ShantanuT01/DACTYL-Pretraining huggingface dataset:
Multiple emitters coherently interacting with an electromagnetic mode give rise to collective effects such as correlated decay and coherent exchange interaction, depending on the separation of the emitters. By diagonalizing the effective non-Hermitian many-body Hamiltonian we reveal the complex-valued eigenvalue spectrum encoding the decay and interaction characteristics. We show that there are significant differences in the emerging effects for an array of interacting anharmonic oscillators compared to those of two-level systems and harmonic oscillators. The bosonic decay rate of the most superradiant state increases linearly as a function of the filling factor and exceeds that of two-level systems in magnitude. Furthermore, with bosonic systems, dark states are formed at each filling factor. These are in strong contrast with two-level systems, where the maximal superradiance is observed at half filling and with larger filling factors superradiance diminishes and no dark states are formed. As an experimentally relevant setup of bosonic waveguide QED, we focus on arrays of transmon devices embedded inside a rectangular waveguide. Specifically, we study the setup of two transmon pairs realized experimentally in M. Zanner et al., arXiv.2106.05623 (2021), and show that it is necessary to consider transmons as bosonic multilevel emitters to accurately recover correct collective effects for the higher excitation manifolds.
A cylindrical Levy process does not enjoy a cylindrical version of the semi-martingale decomposition which results in the need to develop a completely novel approach to stochastic integration. In this work, we introduce a stochastic integral for random integrands with respect to cylindrical Levy processes in Hilbert spaces. The space of admissible integrands consists of adapted stochastic processes with values in the space of Hilbert-Schmidt operators. Neither the integrands nor the integrator is required to satisfy any moment or boundedness condition. The integral process is characterised as an adapted, Hilbert space valued semi-martingale with cadlag trajectories.
We analyze a non-reversible mean-field jump dynamics for discrete q-valued rotators and show in particular that it exhibits synchronization. The dynamics is the mean-field analogue of the lattice dynamics investigated by the same authors in [26] which provides an example of a non-ergodic interacting particle system on the basis of a mechanism suggested by Maes and Shlosman [32]. Based on the correspondence to an underlying model of continuous rotators via a discretization transformation we show the existence of a locally attractive periodic orbit of rotating measures. We also discuss global attractivity, using a free energy as a Lyapunov function and the linearization of the ODE which describes typical behavior of the empirical distribution vector.
In this paper we compute the cohomology groups of GL(4,Z) with coefficients in symmetric powers of the standard representation twisted by the determinant. This problem arises in Goncharov's approach to the study of motivic multiple zeta values of depth 4. The techniques that we use include Kostant's formula for cohomology groups of nilpotent Lie subalgebras of a reductive Lie algebra, Borel-Serre compactification, a result of Harder on Eisenstein cohomology. Finally, we need to show that the ghost class, which is present in the cohomology of the boundary of the Borel-Serre compactification, disappears in the Eisenstein cohomology of GL(4,Z). For this we use a computationally effective version for the homological Euler characteristic of GL(4,Z) with non-trivial coefficients.
Multi-zone chemical evolution models (CEMs), differing in the nucleosynthesis prescriptions (yields) and prescriptions of star formation, have been computed for the Milky Way. All models fit the observed O/H and Fe/H gradients well and reproduce the main characteristics of the gas distribution, but they are also designed to do so. For the C/H gradient the results are inconclusive with regards to yields and star formation. The C/Fe and O/Fe vs. Fe/H, as well as C/O vs. O/H trends predicted by the models for the solar neighbourhood zone were compared with stellar abundances from the literature. For O/Fe vs. Fe/H all models fit the data, but for C/O vs. O/H, only models with increased carbon yields for zero-metallicity stars or an evolving initial mass function provide good fits. Furthermore, a steep star formation threshold in the disc can be ruled out since it predicts a steep fall-off in all abundance gradients beyond a certain galactocentric distance (~ 13 kpc) and cannot explain the possible flattening of the C/H and Fe/H gradients in the outer disc seen in observations. Since in the best-fit models the enrichment scenario is such that carbon is primarily produced in low-mass stars, it is suggested that in every environment where the peak of star formation happened a few Gyr back in time, winds of carbon-stars are responsible for most of the carbon enrichment. However, a significant contribution by zero-metallicity stars, especially at very early stages, and by winds of high-mass stars, which are increasing in strength with metallicity, cannot be ruled out by the CEMs presented here. In the solar neighbourhood, as much as 80%, or as little as 40% of the carbon may have been injected to the interstellar medium by low- and intermediate-mass stars. The stellar origin of carbon remains an open question, although production in low- and intermediate-mass stars appears to be the simplest explanation of observed carbon abundance trends.
