ShantanuT01/DACTYL-Pretraining huggingface dataset:
This study aims to develop the limit theorems on the sample autocovariances and sample autocorrelations for certain stationary infinitely divisible processes. We consider the case where the infinitely divisible process has heavy tail marginals and is generated by a conservative flow. Interestingly, the growth rate of the sample autocovariances is determined by not only heavy tailedness of the marginals but also memory length of the process. Although this feature was first observed by \cite{resnick:samorodnitsky:xue:2000} for some very specific processes, we will propose a more general framework from the viewpoint of infinite ergodic theory. Consequently, the asymptotics of the sample autocovariances can be more comprehensively discussed.
We present a procedure in which known solutions to reflection equations for interaction-round-a-face lattice models are used to construct new solutions. The procedure is particularly well-suited to models which have a known fusion hierarchy and which are based on graphs containing a node of valency $1$. Among such models are the Andrews-Baxter-Forrester models, for which we construct reflection equation solutions for fixed and free boundary conditions.
We prove that an irreducible aperiodic Markov chain is geometrically ergodic if and only if any separately bounded functional of the stationary chain satisfies an appropriate subgaussian deviation inequality from its mean.
The Solar Optical Telescope (SOT) on board Hinode satellite observed an X3.4 class flare on 2006 December 13. Typical two-ribbon structure was observed, not only in the chromospheric CaII H line but also in G-band and FeI 6302A line. The high-resolution, seeing-free images achieved by SOT revealed, for the first time, the sub-arcsec fine structures of the "white light" flare. The G-band flare ribbons on sunspot umbrae showed a sharp leading edge followed by a diffuse inside, as well as previously known core-halo structure. The underlying structures such as umbral dots, penumbral filaments and granules were visible in the flare ribbons. Assuming that the sharp leading edge was directly heated by particle beam and the diffuse parts were heated by radiative back-warming, we estimate the depth of the diffuse flare emission using the intensity profile of the flare ribbon. We found that the depth of the diffuse emission is about 100 km or less from the height of the source of radiative back-warming. The flare ribbons were also visible in the Stokes-V images of FeI 6302A, as a transient polarity reversal. This is probably related to "magnetic transient" reported in the literature. The intensity increase in Stokes-I images indicates that the FeI 6302A line was significantly deformed by the flare, which may cause such a magnetic transient.
We present measurements of the $E$-mode polarization angular auto-power spectrum ($EE$) and temperature-$E$-mode cross-power spectrum ($TE$) of the cosmic microwave background (CMB) using 150 GHz data from three seasons of SPTpol observations. We report the power spectra over the spherical harmonic multipole range $50 < \ell \leq 8000$, and detect nine acoustic peaks in the $EE$ spectrum with high signal-to-noise ratio. These measurements are the most sensitive to date of the $EE$ and $TE$ power spectra at $\ell > 1050$ and $\ell > 1475$, respectively. The observations cover 500 deg$^2$, a fivefold increase in area compared to previous SPTpol analyses, which increases our sensitivity to the photon diffusion damping tail of the CMB power spectra enabling tighter constraints on \LCDM model extensions. After masking all sources with unpolarized flux $>50$ mJy we place a 95% confidence upper limit on residual polarized point-source power of $D_\ell = \ell(\ell+1)C_\ell/2\pi <0.107\,\mu{\rm K}^2$ at $\ell=3000$, suggesting that the $EE$ damping tail dominates foregrounds to at least $\ell = 4050$ with modest source masking. We find that the SPTpol dataset is in mild tension with the $\Lambda CDM$ model ($2.1\,\sigma$), and different data splits prefer parameter values that differ at the $\sim 1\,\sigma$ level. When fitting SPTpol data at $\ell < 1000$ we find cosmological parameter constraints consistent with those for $Planck$ temperature. Including SPTpol data at $\ell > 1000$ results in a preference for a higher value of the expansion rate ($H_0 = 71.3 \pm 2.1\,\mbox{km}\,s^{-1}\mbox{Mpc}^{-1}$ ) and a lower value for present-day density fluctuations ($\sigma_8 = 0.77 \pm 0.02$).
