ShantanuT01/DACTYL-Pretraining huggingface dataset:
We construct global observable algebras and global DHR morphisms for the Virasoro minimal models with central charge c(2,q), q odd. To this end, we pass {}from the irreducible highest weight modules to path representations, which involve fusion graphs of the c(2,q) models. The paths have an interpretation in terms of quasi-particles which capture some structure of non-conformal perturbations of the c(2,q) models. The path algebras associated to the path spaces serve as algebras of bounded observables. Global morphisms which implement the superselection sectors are constructed using quantum symmetries: We argue that there is a canonical semi-simple quantum symmetry algebra for each quasi-rational CFT, in particular for the c(2,q) models. These symmetry algebras act naturally on the path spaces, which allows to define a global field algebra and covariant multiplets therein.
Preferential attachment is a widely adopted paradigm for understanding the dynamics of social networks. Formal statistical inference,for instance GLM techniques, and model verification methods will require knowing test statistics are asymptotically normal even though node or count based network data is nothing like classical data from independently replicated experiments. We therefore study asymptotic normality of degree counts for a sequence of growing simple undirected preferential attachment graphs. The methods of proof rely on identifying martingales and then exploiting the martingale central limit theorems.
We investigate the effects of quenched disorder on the coherent response in a driven system of coupled oscillators. In particular, the interplay between quenched noise and periodic driving is explored, with particular attention to the possibility of resonance. The phase velocity is examined as the response of the system; revealed is the enhancement of the fraction of oscillators locked to the periodic driving, displaying resonance behavior. It is thus concluded that resonance behavior may also be induced by quenched disorder which does not have time-dependent correlations.
Let f(z) = sum_n a(n) n^{(k-1)/2} e(nz) be a cusp form for Gamma_0(N), character chi and weight k geq 4. Let q(x) = x^2 + sx + t be a polynomial with integral coefficients. It is shown that sum_{n \leq X} a(q(n)) = cX + O(X^{6/7+eps}) for some constant c depending on f and q. The constant vanishes in many cases, for example if k is even. On the way a Kuznetsov formula for half-integral weight and entries having different sign is derived.
N=1 curve is defined for four dimensional class S theory using Cayley-Hamilton theorem for two commuting matrices. The curve consists of three ingredients: 1: A set of N+1 degree N equations defining a curve; 2: a set of constraints relating the coefficients in the curve; 3: a canonically defined differential. We then extract from spectral curve various physical information such as the space of moduli fields, chiral ring relations, full moduli space, etc. Many examples are discussed, and the curve recovers the intricate vacua structure which often involves highly non-trivial field theory dynamics such as monopole condensation, dynamical generated superpotential, Seiberg duality, etc.
The on-site Coulomb potential, U, and the covalent state of electronic orbitals play key roles for the Cooper pair symmetry and exotic electromagnetic properties of high-Tc superconducting cuprates. In this paper, we demonstrate a way to determine the value of U and present the whole picture of the covalent state of Cu spins in the mother system of the La-based high-Tc superconducting cuprate, La2CuO4, by combining the muon spin rotation ({\mu}SR) and the density functional theory (DFT) calculation. We reveal local deformations of the CuO6 octahedron followed by changes in Cu-spin distributions caused by the injected muon. Adjusting the DFT and muSR results, U and the minimum charge-transfer energy between the upper Hubbard band and the O 2p band were optimized to be 4.87(4) and 1.24(1) eV, respectively.
We introduce a new ``greedy cleaning'' model where a star-like state space (containing N half-lines connected by the origin) is covered by a homogeneous Poisson process of ``dust particles'', and N^{\alpha} cleaners/workers proceed with cleaning in a ``greedy'' manner: each worker chooses the closest particle next. Assuming \alpha \in (0,1), we analyse the asymptotic behaviour of the workers, as N\to\infty. We show that eventually all of them escape to infinity and that the way how do they do it depends on the value of \alpha.
