ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper we focus on the problem of finding (small) subhypergraphs in a (large) hypergraph. We use this problem to illustrate that reducing hypergraph problems to graph problems by working with the 2-section is not always a reasonable approach. We begin by defining a generalization of the binomial random graph model to hypergraphs and formalizing several definitions of subhypergraph. The bulk of the paper focusses on determining the expected existence of these types of subhypergraph in random hypergraphs. We also touch on the problem of determining whether a given subgraph appearing in the 2-section is likely to have been induced by a certain subhypergraph in the hypergraph. To evaluate the model in relation to real-world data, we compare model prediction to two datasets with respect to (1) the existence of certain small subhypergraphs, and (2) a clustering coefficient.
We report new, as yet unpublished HST/WFPC2 V, I photometry of 9 globular clusters in M31. These are part of a total sample of 19 clusters on M31 with well observed CMDs from HST. The clusters have the full range of horizontal branch morphologies from blue HB to red clump, but none are found with an extreme (blue only) horizontal branch. Plots of HB type vs [Fe/H] are similar to those of Galactic clusters, including a hint of second parameter clusters. Sixteen halo fields adjacent to the observed clusters included in our images have been analysed. The M31 halo metallicity distribution peaks at [Fe/H]=--0.7 with a tail toward low metallicity, resembling the halo of NGC 5128; metal rich giants appear to be centrally concentrated.
Solid electrolytes are considered a potentially enabling component in rechargeable batteries that use lithium metal as the negative electrode, and thereby can safely access higher energy density than available with today's lithium ion batteries. To do so, the solid electrolyte must be able to suppress morphological instabilities that lead to poor coulombic efficiency and, in the worst case, internal short circuits. In this work, lithium electrodeposition experiments were performed using single-crystal Li6La3ZrTaO12 garnet as solid electrolyte layers to investigate the factors that determine whether lithium penetration occurs through brittle inorganic solid electrolytes. In these single crystals, grain boundaries are excluded as possible paths for lithium metal propagation. However, Vickers microindentation was used to introduce sharp surface flaws of known size. Using operando optical microscopy, it was found that lithium metal penetration sometimes initiates at these controlled surface defects, and when multiple indents of varying size were present, propagates preferentially from the largest defect. However, a second class of flaws was found to be equally or more important. At the perimeter of surface current collectors, an enhanced electrodeposition current density causes lithium metal filled cracks to initiate and grow to penetration, even when the large Vickers defects are in close proximity. Modeling the electric field concentration for the experimental configurations, it was shown that a factor of 5 enhancement in field can readily occur within 10 micrometers of current collector discontinuities, which we interpret as the origin of electrochemomechanical stresses leading to failure. Such field amplification may determine the sites where supercritical surface defects dominate lithium metal propagation during electrodeposition, overriding the presence of larger defects elsewhere.
We present first ab initio no-core shell model (NCSM) calculations using similarity renormalization group (SRG) transformed chiral two-nucleon (NN) plus three-nucleon (3N) interactions for nuclei throughout the p-shell, particularly 12-C and 16-O. By introducing an adaptive importance truncation for the NCSM model space and an efficient JT-coupling scheme for the 3N matrix elements, we are able to surpass previous NCSM studies including 3N interactions regarding, both, particle number and model-space size. We present ground and excited states in 12-C and 16-O for model spaces up to N_max=12 including full 3N interactions, which is sufficient to obtain converged results for soft SRG-transformed interactions. We analyze the contributions of induced and initial 3N interactions and probe induced 4N terms through the sensitivity of the energies on the SRG flow parameter. Unlike for light p-shell nuclei, SRG-induced 4N contributions originating from the long-range two-pion terms of the chiral 3N interaction are sizable in 12-C and 16-O.