An influence of high magnetic fields on hyperfine interaction in the rare-earth ions with non-magnetic ground state (Van Vleck ions) is theoretically investigated for the case of $Tm^{3+}$ ion in axial symmetrical crystal electric field (ethylsulphate crystal). It is shown that magnetic-field induced distortions of $4f$-electron shell lead to essential changes in hyperfine magnetic field at the nucleus. The proposed theoretical model is in agreement with recent experimental data.
We apply a combination of numerical renormalization group (NRG) and renormalized perturbation theory (RPT) to a model of two quantum dots (impurities) described by two Anderson impurity models hybridized to their respective baths. The dots are coupled via a direct interaction $U_{12}$ and an exchange interaction $J$. The model has two types of quantum critical points, one at $J=J_c$ to a local singlet state and one at $U_{12}=U_{12}^c$ to a locally charge ordered state. The renormalized parameters which determine the low energy behavior are calculated from the NRG. The results confirm the values predicted from the RPT on the approach to the critical points, which can be expressed in terms of a single energy scale $T^*$ in all cases. This includes cases without particle-hole symmetry, and cases with asymmetry between the dots, where there is also a transition at $J=J_c$. The results give a comprehensive quantitative picture of the behavior of the model in the low energy Fermi liquid regimes, and some of the conclusions regarding the emergence of a single energy scale may apply to a more general class of quantum critical points, such as those observed in some heavy fermion systems.
Common envelope evolution is a fundamental ingredient in our understanding of the formation of close binary stars containing compact objects which includes the progenitors of type Ia supernovae, short gamma ray bursts and most stellar gravitational wave sources. To predict the outcome of common envelope evolution we still rely to a large degree on a simplified energy conservation equation. Unfortunately, this equation contains a theoretically rather poorly constrained efficiency parameter ($\alpha_{\mathrm{CE}}$) and, even worse, it is unclear if energy sources in addition to orbital energy (such as recombination energy) contribute to the envelope ejection process. In previous works we reconstructed the evolution of observed populations of post common envelope binaries (PCEBs) consisting of white dwarfs with main sequence star companions and found indications that the efficiency is rather small ($\alpha_{\mathrm{CE}}\simeq0.2-0.3$) and that extra energy sources are only required in very few cases. Here we used the same reconstruction tool to investigate the evolutionary history of a sample of observed PCEBs with brown dwarf companions. In contrast to previous works, we found that the evolution of observationally well characterized PCEBs with brown dwarf companions can be understood assuming a low common envelope efficiency ($\alpha_{\mathrm{CE}}=0.24-0.41$), similar to that required to understand PCEBs with main sequence star companions, and that contributions from recombination energy are not required. We conclude that the vast majority of PCEBs form from common envelope evolution that can be parameterized with a small efficiency and without taking into account additional energy sources.
We investigate frequency correlations of low frequency (LF, <80 Hz) and kHz quasi-periodic oscillations (QPOs) using the complete RXTE data sets on 6 accreting millisecond X-ray pulsars (AMXPs) and compare them to those of non-pulsating neutron star low mass X-ray binaries with known spin. For the AMXPs SAX J1808.4-3658 and XTE J1807-294, we find frequency-correlation power law indices that, surprisingly, are significantly lower than in the non-pulsars, and consistent with the relativistic precession model (RPM) prediction of 2.0 appropriate to test-particle orbital and Lense-Thirring precession frequencies. As previously reported, power law normalizations are significantly higher in these AMXPs than in the non-pulsating sources, leading to requirements on the neutron star specific moment of inertia in this model that cannot be satisfied with realistic equations of state. At least two other AMXPs show frequency correlations inconsistent with those of SAX J1808.4-3658 and XTE J1807-294, and possibly similar to those of the non-pulsating sources; for two AMXPs no conclusions could be drawn. We discuss these results in the context of a model that has had success in black hole (BH) systems involving a torus-like hot inner flow precessing due to (prograde) frame dragging, and a scenario in which additional (retrograde) magnetic and classical precession torques not present in BH systems are also considered. We show that a combination of these interpretations may accommodate our results.