We study inhomogeneous states in the t-J model using an unrestricted Gutzwiller approximation. We find that $pa\times pa$ checkerboard order, where $p$ is a doping dependent number, emerges from Fermi surface instabilities of both the staggered flux phase and the Fermi liquid state with realistic band parameters. In both cases, the checkerboard order develops at wave vectors $(\pm 2\pi/pa,0)$, $(0,\pm2\pi/pa)$ that are tied to the peaks of the wave-vector dependent susceptibility, and is of the Lomer-Rice-Scott type. The properties of such periodic, inhomogeneous states are discussed in connection to the checkerboard patterns observed by STM in underdoped cuprates.
Octupole deformed shapes in neutron-rich actinides and superheavy nuclei as well as extremely deformed shapes of the N~Z light nuclei have been investigated within the framework of covariant density functional theory. We confirmed the presence of new region of octupole deformation in neutron-rich actinides with the center around Z~96, N~196 but our calculations do not predict octupole deformation in the ground states of superheavy Z~108 nuclei. As exemplified by the study of 36Ar, the nodal structure of the wavefunction of occupied single-particle orbitals in extremely deformed structures allows to understand the formation of the alpha-clusters in very light nuclei, the suppression of the alpha-clusterization with the increase of mass number, the formation of ellipsoidal mean-field type structures and nuclear molecules.
In the energy range from ~ 10^12 eV to ~ 10^15 eV, the Galactic cosmic ray flux has anisotropies both on large scales, with an amplitude of the order of 0.1%, and on scales between ~ 10 and ~ 30 degrees, with amplitudes smaller by a factor of a few. With a diffusion coefficient inferred from Galactic cosmic ray chemical abundances, the diffusion approximation predicts a dipolar anisotropy of comparable size, but does not explain the smaller scale anisotropies. We demonstrate here that energy dependent smaller scale anisotropies naturally arise from the local concrete realization of the turbulent magnetic field within the cosmic ray scattering length. We show how such anisotropies could be calculated if the magnetic field structure within a few tens of parsecs from Earth were known.
We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando--Trebeschi (2008) [20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain \emph{a priori} tame estimates on the effective linear problem {in the usual Sobolev spaces} and a suitable Nash--Moser iteration scheme.
We summarize observational results on the stellar population and star formation history of the Scorpius-Centaurus OB Association (Sco OB2), the nearest region of recent massive star formation. It consists of three subgroups, Upper Scorpius (US), Upper Centaurus-Lupus (UCL), and Lower Centaurus-Crux (LCC) which have ages of about 5, 17, and 16 Myr. In Upper Scorpius, numerous studies have recently revealed hundreds of low-mass association members, including dozens of brown dwarfs. The empirical mass function could be established over the full stellar mass range from 0.1 M_sun up to 20 M_sun, and was found to be consistent with recent determinations of the field initial mass function. A narrow range of ages around 5 Myr was found for the low-mass stars, the same age as had previously (and independently) been derived for the high-mass members. This supports earlier indications that the star formation process in US was triggered, and agrees with previous conjectures that the triggering event was a supernova- and wind-driven shock-wave originating from the nearby UCL group. In the older UCL and LCC regions, large numbers of low-mass members have recently been identified among X-ray and proper-motion selected candidates. In both subgroups, low-mass members have also been serendipitously discovered through investigations of X-ray sources in the vicinity of better known regions (primarily the Lupus and TW Hya associations). While both subgroups appear to have mean ages of ~16 Myr, they both show signs of having substructure. Their star-formation histories may be more complex than that of the younger, more compact US group. ... (abstract abbreviated; see paper for full abstract).
We study the singular part of the free boundary in the obstacle problem for the fractional Laplacian, \ $\min\bigl\{(-\Delta)^su,\,u-\varphi\bigr\}=0$ in $\mathbb R^n$, for general obstacles $\varphi$. Our main result establishes the complete structure and regularity of the singular set. To prove it, we construct new monotonicity formulas of Monneau-type that extend those in \cite{GP} to all $s\in(0,1)$.
