ShantanuT01/DACTYL-Pretraining huggingface dataset:
The inverse scattering problem for the relativistic three-dimensional equation $\Bigl(2E_{\bf p'}-2E_{\bf p}\Bigr)<{\bf p'}|\Psi_{\bf p}>= -\int V(t)d^3{\bf p''}<{\bf p''}|\Psi_{\bf p}>$ with $E_{\bf p}=\sqrt{m^2+{\bf p}^2}$ and $t=\Bigl(E_{\bf p'}-E_{\bf p''}\Bigr)^2 -\Bigl({\bf p'}-{\bf p''}\Bigr)^2$ is considered. The field-theoretical potential $V(t)$ of this equation is constructed in the framework of the old perturbation theory. It contains all contributions of diagrams with intermediate off-mass shell particles. In particular, this potential reproduces the OBE Bonn model of the $NN$ potential exactly.For the $\pi N$ scattering it is generated by $\sigma,\rho, \omega$-meson exchange diagrams. The inverse scattering problem is solved by reduction of these relativistic equations to the standard Schr\"odinger equations $\Bigl(\Delta_{\bf r}+{\bf k}^2\Bigr)<{\bf r}|\phi_{\bf p}>= - v({\bf r})<{\bf r}|\phi_{\bf k}>$ with $E_{\bf p}={\bf k}^2/2m+m$. The relation between the relativistic potential $V(t)$ and its nonrelativistic representation $v({\bf r})$ is obtained.
In this paper we investigate the relation between the maximal luminosity of X-ray outburst and the orbital period in transient low mass X-ray binaries (or soft X-ray transients) observed by the Rossi X-ray Timing Explorer (RXTE) in the past decade. We find that the maximal luminosity (3-200 keV) in Eddington unit generally increases with increasing orbital period, which does not show a luminosity saturation but in general agrees with theoretical prediction. The peak luminosities in ultra-compact binaries might be higher than those with orbital period of 2-4 h, but more data are needed to make the claim. We also find that there is no significant difference in the 3-200 keV outburst peak luminosity between neutron star systems and black hole systems with orbital periods above 4 h; however, there might be significant difference at smaller orbital period where only neutron star systems are observed and radiatively ineffcient accretion flow is expected to work at the low luminosities for black hole accreters.
Deep learning models show remarkable results in automated skin lesion analysis. However, these models demand considerable amounts of data, while the availability of annotated skin lesion images is often limited. Data augmentation can expand the training dataset by transforming input images. In this work, we investigate the impact of 13 data augmentation scenarios for melanoma classification trained on three CNNs (Inception-v4, ResNet, and DenseNet). Scenarios include traditional color and geometric transforms, and more unusual augmentations such as elastic transforms, random erasing and a novel augmentation that mixes different lesions. We also explore the use of data augmentation at test-time and the impact of data augmentation on various dataset sizes. Our results confirm the importance of data augmentation in both training and testing and show that it can lead to more performance gains than obtaining new images. The best scenario results in an AUC of 0.882 for melanoma classification without using external data, outperforming the top-ranked submission (0.874) for the ISIC Challenge 2017, which was trained with additional data.
We present radial velocities of the double-lined spectroscopic binary NP Aqr. The radial velocities and the optical light curves obtained by Hipparcos and ASAS-3 are analyzed separately. The masses of the primary and secondary components have been found to be 1.65$\pm$0.09 and 0.99$\pm$0.05 M$_{\odot}$, respectively. The cross-correlation functions indicate triple peaks which show presence of a tertiary star. The spectroscopic properties of this additional component resemble to that of the primary star. The analysis of the light curves yielded that the more massive primary star fills its corresponding Roche lobe. The secondary component is at or near Roche lobe indicating a new $\beta$ Lyrae-type near-contact binary. The orbital inclination is about 40$^{\circ}$ and, therefore, the observed light variations are produced only by the proximity effects. Due to the absence of eclipses, the effective temperature of the secondary star and the radii of the components could not be determined accurately. We conclude that NP Aqr is a non-eclipsing double-lined spectroscopic binary with a distance of about 134$\pm$7 pc. The absolute parameters of the components are also compared with the evolutionary models. While the location of the primary star seems to be suitable with respect to its mass in the Hertzsprung-Russell diagram, the secondary component is located as if a star having a mass less than 0.6 M$_{\odot}$. This discrepancy is originated from very low effective temperature determined only from the light curve produced by proximity effects. The distance to the third star appears to be very close to that of the close binary which indicates that it may be dynamically bounded to the binary.
