ShantanuT01/DACTYL-Pretraining huggingface dataset:
The Tsetlin library is a very well studied model for the way an arrangement of books on a library shelf evolves over time. One of the most interesting properties of this Markov chain is that its spectrum can be computed exactly and that the eigenvalues are linear in the transition probabilities. In this paper we consider a generalization which can be interpreted as a self-organizing library in which the arrangements of books on each shelf are restricted to be linear extensions of a fixed poset. The moves on the books are given by the extended promotion operators of Ayyer, Klee, and Schilling while the shelves, bookcases, etc. evolve according to the move-to-back moves as in the the self-organizing library of Bj\"orner. We show that the eigenvalues of the transition matrix of this Markov chain are $\pm 1$ integer combinations of the transition probabilities if the posets that prescribe the restrictions on the book arrangements are rooted forests or more generally, if they consist of ordinal sums of a rooted forest and so called ladders. For some of the results we show that the monoids generated by the moves are either $\mathcal{R}$-trivial or, more generally, in $\textbf{DO(Ab)}$ and then we use the theory of left random walks on the minimal ideal of such monoids to find the eigenvalues. Moreover, in order to give a combinatorial description of the eigenvalues in the more general case, we relate the eigenvalues when the restrictions on the book arrangements change only by allowing for one additional transposition of two fixed books.
We investigate the quantum dynamics of site diluted S=1/2 Heisenberg antiferromagnetic clusters at the percolation threshold. We use Lanczos diagonalization to calculate the lowest excitation gap Delta and, to reach larger sizes, study an upper bound for Delta obtained from sum rules involving the staggered structure factor and susceptibility, which we evaluate by quantum Monte Carlo simulations. Scaling the gap distribution with the cluster length L, Delta sim 1/L^z, we obtain a dynamic exponent z approximate 2D_f, where D_f=91/48 is the fractal dimensionality of the percolating cluster. This is in contrast to previous expectations of z=D_f. We argue that the low-energy excitations are due to weakly coupled effective moments formed due to local imbalance in sublattice occupation.
Publicly available clock correction data from the Global Positioning System was analyzed and used in combination with the results of terrestrial clock comparison experiments to confirm the local position invariance (LPI) of Planck's constant within the context of general relativity. The results indicate that h is invariant within a limit of |beta_h|<0.007, where beta_h is a dimensionless parameter that represents the extent of LPI violation.
In odd-dimensional spaces, gauge invariance permits a Chern-Simons mass term for the gauge fields in addition to the usual Maxwell-Yang-Mills kinetic energy term. We study the Casimir effect in such a (2+1)-dimensional Abelian theory. For the case of parallel conducting lines the result is the same as for a scalar field. For the case of circular boundary conditions the results are completely different, with even the sign of the effect being opposite for Maxwell-Chern-Simons fields and scalar fields. We further examine the effect of finite temperature. The Casimir stress is found to be attractive at both low and high temperature. Possibilities of observing this effect in the laboratory are discussed.
We show a probabilistic functional limit result for one-dimensional diffusion processes that are reflected at an elastic boundary which is a function of the reflection local time. Such processes are constructed as limits of a sequence of diffusions which are discretely reflected by small jumps at an elastic boundary, with reflection local times being approximated by $\varepsilon$-step processes. The construction yields the Laplace transform of the inverse local time for reflection. Processes and approximations of this type play a role in finite fuel problems of singular stochastic control.
Deep learning (DL) has demonstrated its powerful capabilities in the field of image inpainting. The DL-based image inpainting approaches can produce visually plausible results, but often generate various unpleasant artifacts, especially in the boundary and highly textured regions. To tackle this challenge, in this work, we propose a new end-to-end, two-stage (coarse-to-fine) generative model through combining a local binary pattern (LBP) learning network with an actual inpainting network. Specifically, the first LBP learning network using U-Net architecture is designed to accurately predict the structural information of the missing region, which subsequently guides the second image inpainting network for better filling the missing pixels. Furthermore, an improved spatial attention mechanism is integrated in the image inpainting network, by considering the consistency not only between the known region with the generated one, but also within the generated region itself. Extensive experiments on public datasets including CelebA-HQ, Places and Paris StreetView demonstrate that our model generates better inpainting results than the state-of-the-art competing algorithms, both quantitatively and qualitatively. The source code and trained models will be made available at https://github.com/HighwayWu/ImageInpainting.