This paper summarizes the results of over 17 years of work searching for low mass stellar and substellar companions to more than 370 nearby white dwarfs. Roughly 60 low mass, unevolved companions were found and studied all together, with over 20 discovered in the last few years, including the first unambiguous brown dwarf companion to a white dwarf, GD 1400B. The resulting spectral type distributions for companions to white dwarfs and nearby cool field dwarfs are compared, and the implications for binary star formation are discussed. A brief analysis of GD 1400B, including new data, is also presented
Efforts to understand unusual weather or abrupt changes in climate have been plagued by deficiencies of the standard solar model (SSM). While it assumes that our primary source of energy began as a homogeneous ball of hydrogen (H) with a steady, well-behaved H-fusion reactor at its core, observations instead reveal a very heterogeneous, dynamic Sun. As examples, the upward acceleration and departure of H+ ions from the surface of the quiet Sun and abrupt climatic changes, including geomagnetic reversals and periodic magnetic storms that eject material from the solar surface are not explained by the SSM. The present magnetic fields are probably deep-seated remnants of very ancient origin. These could have been generated from two mechanisms. These are: a) Bose-Einstein condensation of iron-rich, zero-spin material into a rotating, superfluid, superconductor surrounding the solar core and/or b) superfluidity and quantized vortices in nucleon-paired Fermions at the core.
This paper proposed a method to imitate handwriting style by style transfer. We proposed an neural network model based on conditional generative adversarial networks (cGAN) for handwriting style transfer. This paper improved the loss function on the basis of the GAN. Compared with other handwriting imitation methods, the handwriting style transfer's effect and efficiency have been significantly improved. The experiments showed that the shape of the generated Chinese characters is clear and the analysis of experimental data showed the Generative adversarial networks showed excellent performance in handwriting style transfer. The generated text image is closer to the real handwriting and achieved a better performance in term of handwriting imitation.
This paper is devoted to the proof Gauss' divergence theorem in the framework of "ultrafunctions". They are a new kind of generalized functions, which have been introduced recently [2] and developed in [4], [5] and [6]. Their peculiarity is that they are based on a non Archimedean field namely on a field which contains infinite and infinitesimal numbers. Ultrafunctions have been introduced to provide generalized solutions to equations which do not have any solutions not even among the distributions.
The proposed shopping assistant model SANIP is going to help blind persons to detect hand held objects and also to get a video feedback of the information retrieved from the detected and recognized objects. The proposed model consists of three python models i.e. Custom Object Detection, Text Detection and Barcode detection. For object detection of the hand held object, we have created our own custom dataset that comprises daily goods such as Parle-G, Tide, and Lays. Other than that we have also collected images of Cart and Exit signs as it is essential for any person to use a cart and also notice the exit sign in case of emergency. For the other 2 models proposed the text and barcode information retrieved is converted from text to speech and relayed to the Blind person. The model was used to detect objects that were trained on and was successful in detecting and recognizing the desired output with a good accuracy and precision.
We present Spitzer Space Telescope observations of the "evolved starless core" L1521F which reveal the presence of a very low luminosity object (L < 0.07 Lsun). The object, L1521F-IRS, is directly detected at mid-infrared wavelengths (>5 micron) but only in scattered light at shorter infrared wavelengths, showing a bipolar nebula oriented east-west which is probably tracing an outflow cavity. The nebula strongly suggests that L1521F-IRS is embedded in the L1521F core. Thus L1521F-IRS is similar to the recently discovered L1014-IRS and the previously known IRAM 04191 in its substellar luminosity and dense core environment. However these objects differ significantly in their core density, core chemistry, and outflow properties, and some may be destined to be brown dwarfs rather than stars.
