision of historical polls.

## Part 1: Collect and Clean

The Real Clear Politics website archives many political polls. In addition, they combine related polls to form an "RCP average" estimate of public opinion over time. For example, the chart on this page shows historical polling data for the Obama-Romney presidential race. The chart is an average of the polling data table below the chart.

The data used to generate plots like this are stored as XML pages, with URLs like:

http://charts.realclearpolitics.com/charts/[id].xml

Here, [id] is a unique integer, found at the end of the URL of the page that displays the graph. The id for the Obama-Romney race is 1171:

http://charts.realclearpolitics.com/charts/1171.xml

Opening this page in Google Chrome or Firefox will show you the XML content in an easy-to-read format. Notice that XML tags are nested inside each other, hierarchically (the jargony term for this is the "Document Object Model", or "DOM"). The first step of webscraping is almost always exploring the HTML/XML source in a browser, and getting a sense of this hierarchy.

#### Problem 0

The above XML page includes 5 distinct tags (one, for example, is chart). List these tags, and depict how they nest inside each other using an indented list. For example:

• Page
• Section
• Paragraph
• Conclusion
• chart
• series
• value
• graphs
• graph
• value

#### Problem 1

We want to download and work with poll data like this. Like most programming tasks, we will break this into many smaller, easier pieces

Fill in the code for the get_poll_xml function, that finds and downloads an XML page discussed above

Hint

requests.get("http://www.google.com").text downloads the text from Google's homepage

In [9]:
"""
Function
--------
get_poll_xml

Given a poll_id, return the XML data as a text string

Inputs
------
poll_id : int
The ID of the poll to fetch

Returns
-------
xml : str
The text of the XML page for that poll_id

Example
-------
>>> get_poll_xml(1044)
u'<?xml version="1.0" encoding="UTF-8"?><chart><series><value xid=\'0\'>1/27/2009</value>
...etc...
"""

def get_poll_xml(poll_id):
url = "http://charts.realclearpolitics.com/charts/%i.xml" % int(poll_id)
return requests.get(url).text

Here are some other functions we'll use later. plot_colors contains hints about parsing XML data.

In [10]:
# "r"egular "e"xpressions is kind of a mini-language to
# do pattern matching on text
import re

def _strip(s):
"""This function removes non-letter characters from a word

for example _strip('Hi there!') == 'Hi there'
"""
return re.sub(r'[\W_]+', '', s)

def plot_colors(xml):
"""
Given an XML document like the link above, returns a python dictionary
that maps a graph title to a graph color.

Both the title and color are parsed from attributes of the <graph> tag:
<graph title="the title", color="#ff0000"> -> {'the title': '#ff0000'}

http://coding.smashingmagazine.com/2012/10/04/the-code-side-of-color/

Example
-------
>>> plot_colors(get_poll_xml(1044))
{u'Approve': u'#000000', u'Disapprove': u'#FF0000'}
"""
dom = web.Element(xml)
result = {}
for graph in dom.by_tag('graph'):
title = _strip(graph.attributes['title'])
result[title] = graph.attributes['color']
return result

#### Problem 2

Even though get_poll_xml pulls data from the web into Python, it does so as a block of text. This still isn't very useful. Use the web module in pattern to parse this text, and extract data into a pandas DataFrame.

Hints

• You might want create python lists for each column in the XML. Then, to turn these lists into a DataFrame, run

pd.DataFrame({'column_label_1': list_1, 'column_label_2':list_2, ...})

• use the pandas function pd.to_datetime to convert strings into dates
In [11]:
"""
Function
---------
rcp_poll_data

Extract poll information from an XML string, and convert to a DataFrame

Parameters
----------
xml : str
A string, containing the XML data from a page like
get_poll_xml(1044)

Returns
-------
A pandas DataFrame with the following columns:
date: The date for each entry
title_n: The data value for the gid=n graph (take the column name from the title tag)

This DataFrame should be sorted by date

Example
-------
Consider the following simple xml page:

<chart>
<series>
<value xid="0">1/27/2009</value>
<value xid="1">1/28/2009</value>
</series>
<graphs>
<graph gid="1" color="#000000" balloon_color="#000000" title="Approve">
<value xid="0">63.3</value>
<value xid="1">63.3</value>
</graph>
<graph gid="2" color="#FF0000" balloon_color="#FF0000" title="Disapprove">
<value xid="0">20.0</value>
<value xid="1">20.0</value>
</graph>
</graphs>
</chart>

Given this string, rcp_poll_data should return
result = pd.DataFrame({'date': pd.to_datetime(['1/27/2009', '1/28/2009']),
'Approve': [63.3, 63.3], 'Disapprove': [20.0, 20.0]})
"""

def rcp_poll_data(xml):
dom = web.Element(xml)
result = {}

dates = dom.by_tag('series')[0]
dates = {n.attributes['xid']: str(n.content) for n in dates.by_tag('value')}

keys = dates.keys()

result['date'] = pd.to_datetime([dates[k] for k in keys])

for graph in dom.by_tag('graph'):
name = graph.attributes['title']
data = {n.attributes['xid']: float(n.content)
if n.content else np.nan for n in graph.by_tag('value')}
result[name] = [data[k] for k in keys]

result = pd.DataFrame(result)
result = result.sort(columns=['date'])

return result

The output from rcp_poll_data is much more useful for analysis. For example, we can plot with it:

In [12]:
def poll_plot(poll_id):
"""
Make a plot of an RCP Poll over time

Parameters
----------
poll_id : int
An RCP poll identifier
"""

# hey, you wrote two of these functions. Thanks for that!
xml = get_poll_xml(poll_id)
data = rcp_poll_data(xml)
colors = plot_colors(xml)

#remove characters like apostrophes
data = data.rename(columns = {c: _strip(c) for c in data.columns})

#normalize poll numbers so they add to 100%
norm = data[colors.keys()].sum(axis=1) / 100
for c in colors.keys():
data[c] /= norm

for label, color in colors.items():
plt.plot(data.date, data[label], color=color, label=label)

plt.xticks(rotation=70)
plt.legend(loc='best')
plt.xlabel("Date")
plt.ylabel("Normalized Poll Percentage")

If you've done everything right so far, the following code should reproduce the graph on this page

In [13]:
poll_plot(1044)
plt.title("Obama Job Approval")

Out[13]:
<matplotlib.text.Text at 0x10661b290>

## Part 2: Aggregate and Visualize

#### Problem 3

Unfortunately, these data don't have any error bars. If a candidate leads by 10% in the RCP average, is she a shoo-in to win? Or is this number too close to call? Does a 10% poll lead mean more 1 day before a race than it does 1 week before? Without error estimates, these questions are impossible to answer.

To get a sense of how accurate the RCP polls are, you will gather data from many previous Governor races, where the outcome is known.

This url has links to many governer races.

http://www.realclearpolitics.com/epolls/2010/governor/2010_elections_governor_map.html

Notice that each link to a governor race has the following URL pattern:

http://www.realclearpolitics.com/epolls/[YEAR]/governor/[STATE]/[TITLE]-[ID].html

Write a function that scans html for links to URLs like this

Hint The fnmatch function is useful for simple string matching tasks.

In [14]:
"""
Function
--------
find_governor_races

Find and return links to RCP races on a page like
http://www.realclearpolitics.com/epolls/2010/governor/2010_elections_governor_map.html

Parameters
----------
html : str
The HTML content of a page to scan

Returns
-------
A list of urls for Governer race pages

Example
-------
For a page like

find_governor_races would return
['http://www.realclearpolitics.com/epolls/2010/governor/ma/massachusetts_governor_baker_vs_patrick_vs_cahill-1154.html',
'http://www.realclearpolitics.com/epolls/2010/governor/ca/california_governor_whitman_vs_brown-1113.html']
"""

def is_gov_race(l):
"""return True if a URL refers to a Governor race"""
pattern = 'http://www.realclearpolitics.com/epolls/????/governor/??/*-*.html'
return fnmatch(l, pattern)

def find_governor_races(html):
dom = web.Element(html)
links = [a.attributes.get('href', '') for a in dom.by_tag('a')]
#eliminate duplicates!

#### Problem 4

At this point, you have functions to find a collection of governor races, download historical polling data from each one, parse them into a numerical DataFrame, and plot this data.

The main question we have about these data are how accurately they predict election outcomes. To answer this question, we need to grab the election outcome data.

Write a function that looks up and returns the election result on a page like this one.

Remember to look at the HTML source!

You can do this by selection view->developer->view source in Chrome, or Tools -> web developer -> page source in Firefox. Altenatively, you can right-click on a part of the page, and select "inspect element"

In [15]:
"""
Function
--------
race_result

Return the actual voting results on a race page

Parameters
----------
url : string
The website to search through

Returns
-------
A dictionary whose keys are candidate names,

If necessary, normalize these numbers so that they add up to 100%.

Example
--------
>>> url = 'http://www.realclearpolitics.com/epolls/2010/governor/ca/california_governor_whitman_vs_brown-1113.html'
>>> race_result(url)
{'Brown': 56.0126582278481, 'Whitman': 43.9873417721519}
"""

def race_result(url):

dom = web.Element(requests.get(url).text)

table = dom.by_tag('div#polling-data-rcp')[0]
result_data = table.by_tag('tr.final')[0]
td = result_data.by_tag('td')

results = [float(t.content) for t in td[3:-1]]
tot = sum(results) / 100

labels = [str(t.content).split('(')[0].strip() for t in headers[3:-1]]

return {l:r / tot for l, r in zip(labels, results)}

Here are some more utility functions that take advantage of what you've done so far.

In [16]:
def id_from_url(url):
"""Given a URL, look up the RCP identifier number"""
return url.split('-')[-1].split('.html')[0]

def plot_race(url):
"""Make a plot summarizing a senate race

Overplots the actual race results as dashed horizontal lines
"""
#hey, thanks again for these functions!
id = id_from_url(url)
xml = get_poll_xml(id)
colors = plot_colors(xml)

if len(colors) == 0:
return

#really, you shouldn't have
result = race_result(url)

poll_plot(id)
plt.xlabel("Date")
plt.ylabel("Polling Percentage")
for r in result:
plt.axhline(result[r], color=colors[_strip(r)], alpha=0.6, ls='--')

Now that this is done, we can easily visualize many historical Governer races. The solid line plots the poll history, the dotted line reports the actual result.

If this code block fails, you probably have a bug in one of your functions.

In [17]:
page = requests.get('http://www.realclearpolitics.com/epolls/2010/governor/2010_elections_governor_map.html').text.encode('ascii', 'ignore')

for race in find_governor_races(page):
plot_race(race)
plt.show()