The classical formalism of the Moment Problem has been combined with a cumulant approach and applied to the extensive many-body problem. This has yielded many new exact results for many-body systems in the thermodynamic limit - for the ground state energy, for excited state gaps, and for arbitrary ground state averages. The method applies to any extensive Hamiltonian system, for any phase or symmetry arising in the model, whether on a lattice or in the continuum, and for any dimensionality. The theorems are of a nonperturbative nature with respect to any couplings occuring in the model.
This paper is aimed to dissociate nonlocality from quantum theory. We demonstrate that the tests on violation of the Bell type inequalities are simply statistical tests of local incompatibility of observables. In fact, these are tests on violation of {\it the Bohr complementarity principle.} Thus, the attempts to couple experimental violations of the Bell type inequalities with "quantum nonlocality" is really misleading. These violations are explained in the quantum theory as exhibitions of incompatibility of observables for a single quantum system, e.g., the spin projections for a single electron or the polarization projections for a single photon. Of course, one can go beyond quantum theory with the hidden variables models (as was suggested by Bell) and then discuss their possible nonlocal features. However, conventional quantum theory is local.
We use Gemini Near-Infrared Integral Field Spectrograph (NIFS) adaptive optics assisted data-cubes to map the stellar population of the inner few hundred parsecs of a sample of 18 nearby Seyfert galaxies. The near-infrared light is dominated by the contribution of young to intermediate old stellar populations, with light-weighted mean ages $<t>_L\ \lesssim $ 1.5\,Gyr. Hot dust ($HD$) emission is centrally peaked (in the unresolved nucleus), but it is also needed to reproduce the continuum beyond the nucleus in nearly half of the sample. We have analysed the stellar population properties of the nuclear region and their relation with more global properties of the galaxies. We find a correlation between the X-ray luminosity and the contributions from the $HD$, featureless continuum $FC$ and reddening $A_V$. We attribute these correlations to the fact that all these properties are linked to the mass accretion rate to the active galactic nuclei (AGN). We also find a correlation of the bolometric luminosity $log(LBol_{obs})$ with the mass-weighted mean age of the stellar population, interpreted as due a delay between the formation of new stars and the triggering/feeding of the AGN. The gas reaching the supermassive black hole is probably originated from mass loss from the already somewhat evolved intermediate-age stellar population ($<t>_L \lesssim $ 1.5\,Gyr). In summary, our results show that there is a significant fraction of young to intermediate age stellar populations in the inner few 100\,pc of active galaxies, suggesting that this region is facing a rejuvenation process in which the AGN, once triggered, precludes further star formation, in the sense that it can be associated with the lack of new star formation in the nuclear region.
We present a pilot search for variable and transient sources at 1.4 GHz with the Australian Square Kilometre Array Pathfinder (ASKAP). The search was performed in a 30 deg$^{2}$ area centred on the NGC 7232 galaxy group over 8 epochs and observed with a near-daily cadence. The search yielded nine potential variable sources, rejecting the null hypothesis that the flux densities of these sources do not change with 99.9% confidence. These nine sources displayed flux density variations with modulation indices m $\geq 0.1$ above our flux density limit of 1.5 mJy. They are identified to be compact AGN/quasars or galaxies hosting an AGN, whose variability is consistent with refractive interstellar scintillation. We also detect a highly variable source with modulation index m $ > 0.5$ over a time interval of a decade between the Sydney University Molonglo Sky Survey (SUMSS) and our latest ASKAP observations. We find the source to be consistent with the properties of long-term variability of a quasar. No transients were detected on timescales of days and we place an upper limit $\rho < 0.01$ deg$^{2}$ with 95% confidence for non-detections on near-daily timescales. The future VAST-Wide survey with 36-ASKAP dishes will probe the transient phase space with a similar cadence to our pilot survey, but better sensitivity, and will detect and monitor rarer brighter events.
