Resolution learning in deep convolutional networks using scale-space theory

Resolution in deep convolutional neural networks (CNNs) is typically bounded by the receptive field size through filter sizes, and subsampling layers or strided convolutions on feature maps. The optimal resolution may vary significantly depending on the dataset. Modern CNNs hard-code their resolution hyper-parameters in the network architecture which makes tuning such hyper-parameters cumbersome. We propose to do away with hard-coded resolution hyper-parameters and aim to learn the appropriate resolution from data. We use scale-space theory to obtain a self-similar parametrization of filters and make use of the N-Jet: a truncated Taylor series to approximate a filter by a learned combination of Gaussian derivative filters. The parameter sigma of the Gaussian basis controls both the amount of detail the filter encodes and the spatial extent of the filter. Since sigma is a continuous parameter, we can optimize it with respect to the loss. The proposed N-Jet layer achieves comparable performance when used in state-of-the art architectures, while learning the correct resolution in each layer automatically. We evaluate our N-Jet layer on both classification and segmentation, and we show that learning sigma is especially beneficial for inputs at multiple sizes

Black hole masses of tidal disruption event host galaxies

The mass of the central black hole in a galaxy that hosted a tidal disruption event (TDE) is an important parameter in understanding its energetics and dynamics. We present the first homogeneously measured black hole masses of a complete sample of 12 optically/UV selected TDE host galaxies (down to $g_{host}$$\leq$22 mag and $z$=0.37) in the Northern sky. The mass estimates are based on velocity dispersion measurements, performed on late time optical spectroscopic observations. We find black hole masses in the range 3$\times$10$^5$ M$_{\odot}$$\leq$M$_{\rm BH}$$\leq$2$\times$10$^7$ M$_{\odot}$. The TDE host galaxy sample is dominated by low mass black holes ($\sim$10$^6$ M$_{\odot}$), as expected from theoretical predictions. The blackbody peak luminosity of TDEs with M$_{\rm BH}$$\leq$10$^{7.1}$ M$_{\odot}$ is consistent with the Eddington limit of the SMBH, whereas the two TDEs with M$_{\rm BH}$$\geq$10$^{7.1}$ M$_{\odot}$ have peak luminosities below their SMBH Eddington luminosity, in line with the theoretical expectation that the fallback rate for M$_{\rm BH}$$\geq$10$^{7.1}$ M$_{\odot}$ is sub-Eddington. In addition, our observations suggest that TDEs around lower mass black holes evolve faster. These findings corroborate the standard TDE picture in 10$^6$ M$_{\odot}$ black holes. Our results imply an increased tension between observational and theoretical TDE rates. By comparing the blackbody emission radius with theoretical predictions, we conclude that the optical/UV emission is produced in a region consistent with the stream self-intersection radius of shallow encounters, ruling out a compact accretion disk as the direct origin of the blackbody radiation at peak brightness.Comment: 16 pages, 9 figures. Submitted to MNRAS; including minor revisions suggested by the refere