A formulation of new six-dimensional theories with (1,0) supersymmetry and E_8 global symmetry is proposed. The model is based on the large n theory describing n D-strings interacting with parallel D-fivebranes in Type I string theory.
We investigate the finite size corrections to the equilibrium magnetization of an Ising model on a random graph with $N$ nodes and $N^{\gamma}$ edges, with $1 < \gamma \leq 2$. By conveniently rescaling the coupling constant, the free energy is made extensive. As expected, the system displays a phase transition of the mean-field type for all the considered values of $\gamma$ at the transition temperature of the fully connected Curie-Weiss model. Finite size corrections are investigated for different values of the parameter $\gamma$, using two different approaches: a replica-based finite $N$ expansion, and a cavity method. Numerical simulations are compared with theoretical predictions. The cavity based analysis is shown to agree better with numerics.
The soft X-ray emission from high density plasma in CTTS is associated with the accretion process. It is still unclear whether this high density cool plasma is heated in the accretion shock, or if it is coronal plasma fed/modified by the accretion process. We conducted a coordinated quasi-simultaneous optical and X-ray observing campaign of the CTTS V2129 Oph (Chandra/HETGS data to constrain the X-ray emitting plasma components, and optical observations to constrain the characteristics of accretion and magnetic field). We analyze a 200 ks Chandra/HETGS observation of V2129 Oph, subdivided into two 100 ks segments, corresponding to two different phases within one stellar rotation. The X-ray emitting plasma covers a wide range of temperatures: 2-34 MK. The cool plasma component of V2129 Oph varies between the two segments of the Chandra observation: high density plasma (log Ne ~ 12.1) with high EM at ~ 3-4 MK is present during the 1st segment; during the 2nd segment this plasma component has lower EM and lower density (log Ne < 11.5), although the statistical significance of these differences is marginal. Hotter plasma components, T > 10 MK, show variability on short time scales (~ 10 ks), typical of coronal plasma. A clear flare, detected in the 1st segment, could be located in a large coronal loop (> 3 Rstar). Our observation provides further confirmation that the dense cool plasma at a few MK in CTTS is material heated in the accretion shock. The variability of this cool plasma component on V2129 Oph may be explained in terms of X-rays emitted in the accretion shock and seen with different viewing angles at the two rotational phases probed by our observation. During the 1st time interval direct view of the shock region is possible, while, during the 2nd, the accretion funnel itself intersects the line of sight to the shock region, preventing us from observing accretion-driven X-rays.
The eccentricity (anti-adjacency) matrix $\varepsilon(G)$ of a graph $G$ is obtained from the distance matrix by retaining the eccentricities in each row and each column. The $\varepsilon$-eigenvalues of a graph $G$ are those of its eccentricity matrix $\varepsilon(G),$ and the eccentricity energy (or the $\varepsilon$-energy) of $G$ is the sum of the absolute values of $\varepsilon$-eigenvalues. In this paper, we establish some bounds for the $\varepsilon$-energy of the complete multipartite graph $K_{n_1, n_2, \ldots,n_p}$ of order $n= \sum_{i=1}^p n_i $ and characterize the extreme graphs.   This partially answers the problem given in Wang {\em et al.} (2019). We finish the paper showing graphs that are not $\varepsilon$-cospectral with the same $\varepsilon$-energy.
In the study of non-Fermi-liquid (NFL) phenomena in correlated metals, U2Pt2In is of special interest as it is one of the rare stoichiometric (undoped) materials that show NFL behaviour at ambient pressure. Here we report on the stability of the NFL phase with respect to hydrostatic pressure (p< 1.8 GPa). Electrical resistivity data under pressure, taken on a single-crystalline sample for a current in the tetragonal plane, show that T_FL, i.e. the temperature below which the Fermi-liquid T^2-term is observed, increases with pressure as T_FL ~ (p-p_c), where p_c~0 is a critical pressure. This provides strong evidence for the location of U2Pt2In at an antiferromagnetic quantum critical point.