In this paper I give a short review of some properties of the colossal magnetoresistance manganites, connected with the orbital degrees of freedom. Ions Mn{3+}, present in most of these compounds, have double orbital degeneracy and are strong Jahn-Teller ions, causing structural distortions and orbital ordering. Mechanisms leading to such ordering are shortly discussed, and the role of orbital degrees of freedom in different parts of the phase diagram of manganites is described. Special attention is paid to the properties of low-doped systems (doping 0.1 - 0.25), to overdoped systems (x > 0.5), and to the possibility of a novel type of orbital ordering in optimally doped ferromagnetic metallic manganites.
ABRIDGED: A detailed 2D study of the central region of NGC5253 has been performed to characterize the stellar and ionized gas structure as well as the extinction distribution, physical properties and kinematics of the ionized gas in the central ~210pc x 130pc. We utilized optical integral field spectroscopy (IFS) data obtained with FLAMES. A detailed extinction map for the ionized gas in NGC5253 shows that the largest extinction is associated with the prominent Giant HII region. There is an offset of ~0.5" between the peak of the optical continuum and the extinction peak in agreement with findings in the infrared. We found that stars suffer less extinction than gas by a factor of 0.33. The [SII]l6717/[SII]l6731 map shows an electron density (N_e) gradient declining from the peak of emission in Ha (790cm^-3) outwards, while the argon line ratio traces areas with $N_e~4200 - 6200cm^(-3). The area polluted with extra nitrogen, as deduced from the excess [NII]/Ha, extends up to distances of 3.3" (~60pc) from the maximum pollution, which is offset by ~1.5" from the peak of continuum emission. Wolf-Rayet features are distributed in an irregular pattern over a larger area (~100pc x 100pc) and associated with young stellar clusters. We measured He^+ abundances over most of the field of view and values of He^++/H^+<~0.0005 in localized areas which do not coincide, in general, with the areas presenting W-R emission or extra nitrogen. The line profiles are complex. Up to three emission components were needed to reproduce them. One of them, associated with the giant HII region, presents supersonic widths and [NII] and [SII] emission lines shifted up to 40km/s with respect to Ha. Similarly, one of the narrow components presents offsets in the [NII] line of <~20km/s. This is the first time that maps with such velocity offsets for a starburst galaxy have been presented.
We summarize the main results from MODEST-1, the first workshop on MOdeling DEnse STellar systems. Our goal is to go beyond traditional population synthesis models, by introducing dynamical interactions between single stars, binaries, and multiple systems. The challenge is to define and develop a software framework to enable us to combine in one simulation existing computer codes in stellar evolution, stellar dynamics, and stellar hydrodynamics. With this objective, the workshop brought together experts in these three fields, as well as other interested astrophysicists and computer scientists. We report here our main conclusions, questions and suggestions for further steps toward integrating stellar evolution and stellar (hydro)dynamics.
We analyze the metastable states near criticality of the bootstrap percolation on Galton-Watson trees. We find that, depending on the exact choice of the offspring distribution, it is possible to have several distinct metastable states, with varying scaling of their duration while approaching criticality.
