ShantanuT01/DACTYL-Pretraining huggingface dataset:
Exploring the analogy between quantum mechanics and statistical mechanics we formulate an integrated version of the Quantropy functional [1]. With this prescription we compute the propagator associated to Boltzmann-Gibbs statistics in the semiclassical approximation as $K=F(T) \exp\left(i S_{cl}/\hbar\right)$. We determine also propagators associated to different non-additive statistics; those are the entropies depending only on the probability $S_{\pm}$ [2] and Tsallis entropy $S_q$ [3]. For $S_{\pm}$ we obtain a power series solution for the probability vs. the energy, which can be analytically continued to the complex plane, and employed to obtain the propagators. Our work is motivated by [4] where a modified q-Schr\"odinger equation is obtained; that provides the wave function for the free particle as a q-exponential. The modified q-propagator obtained with our method, leads to the same q-wave function for that case. The procedure presented in this work allows to calculate q-wave functions in problems with interactions; determining non-linear quantum implications of non-additive statistics. In a similar manner the corresponding generalized wave functions associated to $S_{\pm}$ can also be constructed. The corrections to the original propagator are explicitly determined in the case of a free particle and the harmonic oscillator for which the semi-classical approximation is exact.
In this article we address the problem of computing the dimension of the space of plane curves of degree $d$ with $n$ general points of multiplicity $m$. A conjecture of Harbourne and Hirschowitz implies that when $d \geq 3m$, the dimension is equal to the expected dimension given by the Riemann-Roch Theorem. Also, systems for which the dimension is larger than expected should have a fixed part containing a multiple $(-1)$-curve. We reformulate this conjecture by explicitly listing those systems which have unexpected dimension. Then we use a degeneration technique developed in a previous article ("Degenerations of Planar Linear Systems", alg-geom/9702015) to show that the conjecture holds for all $m \leq 12$.
The Hubble Space Telescope composite quasar spectra presented in Telfer et al. show a significant deficit of emission in the extreme ultraviolet (EUV) for the radio loud component of the quasar population (RLQs), compared to the radio quiet component of the quasar population (RQQs). The composite quasar continuum emission between 1100 \AA\, and $\sim$580 \AA\, is generally considered to be associated with the innermost regions of the accretion flow onto the central black hole. The deficit between 1100 \AA\, and 580 \AA\, in RLQs has a straightforward interpretation as a missing or a suppressed innermost region of local energy dissipation in the accretion flow. It is proposed that this can be the result of islands of large scale magnetic flux in RLQs that are located close to the central black hole that remove energy from the accretion flow as Poynting flux (sometimes called magnetically arrested accretion). These magnetic islands are natural sites for launching relativistic jets. Based on the Telfer et al. data and the numerical simulations of accretion flows in Penna et al., the magnetic islands are concentrated between the event horizon and an outer boundary of $<2.8 M$ (in geometrized units) for rapidly rotating black holes and $< 5.5M$ for modestly rotating black holes.
We have carried out a systematic study of the crystal electric field excitations in the family of cubic pyrochlores Er$_2B_2$O$_7$, with $B=$~Ti, Ge, Pt, and Sn, using neutron spectroscopy. All members of this family are magnetic insulators based on 4$f^{11}$ Er$^{3+}$ and non-magnetic $B^{4+}$. At sufficiently low temperatures, long-range antiferromagnetic order is observed in each of these Er$_2B_2$O$_7$ pyrochlores. Our inelastic neutron scattering measurements probe the transitions from the ground state doublet to excited crystal electric field states belonging to the $J=15/2$ Hund's rules manifold. This allows us to quantitatively determine the energy eigenvalues and eigenfunctions of these $(2J+1)=16$ states across the Er$_2B_2$O$_7$ series. The different ionic sizes associated with different non-magnetic $B^{4+}$ cations correspond to positive or negative chemical pressure, depending on the relative contraction or expansion of the crystal lattice, which gives rise to slightly different local environments at the Er$^{3+}$ site. Our results show that the $g$-tensor components, which characterize the anisotropy of the ground state doublet eigenfunctions, are XY-like for all four members of the Er$_2B_2$O$_7$ series. However, the XY anisotropy is much stronger for Er$_2$Pt$_2$O$_7$ and Er$_2$Sn$_2$O$_7$ ($\frac{g_{\perp}}{g_z} > 25$), than for Er$_2$Ge$_2$O$_7$ and Er$_2$Ti$_2$O$_7$ ($\frac{g_{\perp}}{g_z} < 4$). The variation in the nature of the XY-anisotropy in these systems correlates strongly with their ground states, as Er$_2$Ge$_2$O$_7$ and Er$_2$Ti$_2$O$_7$ order into $\Gamma_5$ magnetic structures, while Er$_2$Pt$_2$O$_7$ and Er$_2$Sn$_2$O$_7$ order in the $\Gamma_7$ Palmer-Chalker structure.