Probing magnetic fields in the interstellar medium (ISM) is notoriously challenging. Motivated by the modern theories of magnetohydrodynamic (MHD) turbulence and turbulence anisotropy, we introduce the Structure-Function Analysis (SFA) as a new approach to measure the magnetic field orientation and estimate the magnetization. We analyze the statistics of turbulent velocities in three-dimensional compressible MHD simulations through the second-order structure functions in both local and global reference frames. In the sub-Alfvenic turbulence with the magnetic energy larger than the turbulent energy, the SFA of turbulent velocities measured in the directions perpendicular and parallel to the magnetic field can be significantly different. Their ratio has a power-law dependence on the Alfven Mach number $M_A$, which is inversely proportional to the magnetic field strength. We demonstrate that the anisotropic structure functions of turbulent velocities can be used to estimate both the orientation and strength of magnetic fields. With turbulent velocities measured using different tracers, our approach can be generally applied to probing the magnetic fields in the multi-phase interstellar medium.
We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as a finite linear combination of geometric terms and present conditions on the structure of these linear combinations such that the resulting measure may yield an invariant measure of a random walk. We demonstrate that each geometric term must individually satisfy the balance equations in the interior of the state space and further show that the geometric terms in an invariant measure must have a pairwise-coupled structure. Finally, we show that at least one of the coefficients in the linear combination must be negative.
We present a multi-epoch radio study of the Taurus-Auriga star-forming complex made with the Karl G. Jansky Very Large Array at frequencies of 4.5 GHz and 7.5 GHz. We detect a total of 610 sources, 59 of which are related to young stellar objects and 18 to field stars. The properties of 56\% of the young stars are compatible with non-thermal radio emission. We also show that the radio emission of more evolved young stellar objects tends to be more non-thermal in origin and, in general, that their radio properties are compatible with those found in other star forming regions. By comparing our results with previously reported X-ray observations, we notice that young stellar objects in Taurus-Auriga follow a G\"{u}del-Benz relation with $\kappa$=0.03, as we previously suggested for other regions of star formation. In general, young stellar objects in Taurus-Auriga and in all the previous studied regions seem to follow this relation with a dispersion of $\sim1$ dex. Finally, we propose that most of the remaining sources are related with extragalactic objects but provide a list of 46 unidentified radio sources whose radio properties are compatible with a YSO nature.
The large density of matter in the interaction region of the proton-nucleus or deuteron-nucleus collisions enables the collective expansion of the fireball. Predictions of the hydrodynamic model for the asymmetric transverse flow are presented and compared to experimental data.
We consider the limit behavior of a one-dimensional random walk with unit jumps whose transition probabilities are modified every time the walk hits zero. The invariance principle is proved in the scheme of series where the size of modifications depends on the number of series. For the natural scaling of time and space arguments the limit process is (i) a Brownian motion if modifications are "small", (ii) a linear motion with a random slope if modifications are "large", and (iii) the limit process satisfies an SDE with a local time of unknown process in a drift if modifications are "moderate".
Future redshift-drift measurements (also known as Sandage-Loeb signal) will be crucial to probe the so called "redshift desert", thus providing a new tool for cosmological studies. In this paper we quantify the ability of a future measurement of the Sandage-Loeb signal by a CODEX-like spectrograph to constrain a phenomenological parametrization of dynamical dark energy, specifically by obtaining constraints on $w_0$ and $w_a$. We also demonstrate that if used alongside CMB data, the Sandage-Loeb measurements will be able to break degeneracies between expansion parameters, thus greatly improving cosmological constraints.
In this paper, we are concerned with the relation between the ordinarity of surfaces of general type and the failure of the BMY inequality in positive characteristic. We consider semistable fibrations $\pi:S \longrightarrow C$ where $S$ is a smooth projective surface and $C$ is a smooth projective curve. Using the exact sequence relating the locally exact differential forms on $S$, $C$, and $S/C$, we prove an inequality relating $c_1^2$ and $c_2$ for ordinary surfaces which admit generically ordinary semistable fibrations. This inequality differs from the BMY inequality by a correcting term which vanishes if the fibration is ordinary.
