Regularisation of mixture density networks

Mixture Density Networks are a principled method to model conditional probability density functions which are non-Gaussian. This is achieved by modelling the conditional distribution for each pattern with a Gaussian Mixture Model for which the parameters are generated by a neural network. This thesis presents a novel method to introduce regularisation in this context for the special case where the mean and variance of the spherical Gaussian Kernels in the mixtures are fixed to predetermined values. Guidelines for how these parameters can be initialised are given, and it is shown how to apply the evidence framework to mixture density networks to achieve regularisation. This also provides an objective stopping criteria that can replace the `early stopping' methods that have previously been used. If the neural network used is an RBF network with fixed centres this opens up new opportunities for improved initialisation of the network weights, which are exploited to start training relatively close to the optimum. The new method is demonstrated on two data sets. The first is a simple synthetic data set while the second is a real life data set, namely satellite scatterometer data used to infer the wind speed and wind direction near the ocean surface. For both data sets the regularisation method performs well in comparison with earlier published results. Ideas on how the constraint on the kernels may be relaxed to allow fully adaptable kernels are presented

Regularisation of mixture density networks

Mixture Density Networks are a principled method to model conditional probability density functions which are non-Gaussian. This is achieved by modelling the conditional distribution for each pattern with a Gaussian Mixture Model for which the parameters are generated by a neural network. This thesis presents a novel method to introduce regularisation in this context for the special case where the mean and variance of the spherical Gaussian Kernels in the mixtures are fixed to predetermined values. Guidelines for how these parameters can be initialised are given, and it is shown how to apply the evidence framework to mixture density networks to achieve regularisation. This also provides an objective stopping criteria that can replace the `early stopping' methods that have previously been used. If the neural network used is an RBF network with fixed centres this opens up new opportunities for improved initialisation of the network weights, which are exploited to start training relatively close to the optimum. The new method is demonstrated on two data sets. The first is a simple synthetic data set while the second is a real life data set, namely satellite scatterometer data used to infer the wind speed and wind direction near the ocean surface. For both data sets the regularisation method performs well in comparison with earlier published results. Ideas on how the constraint on the kernels may be relaxed to allow fully adaptable kernels are presented

The Optically Unbiased GRB Host (TOUGH) survey. IV. Lyman-alpha emitters

We report the results of a spectroscopic search for Lyman-alpha emission from gamma-ray burst host galaxies. Based on the well-defined TOUGH sample of 69 X-ray selected Swift GRBs, we have targeted the hosts of a subsample of 20 GRBs known from afterglow spectroscopy to be in the redshift range 1.8-4.5. We detect Lya emission from 7 out of the 20 hosts, with the typical limiting 3sigma line flux being 8E-18 erg/cm2/s, corresponding to a Lya luminosity of 6E41 erg/s at z=3. The Lya luminosities for the 7 hosts in which we detect Lya emission are in the range (0.6-2.3)E42 erg/s corresponding to star-formation rates of 0.6-2.1 Msun/yr (not corrected for extinction). The rest-frame Lya equivalent widths (EWs) for the 7 hosts are in the range 9-40A. For 6 of the 13 hosts for which Lya is not detected we place fairly strong 3sigma upper limits on the EW (<20A), while for others the EW is either unconstrained or has a less constraining upper limit. We find that the distribution of Lya EWs is inconsistent with being drawn from the Lya EW distribution of bright Lyman break galaxies at the 98.3% level, in the sense that the TOUGH hosts on average have larger EWs than bright LBGs. We can exclude an early indication, based on a smaller, heterogeneous sample of pre-Swift GRB hosts, that all GRB hosts are Lya emitters. We find that the TOUGH hosts on average have lower EWs than the pre-Swift GRB hosts, but the two samples are only inconsistent at the 92% level. The velocity centroid of the Lya line is redshifted by 200-700 km/s with respect to the systemic velocity, similar to what is seen for LBGs, possibly indicating star-formation driven outflows from the host galaxies. There seems to be a trend between the Lya EW and the optical to X-ray spectral index of the afterglow (beta_OX), hinting that dust plays a role in the observed strength and even presence of Lya emission. [ABRIDGED]Comment: ApJ accepted (v2: minor changes in the Subject headings and reference list