We carry out the microscopic calculations of the atomic EDM in deuterium, Xe and Hg atomic systems. Due to Schiff's theorem, we obtain the atomic EDM only from the finite nuclear size effects, but it is found that the atomic EDM is appreciably larger than expected. This is essentially due to the new mechanism in which the nuclear excitations are taken into account while atomic states stay in the ground state. The EDM of deuterium is found to be $d_D \simeq 0.017 d_n$ while the EDM of Xe and Hg become $d_{\rm Xe} \simeq 1.6 d_n$ and $d_{{\rm Hg}} \simeq -2.8 d_n$, respectively. It turns out that the new constraint on the neutron EDM becomes $d_n \simeq (0.37\pm 0.17 \pm 0.14)\times 10^{-28} {\rm e}\cdot {\rm cm}$.
We show that any extremal contraction from a smooth projective variety with dimension less than or equal to three appears as a moduli space of (semi)stable objects in the derived category of coherent sheaves.
In this paper, we study the formation and early evolution of a limb coronal mass ejection (CME) and its associated shock wave that occurred on 2014 January 8. The extreme ultraviolet (EUV) images provided by the Atmospheric Imaging Assembly (AIA) on board \textit{Solar Dynamics Observatory} disclose that the CME first appears as a bubble-like structure. Subsequently, its expansion forms the CME and causes a quasi-circular EUV wave. Interestingly, both the CME and the wave front are clearly visible at all of the AIA EUV passbands. Through a detailed kinematical analysis, it is found that the expansion of the CME undergoes two phases: a first phase with a strong but transient lateral over-expansion followed by a second phase with a self-similar expansion. The temporal evolution of the expansion velocity coincides very well with the variation of the 25--50 keV hard X-ray flux of the associated flare, which indicates that magnetic reconnection most likely plays an important role in driving the expansion. Moreover, we find that, when the velocity of the CME reaches $\sim$600 km s$^{-1}$, the EUV wave starts to evolve into a shock wave, which is evidenced by the appearance of a type II radio burst. The shock's formation height is estimated to be $\sim$0.2$R_{sun}$, which is much lower than the height derived previously. Finally, we also study the thermal properties of the CME and the EUV wave. We find that the plasma in the CME leading front and the wave front has a temperature of $\sim$2 MK, while that in the CME core region and the flare region has a much higher temperature of $\ge$8 MK.
We show that the pseudoeffective cone of $k$-cycles on a complete complexity one $T$-variety is rational polyhedral for any $k$, generated by classes of $T$-invariant subvarieties. When $X$ is also rational, we give a presentation of the Chow groups of $X$ in terms of generators and relations, coming from the combinatorial data defining $X$ as a $T$-variety.
In this work we matched the AKARI archival data to the Optical Gravitational Lensing Experiment-III (OGLE-III) catalog to derive the mid-infrared period luminosity (PL) relations for Small Magellanic Cloud (SMC) Cepheids. Mismatched AKARI sources were eliminated using random-phase colors obtained from the full I-band light curves from OGLE-III. It was possible to derive PL relations in the N3 and N4 bands only, although the S7, S11, L15, and L24 band data were also tested. Random-phase correction was included when deriving the PL relation in the N3 and N4 bands using the available time of observations from AKARI data. The final adopted PL relations were: N3 = -3.370 logP + 16.527 and N4 = -3.402 logP + 16.556. However, these PL relations may be biased due to the small number of Cepheids in the sample.
This paper is a continuation of \cite{zhang}, in which we established the wellposedness result and a comparison theorem for a class of one dimensional Forward-Backward SDEs. In this paper we extend the wellposedness result to high dimensional FBSDEs, and weaken the key condition in \cite{zhang} significantly. Compared to the existing methods in the literature, our result has the following features: (i) arbitrary time duration; (ii) random coefficients; (iii) (possibly) degenerate forward diffusion; and (iv) no monotonicity condition.