It is only now, with low-frequency radio telescopes, long exposures with high-resolution X-ray satellites and gamma-ray telescopes, that we are beginning to learn about the physics in the periphery of galaxy clusters. In the coming years, Sunyaev-Zeldovich telescopes are going to deliver further great insights into the plasma physics of these special regions in the Universe. The last years have already shown tremendous progress with detections of shocks, estimates of magnetic field strengths and constraints on the particle acceleration efficiency. X-ray observations have revealed shock fronts in cluster outskirts which have allowed inferences about the microphysical structure of shocks fronts in such extreme environments. The best indications for magnetic fields and relativistic particles in cluster outskirts come from observations of so-called radio relics, which are megaparsec-sized regions of radio emission from the edges of galaxy clusters. As these are difficult to detect due to their low surface brightness, only few of these objects are known. But they have provided unprecedented evidence for the acceleration of relativistic particles at shock fronts and the existence of muG strength fields as far out as the virial radius of clusters. In this review we summarise the observational and theoretical state of our knowledge of magnetic fields, relativistic particles and shocks in cluster outskirts.
We prove a sum formula with 4 parameters among finite alternating multiple zeta values which can be regarded as an alternating version of the result of Kamano on finite multiple zeta values.
Sliding and twisting van der Waals layers with respect to each other gives rise to moir\'e structures with emergent electronic properties. Electrons in these moir\'e structures feel weak potentials that are typically in the tens of millielectronvolt range when the moir\'e structures are smooth at the atomic scale. Here we report a facile technique to achieve deep, deterministic trapping potentials via strain-based moir\'e engineering in van der Waals bilayers. We use elasto-scanning tunneling microscopy to show that uniaxial strain drives a commensurate-incommensurate lattice transition in a multilayer MoSe$_2$ system. In the incommensurate state, the top monolayer is partially detached from the bulk through the spontaneous formation of topological solitons where stress is relieved. Intersecting solitons form a honeycomb-like network resulting from the three-fold symmetry of the adhesion potential between layers. The vertices of the honeycomb network occur in bound pairs with different interlayer stacking arrangements. One vertex of the pair is found to be an efficient trap for electrons, displaying two states that are deeply confined within the semiconductor gap and have a spatial extent of 2 nm. Honeycomb soliton networks thus provide a unique path to engineer an array of identical deeply confined states with a strain-dependent tunable spatial separation, without the necessity of introducing chemical defects into the host materials.
We investigate a universal behavior of thermodynamics and evaporation process for the regular black holes. We newly observe an important point where the temperature is maximum, the heat capacity is changed from negative infinity to positive infinity, and the free energy is minimum. Furthermore, this point separates the evaporation process into the early stage with negative heat capacity and the late stage with positive heat capacity. The latter represents the quantum cooling evaporation process. As a result, the whole evaporation process could be regarded as the inverse Hawking-Page phase transition.
In this presented work, we propose a realistic hair simulator using image blending for dermoscopic images. This hair simulator can be used for benchmarking and validation of the hair removal methods and in data augmentation for improving computer aided diagnostic tools. We adopted one of the popular implementation of image blending to superimpose realistic hair masks to hair lesion. This method was able to produce realistic hair masks according to a predefined mask for hair. Thus, the produced hair images and masks can be used as ground truth for hair segmentation and removal methods by inpainting hair according to a pre-defined hair masks on hairfree areas. Also, we achieved a realism score equals to 1.65 in comparison to 1.59 for the state-of-the-art hair simulator.
In this paper, we develop a new method to classify abelian automorphism groups of hypersurfaces. We use this method to classify (Theorem 4.2) abelian groups that admit a liftable action on a smooth cubic fourfold. A parallel result (Theorem 5.1) is obtained for quartic surfaces.
Recently, very high-energy photons above 100 GeV were reported to be detected from GRB~190114C and GRB~180720B at, respectively, 100-1000 s and 10 hours after the burst. We model the available broad-band data of both GRBs with the synchrotron plus synchrotron self-Compton (SSC) emission of the afterglow shocks. We find that the sub-TeV emission of GRB~180720B can be interpreted as the SSC emission from afterglow shocks expanding in a constant density circum-burst medium. The SSC emission of GRB~190114C dominates over the synchrotron component from GeV energies at $\sim100$ s, which can explain the possible hard spectrum of the GeV emission at this time. The extrapolated flux of this SSC component to sub-TeV energies can explain the high-significance detection of GRB~190114C by the MAGIC telescope. The parameter values (such as the circum-burst density and shock microphysical parameters) in the modeling are not unusual for both GRBs, implying that the detection of sub-TeV photons from these two bursts should be attributed to their large burst energies and low redshifts.