Swift Identification of Dark Gamma-Ray Bursts

We present an optical flux vs. X-ray flux diagram for all known gamma-ray bursts (GRBs) for which an X-ray afterglow has been detected. We propose an operational definition of dark bursts as those bursts that are optically subluminous with respect to the fireball model, i.e., which have an optical-to-X-ray spectral index beta_OX < 0.5. Out of a sample of 52 GRBs we identify 5 dark bursts. The definition and diagram serve as a simple and quick diagnostic tool for identifying dark GRBs based on limited information, particularly useful for early and objective identification of dark GRBs observed with the Swift satellite.Comment: 4 pages, 1 figure. ApJ Letters, in pres

The galaxies in the field of the nearby GRB980425/SN1998bw

We present spectroscopic observations of ESO 184-G82, the host galaxy of GRB980425/SN1998bw, and six galaxies in its field. A host redshift of z=0.0087+/-0.0006 is derived, consistent with that measured by Tinney et al. (1998). Redshifts are obtained for the six surrounding galaxies observed. Three of these galaxies lie within 11 Mpc of each other, confirming the suggestion that some of these galaxies form a group. However, all of the field galaxies observed lie at significantly greater distances than ESO 184-G82 and are therefore not associated with it. The host galaxy of GRB980425/SN1998bw thus appears to be an isolated dwarf galaxy and interactions with other galaxies do not seem to be responsible for its star formation.Comment: 5 pages, 2 figures, accepted for publication in A&

Gamma-ray burst host galaxies and the link to star-formation

We briefly review the current status of the study of long-duration gamma-ray burst (GRB) host galaxies. GRB host galaxies are mainly interesting to study for two reasons: 1) they may help us understand where and when massive stars were formed throughout cosmic history, and 2) the properties of host galaxies and the localisation within the hosts where GRBs are formed may give essential clues to the precise nature of the progenitors. The main current problem is to understand to what degree GRBs are biased tracers of star formation. If GRBs are only formed by low-metallicity stars, then their host galaxies will not give a representative view of where stars are formed in the Universe (at least not a low redshifts). On the other hand, if there is no dependency on metallicity then the nature of the host galaxies leads to the perhaps surprising conclusion that most stars are formed in dwarf galaxies. In order to resolve this issue and to fully exploit the potential of GRBs as probes of star-forming galaxies throughout the observable universe it is mandatory that a complete sample of bursts with redshifts and host galaxy detections is built.Comment: 9 pages, 3 figures. To appear in the proceedings of the Eleventh Marcel Grossmann Meeting on General Relativity, eds. H. Kleinert, R. T. Jantzen & R. Ruffini, World Scientific, Singapore, 200

The Redshift Distribution of the TOUGH Survey

We present the redshift results from a Very Large Telescope program aimed at optimizing the legacy value of the Swift mission: to characterize a homogeneous, X-ray selected, sample of 69 GRB host galaxies. 19 new redshifts have been secured, resulting in a 83% (57/69) redshift completion, making the survey the most comprehensive in terms of redshift completeness of any sample to the full Swift depth, available to date. We present the cumulative redshift distribution and derive a conservative, yet small, associated uncertainty. We constrain the fraction of Swift GRBs at high redshift to a maximum of 10% (5%) for z > 6 (z > 7). The mean redshift of the host sample is assessed to be > 2.2. Using this more complete sample, we confirm previous findings that the GRB rate at high redshift (z > 3) appears to be in excess of predictions based on assumptions that it should follow conventional determinations of the star formation history of the universe, combined with an estimate of its likely metallicity dependence. This suggests that either star formation at high redshifts has been significantly underestimated, for example due to a dominant contribution from faint, undetected galaxies, or that GRB production is enhanced in the conditions of early star formation, beyond those usually ascribed to lower metallicity.Comment: 7th Huntsville Gamma-Ray Burst Symposium, GRB 2013: paper 34 in eConf Proceedings C130414