We compare ground state energies by variational Monte Carlo of the spin unpolarized Halperin 331 and the spin polarized Moore-Read (MR) Pfaffian fractional quantum Hall states at half-filling of the lowest Landau level (LLL) and the second Landau level (SLL) as a function of small deviations around the Coulomb point via the finite thickness effect and direct alterations to the the first two Haldane pseudopotentials. In the comparison we find that in the LLL, either the 331 state or the MR Pfaffian may be lower in energy depending on the deviations. In the SLL, however, the MR Pfaffian is consistently lower in energy except for large deviations. These results suggest that even under moderate deviations in the interaction potential (through various physical processes such as finite thickness, Landau level mixing, etc.), the MR Pfaffian description is more energetically favorable than the Halperin 331 state in the half-filled SLL (i.e. $\nu = 5/2$), consistent with recent experimental investigations.
In this paper we report the experimental implementation of a theoretically-proposed technique for creating a photoionized plasma in the laboratory using X-ray line radiation. Using a Sn laser-plasma to irradiate an Ar gas target, the photoionization parameter, \xi = 4{\pi}F/Ne, reached values of order 50 erg cm/s, where F is the radiation flux in erg/cm2/s. The significance of this is that this technique allows us to mimic effective spectral radiation temperatures in excess of 1 keV. We show that our plasma starts to be collisionally dominated before the peak of the X-ray drive. However, the technique is extendable to higher energy laser systems to create plasmas with parameters relevant to benchmarking codes used to model astrophysical objects.
In this paper, we propose a novel Deep Micro-Dictionary Learning and Coding Network (DDLCN). DDLCN has most of the standard deep learning layers (pooling, fully, connected, input/output, etc.) but the main difference is that the fundamental convolutional layers are replaced by novel compound dictionary learning and coding layers. The dictionary learning layer learns an over-complete dictionary for the input training data. At the deep coding layer, a locality constraint is added to guarantee that the activated dictionary bases are close to each other. Next, the activated dictionary atoms are assembled together and passed to the next compound dictionary learning and coding layers. In this way, the activated atoms in the first layer can be represented by the deeper atoms in the second dictionary. Intuitively, the second dictionary is designed to learn the fine-grained components which are shared among the input dictionary atoms. In this way, a more informative and discriminative low-level representation of the dictionary atoms can be obtained. We empirically compare the proposed DDLCN with several dictionary learning methods and deep learning architectures. The experimental results on four popular benchmark datasets demonstrate that the proposed DDLCN achieves competitive results compared with state-of-the-art approaches.
We perform a systematic analysis of several HBT parameters in heavy ion collisions from $E_{\rm beam}=2$ AGeV to $\sqrt {s_{\rm NN}}=200$ GeV within the UrQMD transport approach and compare the results to experimental data where available. We find that the 'lifetime' of the emission source as calculated from $\tau \sim \sqrt{R_O^{2}-R_S^{2}}$, is larger than the experimentally observed values at all investigated energies. The calculated volume of the pion source ($V_f$) is found to increase monotonously with increasing beam energy and the experimentally observed decrease of the measured $V_f$ at AGS is not seen. Finally, we calculate the mean free path $\lambda_f=0.5-1$ fm of pions at freeze-out and find a good description of the experimental data above the AGS energy region, supporting the suggestion of a universal kinetic decoupling criterion up to the highest RHIC energies.
We note that the model discussed in the communication of S. Bornholdt and H. Ebel (World Wide Web scaling exponent from Simon's 1955 model, cond-mat/0008465) is the particular case of the model considered and solved exactly in our paper, cond-mat/0004434. These models may be used for estimation of the order of the deviation of the scaling exponent from 2 both for the distributions of incoming links and links coming out from nodes but not for the obtaining some specific values of the exponents from the WWW growth data. We emphasize that, unlike the statement of Bornholdt and Ebel, both the network under consideration and the model of Barab\'{a}si and Albert provide quite equal possibilities for individual growth. There is no great difference between them in this respect. The resulting distributions for individual nodes and arising scaling relations have been obtained in our paper, cond-mat/0004434. We discuss briefly the modern state of art in the physics of the evolving networks and the great role of the general principle -- {\em popularity is attractive} -- in the self-organization of complex communications networks, in physics of nonequilibrium phenomena, and in Nature.