We have numerically investigated whether or not a mean-field theory of spin textures generate fictitious flux in the doped two dimensional $t-J$-model. First we consider the properties of uniform systems and then we extend the investigation to include models of striped phases where a fictitious flux is generated in the domain wall providing a possible source for lowering the kinetic energy of the holes. We have compared the energetics of uniform systems with stripes directed along the (10)- and (11)-directions of the lattice, finding that phase-separation generically turns out to be energetically favorable. In addition to the numerical calculations, we present topological arguments relating flux and staggered flux to geometric properties of the spin texture. The calculation is based on a projection of the electron operators of the $t-J$ model into a spin texture with spinless fermions.
Let $X\subset \mathbb{R}^n$ be a compact semialgebraic set and let $f:X\to \mathbb{R}$ be a nonzero Nash function. We give a Solern\'o and D'Acunto-Kurdyka type estimation of the exponent $\varrho\in[0,1)$ in the {\L}ojasiewicz gradient inequality $|\nabla f(x)|\ge C|f(x)|^\varrho$ for $x\in X$, $|f(x)|<\varepsilon$ for some constants $C,\varepsilon>0$, in terms of the degree of a polynomial $P$ such that $P(x,f(x))=0$, $x\in X$. As a corollary we obtain an estimation of the degree of sufficiency of non-isolated Nash functions singularities
The second law of thermodynamics is probabilistic in nature. Its formulation requires that the state of a system be described by a probability distribution. A natural question, thereby, arises as to whether a prior knowledge about the state of the system affects the second law. This question has now been nurtured over a century and its inception was done by C. Maxwell through his famous thought experiment wherein comes the idea of Maxwell's demon. The next important step in this direction was provided by L. Szilard who demonstrated a theoretical model for an information engine incorporating Maxwell's demon. The final step that lead to the inter-linkage between information theory and thermodynamics was through Landauer's principle of information erasure that established the fact that information is physical. Here we will present an overview of these three major works that laid the foundations of information thermodynamics.
We use data taken as part of HST/WFC3 observations of the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) to identify massive and evolved galaxies at 3<z<4.5. This is performed using the strength of the Balmer break feature at rest-frame 3648A, which is a diagnostic of the age of the stellar population in galaxies. Using WFC3 H-band selected catalog for the CANDELS GOODS-S field and deep multi-waveband photometry from optical (HST) to mid-infrared (Spitzer) wavelengths, we identify a population of old and evolved post-starburst galaxies based on the strength of their Balmer breaks (Balmer Break Galaxies- BBGs). The galaxies are also selected to be bright in rest-frame near-IR wavelengths and hence, massive. We identify a total of 16 BBGs. Fitting the spectral energy distribution (SED) of the BBGs show that the candidate galaxies have average estimated ages of ~800 Myr and average stellar masses of ~5x10^10 M_sun, consistent with being old and massive systems. Two of our BBG candidates are also identified by the criteria that is sensitive to star forming galaxies (LBG selection). We find a number density of ~3.2x10^-5 Mpc^-3 for the BBGs corresponding to a mass density of ~2.0x10^6 M_sun/Mpc^3 in the redshift range covering the survey. Given the old age and the passive evolution, it is argued that some of these objects formed the bulk of their mass only a few hundred million years after the Big Bang.
We investigate the effects of noise on parameterised quantum circuits using spectral analysis and classical signal processing tools. For different noise models, we quantify the additional, higher frequency modes in the output signal caused by device errors. We show that filtering these noise-induced modes effectively mitigates device errors. When combined with existing methods, this yields an improved reconstruction of the noiseless variational landscape. Moreover, we describe the classical and quantum resource requirements for these techniques and test their effectiveness for application motivated circuits on quantum hardware.