[Abridged] We use the ATLAS3D sample of 260 early-type galaxies (ETGs) to study the apparent kinematic misalignment angle, Psi, defined as the angle between the photometric and kinematic major axis. We find that 71% of nearby ETGs are strictly aligned systems (Psi > 5 deg), an additional 14% have 5 < Psi < 10 deg and 90% of galaxies have Psi < 15 deg. Taking into account measurement uncertainties, 90% of galaxies can be considered aligned to better than 5 deg, suggesting that only a small fraction of early-type galaxies (~10%) are not consistent with axisymmetry within the projected half-light radius. We identify morphological features such as bars and rings (30%), dust structures (16%), blue nuclear colours (6%) and evidence of interactions (8%). We use kinemetry to analyse the mean velocity maps and separate galaxies in two broad types of regular and non-regular rotators. We find 82% of regular rotators and 17% non-regular rotators, with 2 galaxies that we were not able to classify due to data quality. The non-regular rotators are typically found in dense regions and are massive. The majority of galaxies do not have any specific kinemetric features, but we highlight here the frequency of the kinematically distinct cores (7%) and the aligned double peaks in the velocity dispersion maps (4%). Most of the galaxies that are misaligned have complex kinematics and are non-regular rotators. While the trends are weak, there is a tendency that large values of Psi are found in galaxies at intermediate environmental densities and among the most massive galaxies in the sample. We suggest that the most common formation mechanism for ETGs preserves the axisymmetry of the disk progenitors. Less commonly, the formation process results in a triaxial galaxy with much lower net angular momentum.

In this letter, we present LHC limits on the minimal universal extra dimension (MUED) model from LHC Run 1 data and current limits from searches of the ongoing Run 2. Typical collider signals of the Kaluza-Klein (KK) states mimic generic degenerate supersymmetry (SUSY) missing transverse momentum signatures since the excited KK particles cascade decay to jets, leptons and the lightest KK particle which is stable due to KK parity and thus evades detection. We test the parameter space against a large number of supersymmetry based missing energy searches implemented in the public code CheckMATE. We demonstrate the complementarity of employing various searches which target a large number of final state signatures, and we derive the most up to date limits on the MUED parameter space from 13 TeV SUSY searches.

Physics-informed neural networks (PINNs) and related methods struggle to resolve sharp gradients in singularly perturbed boundary value problems without resorting to some form of domain decomposition, which often introduce complex interface penalties. While the Extreme Theory of Functional Connections (X-TFC) avoids multi-objective optimization by employing exact boundary condition enforcement, it remains computationally inefficient for boundary layers and incompatible with decomposition. We propose Gated X-TFC, a novel framework for both forward and inverse problems, that overcomes these limitations through a soft, learned domain decomposition. Our method replaces hard interfaces with a differentiable logistic gate that dynamically adapts radial basis function (RBF) kernel widths across the domain, eliminating the need for interface penalties. This approach yields not only superior accuracy but also dramatic improvements in computational efficiency: on a benchmark one dimensional (1D) convection-diffusion, Gated X-TFC achieves an order-of-magnitude lower error than standard X-TFC while using 80 percent fewer collocation points and reducing training time by 66 percent. In addition, we introduce an operator-conditioned meta-learning layer that learns a probabilistic mapping from PDE parameters to optimal gate configurations, enabling fast, uncertainty-aware warm-starting for new problem instances. We further demonstrate scalability to multiple subdomains and higher dimensions by solving a twin boundary-layer equation and a 2D Poisson problem with a sharp Gaussian source. Overall, Gated X-TFC delivers a simple alternative alternative to PINNs that is both accurate and computationally efficient for challenging boundar-layer regimes. Future work will focus on nonlinear problems.