Fitzpatrick's variational representation of maximal monotone operators is here extended to a class of pseudo-monotone operators in Banach spaces. On this basis, the initial-value problem associated with the first-order flow of such an operator is here reformulated as a minimization principle, extending a method that was pioneered by Brezis, Ekeland and Nayroles for gradient flows. This formulation is used to prove that the problem is stable w.r.t.\ arbitrary perturbations not only of data but also of operators. This is achieved by using the notion of evolutionary $\Gamma$-convergence w.r.t.\ a nonlinear topology of weak type.   These results are applied to the Cauchy problem for quasilinear parabolic PDEs. This provides the structural compactness and stability of the model of several physical phenomena: nonlinear diffusion, incompressible viscous flow, phase transitions, and so on.
We review the application of field-theoretic renormalization group (RG) methods to the study of fluctuations in reaction-diffusion problems. We first investigate the physical origin of universality in these systems, before comparing RG methods to other available analytic techniques, including exact solutions and Smoluchowski-type approximations. Starting from the microscopic reaction-diffusion master equation, we then pedagogically detail the mapping to a field theory for the single-species reaction k A -> l A (l < k). We employ this particularly simple but non-trivial system to introduce the field-theoretic RG tools, including the diagrammatic perturbation expansion, renormalization, and Callan-Symanzik RG flow equation. We demonstrate how these techniques permit the calculation of universal quantities such as density decay exponents and amplitudes via perturbative eps = d_c - d expansions with respect to the upper critical dimension d_c. With these basics established, we then provide an overview of more sophisticated applications to multiple species reactions, disorder effects, L'evy flights, persistence problems, and the influence of spatial boundaries. We also analyze field-theoretic approaches to nonequilibrium phase transitions separating active from absorbing states. We focus particularly on the generic directed percolation universality class, as well as on the most prominent exception to this class: even-offspring branching and annihilating random walks. Finally, we summarize the state of the field and present our perspective on outstanding problems for the future.
TlCuCl$_3$ has a singlet ground state with the excitation gap $\Delta =0.65$ meV. The magnetic excitations in TlCuCl$_3$ have been investigated by means of neutron inelastic scattering experiments. The constant-$\it{\pmb Q}$ energy scan profiles were collected in the $a^*-c^*$ plane. A well-defined single magnetic excitation mode was observed. The dispersion relations along four different directions were determined. The lowest excitation occurs at ${\it{\pmb Q}}=(h, 0, l)$ with integer $h$ and odd $l$, as observed in KCuCl$_3$. A cluster series expansion up to the sixth order was applied to analyze the dispersion relations, and the individual exchange interactions were evaluated. It was demonstrated that TlCuCl$_3$ is a strongly coupled spin-dimer system.
Understanding, reasoning, and manipulating semantic concepts of images have been a fundamental research problem for decades. Previous work mainly focused on direct manipulation on natural image manifold through color strokes, key-points, textures, and holes-to-fill. In this work, we present a novel hierarchical framework for semantic image manipulation. Key to our hierarchical framework is that we employ a structured semantic layout as our intermediate representation for manipulation. Initialized with coarse-level bounding boxes, our structure generator first creates pixel-wise semantic layout capturing the object shape, object-object interactions, and object-scene relations. Then our image generator fills in the pixel-level textures guided by the semantic layout. Such framework allows a user to manipulate images at object-level by adding, removing, and moving one bounding box at a time. Experimental evaluations demonstrate the advantages of the hierarchical manipulation framework over existing image generation and context hole-filing models, both qualitatively and quantitatively. Benefits of the hierarchical framework are further demonstrated in applications such as semantic object manipulation, interactive image editing, and data-driven image manipulation.
