ShantanuT01/DACTYL-Pretraining huggingface dataset:
We experimentally investigate the properties of hyperentangled states displaying simultaneous entanglement in multiple degrees of freedom, and find that Bell tests beyond the standard Clauser, Horne, Shimony, Holt inequality can reveal a higher-dimensional nature in a device-independent way. Specifically, we show that hyperentangled states possess more than just simultaneous entanglement in separate degrees of freedom but also entanglement in a higher dimensional Hilbert space. We also verify the steerability of hyperentangled quantum states by steering different photonic degrees of freedom.
The hyper Zagreb index is a kind of extensions of Zagreb index, used for predicting physicochemical properties of organic compounds. Given a graph $G= (V(G), E(G))$, the first hyper-Zagreb index is the sum of the square of edge degree over edge set $E(G)$ and defined as $HM_1(G)=\sum_{e=uv\in E(G)}d(e)^2$, where $d(e)=d(u)+d(v)$ is the edge degree. In this work we define the second hyper-Zagreb index on the adjacent edges as $HM_2(G)=\sum_{e\sim f}d(e)d(f)$, where $e\sim f$ represents the adjacent edges of $G$. By inequalities, we explore some upper and lower bounds of these hyper-Zagreb indices, and provide the relation between Zagreb indices and hyper Zagreb indices.
A detailed study of an inhomogeneous dust cosmology contained in a $\gamma$-law family of perfect-fluid metrics recently presented by Mars and Senovilla is performed. The metric is shown to be the most general orthogonally transitive, Abelian, $G_2$ on $S_2$ solution admitting an additional homothety such that the self-similar group $H_3$ is of Bianchi type VI and the fluid flow is tangent to its orbits. The analogous cases with Bianchi types I, II, III, V, VIII and IX are shown to be impossible thus making this metric privileged from a mathematical viewpoint. The differential equations determining the metric are partially integrated and the line-element is given up to a first order differential equation of Abel type of first kind and two quadratures. The solutions are qualitatively analyzed by investigating the corresponding autonomous dynamical system. The spacetime is regular everywhere except for the big bang and the metric is complete both into the future and in all spatial directions. The energy-density is positive, bounded from above at any instant of time and with an spatial profile (in the direction of inhomogeneity) which is oscillating with a rapidly decreasing amplitude. The generic asymptotic behaviour at spatial infinity is a homogeneous plane wave. Well-known dynamical system results indicate that this metric is very likely to describe the asymptotic behaviour in time of a much more general class of inhomogeneous $G_2$ dust cosmologies.
Among stars in Galactic globular clusters the carbon abundance tends to decrease with increasing luminosity on the upper red giant branch, particularly within the lowest metallicity clusters. While such a phenomena is not predicted by canonical models of stellar interiors and evolution, it is widely held to be the result of some extra mixing operating during red giant branch ascent which transports material exposed to the CN(O)-cycle across the radiative zone in the stellar interior and into the base of the convective envelope, whereupon it is brought rapidly to the stellar surface. Here we present measurements of [C/Fe] abundances among 67 red giants in 19 globular clusters within the Milky Way. Building on the work of Martell et al., we have concentrated on giants with absolute magnitudes of $M_\mathrm{V} \sim -1.5$ within clusters encompassing a range of metallicity (-2.4 $<$ [Fe/H] $<$ -0.3). The Kitt Peak National Observatory (KPNO) 4 m and Southern Astrophysical Research (SOAR) 4.1 m telescopes were used to obtain spectra covering the $\lambda$4300 CH and $\lambda$3883 CN bands. The CH absorption features in these spectra have been analyzed via synthetic spectra in order to obtain [C/Fe] abundances. These abundances and the luminosities of the observed stars were used to infer the rate at which C abundances change with time during upper red giant branch evolution (i.e., the mixing efficiency). By establishing rates over a range of metallicity, the dependence of deep mixing on metallicity is explored. We find that the inferred carbon depletion rate decreases as a function of metallicity, although our results are dependent on the initial [C/Fe] composition assumed for each star.
We study E1 resonances, breakup and fusion reactions for weakly bound Be nuclei. The absorbing-boundary condition (ABC) is used to describe both the outgoing and incoming boundary conditions. The neutron continuum plays important roles in response and reaction of neutron drip-line nuclei.