An important component of the Extragalactic Distance Database (EDD) at this http URL is a group of catalogs related to the measurement of HI line profile parameters. One of these is the All Digital HI catalog which contains an amalgam of information from new data and old. The new data results from observations with Arecibo and Parkes telescopes and with the Green Bank Telescope (GBT), including continuing input since the award of the NRAO Cosmic Flows Large Program. The old data has been collected from archives, wherever available, particularly the Cornell University Digital HI Archive, the Nancay Telescope extragalactic HI archive, and the Australia Telescope archive. The catalog currently contains information on ~15,000 profiles relating to ~13,000 galaxies. The channel - flux per channel files, from whatever source, are carried through a common pipeline. The derived parameter of greatest interest is W_m50, the profile width at 50% of the mean flux. After appropriate adjustment, the parameter W_mx is derived, the linewidth which statistically approximates the peak to peak maximum rotation velocity before correction for inclination, 2 V_max sin(i).

These are the notes of five lectures given at the Summer School {\em Geometric and Topological Methods for Quantum Field Theory}, held in Villa de Leyva (Colombia), July 2--20, 2007. The lectures are meant for graduate or almost graduate students in physics or mathematics. They include references, many examples and some exercices. The content is the following. The first lecture is a short introduction to algebraic and proalgebraic groups, based on some examples of groups of matrices and groups of formal series, and their Hopf algebras of coordinate functions. The second lecture presents a very condensed review of classical and quantum field theory, from the Lagrangian formalism to the Euler-Lagrange equation and the Dyson-Schwinger equation for Green's functions. It poses the main problem of solving some non-linear differential equations for interacting fields. In the third lecture we explain the perturbative solution of the previous equations, expanded on Feynman graphs, in the simplest case of the scalar $\phi^3$ theory. The forth lecture introduces the problem of divergent integrals appearing in quantum field theory, the renormalization procedure for the graphs, and how the renormalization affects the Lagrangian and the Green's functions given as perturbative series. The last lecture presents the Connes-Kreimer Hopf algebra of renormalization for the scalar theory and its associated proalgebraic group of formal series.

In these lectures we present five interpretations of the Fa' di Bruno formula which computes the n-th derivative of the composition of two functions of one variable: in terms of groups, Lie algebras and Hopf algebras, in combinatorics and within operads.

We explore the pMSSM parameter space in view of the constraints from SUSY and monojet searches at the LHC, from Higgs data and flavour physics observables, as well as from dark matter searches. We show that whilst the simplest SUSY scenarios are already ruled out, there are still many possibilities left over in the pMSSM. We discuss the complementarity between different searches and consistency checks which are essential in probing the pMSSM and will be even more important in the near future with the next round of data becoming available.

We study the stochastically forced system of isentropic Euler equations of gas dynamics with a $\gamma$-law for the pressure. We show the existence of martingale weak entropy solutions; we also discuss the existence and characterization of invariant measures in the concluding section.

It was noted already in the 90s that many classic graph classes, such as interval, chordal, and bipartite graphs, can be characterized by the existence of an ordering of the vertices avoiding some ordered subgraphs, called patterns. Very recently, all the classes corresponding to patterns on three vertices (including the ones mentioned above) have been listed, and proved to be efficiently recognizable. In contrast, very little is known about patterns on four vertices. One of the few graph classes characterized by a pattern on four vertices is the class of intersection graphs of rectangles that are said to be grounded on a line. This class appears naturally in the study of intersection graphs, and similar grounded classes have recently attracted a lot of attention. This paper contains three parts. First, we make a survey of grounded intersection graph classes, summarizing all the known inclusions between these various classes. Second, we show that the correspondence between a pattern on four vertices and grounded rectangle graphs is not an isolated phenomenon. We establish several other pattern characterizations for geometric classes, and show that the hierarchy of grounded intersection graph classes is tightly interleaved with the classes defined patterns on four vertices. We claim that forbidden patterns are a useful tool to classify grounded intersection graphs. Finally, we give an overview of the complexity of the recognition of classes defined by forbidden patterns on four vertices and list several interesting open problems.