We analize semi-inclusive electron-nucleus processes e+A->e'+h+X at moderate Q**2 and energy transfer nu. Our results show that nucleons bound in the nuclear medium are distributed according to a function f_A that reduces to the standard light-cone distribution in the Bjorken limit and exhibits a sizeable Q**2-dependence at lower Q**2, particular Q**2 is order of nu**2.
In this paper we study the finite time emergence of one shock for the solution of scalar conservation laws in one space dimension with general flux f . We give a necessary and sufficient condition to the initial data connecting to flux. The proof relies on the structure theorem for the linear degenerate flux and the finer analysis of characteristic curves.
Data-driven saliency has recently gained a lot of attention thanks to the use of Convolutional Neural Networks for predicting gaze fixations. In this paper we go beyond standard approaches to saliency prediction, in which gaze maps are computed with a feed-forward network, and present a novel model which can predict accurate saliency maps by incorporating neural attentive mechanisms. The core of our solution is a Convolutional LSTM that focuses on the most salient regions of the input image to iteratively refine the predicted saliency map. Additionally, to tackle the center bias typical of human eye fixations, our model can learn a set of prior maps generated with Gaussian functions. We show, through an extensive evaluation, that the proposed architecture outperforms the current state of the art on public saliency prediction datasets. We further study the contribution of each key component to demonstrate their robustness on different scenarios.
We study the evaporation of two-dimensional black holes in JT gravity from a three-dimensional point of view. A partial dimensional reduction of AdS$_3$ in Poincar\'e coordinates leads to an extremal 2D black hole in JT gravity coupled to a 'bath': the holographic dual of the remainder of the 3D spacetime. Partially reducing the BTZ black hole gives us the finite temperature version. We compute the entropy of the radiation using geodesics in the three-dimensional spacetime. We then focus on the finite temperature case and describe the dynamics by introducing time-dependence into the parameter controlling the reduction. The energy of the black hole decreases linearly as we slowly move the dividing line between black hole and bath. Through a re-scaling of the BTZ parameters we map this to the more canonical picture of exponential evaporation. Finally, studying the entropy of the radiation over time leads to a geometric representation of the Page curve. The appearance of the island region is explained in a natural and intuitive fashion.
We extend to higher order a recently published method for calculating the deflection angle of light in a general static and spherically symmetric metric. Since the method is convergent we obtain very accurate analytical expressions that we compare with numerical results.
The coupled-channel theory is a natural way of treating nonelastic channels, in particular those arising from collective excitations characterized by nuclear deformations. A proper treatment of such excitations is often essential to the accurate description of experimental nuclear-reaction data and to the prediction of a wide variety of scattering observables. Stimulated by recent work substantiating the near validity of the adiabatic approximation in coupled-channel calculations for scattering on statically deformed nuclei, we explore the possibility of generalizing a global spherical optical model potential (OMP) to make it usable in coupled-channel calculations on this class of nuclei. To do this, we have deformed the Koning-Delaroche global spherical potential for neutrons, coupling a sufficient number of states of the ground state band to ensure convergence. We present an extensive study of the effects of collective couplings and nuclear deformations on integrated cross sections as well as on angular distributions for neutron-induced reactions on statically deformed nuclei in the rare-earth region. We choose isotopes of three rare-earth elements (Gd, Ho, W), which are known to be nearly perfect rotors, to exemplify the results of the proposed method. Predictions from our model for total, elastic and inelastic cross sections, as well as for elastic and inelastic angular distributions, are in reasonable agreement with measured experimental data. These results suggest that the deformed Koning-Delaroche potential provides a useful regional neutron optical potential for the statically deformed rare earth nuclei.
