We observed with ALMA three deeply buried nuclei in two galaxies, NGC 4418 and Arp 220, at $sim$0.2$$ resolution over a total bandwidth of 67 GHz in $f_{rm rest}$ = 215 - 697 GHz. Here we (1) introduce our program, (2) describe our data reduction met
hod for wide-band, high-resolution imaging spectroscopy, (3) analyze in visibilities the compact nuclei with line forests, (4) develop a continuum-based estimation method of dust opacity and gas column density in heavily obscured nuclei, which uses the BGN (buried galactic nuclei) model and is sensitive to $log(N_{rm H_2}/{rm cm}^{-2}) sim $ 25 - 26 at $lambda sim 1$ mm, and (5) present the continuum data and diagnosis of our targets. The three continuum nuclei have major-axis FWHM of $sim$0.1$$-0.3$$ (20-140 pc) aligned to their rotating nuclear disks of molecular gas. However, each nucleus is described better with two or three concentric components than with a single Gaussian. The innermost cores have sizes of 0.05$$-0.10$$ (8-40 pc), peak brightness temperatures of ~100-500 K at 350 GHz, and more fractional flux at lower frequencies. The intermediate components correspond to the nuclear disks. They have axial ratios of $approx$0.5 and hence inclinations $stackrel{>}{sim} 60$ deg. The outermost elements include the bipolar outflow from Arp 220W. We estimate 1 mm dust opacity of $tau_{rm d,1mm} approx 2.2$, $1.2$, and $stackrel{<}{sim} 0.4$ respectively for NGC 4418, Arp 220W, and Arp 220E. The first two correspond to $log(N_{rm H}/{rm cm}^{-2}) sim 26$ for conventional dust-opacity laws, and hence the nuclei are highly Compton thick.
We study the impact of quenched disorder on the dynamics of locally constrained quantum spin chains, that describe 1D arrays of Rydberg atoms in both frozen (Ising-type) and dressed (XY-type) regime. Performing large-scale numerical experiments, we o
bserve no trace of many-body localization even at large disorder. Analyzing the role of quenched disorder terms in constrained systems we show that they act in two, distinct and competing ways: as an on-site disorder term for the basic excitations of the system, and as an interaction between excitations. The two contributions are of the same order, and as they compete (one towards localization, the other against it), one does never enter a truly strong disorder, weak interaction limit, where many-body localization occurs. Such a mechanism is further clarified in the case of XY-type constrained models: there, a term which would represent a bona-fide local quenched disorder term acting on the excitations of the clean model must be written as a series of non-local terms in the unconstrained variables. Our observations provide a simple picture to interpret the role of quenched disorder that could be immediately extended to other constrained models or quenched gauge theories.
Quantum scars are non-thermal eigenstates characterized by low entanglement entropy, initially detected in systems subject to nearest-neighbor Rydberg blockade, the so called PXP model. While most of these special eigenstates elude an analytical desc
ription and seem to hybridize with nearby thermal eigenstates for large systems, some of them can be written as matrix product states (MPS) with size-independent bond dimension. We study the response of these exact quantum scars to perturbations by analysing the scaling of the fidelity susceptibility with system size. We find that some of them are anomalously stable at first order in perturbation theory, in sharp contrast to the eigenstate thermalization hypothesis. However, this stability seems to breakdown when all orders are taken into account. We further investigate models with larger blockade radius and find a novel set of exact quantum scars, that we write down analytically and compare with the PXP exact eigenstates. We show that they exhibit the same robustness against perturbations at first order.
For G a complex reductive group and X a smooth projective or convex quasi-projective polarized G-variety we construct a formal map in quantum K-theory from the equivariant quantum K-theory QK^G(X) to the quantum K-theory of the git quotient X//G assu
ming the quotient X//G is a smooth Deligne-Mumford stack with projective coarse moduli space. As an example, we give a presentation of the (possibly bulk-shifted) quantum K-theory of any smooth proper toric Deligne-Mumford stack with projective coarse moduli space. We also provide awall-crossing formula for the K-theoretic gauged potential under variation of git quotient, a proof of the invariance of certain K-theoretic Gromov-Witten invariants under (strong) crepant transformation assumptions, and a proof of a version of the abelian non-abelian correspondence.