We report on spin coherence lifetime extension on Tm$^{3+}$:YAG obtained through dynamically decoupling the thulium spins from their magnetic environment. The coherence lifetime reached with a Carr-Purcell-Meiboom-Gill sequence revealed a 450-fold extension [$\sim$$(230 \pm 30)$ ms] with respect to previously measured values. Comparison to a simple theoretical model allowed us to estimate the correlation time of the fluctuations of the ground level transition frequency to $(172 \pm 30)$ $\mu$s at 1.7 K. For attaining efficient decoupling sequences, we developed a strategy inspired by the \emph{zero-first-order Zeeman} effect to minimize the large inhomogeneous broadening of the ground level spin transition.
The Newman-Penrose formalism in transverse tetrads, namely those tetrads where \Psi_1=\Psi_3=0, is studied. In particular it is shown that the equations governing the dynamics within this formalism can be recast in a particularly compact way, leading to a better understanding of the formalism itself. The particular choice of tetrad allows not only to obtain the expression of Weyl scalars as simple functions of curvature invariants, but also the spin coefficients can be partly determined in an invariant way, by means of a new expression for the Bianchi identities that shows the various degrees of freedom in a more intuitive and direct way. We expect this approach to be very promising for a better understanding of all the equations governing the Newman-Penrose formalism. Such a new insight to the equations can also turn out to be useful for a generalization of the Newman- Penrose formalism to higher dimensions, thus allowing a better analysis of the various degrees of freedom, in view of extending to this case results already known in four dimensions.
Using two Chandra observations we have derived estimates of the dust distribution and distance to the eclipsing high mass X-ray binary (HMXB) Cen X-3 using the energy-resolved dust-scattered X-ray halo. By comparing the observed X-ray halos in 200 eV bands from 2-5 keV to the halo profiles predicted by the Weingartner & Draine interstellar grain model, we find that the vast majority (about 70%) of the dust along the line of sight to the system is located within about 300 pc of the Sun, although the halo measurements are insensitive to dust very close to the source. One of the Chandra observations occurred during an egress from eclipse as the pulsar emerged from behind the mass-donating primary. By comparing model halo light curves during this transition to the halo measurements, a source distance of 5.7 +/- 1.5 kpc (68% confidence level) is estimated, although we find this result depends on the distribution of dust on very small scales. Nevertheless, this value is marginally inconsistent with the commonly accepted distance to Cen X-3 of 8 kpc. We also find that the energy scaling of the scattering optical depth predicted by the Weingartner & Draine interstellar grain model does not accurately represent the results determined by X-ray halo studies of Cen X-3. Relative to the model, there appears to be less scattering at low energies or more scattering at high energies in Cen X-3.
In this paper, following the techniques of Foias and Temam, we establish suitable Gevrey class regularity of solutions to the supercritical quasi-geostrophic equations in the whole space, with initial data in "critical" Sobolev spaces. Moreover, the Gevrey class that we obtain is "near optimal" and as a corollary, we obtain temporal decay rates of higher order Sobolev norms of the solutions. Unlike the Navier-Stokes or the subcritical quasi-geostrophic equations, the low dissipation poses a difficulty in establishing Gevrey regularity. A new commutator estimate in Gevrey classes, involving the dyadic Littlewood-Paley operators, is established that allow us to exploit the cancellation properties of the equation and circumvent this difficulty.
We compute supersymmetric contributions to pion leptonic (\pi_{l2}) decays in the Minimal Supersymmetric Standard Model (MSSM). When R-parity is conserved, the largest contributions to the ratio R_{e/\mu} = \Gamma[ \pi^+ \to e^+ \nu_e(\gamma)]/\Gamma[ \pi^+ \to \mu^+ \nu_\mu(\gamma)] arise from one-loop (V-A)x(V-A) corrections. These contributions can be potentially as large as the sensitivities of upcoming experiments; if measured, they would imply significant bounds on the chargino and slepton sectors complementary to current collider limits. We also analyze R-parity violating interactions, which may produce a detectable deviation in R_{e/\mu} while remaining consistent with all other precision observables.