Statistical modeling of data sets by neural-network techniques is offered as an alternative to traditional semiempirical approaches to global modeling of nuclear properties. New results are presented to support the position that such novel techniques can rival conventional theory in predictive power, if not in economy of description. Examples include the statistical inference of atomic masses and beta-decay halflives based on the information contained in existing databases. Neural network modeling, as well as other statistical strategies based on new algorithms for artificial intelligence, may prove to be a useful asset in the further exploration of nuclear phenomena far from stability.
We introduce a notion of the De Rham complex of a Gerstenhaber algebra which produces a notion of a "quasi-BV structure", and allows to classify these structures, generalizing the classical results for polyvector fields.
In this paper, we investigate the energy-source models for the most luminous supernova ASASSN-15lh. We revisit the ejecta-circumstellar medium (CSM) interaction (CSI) model and the CSI plus magnetar spin-down with full gamma-ray/X-ray trapping which were adopted by \cite{Chatzopoulos16} and find that the two models cannot fit the bolometric LC of ASASSN-15lh. Therefore, we consider a CSI plus magnetar model with the gamma-rays/X-rays leakage effect to eliminate the late-time excess of the theoretical LC. We find that this revised model can reproduce the bolometric LC of ASASSN-15lh. Moreover, we construct a new hybrid model (i.e., the CSI plus fallback model), and find that it can also reproduce the bolometric LC of ASASSN-15lh. Assuming that the conversion efficiency ($\eta$) of fallback accretion to the outflow is typically $\sim10^{-3}$, we derive that the total mass accreted is $\sim3.9~M_\odot$. The inferred CSM mass in the two models is rather large, indicating that the progenitor could have experienced an eruption of hydrogen-poor materials followed by an energetic core-collapse explosion leaving behind a magnetar or a black hole.
There is a large degree of variety in the optical variability of quasars and it is unclear whether this is all attributable to a single (set of) physical mechanism(s). We present the results of a systematic search for major flares in AGN in the Catalina Real-time Transient Survey as part of a broader study into extreme quasar variability. Such flares are defined in a quantitative manner as being atop of the normal, stochastic variability of quasars. We have identified 51 events from over 900,000 known quasars and high probability quasar candidates, typically lasting 900 days and with a median peak amplitude of $\Delta m = 1.25$ mag. Characterizing the flare profile with a Weibull distribution, we find that nine of the sources are well described by a single-point single-lens model. This supports the proposal by Lawrence et al. (2016) that microlensing is a plausible physical mechanism for extreme variability. However, we attribute the majority of our events to explosive stellar-related activity in the accretion disk: superluminous supernovae, tidal disruption events, and mergers of stellar mass black holes.
GRB 160625B is an extremely bright GRB with three distinct emission episodes. By analyzing its data observed with the GBM and LAT on board the {\em Fermi} mission, we find that a multi-color black body (mBB) model can be used to fit the spectra of initial short episode (Episode I) very well within the hypothesis of photosphere emission of a fireball model. The time-resolved spectra of its main episode (Episode II), which was detected with both GBM and LAT after a long quiet stage ($\sim 180$ seconds) of the initial episode, can be fitted with a model composing of an mBB component plus a cutoff power-law (CPL) component. This GRB was detected again in the GBM and LAT bands with a long extended emission (Episode III) after a quiet period of $\sim 300$ seconds. The spectrum of Episode III is adequately fitted with a CPL plus a single power-law models, and no mBB component is required. These features may imply that the emission of three episodes are dominated by distinct physics process, i.e., Episode I is possible from cocoon emission surrounding the relativistic jet, Episode II may be from photosphere emission and internal shock of relativistic jet, and Episode III is contributed by internal and external shocks of relativistic jet. On the other hand, both X-ray and optical afterglows are consistent with standard external shocks model.