Integral field spectroscopy:a glance to chemo-dynamics in galaxies

Abstract. 3D information of the structures in galaxies is not directly available from the morphologies that are, however, needed to target studies on the structures. Alternatively, the spectra of galaxies broadened by the line-of-sight-velocity-distribution (LOSVD) can be used as LOS spatial distribution probes and hold the chemical footprints left along the evolution of galaxies. Knowledge gained from the density distributions and the stellar populations narrows down the processes involved in building these observed morphologies. Integral field spectroscopy (IFS) is an ideal technique for such cases as it instantaneously provides simultaneous morphological and spectral information from the targets. Thick disks and X/B/P bulges are both structures that are often most directly observable in a near edge-on orientation. The vertical density distribution in these structures are the result of evolutional processes that produce stellar populations accordingly but direct information on the distribution vanishes sharply with decreasing inclination ($i$) as does our consensus of the structures in the LOS. Investigating such structures and the LOSVDs in simulations can lift some of the doubt and improve our knowledge to be adapted on the search of these structures over various galaxy inclinations. In this thesis Gauss-Hermite series are deployed to scrutinise the LOSVDs in thin-thick disk and X/B/P simulations (A and B) against the IFS data from central regions of 13 ($\textrm{SA-S}\underline{\textrm{A}}\textrm{B}$) galaxies with $\langle M_{*}\rangle \approx 2\times10^{10.5}\textrm{M}_{\odot}$, $\langle T \rangle \approx 2$, $\langle i \rangle \approx 45°$ from the Spitzer Survey Stellar Structures in Galaxies ($\mathrm{S}^{4}\mathrm{G}$) sample. Thin-thick disk superposition in simulation-A produces radially increasing amplitudes of the fourth Gauss-Hermite moment ($h_{4}$). The third Gauss-Hermite moment ($h_{3}$) shows mainly anti-correlation with LOSV and persist relatively strong even for low inclinations. These signatures are observed in the IFS data but due to limited field-of-view (FoV) and on-plane rings observed in the systems they are not unambiguous. In simulation-B, negative $h_{4}$ minima are found on average at $r \approx 2h_{r}$ and corresponds to the X-shape structure on edge-on view. Regarding observations, the nuclear region also highlights a $h_{4}$-ring that is a signature observed frequently in the sample. In simulation-B the $h_{4}$ ring is produced by the disk-bulge superposition in the LOS and is observable independent of inclination. NGC 1068 and NGC 1387 are found to be X/B/P bulge candidates as both are observed in low $i$, in which the fourth vertical density distribution moment ($d_{4}$) is probed by the $h_{4}$ moment, and are observed with negative $h_{4}$ at a radial distance $h_{r} \lt r \lt 2h_{r}$. In low $i$ the $h_{4}$ minima in simulation-B are found with weak $h_{3}-V$ correlation that is observed with NGC 1387 but not clearly with NGC 1068.2D spektroskopia : katsaus galaksien kemo-dynamiikkaan. Tiivistelmä. 3D informaatio galaksien rakenteista ei ole suoraan havaittavissa niiden morfologiasta, jota kuitenkin tarvitaan näiden rakenteiden tutkimiseen. Toisaalta galaksien spektrit laajentuessaan katseen suuntaisten nopeusjakaumien (LOSVD) mukaisesti mahdollistavat rakenteiden syvyyssuuntaisen ulottuvuuden tutkimisen ja pitävät sisällään kemialliset jalanjäljet galaksien evoluutiosta. Tiheys/nopeusjakaumista ja tähtipopulaatiosta saatava tieto tuottaa tarkemman kuvan siitä, mitkä prosessit kykenevät muodostamaan galakseissa havaitut rakenteet. 2D-spektroskopia (IFS) on ideaali keino galaksien rakenteiden tutkimiseen sen välittömästi tuottaman yhtäaikaisen morfologisen ja spektroskooppisen informaation ansiosta. Paksukiekot ja X/B/P keskuspullistumat ovat rakenteita, jotka ovat usein havaittavissa suuren inklinaation omaavissa galakseissa. Näiden rakenteiden pystysuuntaiset tiheys/nopeusjakaumat ja tähtipopulaatiot ovat evoluutionaalisten prosessien tulosta, mutta havaittavan galaksin inklinaation ollessa pieni, suora informaatio rakenteiden pystysuuntaisista tiheysjakaumista ja identiteetistä katoaa. Siksi rakenteiden muodon ja niiden katseen suuntaisten nopeushajontojen tutkiminen simulaatiossa vahvistaa käsitystämme galakseissa esiintyvistä rakenteista. Työssä hyödynnetään Gauss-Hermite sarjoja nopeusjakaumien analyysiin kahdessa simulaatiossa ja 2D spektroskopiassa 13:lle ($\textrm{SA-S}\underline{\textrm{A}}\textrm{B}$) galaksille ($\langle M_{*}\rangle \approx 2\times10^{10.5}\textrm{M}_{\odot}$, $\langle T \rangle \approx 2$, $\langle i \rangle \approx 45°$) ”Spitzer Survey of Stellar Structures in Galaxies (S4G)” havaintojoukosta. Kaksoiskiekkosimulaatiossa kiekkojen superpositio-LOSVD tuottaa radiaalisesti ulospäin kasvavan Gauss-Hermite sarjan neljännen momentin ($h_{4}$). Gauss-Hermite sarjan kolmas momentti ($h_{3}$) anti-korreloi LOSV kanssa ja on havaittavissa suhteellisen selvästi, myös matalilla simulaatio inklinaatiolla. Vastaavat merkit ovat havaittavissa IFS datasta, mutta rajallisesta havaintoalueesta ja häiriöitä tuottavista rengasrakenteista johtuen ne eivät ole yksiselitteisiä. X/B/P simulaatiossa negatiiviset $h_{4}$ minimit esiintyvät keskimäärin etäisyydellä $r \approx 2h_{r}$, joka vastaa X-rakennetta kylki-edessä orientaatiossa. Simulaation keskustassa havaitaan keskuspullistuman ja kiekon tuottama $h_{4}$ rengas, joka on usein esiintyvä piirre havaintojoukon IFS datassa. NGC 1068 ja NGC 1387 ovat X/B/P keskuspullistuma kandidaatteja, sillä molemmat ovat inklinaatiossa, jossa vertikaalisen tiheysjakauman neljännen momentin ($d_{4}$) tulkinta $h_{4}$ arvoista on mahdollista ja molemmissa tapauksissa negatiiviset $h_{4}$ minimit löytyvät radiaalisella etäisyydellä $h_{r} \lt r \lt 2h_{r}$. Matalilla inklinaatiolla simulaation $h_{4}$ minimit havaitaan heikon $h_{3}-V$ korrelaation kanssa, joka on havaittavissa NGC 1387:ssä, mutta ei selkeästi NGC 1068:ssa