On the Distribution of Stellar Masses in Gamma-ray Burst Host Galaxies

We analyze Spitzer images of 30 long-duration gamma-ray burst (GRB) host galaxies. We estimate their total stellar masses (M_*) based on the rest-frame K-band luminosities (L_K_(rest)) and constrain their star formation rates (SFRs; not corrected for dust extinction) based on the rest-frame UV continua. Further, we compute a mean M_*/ L_K_(rest) = 0.45 M_☉/L_☉. We find that the hosts are low M_*, star-forming systems. The median M_* in our sample ( = 10^(9.7) M_☉) is lower than that of "field" galaxies (e.g., Gemini Deep Deep Survey). The range spanned by M_* is 10^7 M_☉ < M_* < 10^(11) M_☉, while the range spanned by the dust-uncorrected UV SFR is 10^(–2) M_☉ yr^(–1) < SFR < 10 M_☉ yr^(–1). There is no evidence for intrinsic evolution in the distribution of M_* with redshift. We show that extinction by dust must be present in at least 25% of the GRB hosts in our sample and suggest that this is a way to reconcile our finding of a relatively lower UV-based, specific SFR (φ ≡ SFR/M_*) with previous claims that GRBs have some of the highest φ values. We also examine the effect that the inability to resolve the star-forming regions in the hosts has on φ

Low frequency radio and X-ray properties of core-collapse supernovae

Radio and X-ray studies of young supernovae probe the interaction between the supernova shock waves and the surrounding medium and give clues to the nature and past of the progenitor star. Here we discuss the early emission from type Ic SN 2002ap and argue that repeated Compton boosting of optical photons by hot electrons presents the most natural explanation of the prompt X-ray emission. We describe the radio spectrum of another type Ic SN 2003dh (GRB030329) obtained with combined GMRT and VLA data. We report on the low frequency radio monitoring of SN 1995N and our objectives of distinguishing between competing models of X-ray emission from this SN and the nature of its progenitor by X-ray spectroscopy. Radio studies on SN 2001gd, SN 2001ig and SN 2002hh are mentioned.Comment: 5 pages, 4 figures. Uses svmult.cls. To appear in proceedings of IAU Colloquium 192 "Supernovae (10 years of SN 1993J)", April 2003, Valencia, Spain, eds. J. M. Marcaide and K. W. Weile

Helium in natal HII regions: the origin of the X-ray absorption in gamma-ray burst afterglows

Soft X-ray absorption in excess of Galactic is observed in the afterglows of most gamma-ray bursts (GRBs), but the correct solution to its origin has not been arrived at after more than a decade of work, preventing its use as a powerful diagnostic tool. We resolve this long-standing problem and find that He in the GRB's host HII region is responsible for most of the absorption. We show that the X-ray absorbing column density (N_Hx) is correlated with both the neutral gas column density and with the optical afterglow extinction (Av). This correlation explains the connection between dark bursts and bursts with high N_Hx values. From these correlations we exclude an origin of the X-ray absorption which is not related to the host galaxy, i.e. the intergalactic medium or intervening absorbers are not responsible. We find that the correlation with the dust column has a strong redshift evolution, whereas the correlation with the neutral gas does not. From this we conclude that the column density of the X-ray absorption is correlated with the total gas column density in the host galaxy rather than the metal column density, in spite of the fact that X-ray absorption is typically dominated by metals. The strong redshift evolution of N_Hx/Av is thus a reflection of the cosmic metallicity evolution of star-forming galaxies. We conclude that the absorption of X-rays in GRB afterglows is caused by He in the HII region hosting the GRB. While dust is destroyed and metals are stripped of all of their electrons by the GRB to great distances, the abundance of He saturates the He-ionising UV continuum much closer to the GRB, allowing it to remain in the neutral or singly-ionised state. Helium X-ray absorption explains the correlation with total gas, the lack of strong evolution with redshift as well as the absence of dust, metal or hydrogen absorption features in the optical-UV spectra.Comment: 10 pages, 4 figures, submitted to Ap