The X-ray emission from accreting black hole (BH) systems displays strong variability. Short reverberation lags are expected between the primary hard X-ray continuum and the reprocessed disc emission. These lags depend on light-travel distances, thus offering the opportunity to map the geometry of the innermost accretion flow. X-ray reverberation lags have been observed in several BH accreting systems. In radio quiet active galactic nuclei (AGN) these lags scale with BH mass and point to a reprocessing region located close to the Comptonizing X-ray corona. On the other hand, reverberation lags detected in the hard state of some BH X-ray binaries (BHXRB) suggest a different accretion flow geometry than in AGN, showing evidence of evolution as a function of luminosity.
Polycrystalline Yb substituted NiZn nanoferrites with the compositions of Ni0.5Zn0.5YbxFe2-xO4 (x= 0.00, 0.04, 0.08, 0.12, 0.16 and 0.20) have been synthesized using sol gel auto combustion technique. Single phase cubic spinel structure has been confirmed by the X ray diffraction (XRD) patterns. Larger lattice constants of the compositions are found with increasing Yb3+ concentration while the average grain size (52 to 18 nm) has noticeable decrease as Yb3+ content is increased. The presence of all existing elements as well as the purity of the samples has also been confirmed from energy dispersive X ray spectroscopic (EDS) analysis. Frequency dependent dielectric constant, dielectric loss, dielectric relaxation time, AC and DC resistivity of the compositions have also been examined at room temperature. The DC resistivity value is found in the order of 10 to power 10 (omega-cm) which is at least four orders greater than the ferrites prepared by conventional method. This larger value of resistivity attributes due to very small grain size and successfully explained using the Verwey and deBoer hopping conduction model. The contribution of grain and grain boundary resistance has been elucidated using Cole Cole plot. The study of temperature dependent DC resistivity confirms the semiconducting nature of all titled compositions wherein bandgap (optical) increases from 2.73 eV to 3.25 eV with the increase of Yb content. The high value of resistivity is of notable achievement for the compositions that make them a potential candidate for implication in the high frequency applications where reduction of eddy current loss is highly required.
The propagation of extremely energetic nu_tau's through the Earth is studied by means of a detailed Monte Carlo simulation. All major mechanisms of nu_tau interactions and tau energy loss as well as all its relevant decay modes are properly taken into account. The detection possibility of nu_tau's emerging from Earth in forthcoming neutrino telescopes is addressed
The physics of gamma-ray bursts (GRBs) and their offsets from the centers of their host galaxies are used to investigate the evolutionary state of their progenitors, motivated by the popular idea that GRBs are linked with the cataclysmic collapse of massive stars. We suggest that GRB progenitors in the inner and outer regions of hosts may be intrinsically different: outer bursts appear to have systematically greater isotropic equivalent energies (or narrower jets). This may provide an interesting clue to the nature of GRBs, and could reflect a relation between metallicity and the evolution of GRB progenitors. If true, then this offset-isotropic luminosity correlation is a strong argument for a collapsar origin of long-duration GRBs.