Using $0.2^{prime prime}$ ($sim3$ pc) ALMA images of vibrationally excited HC$_3$N emission (HC$_3$N$^*$) we reveal the presence of $8$ unresolved Super Hot Cores (SHCs) in the inner $160$ pc of NGC,253. Our LTE and non-LTE modelling of the HC$_3$N$^
*$ emission indicate that SHCs have dust temperatures of $200-375$ K, relatively high H$_2$ densities of $1-6times 10^{6}$ cm$^{-3}$ and high IR luminosities of $0.1-1times 10^8$ L$_odot$. As expected from their short lived phase ($sim 10^4$ yr), all SHCs are associated with young Super Star Clusters (SSCs). We use the ratio of luminosities form the SHCs (protostar phase) and from the free-free emission (ZAMS star phase), to establish the evolutionary stage of the SSCs. The youngest SSCs, with the larges ratios, have ages of a few $10^4$ yr (proto-SSCs) and the more evolved SSCs are likely between $10^5$ and $10^6$ yr (ZAMS-SSCs). The different evolutionary stages of the SSCs are also supported by the radiative feedback from the UV radiation as traced by the HNCO/CS ratio, with this ratio being systematically higher in the young proto-SSCs than in the older ZAMS-SSCs. We also estimate the SFR and the SFE of the SSCs. The trend found in the estimated SFE ($sim40%$ for proto-SSCs and $>85%$ for ZAMS-SSCs) and in the gas mass reservoir available for star formation, one order of magnitude higher for proto-SSCs, suggests that star formation is still going on in proto-SSCs. We also find that the most evolved SSCs are located, in projection, closer to the center of the galaxy than the younger proto-SSCs, indicating an inside-out SSC formation scenario.
Recent interferometric observations have shown bright HCN emission from the nu2=1 vibrational state arising in buried nuclear regions of galaxies, indicating an efficient pumping of the nu2=1 state through absorption of 14 $mu$m continuum photons. We
have modeled the continuum and HCN vibrational line emission in these regions, characterized by high column densities of dust and high luminosities, with a spherically symmetric approach, simulating both a central heating source (AGN) and a compact nuclear starburst (SB). We find that when the H2 columns become very high, N_{H2}>~10^{25} cm-2, trapping of continuum photons within the nuclear region dramatically enhances the dust temperature (Tdust) in the inner regions, even though the predicted spectral energy distribution as seen from outside becomes relatively cold. The models thus predict bright continuum at millimeter wavelengths for luminosity surface brightness (averaged over the model source) of ~10^{8} Lsun pc^{-2}. This {it greenhouse} effect significantly enhances the mean mid-infrared intensity within the dusty volume, populating the nu2=1 state to the extent that the HCN vibrational lines become optically thick. AGN models yield higher Tdust in the inner regions and higher peak (sub)millimeter continuum brightness than SB models, but similar HCN vibrational J=3-2 and 4-3 emission owing to both optical depth effects and a moderate impact of high tdust on these low-J lines. The observed HCN vibrational emission in several galaxies can be accounted for with a HCN abundance of ~10^{-6} (relative to H2) and luminosity surface brightness in the range (0.5-2)x10^{8}$ Lsun pc^{-2}, predicting a far-infrared photosphere with Tdust}~80-150 K --in agreement with the values inferred from far-infrared molecular absorption.