We report the discovery of a unique $z=6.027$ galaxy, multiply imaged by the cluster Abell 383 and detected in new Hubble Space Telescope ACS and WFC3 imaging, as well as in Warm Spitzer observations. This galaxy was selected as a pair of i-dropouts; its suspected high redshift was confirmed by the measurement of a strong Lyman-alpha line in both images using Keck/DEIMOS. Combining Hubble and Spitzer photometry after correcting for contamination by line emission (estimated to be a small effect), we identify a strong Balmer break of 1.5 magnitudes. Taking into account the magnification factor of 11.4+/-1.9 (2.65+/-0.17 mag) for the brightest image, the unlensed AB magnitude for the source is 27.2+/-0.05 in the H band, corresponding to a 0.4 L* galaxy, and 25.7+/-0.08 at 3.6 um. The UV slope is consistent with beta~2.0, and from the rest-frame UV continuum we measure a current star formation rate of 2.4+/-1.1 Msol/yr. The unlensed half-light radius is measured to be 300 pc, from which we deduce a star-forming surface density of ~10 Msol/yr/kpc2. The Lyman-alpha emission is found to be extended over ~3" along the slit, corresponding to ~5 kpc in the source plane. This can be explained by the presence of a much larger envelope of neutral hydrogen around the star-forming region. Finally, fitting the spectral energy distribution using 7 photometric data points with simple SED models, we derive the following properties: very little reddening, an inferred stellar mass of M*=6e9 Msol, and an inferred age of ~800 Myrs (corresponding to a redshift of formation of ~18). The star-formation rate of this object was likely much stronger in the past than at the time of observation, suggesting that we may be missing a fraction of galaxies at z~6 which have already faded in rest-frame UV wavelengths.

We present the rationale for and the observational description of ASPECS: The ALMA SPECtroscopic Survey in the Hubble Ultra-Deep Field (UDF), the cosmological deep field that has the deepest multi-wavelength data available. Our overarching goal is to obtain an unbiased census of molecular gas and dust continuum emission in high-redshift (z&gt;0.5) galaxies. The $\sim$1$'$ region covered within the UDF was chosen to overlap with the deepest available imaging from HST. Our ALMA observations consist of full frequency scans in band 3 (84-115 GHz) and band 6 (212-272 GHz) at approximately uniform line sensitivity ($L'_{\rm CO}\sim$2$\times$10$^{9}$ K km/s pc$^2$), and continuum noise levels of 3.8 $\mu$Jy beam$^{-1}$ and 12.7 $\mu$Jy beam$^{-1}$, respectively. The molecular surveys cover the different rotational transitions of the CO molecule, leading to essentially full redshift coverage. The [CII] emission line is also covered at redshifts $6.0

We analyze the decays $K\to\pi\ell\nu$ and $P\to\ell\nu$ ($P=K,\pi$, $\ell=e,\,\mu$) using a low-energy Effective-Field-Theory approach to parametrize New Physics and study the complementarity with baryon $\beta$ decays. We then provide a road map for a global analysis of the experimental data, with all the Wilson coefficients simultaneously, and perform a fit leading to numerical bounds for them and for $V_{us}$. A prominent result of our analysis is a reinterpretation of the well-known $V_{ud}-V_{us}$ diagram as a strong constraint on new physics. Finally, we reinterpret our bounds in terms of the $SU(2)_L\times~U(1)_Y$-invariant operators, provide bounds to the corresponding Wilson coefficients at the TeV scale and compare our results with collider searches at the LHC.