Let $P$ be an irreducible and reversible transition matrix on a finite state space $V$ with invariant distribution $\pi$. We let $k$ chains start by choosing independent locations distributed according to $\pi$ and then they evolve independently according to $P$. Let $\tau_{\mathrm{cov}}(k)$ be the first time that every vertex of $V$ has been visited at least once by at least one chain and let $t_{\rm{cov}}(k)=\mathbb{E}[\tau_{\mathrm{cov}}(k)]$ with $t_{\rm{cov}}=t_{\rm{cov}}(1)$. We prove that $t_{\rm{cov}}(k)\lesssim t_{\rm{cov}}/k$. When $k\leq t_{\mathrm{cov}}/t_{\rm{rel}}$, where $t_{\rm{rel}}$ is the inverse of the spectral gap, we show that this bound is sharp. For $k\leq t_{\mathrm{cov}}/t_{\rm{mix}}$ with $t_{\rm{mix}}$ the total variation mixing time of $(P+I)/2$ we prove that $k \cdot \max_{x_1,\ldots,x_k}\mathbb{E}_{x_1,\ldots,x_k}[\tau_{\rm{cov}}(k)] \asymp t_{\rm{cov}}$.
We analyze the broadband photometric light curves of Seyfert 1 galaxies from the Sergeev et al. (2005) sample and find that a) perturbations propagating across the continuum emitting region are a general phenomenon securely detected in most cases, b) it is possible to obtain reliable time-delays between continuum emission in different wavebands, which are not biased by the contribution of broad emission lines to the signal, and that c) such lags are consistent with the predictions of standard irradiated accretion disk models, given the optical luminosity of the sources. These findings provide new and independent support for standard accretion disks being responsible for the bulk of the (rest) optical emission in low-luminosity active galactic nuclei (AGN). We interpret our lag measurements in individual objects within the framework of this model and estimate the typical mass accretion rate to be <~0.1Msol/yr, with little dependence on the black hole mass. Assuming bolometric corrections typical of type-I sources, we find tentative evidence for the radiative efficiency of accretion flows being a rising function of the black hole mass. With upcoming surveys that will regularly monitor the sky, we may be able to better quantify possible departures from standard self-similar models, and identify other modes of accretion in AGN.
We show that the sequential closure of a family of probability measures on the canonical space of c{\`a}dl{\`a}g paths satisfying Stricker's uniform tightness condition is a weak${}^*$ compact set of semimartingale measures in the pairing of the Riesz representation theorem under topological assumptions on the path space. Similar results are obtained for quasi- and supermartingales under analogous conditions. In particular, we give a full characterization of the strongest topology on the Skorokhod space for which these results are true.
We propose the use of a gravitational uncertainty principle for gravitation. We define the corresponding gravitational Planck's constant and the gravitational quantum of mass. We define entropy in terms of the quantum of gravity with the property of having an extensive quality. The equivalent 2nd law of thermodynamics is derived, the entropy increasing linearly with cosmological time. These concepts are applied to the case of black holes, finding their entropy and discussing their radiation.
We present a detailed photometric and spectroscopic analysis of DD CMa, based on published survey photometry and new spectroscopic data. We find an improved orbital period of $P_\mathrm{o}= 2.0084530 \pm 0.0000006 ~\mathrm{d}$. Our spectra reveal H$\beta$ and H$\alpha$ absorptions with weak emission shoulders and we also find color excess in the WISE multiband photometry, interpreted as signatures of circumstellar matter. We model the $V$-band orbital light curve derived from the ASAS and ASAS-SN surveys, assuming a semidetached configuration and using the mass ratio and temperature of the hotter star derived from our spectroscopic analysis. Our model indicates that the system consists of a B 2.5 dwarf and a B 9 giant of radii 3.2 and 3.7 $\mathrm{R_{\odot}}$, respectively, orbiting in a circular orbit of radius 6.75 $\mathrm{R_{\odot}}$. We also found $M_{\mathrm{c}} = 1.7 \pm 0.1 ~\mathrm{M_{\odot}}$, $T_{\mathrm{c}} = 11350 \pm 100 ~\mathrm{K}$ and $M_{\mathrm{h}} = 6.4 \pm 0.1 ~\mathrm{M_{\odot}}$, $T_{\mathrm{h}} = 20000 \pm 500 ~\mathrm{K}$, for the cooler and hotter star, respectively. We find broad single emission peaks in H$\alpha$ and H$\beta$ after subtracting the synthetic stellar spectra. Our results are consistent with mass exchange between the stars, and suggest the existence of a stream of gas being accreted onto the early B-type star.