This paper presents a new toolbox for MEEG source activity and connectivity estimation: Brain Connectivity Variable Resolution Tomographic Analysis version 1.0 (BC-VARETA 1.0). It relies on the third generation of nonlinear methods for the analysis o
f resting state MEEG Time Series. Into the state of the art of MEEG analysis, the methodology underlying our tool (BC-VARETA) brings out several assets. First: Constitutes a Bayesian Identification approach of Linear Dynamical Systems in the Frequency Domain, grounded in more consistent models (third generation). Second: Achieves Super-Resolution, through the iterative solution of a Sparse Hermitian Source Graphical Model. Third: Tackles efficiently in High Dimensional and Complex set up the estimation of connectivity. Fourth: Incorporates priors at the connectivity level by penalizing the groups of variables, corresponding to the Gray Matter anatomical segmentation, and including a probability mask of the anatomically plausible connections. Along with the implementation of our method, we include in this toolbox a benchmark for the validation of MEEG source analysis methods, that would serve for the evaluation of sophisticated methodologies (third generation). It incorporates two elements. First: A realistic simulation framework, for the generation of MEEG synthetic data, given an underlying source connectivity structure. Second: Sensitive quality measures that allow for a reliable evaluation of the source activity and connectivity reconstruction performance, based on the Spatial Dispersion and Earth Movers Distance, in both source and connectivity space.
The noninvasive procedures for neural connectivity are under questioning. Theoretical models sustain that the electromagnetic field registered at external sensors is elicited by currents at neural space. Nevertheless, what we observe at the sensor sp
ace is a superposition of projected fields, from the whole gray-matter. This is the reason for a major pitfall of noninvasive Electrophysiology methods: distorted reconstruction of neural activity and its connectivity or leakage. It has been proven that current methods produce incorrect connectomes. Somewhat related to the incorrect connectivity modelling, they disregard either Systems Theory and Bayesian Information Theory. We introduce a new formalism that attains for it, Hidden Gaussian Graphical State-Model (HIGGS). A neural Gaussian Graphical Model (GGM) hidden by the observation equation of Magneto-encephalographic (MEEG) signals. HIGGS is equivalent to a frequency domain Linear State Space Model (LSSM) but with sparse connectivity prior. The mathematical contribution here is the theory for high-dimensional and frequency-domain HIGGS solvers. We demonstrate that HIGGS can attenuate the leakage effect in the most critical case: the distortion EEG signal due to head volume conduction heterogeneities. Its application in EEG is illustrated with retrieved connectivity patterns from human Steady State Visual Evoked Potentials (SSVEP). We provide for the first time confirmatory evidence for noninvasive procedures of neural connectivity: concurrent EEG and Electrocorticography (ECoG) recordings on monkey. Open source packages are freely available online, to reproduce the results presented in this paper and to analyze external MEEG databases.
Simplistic estimation of neural connectivity in MEEG sensor space is impossible due to volume conduction. The only viable alternative is to carry out connectivity estimation in source space. Among the neuroscience community this is claimed to be impo
ssible or misleading due to Leakage: linear mixing of the reconstructed sources. To address this problematic we propose a novel solution method that caulks the Leakage in MEEG source activity and connectivity estimates: BC-VARETA. It is based on a joint estimation of source activity and connectivity in the frequency domain representation of MEEG time series. To achieve this, we go beyond current methods that assume a fixed gaussian graphical model for source connectivity. In contrast we estimate this graphical model in a Bayesian framework by placing priors on it, which allows for highly optimized computations of the connectivity, via a new procedure based on the local quadratic approximation under quite general prior models. A further contribution of this paper is the rigorous definition of leakage via the Spatial Dispersion Measure and Earth Movers Distance based on the geodesic distances over the cortical manifold. Both measures are extended for the first time to quantify Connectivity Leakage by defining them on the cartesian product of cortical manifolds. Using these measures, we show that BC-VARETA outperforms most state of the art inverse solvers by several orders of magnitude.
We prove a quantum version of the localization formula of Witten that relates invariants of a git quotient with the equivariant invariants of the action. Using the formula we prove a quantum version of an abelianization formula of S. Martin relating
invariants of geometric invariant theory quotients by a group and its maximal torus, conjectured by Bertram, Ciocan-Fontanine, and Kim. By similar techniques we prove a quantum Lefschetz principle for holomorphic symplectic reductions. As an application, we give a formula for the fundamental solution to the quantum differential equation (qde) for the moduli space of points on the projective line and for the smoothed moduli space of framed sheaves on the projective plane (a Nakajima quiver variety).