In this paper, we consider a kind of $k$-Hessian type equations $S_k^{\frac{1}{k}}(D^2u+\mu|D u|I)= f(u)$ in $\mathbb{R}^n$, and provide a necessary and sufficient condition of $f$ on the existence and nonexistence of entire admissible subsolutions, which can be regarded as a generalized Keller-Osserman condition. The existence and nonexistence results are proved in different ranges of the parameter $\mu$ respectively, which embrace the standard Hessian equation case ($\mu=0$) by Ji and Bao (Proc Amer Math Soc 138: 175--188, 2010) as a typical example. The difference between the semilinear case ($k=1$) and the fully nonlinear case ($k\ge 2$) is also concerned.
In recent years, two-dimensional boron sheets (borophene) have been experimentally synthesized and theoretically observed as promising conductor or transistor with novel thermal and electronic properties. We first give a general survey of some notable electronic properties of borophene, including the superconductivity and topological characters. We then mainly review the basic approaches, thermal transport, as well as the mechanical properties of borophene with different configurations. This review gives a general understanding of some of the crucial thermal transport and electronic properties of borophene, and also calls for further experimental investigations and applications on certain scientific community.
The status quo approach to training object detectors requires expensive bounding box annotations. Our framework takes a markedly different direction: we transfer tracked object boxes from weakly-labeled videos to weakly-labeled images to automatically generate pseudo ground-truth boxes, which replace manually annotated bounding boxes. We first mine discriminative regions in the weakly-labeled image collection that frequently/rarely appear in the positive/negative images. We then match those regions to videos and retrieve the corresponding tracked object boxes. Finally, we design a hough transform algorithm to vote for the best box to serve as the pseudo GT for each image, and use them to train an object detector. Together, these lead to state-of-the-art weakly-supervised detection results on the PASCAL 2007 and 2010 datasets.
We argue that the detection of neutrino signature from the Earth core is an ideal approach for probing the coupling of heavy dark matter ($m_{\chi}>10^{4}$ GeV) to nucleons. We first note that direct searches for dark matter (DM) in such a mass range do not provide stringent constraints. Furthermore the energies of neutrinos arising from DM annihilations inside the Sun cannot exceed a few TeV at the Sun surface due to the attenuation effect. Therefore the sensitivity to the heavy DM coupling is lost. Finally, the detection of neutrino signature from galactic halo can only probe DM annihilation cross sections. After presenting the rationale of our studies, we discuss the event rates in IceCube and KM3NeT arising from the neutrino flux produced by annihilations of Earth-captured DM heavier than $10^{4}$ GeV. The IceCube and KM3NeT sensitivities to spin independent DM-proton scattering cross section $\sigma_{\chi p}$ and isospin violation effect in this mass range are presented. The implications of our results are also discussed.
An anisotropy signal for the arrival directions of ultra-high energy cosmic rays (UHECR) of more than 99% confidence level was established using data collected by the Pierre Auger Observatory. Cosmic rays with energy above $\sim 6 \times 10^{19}$ eV show a correlation with the positions of extragalactic nearby active galactic nuclei (AGN), being maximum for sources at less than $\sim$100 Mpc and angular separation of a few degrees. The evolution of the correlation signal with the energy shows that the departure from anisotropy coincides with the flux suppression observed in the spectrum, being therefore consistent with the hypothesis that the correlated events have their origin in extragalactic sources close enough to avoid significant interaction with the cosmic microwave background (the Greisen-Zatsepin-Kuz'min effect). Even though the observed signal cannot unambiguously identify AGNs as the production sites of UHECRs, the potential sources have to be distributed in a similar way. A number of additional statistical tests were performed in order to further understand the nature of the correlation signal.