It is shown that statistics of records for time series generated by random walks are independent of the details of the jump distribution, as long as the latter is continuous and symmetric. In N steps, the mean of the record distribution grows as the sqrt(4N/pi) while the standard deviation grows as sqrt((2-4/pi) N), so the distribution is non-self-averaging. The mean shortest and longest duration records grow as sqrt(N/pi) and 0.626508... N, respectively. The case of a discrete random walker is also studied, and similar asymptotic behavior is found.
A model for nonequilibrium wetting in 1+1 dimensions is introduced. It comprises adsorption and desorption processes with a dynamics which generically does not obey detailed balance. Depending on the rates of the dynamical processes the wetting transition is either of first or second order. It is found that the wet (unbound) and the non-wet (pinned) states coexist and are both thermodynamically stable in a domain of the dynamical parameters which define the model. This is in contrast with equilibrium transitions where coexistence of thermodynamically stable states takes place only on the transition line.
A genus one labeled circle tree is a tree with its vertices on a circle, such that together they can be embedded in a surface of genus one, but not of genus zero. We define an e-reduction process whereby a special type of subtree, called an e-graph, is collapsed to an edge. We show that genus is invariant under e-reduction. Our main result is a classification of genus one labeled circle trees through e-reduction. Using this we prove a modified version of a conjecture of David Hough, namely, that the number of genus one labeled circle trees on $n$ vertices is divisible by $n$ or if it is not divisible by $n$ then it is divisible by $n/2$. Moreover, we explicitly characterize when each of these possibilities occur.
We apply Wildeshaus's theory of motivic intermediate extensions to the motivic decomposition conjecture, formulated by Deninger-Murre and Corti-Hanamura. We first obtain a general motivic decomposition for the Chow motive of an arbitrary smooth projective family $f:X \rightarrow S$ whose geometric fibers are Tate. Using Voevodsky's motives with rational coefficients, the formula is valid for an arbitrary regular base $S$, without assuming the existence of a base field or even of a prime integer $\ell$ invertible on $S$. This result, and some of Bondarko' ideas, lead us to a generalized formulation of Corti-Hanamura's conjecture. Secondly we establish the existence of the motivic decomposition when $f:X \rightarrow S$ is a projective quadric bundle over a characteristic $0$ base, which is either sufficiently general or whose discriminant locus is a normal crossing divisor. This provides a motivic lift of the Bernstein-Beilinson-Deligne decomposition in this setting.
We calculate the ionisation fraction in protostellar disk models using two different gas-phase chemical networks, and examine the effect of turbulent mixing by modelling the diffusion of chemical species vertically through the disk. The aim is to determine in which regions of the disk gas can couple to a magnetic field and sustain MHD turbulence. We find that the effect of diffusion depends crucially on the elemental abundance of heavy metals (magnesium) included in the chemical model. In the absence of heavy metals, diffusion has essentially no effect on the ionisation structure of the disks, as the recombination time scale is much shorter than the turbulent diffusion time scale. When metals are included with an elemental abundance above a threshold value, the diffusion can dramatically reduce the size of the magnetically decoupled region, or even remove it altogther. For a complex chemistry the elemental abundance of magnesium required to remove the dead zone is 10(-10) - 10(-8). We also find that diffusion can modify the reaction pathways, giving rise to dominant species when diffusion is switched on that are minor species when diffusion is absent. This suggests that there may be chemical signatures of diffusive mixing that could be used to indirectly detect turbulent activity in protoplanetary disks. We find examples of models in which the dead zone in the outer disk region is rendered deeper when diffusion is switched on. Overall these results suggest that global MHD turbulence in protoplanetary disks may be self-sustaining under favourable circumstances, as turbulent mixing can help maintain the ionisation fraction above that necessary to ensure good coupling between the gas and magnetic field.
In this paper, we study the entanglement contour in a general excited state in the holographic 2d CFT using the partial entanglement entropy proposal. We show how thermodynamics fixes the entanglement contour relating it to the first law of entanglement. We derive the entanglement contour for a general time-dependent excited state and consider a quenched initial state in the presence of spatial boundaries as an explicit example. Finally, we comment on the coarse-graining and the complexity contour in the $AdS_3/CFT_2$.