We study graphs which admit an acyclic orientation that contains an out-branching and in-branching which are arc-disjoint (such an orientation is called {\bf good}). A {\bf 2T-graph} is a graph whose edge set can be decomposed into two edge-disjoint spanning trees. Clearly a graph has a good orientation if and only if it contains a spanning 2T-graph with a good orientation, implying that 2T-graphs play a central role. Vertex-minimal 2T-graphs with at least two vertices, also known as {\bf generic circuits}, play an important role in rigidity theory for graphs. It was shown in \cite{bangGOpaper} that every generic circuit has a good orientation. Using this, several results on good orientations of 2T-graphs were obtained in \cite{bangGOpaper}. It is an open problem whether there exist a polynomial algorithm for deciding whether a given 2T-graph has a good orientation. In \cite{bangGOpaper} complex constructions of 2T-graphs with no good orientation were given, indicating that the problem might be very difficult. In this paper we focus on so-called {\bf quartics} which are 2T-graphs where every vertex has degree 3 or 4. We identify a sufficient condition for a quartic to have a good orientation, give a polynomial algorithm to recognize quartics satisfying the condition and a polynomial algorithm to produce such an orientation when this condition is met. As a consequence of these results we prove that every 4-regular and 4-connected graph has a good orientation. \iffalse We also provide evidence that even for quartics it may be difficult to find a characterization of those instances which have a good orientation.\fi We also show that every graph on $n\geq 8$ vertices and of minimum degree at least $\lfloor{}n/2\rfloor$ has a good orientation. Finally we pose a number of open problems.
We analyze mathematically the acoustic imaging modality using bubbles as contrast agents. These bubbles are modeled by mass densities and bulk moduli enjoying contrasting scales. These contrasting scales allow them to resonate at certain incident frequencies. We consider two types of such contrasts. In the first one, the bubbles are light with small bulk modulus, as compared to the ones of the background, so that they generate the Minnaert resonance (corresponding to a local surface wave). In the second one, the bubbles have moderate mass density but still with small bulk modulus so that they generate a sequence of resonances (corresponding to local body waves).   We propose to use as measurements the far-fields collected before and after injecting a bubble, set at a given location point in the target domain, generated at a band of incident frequencies and at a fixed single backscattering direction. Then, we scan the target domain with such bubbles and collect the corresponding far-fields. The goal is to reconstruct both the, variable, mass density and bulk modulus of the background in the target region.   1. We show that, for each fixed used bubble, the contrasted far-fields reach their maximum value at, incident, frequencies close to the Minneart resonance (or the body-wave resonances depending on the types of bubbles we use). Hence, we can reconstruct this resonance from our data. The explicit dependence of the Minnaert resonance in terms of the background mass density of the background allows us to recover it, i.e. the mass density, in a straightforward way.   2. In addition, this measured contrasted far-fields allow us to recover the total field at the location points of the bubbles (i.e. the total field in the absence of the bubbles). A numerical differentiation argument, for instance, allows us to recover the bulk modulus of the targeted region as well.
Let $A$ be a finite nonempty set of integers. An asymptotic estimate of several dilates sum size was obtained by Bukh. The unique known exact bound concerns the sum $|A+k\cdot A|,$ where $k$ is a prime and $|A|$ is large. In its full generality, this bound is due to Cilleruelo, Serra and the first author.   Let $k$ be an odd prime and assume that $|A|>8k^{k}.$ A corollary to our main result states that $|2\cdot A+k\cdot A|\ge (k+2)|A|-k^2-k+2.$ Notice that $|2\cdot P+k\cdot P|=(k+2)|P|-2k,$ if $P$ is an arithmetic progression.