Symmetry Groups, Quantum Mechanics and Generalized Hermite Functions

This is a review paper on the generalization of Euclidean as well as pseudo-Euclidean groups of interest in quantum mechanics. The Weyl–Heisenberg groups, Hn, together with the Euclidean, En, and pseudo-Euclidean Ep,q, groups are two families of groups with a particular interest due to their applications in quantum physics. In the present manuscript, we show that, together, they give rise to a more general family of groups, Kp,q, that contain Hp,q and Ep,q as subgroups. It is noteworthy that properties such as self-similarity and invariance with respect to the orientation of the axes are properly included in the structure of Kp,q. We construct generalized Hermite functions on multidimensional spaces, which serve as orthogonal bases of Hilbert spaces supporting unitary irreducible representations of groups of the type Kp,q. By extending these Hilbert spaces, we obtain representations of Kp,q on rigged Hilbert spaces (Gelfand triplets). We study the transformation laws of these generalized Hermite functions under Fourier transform

Implementation of dynamical systems with plastic self-organising velocity fields

To describe learning, as an alternative to a neural network recently dynamical systems were introduced whose vector fields were plastic and self-organising. Such a system automatically modifies its velocity vector field in response to the external stimuli. In the simplest case under certain conditions its vector field develops into a gradient of a multi-dimensional probability density distribution of the stimuli. We illustrate with examples how such a system carries out categorisation, pattern recognition, memorisation and forgetting without any supervision. [Continues.

The SAMI Galaxy Survey: the cluster redshift survey, target selection and cluster properties

We describe the selection of galaxies targeted in eight low redshift clusters (APMCC0917, A168, A4038, EDCC442, A3880, A2399, A119 and A85; $0.029 < z < 0.058$) as part of the Sydney-AAO Multi-Object integral field Spectrograph Galaxy Survey (SAMI-GS). We have conducted a redshift survey of these clusters using the AAOmega multi-object spectrograph on the 3.9m Anglo-Australian Telescope. The redshift survey is used to determine cluster membership and to characterise the dynamical properties of the clusters. In combination with existing data, the survey resulted in 21,257 reliable redshift measurements and 2899 confirmed cluster member galaxies. Our redshift catalogue has a high spectroscopic completeness ($\sim 94\%$) for $r_{\rm petro} \leq 19.4$ and clustercentric distances $R< 2\rm{R}_{200}$. We use the confirmed cluster member positions and redshifts to determine cluster velocity dispersion, $\rm{R}_{200}$, virial and caustic masses, as well as cluster structure. The clusters have virial masses $14.25 \leq {\rm log }({\rm M}_{200}/\rm{M}_{\odot}) \leq 15.19$. The cluster sample exhibits a range of dynamical states, from relatively relaxed-appearing systems, to clusters with strong indications of merger-related substructure. Aperture- and PSF-matched photometry are derived from SDSS and VST/ATLAS imaging and used to estimate stellar masses. These estimates, in combination with the redshifts, are used to define the input target catalogue for the cluster portion of the SAMI-GS. The primary SAMI-GS cluster targets have $R< \rm{R}_{200}$, velocities $|v_{\rm pec}| < 3.5\sigma_{200}$ and stellar masses $9.5 \leq {\rm log(M}^*_{approx}/\rm{M}_{\odot}) \leq 12$. Finally, we give an update on the SAMI-GS progress for the cluster regions