Unusually high velocities (< ~0.1c) and correspondingly high kinetic energies have been observed in a subset of Type Ic supernovae (so-called "broad-lined Ic" supernovae; SNe Ic-BL), prompting a search for a central engine model capable of generating such energetic explosions. A clue to the explosion mechanism may lie in the fact that all supernovae that accompany long-duration gamma-ray bursts belong to the SN Ic-BL class. Using a combination of two-dimensional relativistic hydrodynamics and radiation transport calculations, we demonstrate that the central engine responsible for long gamma-ray bursts can also trigger a SN Ic-BL. We find that a reasonable gamma-ray burst engine injected into a stripped Wolf-Rayet progenitor produces a relativistic jet with energy ~10^51 ergs, as well as a SN whose synthetic light curves and spectra are fully consistent with observed SNe Ic-BL during the photospheric phase. As a result of the jet's asymmetric energy injection, the SN spectra and light curves depend on viewing angle. The impact of viewing angle on the spectrum is particularly pronounced at early times, while the viewing angle dependence for the light curves (~10% variation in bolometric luminosity) persists throughout the photospheric phase.
An algorithm is presented for generating finite modular, semimodular, graded, and geometric lattices up to isomorphism. Isomorphic copies are avoided using a combination of the general-purpose graph-isomorphism tool nauty and some optimizations that handle simple cases directly. For modular and semimodular lattices, the algorithm prunes the search tree much earlier than the method of Jipsen and Lawless, leading to a speedup of several orders of magnitude. With this new algorithm modular lattices are counted up to 30 elements, semimodular lattices up to 25 elements, graded lattices up to 21 elements, and geometric lattices up to 34 elements. Some statistics are also provided on the typical shape of small lattices of these types.
In this article, we examine $L^2$ well-posedness and stabilization property of the dispersion-generalized Benjamin-Ono equation with periodic boundary conditions. The main ingredient of our proof is a development of dissipation-normalized Bourgain space, which gains smoothing properties simultaneously from dissipation and dispersion within the equation. We will establish a bilinear estimate for the derivative nonlinearity using this space and prove the linear observability inequality leading to small-data stabilization.
We consider problems about packing and counting Hamilton $\ell$-cycles in hypergraphs of large minimum degree. Given a hypergraph $\mathcal H$, for a $d$-subset $A\subseteq V(\mathcal H)$, we denote by $d_{\mathcal H}(A)$ the number of distinct \emph{edges} $f\in E(\mathcal H)$ for which $A\subseteq f$, and set $\delta_d(\mathcal H)$ to be the minimum $d_{\mathcal H}(A)$ over all $A\subseteq V(\mathcal H)$ of size $d$. We show that if a $k$-uniform hypergraph on $n$ vertices $\mathcal H$ satisfies $\delta_{k-1}(\mathcal H)\geq \alpha n$ for some $\alpha>1/2$, then for every $\ell<k/2$ $\mathcal H$ contains $(1-o(1))^n\cdot n!\cdot \left(\frac{\alpha}{\ell!(k-2\ell)!}\right)^{\frac{n}{k-\ell}}$ Hamilton $\ell$-cycles. The exponent above is easily seen to be optimal. In addition, we show that if $\delta_{k-1}(\mathcal H)\geq \alpha n$ for $\alpha>1/2$, then $\mathcal H$ contains $f(\alpha)n$ edge-disjoint Hamilton $\ell$-cycles for an explicit function $f(\alpha)>0$. For the case where every $(k-1)$-tuple $X\subset V({\mathcal H})$ satisfies $d_{\mathcal H}(X)\in (\alpha\pm o(1))n$, we show that $\mathcal H$ contains edge-disjoint Haimlton $\ell$-cycles which cover all but $o\left(|E(\mathcal H)|\right)$ edges of $\mathcal H$. As a tool we prove the following result which might be of independent interest: For a bipartite graph $G$ with both parts of size $n$, with minimum degree at least $\delta n$, where $\delta>1/2$, and for $p=\omega(\log n/n)$ the following holds. If $G$ contains an $r$-factor for $r=\Theta(n)$, then by retaining edges of $G$ with probability $p$ independently at random, w.h.p the resulting graph contains a $(1-o(1))rp$-factor.