We study the unbiased WalkerMaker-WalkerBreaker games on the edge set of the complete graph on $n$ vertices, $K_n$, a variant of well-known Maker-Breaker positional games, where both players have the restriction on the way of playing. Namely, each player has to choose her/his edges according to a walk. Here, we focus on two standard graph games - the Connectivity game and the Hamilton cycle game and show how quickly WalkerMaker can win both games.
We address semantic segmentation on omnidirectional images, to leverage a holistic understanding of the surrounding scene for applications like autonomous driving systems. For the spherical domain, several methods recently adopt an icosahedron mesh, but systems are typically rotation invariant or require significant memory and parameters, thus enabling execution only at very low resolutions. In our work, we propose an orientation-aware CNN framework for the icosahedron mesh. Our representation allows for fast network operations, as our design simplifies to standard network operations of classical CNNs, but under consideration of north-aligned kernel convolutions for features on the sphere. We implement our representation and demonstrate its memory efficiency up-to a level-8 resolution mesh (equivalent to 640 x 1024 equirectangular images). Finally, since our kernels operate on the tangent of the sphere, standard feature weights, pretrained on perspective data, can be directly transferred with only small need for weight refinement. In our evaluation our orientation-aware CNN becomes a new state of the art for the recent 2D3DS dataset, and our Omni-SYNTHIA version of SYNTHIA. Rotation invariant classification and segmentation tasks are additionally presented for comparison to prior art.
We consider a Cops-and-Robber game played on the subsets of an $n$-set. The robber starts at the full set; the cops start at the empty set. On each turn, the robber moves down one level by discarding an element, and each cop moves up one level by gaining an element. The question is how many cops are needed to ensure catching the robber when the robber reaches the middle level. Aaron Hill posed the problem and provided a lower bound of $2^{n/2}$ for even $n$ and $\binom{n}{\lceil n/2 \rceil}2^{-\lfloor n/2 \rfloor}$ for odd $n$. We prove an upper bound (for all $n$) that is within a factor of $O(\ln n)$ times this lower bound.
We prove a central limit theorem for the normalized overlap between two replicas in the spherical SK model in the high temperature phase. The convergence holds almost surely with respect to the disorder variables, and the inverse temperature can approach the criticial value at a polynomial rate with any exponent strictly greater than $1/3$.
HST finds galaxies whose Tolman dimming should exceed 10 mag. Could evolution alone explain these as our ancestor galaxies? Or could they be representatives of quite a different dynasty whose descendants are no longer prominent today? We explore this latter hypothesis and argue that Surface Brightness Selection Effects naturally bring into focus quite different dynasties from different redshifts. Thus the HST z=7 galaxies could be examples of galaxies whose descendants are both too small and too choked with dust to be recognizable in our neighborhood easily today. Conversely the ancestors of the Milky Way and its obvious neighbors will have completely sunk below the sky at z>1.2 although their diffuse light could account for the missing Reionization flux. This Succeeding Prominent Dynasties Hypothesis (SPDH) fits the existing observations both naturally and well,including the bizarre distributions of galaxy surface brightnesses found in deep fields, the angular size ~ inverse (1+z) law,'Downsizing' which turns out to be an 'illusion' in the sense that it does not imply evolution, 'Infant Mortality', i.e. the discrepancy between stars born and stars seen, and finally the recently discovered and unexpected excess of QSOAL DLAs at high redshift. If the SPDH is true then a large proportion of galaxies remain sunk from sight, probably at all redshifts. We show that fishing them out of the sky by their optical emissions alone will be practically impossible, even when they are nearby. More ingenious methods will be needed to detect them. It follows that disentangling galaxy evolution through studying ever higher redshift galaxies may be a forlorn hope because one will be comparing young apples with old oranges, not descendants with their own ancestors.