We investigate the evolution of different measures of ``Gravitational Entropy'' in Bianchi type I and Lema\^itre-Tolman universe models.   A new quantity behaving in accordance with the second law of thermodynamics is introduced. We then go on and investigate whether a quantum calculation of initial conditions for the universe based upon the Wheeler-DeWitt equation supports Penrose's Weyl Curvature Conjecture, according to which the Ricci part of the curvature dominates over the Weyl part at the initial singularity of the universe. The theory is applied to the Bianchi type I universe models with dust and a cosmological constant and to the Lema\^itre-Tolman universe models. We investigate two different versions of the conjecture. First we investigate a local version which fails to support the conjecture. Thereafter we construct a non-local entity which shows more promising behaviour concerning the conjecture.
Aside from being a one-neutron halo nucleus, $^{15}$C is interesting because it is involved in reactions of relevance for several nucleosynthesis scenarios. The aim of this work is to analyze various reactions involving $^{15}$C, using a single structure model based on Halo EFT. To develop a Halo-EFT model of $^{15}$C at NLO, we first extract the ANC of its ground state by analyzing $^{14}$C(d,p)$^{15}$C transfer data at low energy. Using this Halo-EFT description, we study the $^{15}$C Coulomb breakup at high (605AMeV) and intermediate (68AMeV) energies using eikonal models with a consistent treatment of nuclear and Coulomb interactions at all orders, and proper relativistic corrections. Finally, we study the $^{14}$C(n,$\gamma$)$^{15}$C radiative capture. Our theoretical cross sections are in good agreement with experimental data for all reactions, thereby assessing the robustness of the $^{15}$C Halo-EFT model. Since a simple NLO description is enough to reproduce all data, the only nuclear-structure observables that matter are the binding energy and its ANC, showing that all the reactions considered are purely peripheral. In particular, it confirms the ANC value obtained for the $^{15}$C ground state: 1.59$\pm$0.06fm$^{-1}$. Our model provides also a new estimate of the radiative-capture cross section at astrophysical energy (23.3keV): 4.66$\pm$0.14$\mu$b. Including a Halo-EFT description of $^{15}$C within precise models of reactions is confirmed to be an excellent way to relate the nucleus reaction cross sections and structure. Its systematic expansion enables us to deduce which nuclear-structure observables are actually probed in the collision. From this, we can infer valuable information on both the structure of $^{15}$C and its synthesis through the $^{14}$C(n,$\gamma$)$^{15}$C radiative capture at astrophysical energies.
Let $n$ be a positive integer and let $0 < \alpha < n.$ In this paper, we continue our study of the integral equation $$ u(x) = \int_{R^{n}} \frac{u(y)^{(n+\alpha)(n-\alpha)}{|x - y|^{n-\alpha}}dy.$$ We mainly consider singular solutions in subcritical, critical, and super critical cases, and obtain qualitative properties, such as radial symmetry, monotonicity, and upper bounds for the solutions.
Several supersonic runaway pulsar wind nebulae (sPWNe) with jet-like extended structures have been recently discovered in X-rays. If these structures are the product of electrons escaping the system and diffusing into the surrounding interstellar medium, they can produce a radio halo extending for several arcmin around the source. We model the expected radio emission in this scenario in the Lighthouse Nebula sPWN. We assume a constant particle injection rate during the source lifetime, and isotropic diffusion into the surrounding medium. Our predictions strongly depend on the low- and high-energy cutoffs given in the particle distribution. Our results indicate that extended radio emission can be detected from the Lighthouse Nebula without the need to invoke extreme values for the model parameters. We provide synthetic synchrotron maps that can be used to constrain these results with observations by current highly sensitive radio instruments.
Structural and static properties of a classical two-dimensional (2D) system consisting of a finite number of charged particles which are laterally confined by a parabolic potential are investigated by Monte Carlo (MC) simulations and the Newton optimization technique. This system is the classical analog of the well-known quantum dot problem. The energies and configurations of the ground and all metastable states are obtained. In order to investigate the barriers and the transitions between the ground and all metastable states we first locate the saddle points between them, then by walking downhill from the saddle point to the different minima, we find the path in configurational space from the ground state to the metastable states, from which the geometric properties of the energy landscape are obtained. The sensitivity of the ground-state configuration on the functional form of the inter-particle interaction and on the confinement potential is also investigated.