We report the results of a joint analysis of data from BICEP2/Keck Array and Planck. BICEP2 and Keck Array have observed the same approximately 400 deg$^2$ patch of sky centered on RA 0h, Dec. $-57.5°$. The combined maps reach a depth of 57 nK deg in Stokes $Q$ and $U$ in a band centered at 150 GHz. Planck has observed the full sky in polarization at seven frequencies from 30 to 353 GHz, but much less deeply in any given region (1.2 $\mu$K deg in $Q$ and $U$ at 143 GHz). We detect 150$\times$353 cross-correlation in $B$-modes at high significance. We fit the single- and cross-frequency power spectra at frequencies $\geq 150$ GHz to a lensed-$\Lambda$CDM model that includes dust and a possible contribution from inflationary gravitational waves (as parameterized by the tensor-to-scalar ratio $r$), using a prior on the frequency spectral behavior of polarized dust emission from previous \planck\ analysis of other regions of the sky. We find strong evidence for dust and no statistically significant evidence for tensor modes. We probe various model variations and extensions, including adding a synchrotron component in combination with lower frequency data, and find that these make little difference to the $r$ constraint. Finally we present an alternative analysis which is similar to a map-based cleaning of the dust contribution, and show that this gives similar constraints. The final result is expressed as a likelihood curve for $r$, and yields an upper limit r_{0.05}&lt;0.12 at 95% confidence. Marginalizing over dust and $r$, lensing $B$-modes are detected at $7.0\,\sigma$ significance.

These tips provide a quick and concentrated guide for beginners in the analysis of network data.

Arguably the main challenge of galactic magnetism studies is to explain how the interstellar medium of galaxies reaches energetic equipartition despite the extremely weak cosmic primordial magnetic fields that are originally predicted to thread the inter-galactic medium. Previous numerical studies of isolated galaxies suggest that a fast dynamo amplification might suffice to bridge the gap spanning many orders of magnitude in strength between the weak early Universe magnetic fields and the ones observed in high redshift galaxies. To better understand their evolution in the cosmological context of hierarchical galaxy growth, we probe the amplification process undergone by the cosmic magnetic field within a spiral galaxy to unprecedented accuracy by means of a suite of constrained transport magnetohydrodynamical adaptive mesh refinement cosmological zoom simulations with different stellar feedback prescriptions. A galactic turbulent dynamo is found to be naturally excited in this cosmological environment, being responsible for most of the amplification of the magnetic energy. Indeed, we find that the magnetic energy spectra of simulated galaxies display telltale inverse cascades. Overall, the amplification process can be divided in three main phases, which are related to different physical mechanisms driving galaxy evolution: an initial collapse phase, an accretion-driven phase, and a feedback-driven phase. While different feedback models affect the magnetic field amplification differently, all tested models prove to be subdominant at early epochs, before the feedback-driven phase is reached. Thus the three-phase evolution paradigm is found to be quite robust vis-a-vis feedback prescriptions.

We present a comparison of nine galaxy formation models, eight semi-analytical and one halo occupation distribution model, run on the same underlying cold dark matter simulation (cosmological box of co-moving width 125$h^{-1}$ Mpc, with a dark-matter particle mass of $1.24\times 10^9 h^{-1}$ Msun) and the same merger trees. While their free parameters have been calibrated to the same observational data sets using two approaches, they nevertheless retain some 'memory' of any previous calibration that served as the starting point (especially for the manually-tuned models). For the first calibration, models reproduce the observed z = 0 galaxy stellar mass function (SMF) within 3-{\sigma}. The second calibration extended the observational data to include the z = 2 SMF alongside the z~0 star formation rate function, cold gas mass and the black hole-bulge mass relation. Encapsulating the observed evolution of the SMF from z = 2 to z = 0 is found to be very hard within the context of the physics currently included in the models. We finally use our calibrated models to study the evolution of the stellar-to-halo mass (SHM) ratio. For all models we find that the peak value of the SHM relation decreases with redshift. However, the trends seen for the evolution of the peak position as well as the mean scatter in the SHM relation are rather weak and strongly model dependent. Both the calibration data sets and model results are publicly available.

As one of the prime contributors to the interstellar medium energy budget, magnetic fields naturally play a part in shaping the evolution of galaxies. Galactic magnetic fields can originate from strong primordial magnetic fields provided these latter remain below current observational upper limits. To understand how such magnetic fields would affect the global morphological and dynamical properties of galaxies, we use a suite of high-resolution constrained transport magneto-hydrodynamic cosmological zoom simulations where we vary the initial magnetic field strength and configuration along with the prescription for stellar feedback. We find that strong primordial magnetic fields delay the onset of star formation and drain the rotational support of the galaxy, diminishing the radial size of the galactic disk and driving a higher amount of gas towards the centre. This is also reflected in mock UVJ observations by an increase in the light profile concentration of the galaxy. We explore the possible mechanisms behind such a reduction in angular momentum, focusing on magnetic braking. Finally, noticing that the effects of primordial magnetic fields are amplified in the presence of stellar feedback, we briefly discuss whether the changes we measure would also be expected for galactic magnetic fields of non-primordial origin.