Visual-Semantic Embedding (VSE) is a prevalent approach in image-text retrieval by learning a joint embedding space between the image and language modalities where semantic similarities would be preserved. The triplet loss with hard-negative mining has become the de-facto objective for most VSE methods. Inspired by recent progress in deep metric learning (DML) in the image domain which gives rise to new loss functions that outperform triplet loss, in this paper, we revisit the problem of finding better objectives for VSE in image-text matching. Despite some attempts in designing losses based on gradient movement, most DML losses are defined empirically in the embedding space. Instead of directly applying these loss functions which may lead to sub-optimal gradient updates in model parameters, in this paper we present a novel Gradient-based Objective AnaLysis framework, or \textit{GOAL}, to systematically analyze the combinations and reweighting of the gradients in existing DML functions. With the help of this analysis framework, we further propose a new family of objectives in the gradient space exploring different gradient combinations. In the event that the gradients are not integrable to a valid loss function, we implement our proposed objectives such that they would directly operate in the gradient space instead of on the losses in the embedding space. Comprehensive experiments have demonstrated that our novel objectives have consistently improved performance over baselines across different visual/text features and model frameworks. We also showed the generalizability of the GOAL framework by extending it to other models using triplet family losses including vision-language model with heavy cross-modal interactions and have achieved state-of-the-art results on the image-text retrieval tasks on COCO and Flick30K.
In spiral galaxies, we explain their non-Keplerian rotation curves (RCs) by means of a non-luminous component embedding their stellar-gaseous disks. Understanding the detailed properties of this component (labelled Dark Matter, DM) is one of the most pressing issues of Cosmology. We investigate the recent relationship (claimed by Walker et al. 2010, hereafter W+10) between $r$, the galaxy radial coordinate, and $V_h(r)$, the dark halo contribution to the circular velocity at $r$, {\it a}) in the framework of the Universal Rotation Curve (URC) paradigm and directly {\it b}) by means of the kinematics of a large sample of DM dominated spirals. We find a general agreement between the W+10 claim, the distribution of DM emerging from the URC and that inferred in the (low luminosity) objects of our sample. We show that such a phenomenology, linking the spiral's luminosity, radii and circular velocities, implies an evident inconsistency with (naive) predictions in the $\Lambda$ Cold Dark Matter ($\Lambda$CDM) scenario.
A grand rotation curve of the Milky Way Galaxy is constructed, which covers a wide range of radius from the Galactic Center to ~1 Mpc, and is deconvolved into bulge, disk and halo components by least-squares fitting. We determined the scale radii and masses of the bulge and disk to be M_b=(1.652 +/-0.083)x10^10 Msun, a_b=(0.522 +/- 0.037) kpc, M_d=(3.41 +/- 0.41)x10^10 Msun and a_d=(3.19 +/- 0.3) kpc. The dark halo was fitted by the Navaro-Frenk-White (NFW) density profile, rho=rho_0/[(R/h) (1+R/h)^2], and the fit yielded h=12.5 +/- 0.9 kpc and rho_0=(1.06 +/- 0.14)x10^-2 Msun pc^-3. The local dark matter density near the Sun at R_0=8 kpc is estimated to be rho_0_sun=(6.12 +/-0.80)x10^-3 Msun pc^-3 = 0.235 +/- 0.030 GeV cm^-3. The total mass inside the gravitational boundary of the Galaxy at R~ 385 kpc, a half distance to M31, is estimated to be M_h ~ (7.03 +/- 1.01)x10^11 Msun. This leads to the stellar baryon fraction of (M_b+M_d)/(M_b+M_d+M_h)=0.072 +/-0.018. Considering expected baryon fraction in the Local Group, we suggest that baryons in the form of hot gas are filling the dark halo with temperature of ~ 10^6 K and emission measure ~ 10^-5 pc cm^-6. Such hot halo gas may share a small fraction of the observed X-ray background emission.
We have used the electromigration technique to fabricate a   $\rm{C_{{60}}}$ single-molecule transistor (SMT). We present a full experimental study as a function of temperature, down to 35 mK, and as a function of magnetic field up to 8 T in a SMT with odd number of electrons, where the usual spin-1/2 Kondo effect occurs, with good agreement with theory. In the case of even number of electrons, a low temperature magneto-transport study is provided, which demonstrates a Zeeman splitting of the zero-bias anomaly at energies well below the Kondo scale.