Using hadronic Lagrangians that include the interaction of pentaquark $\Theta^+$ baryon with $K$ and $N$, we evaluate the cross sections for its production from meson-proton, proton-proton, and photon-proton reactions near threshold. With empirical coupling constants and form factors, the predicted cross sections are about 1.5 mb in kaon-proton reactions, 0.1 mb in rho-nucleon reactions, 0.05 mb in pion-nucleon reactions, 20 $\mu$b in proton-proton reactions, and 40 nb in photon-proton reactions.
Let $(M,g)$ be a complete manifold of nonpositive scalar curvature, let $\Omega\subset M$ be a suitable domain, and let $\lambda(\Omega)$ be the first Dirichlet eigenvalue of the Laplace-Beltrami operator on $\Omega$. We prove several bounds for the rate of decrease of $\lambda(\Omega)$ and $\Omega$ increases, and a result comparing the rate of decrease of $\lambda$ before and after a conformal diffeomorphism. Along the way, we prove a reverse-Holder inequality for the first eigenfunction, which generalizes results of Chiti to the monifold setting and may be of independent interest
We present a wide-field optical imaging search for electromagnetic counterparts to the likely neutron star - black hole (NS-BH) merger GW190814/S190814bv. This compact binary merger was detected through gravitational waves by the LIGO/Virgo interferometers, with masses suggestive of a NS-BH merger. We imaged the LIGO/Virgo localization region using the MegaCam instrument on the Canada-France-Hawaii Telescope. We describe our hybrid observing strategy of both tiling and galaxy-targeted observations, as well as our image differencing and transient detection pipeline. Our observing campaign produced some of the deepest multi-band images of the region between 1.7 and 8.7 days post-merger, reaching a 5sigma depth of g > 22.8 (AB mag) at 1.7 days and i > 23.1 and i > 23.9 at 3.7 and 8.7 days, respectively. These observations cover a mean total integrated probability of 67.0% of the localization region. We find no compelling candidate transient counterparts to this merger in our images, which suggests that either the lighter object was tidally disrupted inside of the BH's innermost stable circular orbit, the transient lies outside of the observed sky footprint, or the lighter object is a low-mass BH. We use 5sigma source detection upper limits from our images in the NS-BH interpretation of this merger to constrain the mass of the kilonova ejecta to be Mej < 0.015Msun for a 'blue' (kappa = 0.5 cm^2 g^-1) kilonova, and Mej < 0.04Msun for a 'red' (kappa = 5-10 cm^2 g^-1) kilonova. Our observations emphasize the key role of large-aperture telescopes and wide-field imagers such as CFHT MegaCam in enabling deep searches for electromagnetic counterparts to gravitational wave events.
A k-ranking of a graph G is a labeling of the vertices of G with values from {1,...,k} such that any path joining two vertices with the same label contains a vertex having a higher label. The tree-depth of G is the smallest value of k for which a k-ranking of G exists. The graph G is k-critical if it has tree-depth k and every proper minor of G has smaller tree-depth.   We establish partial results in support of two conjectures about the order and maximum degree of k-critical graphs. As part of these results, we define a graph G to be 1-unique if for every vertex v in G, there exists an optimal ranking of G in which v is the unique vertex with label 1. We show that several classes of k-critical graphs are 1-unique, and we conjecture that the property holds for all k-critical graphs. Generalizing a previously known construction for trees, we exhibit an inductive construction that uses 1-unique k-critical graphs to generate large classes of critical graphs having a given tree-depth.
Angular momentum transport is one of the cornerstones of spintronics. Spin angular momentum is not only transported by mobile charge carriers, but also by the quantized excitations of the magnetic lattice in magnetically ordered systems. In this regard, magnetically ordered insulators provide a platform for magnon spin transport experiments without additional contributions from spin currents carried by mobile electrons. In combination with charge-to-spin current conversion processes in conductors with finite spin-orbit coupling it is possible to realize all-electrical magnon transport schemes in thin film heterostructures. This review provides an insight into such experiments and recent breakthroughs achieved. Special attention is given to charge current based manipulation via an adjacent normal metal of magnon transport in magnetically ordered insulators in terms of spin-transfer torque. Moreover, the influence of two magnon modes with opposite spin in antiferromagnetic insulators on all-electrical magnon transport experiments is discussed.