The SAMI Galaxy Survey: the cluster redshift survey, target selection and cluster properties

We describe the selection of galaxies targeted in eight low-redshift clusters (APMCC0917, A168, A4038, EDCC442, A3880, A2399, A119 and A85; 0.029 < z < 0.058) as part of the Sydney-AAO Multi-Object Integral field spectrograph Galaxy Survey (SAMI-GS). We have conducted a redshift survey of these clusters using the AAOmega multi-object spectrograph on the 3.9-m Anglo-Australian Telescope. The redshift survey is used to determine cluster membership and to characterize the dynamical properties of the clusters. In combination with existing data, the survey resulted in 21 257 reliable redshift measurements and 2899 confirmed cluster member galaxies. Our redshift catalogue has a high spectroscopic completeness (∼94 per cent) for rpetro ≤ 19.4 and cluster-centric distances R < 2R200. We use the confirmed cluster member positions and redshifts to determine cluster velocity dispersion, R200, virial and caustic masses, as well as cluster structure. The clusters have virial masses 14.25 ≤ log(M200/M_⊙) ≤ 15.19. The cluster sample exhibits a range of dynamical states, from relatively relaxed-appearing systems, to clusters with strong indications of merger-related substructure. Aperture- and point spread function matched photometry are derived from Sloan Digital Sky Survey and VLT Survey Telescope/ATLAS imaging and used to estimate stellar masses. These estimates, in combination with the redshifts, are used to define the input target catalogue for the cluster portion of the SAMI-GS. The primary SAMI-GS cluster targets have R <R200, velocities |vpec| < 3.5σ200 and stellar masses 9.5 ≤ log(M^∗_(approx)/M_⊙) ≤ 12. Finally, we give an update on the SAMI-GS progress for the cluster regions

Aspects of Supermassive Black Hole Growth in Nearby Active Galactic Nuclei

Super-massive black holes (SBHs) have long been identified as the engines of active galactic nuclei (AGNs) and are now considered to play a key role in galaxy evolution. In this dissertation I present results from two observational studies conducted on nearby AGNs with the aim of furthering our understanding of SBH growth and their interplay with the host galaxies. The first study is an observational search for SBHs spatially offset from the center of their host galaxies. Such offsets can be considered signatures of gravitational recoil following the coalescence of an SBH binary system (formed in the aftermath of a galaxy merger) due to emission of gravitational waves. The study is based on a photometric analysis of fourteen nearby elliptical galaxies observed with the Hubble Space Telescope. I find that parsec-scale offsets are common. However, while these are individually consistent with residual gravitational recoil oscillations, there is a high probability that larger offsets than those actually observed should have been found in the sample as a whole. There are a number of possible explanations for this result: the galaxy merger rate may be lower than current estimates; SBH-binaries may reach the merger stage with a configuration which minimizes recoil velocities; or the SBH oscillations are more quickly damped than predicted. In the second study I use integral field spectroscopy obtained with the Gemini South telescope to investigate the kinematics of the circum-nuclear ionized gas in two active galaxies: NGC 1386, a Seyfert 2, and NGC 1365, a Seyfert 1. The goal of the study is to investigate outflows in low-luminosity AGNs, and the mechanisms channeling gas (the SBH fuel) from the inner kiloparsec down to a few tens of parsecs from the SBH. I find that the dominant kinematic components can be explained as a combination of rotation in the large-scale galactic disk and compact outflows along the axis of the AGN “radiation cone”. However, in the case of NGC 1386, there is also compelling evidence for an equatorial outflow, which provides a new clue to the physical processes operating in AGNs