Nucleon electromagnetic form factor data (including recent data) is fitted with models that respect the confinement and asymptotic freedom properties of QCD. Gari-Krumpelmann (GK) type models, which include the major vector meson pole contributions and at high momentum transfer conform to the predictions of perturbative QCD, are combined with Hohler-Pietarinen (HP) models, which also include the width of the rho meson and the addition of higher mass vector meson exchanges, but do not evolve into the explicit form of PQCD at high momentum transfer. Different parameterizations of the GK model's hadronic form factors, the effect of including the width of the rho meson and the addition of the next (in mass) isospin 1 vector meson are considered. The quality of fit and the consistency of the parameters select three of the combined HP/GK type models. Projections are made to the higher momentum transfers which are relevant to electron-deuteron experiments. The projections vary little for the preferred models, removing much of the ambiguity in electron-nucleus scattering predictions.
Nowadays, billions of videos are online ready to be viewed and shared. Among an enormous volume of videos, some popular ones are widely viewed by online users while the majority attract little attention. Furthermore, within each video, different segments may attract significantly different numbers of views. This phenomenon leads to a challenging yet important problem, namely fine-grained video attractiveness prediction. However, one major obstacle for such a challenging problem is that no suitable benchmark dataset currently exists. To this end, we construct the first fine-grained video attractiveness dataset, which is collected from one of the most popular video websites in the world. In total, the constructed FVAD consists of 1,019 drama episodes with 780.6 hours covering different categories and a wide variety of video contents. Apart from the large amount of videos, hundreds of millions of user behaviors during watching videos are also included, such as "view counts", "fast-forward", "fast-rewind", and so on, where "view counts" reflects the video attractiveness while other engagements capture the interactions between the viewers and videos. First, we demonstrate that video attractiveness and different engagements present different relationships. Second, FVAD provides us an opportunity to study the fine-grained video attractiveness prediction problem. We design different sequential models to perform video attractiveness prediction by relying solely on video contents. The sequential models exploit the multimodal relationships between visual and audio components of the video contents at different levels. Experimental results demonstrate the effectiveness of our proposed sequential models with different visual and audio representations, the necessity of incorporating the two modalities, and the complementary behaviors of the sequential prediction models at different levels.
It is shown that the results presented in the article 'The influence of the temperature and pressure on a fractal dimension of defects in crystal structures' by V.B. Fedoseev (Butlerov communications. 2010. V23. Number 14. P.36-42) are not correct, because the results are based on impracticable conditions, conflicting assumptions and incorrect distributions.
In this paper a fast and novel method is proposed for multi-font multi-size Kannada numeral recognition which is thinning free and without size normalization approach. The different structural feature are used for numeral recognition namely, directional density of pixels in four directions, water reservoirs, maximum profile distances, and fill hole density are used for the recognition of Kannada numerals. A Euclidian minimum distance criterion is used to find minimum distances and K-nearest neighbor classifier is used to classify the Kannada numerals by varying the size of numeral image from 16 to 50 font sizes for the 20 different font styles from NUDI and BARAHA popular word processing Kannada software. The total 1150 numeral images are tested and the overall accuracy of classification is found to be 100%. The average time taken by this method is 0.1476 seconds.
We propose a scheme for the controllable preparation of a cold indirect exciton condensate using dipolaritonic setup with an optical pumping. Dipolaritons are bosonic quasiparticles which arise from the coupling between cavity photon (C), direct exciton (DX), and indirect exciton (IX) modes, and appear in a double quantum well embedded in a semiconductor microcavity. Controlling the detuning between modes of the system, the limiting cases of exciton-polaritons and indirect excitons can be realized. Our protocol relies on the initial preparation of an exciton polariton condensate for the far blue-detuned IX mode, with its subsequent adiabatic transformation to an indirect exciton condensate by lowering IX energy via applied electric field. The following allows for generation of a spatially localized cold exciton gas, on the contrary to currently used methods, where IX cloud appears due to diffusion of carriers from spatially separated electron- and hole-rich areas.
Entanglement of four qubit pure states defined by the $\eta$-trigonometric functions is studied. We analyze the behavior of two recently proposed symmetric entanglement monotones on the chosen $n=4$ qubit states .
The interior of gravitationally collapsed objects in alternate theories of gravity in which event horizons and singularities do not occur in strong field gravity were generically investigated. These objects, called red holes, were found to contain dynamic configurations of matter, radiation and spacetime similar to inside out accretion disks well inside the photon orbit. Applications to astrophysical phenomena are briefly described.