Many algorithms have been proposed in the last ten years for the discovery of dynamic communities. However, these methods are seldom compared between themselves. In this article, we propose a generator of dynamic graphs with planted evolving community structure, as a benchmark to compare and evaluate such algorithms. Unlike previously proposed benchmarks, it is able to specify any desired evolving community structure through a descriptive language, and then to generate the corresponding progressively evolving network. We empirically evaluate six existing algorithms for dynamic community detection in terms of instantaneous and longitudinal similarity with the planted ground truth, smoothness of dynamic partitions, and scalability. We notably observe different types of weaknesses depending on their approach to ensure smoothness, namely Glitches, Oversimplification and Identity loss. Although no method arises as a clear winner, we observe clear differences between methods, and we identified the fastest, those yielding the most smoothed or the most accurate solutions at each step.

We present a comparison of the observed evolving galaxy stellar mass functions with the predictions of eight semi-analytic models and one halo occupation distribution model. While most models are able to fit the data at low redshift, some of them struggle to simultaneously fit observations at high redshift. We separate the galaxies into 'passive' and 'star-forming' classes and find that several of the models produce too many low-mass star-forming galaxies at high redshift compared to observations, in some cases by nearly a factor of 10 in the redshift range 2.5 &lt; z &lt; 3.0. We also find important differences in the implied mass of the dark matter haloes the galaxies inhabit, by comparing with halo masses inferred from observations. Galaxies at high redshift in the models are in lower mass haloes than suggested by observations, and the star formation efficiency in low-mass haloes is higher than observed. We conclude that many of the models require a physical prescription that acts to dissociate the growth of low-mass galaxies from the growth of their dark matter haloes at high redshift.

We provide a census of the apparent stellar angular momentum within 1 Re of a volume-limited sample of 260 early-type galaxies (ETGs) in the nearby Universe, using integral-field spectroscopy obtained in the course of the ATLAS3D project. We exploit the LambdaR parameter to characterise the existence of two families of ETGs: Slow Rotators which exhibit complex stellar velocity fields and often include stellar kinematically Distinct Cores (KDCs), and Fast Rotators which have regular velocity fields. Our complete sample of 260 ETGs leads to a new criterion to disentangle Fast and Slow Rotators which now includes a dependency on the apparent ellipticity (Epsilon). It separates the two classes significantly better than the previous prescription, and than a criterion based on V/Sigma: Slow Rotators and Fast Rotators have LambdaR lower and larger than kFSxSQRT(Epsilon), respectively, where kFS=0.31 for measurements made within 1 Re. We show that the vast majority of early-type galaxies are Fast Rotators: these have regular stellar rotation, with aligned photometric and kinematic axes (Paper II, Krajnovic et al. 2011}, include discs and often bars and represent 86% (224/260) of all early-type galaxies in the volume-limited ATLAS3D sample. Fast Rotators span the full range of apparent ellipticities from 0 to 0.85, and we suggest that they cover intrinsic ellipticities from about 0.35 to 0.85, the most flattened having morphologies consistent with spiral galaxies. Only a small fraction of ETGs are Slow Rotators representing 14% (36/260) of the ATLAS3D sample of ETGs. Of all Slow Rotators, 11% (4/36) exhibit two counter-rotating stellar disc-like components and are rather low mass objects (Mdyn<10^10.5 M_Sun). All other Slow Rotators (32/36) appear relatively round on the sky (Epsilon_e<0.4), tend to be massive (Mdyn>10^10.5 M_Sun), and often (17/32) exhibit KDCs.