We present a detailed investigation of the structure and activity of extended defects namely monoatomic steps on (1x1)-TiO2(110). Specifically, the two most stable <001> and <1-11> step edges are considered. Employing an automated genetic algorithm that samples a large number of candidates for each step edge, more stable, reconstructed structures were found for the <1-11> step edge, while the bulk truncated structures were recovered for the <001> step edge. We demonstrate how oxygen vacancies along these defects have lower formation energies than on flat terraces and how water and methanol molecules adsorb dissociatively on reduced <1-11> step edges. Our findings are in agreement with earlier experimental results and indicate an important contribution from step edges to the reactivity of the TiO2(110) surface.
Let $p$ be an odd prime and $q$ a power of $p$. We examine the deformation theory of reducible and indecomposable Galois representations $\bar{\rho}:G_{\mathbb{Q}}\rightarrow \text{GSp}_{2n}(\mathbb{F}_q)$ that are unramified outside a finite set of primes $S$ and whose image lies in a Borel subgroup. We show that under some additional hypotheses, such representations have geometric lifts to the Witt vectors $\text{W}(\mathbb{F}_q)$. The main theorem extends that of Hamblen and Ramakrishna in which the $n=1$ case was treated.
Person re-identification (re-ID) aims at recognizing the same person from images taken across different cameras. To address this challenging task, existing re-ID models typically rely on a large amount of labeled training data, which is not practical for real-world applications. To alleviate this limitation, researchers now targets at cross-dataset re-ID which focuses on generalizing the discriminative ability to the unlabeled target domain when given a labeled source domain dataset. To achieve this goal, our proposed Pose Disentanglement and Adaptation Network (PDA-Net) aims at learning deep image representation with pose and domain information properly disentangled. With the learned cross-domain pose invariant feature space, our proposed PDA-Net is able to perform pose disentanglement across domains without supervision in identities, and the resulting features can be applied to cross-dataset re-ID. Both of our qualitative and quantitative results on two benchmark datasets confirm the effectiveness of our approach and its superiority over the state-of-the-art cross-dataset Re-ID approaches.
The extension of the Ramo-Schockley-Pellegrini theorem for quantum systems allows to define a positive-operator valued measure (POVM) for the total conduction plus displacement electrical current. The resulting current operator is characterized by two parameters, viz. the width of the associated Gaussian functions and the lapse of time between consecutive measurements. For large Gaussian dispersions and small time intervals, the operator obeys to a continuous weak-measurement scheme. Contrarily, in the limit of very narrow Gaussian widths and a single-shot measurement, the operator corresponds to a standard von Neumann (projective) measurement. We have implemented the resulting measurement protocol into a quantum electron transport simulator. Numerical results for a resonant tunneling diode show the great sensibility of current-voltage characteristics to different parameter configurations of the total current operator.
Within hydrodynamic approach, we study the Bose-Einstein correlation of identical pions by taking into account both event-by-event fluctuating initial conditions and continuous pion emission during the whole development of the hot and dense matter formed in high-energy collisions. Considerable deviations occur, compared to the usual hydro calculations with smooth initial conditions and a sudden freeze-out on a well defined hypersurface. Comparison with data at RHIC shows that, despite rather rough approximation we used here, this description can give account of the $m_T$ dependence of $R_L$ and $R_s$ and improves considerably the one for $R_o$ with respect to the usual version.
We present optical and X-ray properties for the first confirmed galaxy cluster sample selected by the Sunyaev-Zel'dovich Effect from 148 GHz maps over 455 square degrees of sky made with the Atacama Cosmology Telescope. These maps, coupled with multi-band imaging on 4-meter-class optical telescopes, have yielded a sample of 23 galaxy clusters with redshifts between 0.118 and 1.066. Of these 23 clusters, 10 are newly discovered. The selection of this sample is approximately mass limited and essentially independent of redshift. We provide optical positions, images, redshifts and X-ray fluxes and luminosities for the full sample, and X-ray temperatures of an important subset. The mass limit of the full sample is around 8e14 Msun, with a number distribution that peaks around a redshift of 0.4. For the 10 highest significance SZE-selected cluster candidates, all of which are optically confirmed, the mass threshold is 1e15 Msun and the redshift range is 0.167 to 1.066. Archival observations from Chandra, XMM-Newton, and ROSAT provide X-ray luminosities and temperatures that are broadly consistent with this mass threshold. Our optical follow-up procedure also allowed us to assess the purity of the ACT cluster sample. Eighty (one hundred) percent of the 148 GHz candidates with signal-to-noise ratios greater than 5.1 (5.7) are confirmed as massive clusters. The reported sample represents one of the largest SZE-selected sample of massive clusters over all redshifts within a cosmologically-significant survey volume, which will enable cosmological studies as well as future studies on the evolution, morphology, and stellar populations in the most massive clusters in the Universe.