We compare signal and noise for observations of the scintillating pulsar B0834+06, using very-long baseline interferometry and a single-dish spectrometer. Comparisons between instruments and with models suggest that amplitude variations of the pulsar strongly affect the amount and distribution of self-noise. We show that noise follows a quadratic polynomial with flux density, in spectral observations. Constant coefficients, indicative of background noise, agree well with expectation; whereas second-order coefficients, indicative of self-noise, are about 3 times values expected for a pulsar with constant on-pulse flux density. We show that variations in flux density during the 10-sec integration account for the discrepancy. In the secondary spectrum, about 97% of spectral power lies within the pulsar's typical scintillation bandwidth and timescale; an extended scintillation arc contains about 3%. For a pulsar with constant on-pulse flux density, noise in the dynamic spectrum will appear as a uniformly-distributed background in the secondary spectrum. We find that this uniform noise background contains 95% of noise in the dynamic spectrum for interferometric observations; but only 35% of noise in the dynamic spectrum for single-dish observations. Receiver and sky dominate noise for our interferometric observations, whereas self-noise dominates for single-dish. We suggest that intermittent emission by the pulsar, on timescales < 300 microseconds, concentrates self-noise near the origin in the secondary spectrum, by correlating noise over the dynamic spectrum. We suggest that intermittency sets fundamental limits on pulsar astrometry or timing. Accounting of noise may provide means for detection of intermittent sources, when effects of propagation are unknown or impractical to invert.
Given a set $\Sg$ of bipartitions of some finite set $X$ of cardinality at least 2, one can associate to $\Sg$ a canonical $X$-labeled graph $\B(\Sg)$, called the Buneman graph. This graph has several interesting mathematical properties - for example, it is a median network and therefore an isometric subgraph of a hypercube. It is commonly used as a tool in studies of DNA sequences gathered from populations. In this paper, we present some results concerning the {\em cut vertices} of $\B(\Sg)$, i.e., vertices whose removal disconnect the graph, as well as its {\em blocks} or 2-{\em connected components} - results that yield, in particular, an intriguing generalization of the well-known fact that $\B(\Sg)$ is a tree if and only if any two splits in $\Sg$ are compatible.
We study a general class of log-gas ensembles on (shifted) quadratic lattices. We prove that the corresponding empirical measures satisfy a law of large numbers and that their global fluctuations are Gaussian with a universal covariance. We apply our general results to analyze the asymptotic behavior of a $q$-boxed plane partition model introduced by Borodin, Gorin and Rains. In particular, we show that the global fluctuations of the height function on a fixed slice are described by a one-dimensional section of a pullback of the two-dimensional Gaussian free field.   Our approach is based on a $q$-analogue of the Schwinger-Dyson (or loop) equations, which originate in the work of Nekrasov and his collaborators, and extends the methods developed by Borodin, Gorin and Guionnet to quadratic lattices.
We introduce a new optimal transport distance between nonnegative finite Radon measures with possibly different masses. The construction is based on non-conservative continuity equations and a corresponding modified Benamou-Brenier formula. We establish various topological and geometrical properties of the resulting metric space, derive some formal Riemannian structure, and develop differential calculus following F. Otto's approach. Finally, we apply these ideas to identify an ideal free distribution model of population dynamics as a gradient flow and obtain new long-time convergence results.
Tumor segmentation from magnetic resonance imaging (MRI) data is an important but time consuming manual task performed by medical experts. Automating this process is a challenging task because of the high diversity in the appearance of tumor tissues among different patients and in many cases similarity with the normal tissues. MRI is an advanced medical imaging technique providing rich information about the human soft-tissue anatomy. There are different brain tumor detection and segmentation methods to detect and segment a brain tumor from MRI images. These detection and segmentation approaches are reviewed with an importance placed on enlightening the advantages and drawbacks of these methods for brain tumor detection and segmentation. The use of MRI image detection and segmentation in different procedures are also described. Here a brief review of different segmentation for detection of brain tumor from MRI of brain has been discussed.