The trace anomaly is relevant to the renormalisation of the unpolarised parton distributions. The role of the trace anomaly in F_2 is compared with the axial anomaly in g_1.
The capability to predict the parameters of an SEP event such as its onset, peak flux, and duration is critical to assessing any potential space weather impact. We present a new flexible modelling system simulating the propagation of Solar Energetic Particles (SEPs) from locations near the Sun to any given location in the heliosphere to forecast the SEP flux profiles. SPARX uses an innovative methodology, that allows implementation within an operational framework, to overcome the time constraints of test particle modelling of SEP profiles, allowing the production of near real time SEP nowcasts and forecasts, when paired with appropriate near real time triggers. SPARX has the capability to produce SEP forecasts within minutes of being triggered by observations of a solar eruptive event. The model is based on the test particle approach and is spatially 3D, thus allowing for the possibility of transport in the direction perpendicular to the magnetic field. The model naturally includes the effects of perpendicular propagation due to drifts and drift-induced deceleration. The modelling framework and the way in which parameters of relevance for Space Weather forecasting are obtained are described. The first results from the modelling system are presented. These results demonstrate that corotation and drift of SEP streams play an important role in shaping SEP flux profiles.
The ability of metal adsorption to transfer charge to the surface of single molecular carbon sheets is explored in this paper. Though other metals are considered we basically will deal with Lithium We concentrate on fairly small sheets and examined the minimum threshold size of a molecular surface needed to separate metals. From our quantum chemical calculations we deduce that a molecular surface of six benzene rings is needed for Lithium dimers to be separated. We further observe symmetry breaking, when two lithium atoms are adsorbed right opposite to each other on the two sides of the sheet.
Blind super-resolution (SR) methods aim to generate a high quality high resolution image from a low resolution image containing unknown degradations. However, natural images contain various types and amounts of blur: some may be due to the inherent degradation characteristics of the camera, but some may even be intentional, for aesthetic purposes (e.g. Bokeh effect). In the case of the latter, it becomes highly difficult for SR methods to disentangle the blur to remove, and that to leave as is. In this paper, we propose a novel blind SR framework based on kernel-oriented adaptive local adjustment (KOALA) of SR features, called KOALAnet, which jointly learns spatially-variant degradation and restoration kernels in order to adapt to the spatially-variant blur characteristics in real images. Our KOALAnet outperforms recent blind SR methods for synthesized LR images obtained with randomized degradations, and we further show that the proposed KOALAnet produces the most natural results for artistic photographs with intentional blur, which are not over-sharpened, by effectively handling images mixed with in-focus and out-of-focus areas.
MoS_2 in its two-dimensional (2D) form is known to exhibit many fundamentally interesting and technologically important properties. One of the most popular routes to form extensive amount of such 2D samples is the chemical exfoliation route. However, the nature and origin of the specific polymorph of MoS_2 primarily responsible for such spectacular properties has remained controversial with claims of both T and T' phases as well as metallic and semiconducting natures. We show that a comprehensive scrutiny of the available literature data of Raman spectra from such samples allow little scope for such ambiguities, providing overwhelming evidence for the formation of the T' phase as the dominant metastable state in all such samples. We also explain that this small band-gap T' phase may attain substantial conductivity due to thermal and chemical doping of charge-carriers, explaining the contradictory claims of metallic and semiconducting nature of such samples, thereby attaining a consistent view of all reports available so far.
The intersection volume of two independent 2-level cut Gaussian random fields is proposed to model the open-cell microstructure of organic aerogels. The experimentally measured X-ray scattering intensity, surface area and solid thermal conductivity of both polymeric and colloidal organic aerogels can be accounted for by the model.