Variation of the speed of light is quite a debated issue in cosmology with some benefits, but also with some controversial concerns. Many approaches to develop a consistent varying speed of light (VSL) theory have been developed recently. Although a lot of theoretical debate has sprout out about their feasibility and reliability, the most obvious and straightforward way to discriminate and check if such theories are really workable has been missed out or not fully employed. What is meant here is the comparison of these theories with observational data in a fully comprehensive way. In this paper we try to address this point i.e., by using the most updated cosmological probes, we test three different candidates for a VSL theory (Barrow \& Magueijo, Avelino \& Martins, and Moffat) signal. We consider many different ans\"{a}tze for both the functional form of $c(z)$ (which cannot be fixed by theoretical motivations) and for the dark energy dynamics, in order to have a clear global picture from which we extract the results. We compare these results using a reliable statistical tool such as the Bayesian Evidence. We find that the present cosmological data is perfectly compatible with any of these VSL scenarios, but in one case (Moffat model) we have a higher Bayesian Evidence ratio in favour of VSL than in the standard $c=$ constant $\Lambda$CDM scenario. Moreover, in such a scenario, the VSL signal can help to strengthen constraints on the spatial curvature (with indication toward an open universe), to clarify some properties of dark energy (exclusion of a cosmological constant at $2\sigma$ level) and is also falsifiable in the nearest future due to some peculiar issues which differentiate this model from the standard model. Finally, we have applied some priors which come from cosmology and, in particular, from information theory and gravitational thermodynamics.
Multi-person pose estimation generally follows top-down and bottom-up paradigms. Both of them use an extra stage ($\boldsymbol{e.g.,}$ human detection in top-down paradigm or grouping process in bottom-up paradigm) to build the relationship between the human instance and corresponding keypoints, thus leading to the high computation cost and redundant two-stage pipeline. To address the above issue, we propose to represent the human parts as adaptive points and introduce a fine-grained body representation method. The novel body representation is able to sufficiently encode the diverse pose information and effectively model the relationship between the human instance and corresponding keypoints in a single-forward pass. With the proposed body representation, we further deliver a compact single-stage multi-person pose regression network, termed as AdaptivePose. During inference, our proposed network only needs a single-step decode operation to form the multi-person pose without complex post-processes and refinements. We employ AdaptivePose for both 2D/3D multi-person pose estimation tasks to verify the effectiveness of AdaptivePose. Without any bells and whistles, we achieve the most competitive performance on MS COCO and CrowdPose in terms of accuracy and speed. Furthermore, the outstanding performance on MuCo-3DHP and MuPoTS-3D further demonstrates the effectiveness and generalizability on 3D scenes. Code is available at https://github.com/buptxyb666/AdaptivePose.
The mergers of two neutron stars are typically accompanied by broad-band electromagnetic emission from either a relativistic jet or a kilonova. It has also been long predicted that coherent radio emission will occur during the merger phase or from a newly formed neutron star remnant, however this emission has not been seen to date. This paper presents the deepest limits for this emission from a neutron star merger folowing triggered LOFAR observations of the short gamma-ray burst (SGRB) 181123B, starting 4.4 minutes after the GRB occurred. During the X-ray plateau phase, a signature of ongoing energy injection, we detect no radio emission to a 3$\sigma$ limit of 153 mJy at 144 MHz (image integration time of 136 seconds), which is significantly fainter than the predicted emission from a standard neutron star. At a redshift of 1.8, this corresponds to a luminosity of $2.5 \times 10^{44}$ erg s$^{-1}$. Snapshot images were made of the radio observation on a range of timescales, targeting short duration radio flashes similar to fast radio bursts (FRBs). No emission was detected in the snapshot images at the location of GRB 181123B enabling constraints to be placed on the prompt coherent radio emission model and emission predicted to occur when a neutron star collapses to form a black hole. At the putative host redshift of 1.8 for GRB 181123B, the non detection of the prompt radio emission is two orders of magnitude lower than expected for magnetic reconnection models for prompt GRB emission and no magnetar emission is expected.
Magnetoresistance (MR) and magnetization (d.c and a.c) measurements have been carried out on the manganites, (La0.7-2xEux)(Ca0.3Srx)MnO3 (0.05<x<0.15), in the temperature range of 5K-320K. At 5K, an unusually large MR of almost 98% is observed in the x=0.15 sample, nearly up to fields of 4-5 Tesla. This large high-field MR occurs in the metallic region, far below the insulator-metal transition temperature, and does not vary linearly with applied field. The unusual magnetoresistance is explained the light of various possibilities of phase segregation and cluster spin-glass behavior. Keywords: Manganites, High field MR, Phase segregation.
We present a non-Hermitian Floquet model with topological edge states in real and imaginary band gaps. The model utilizes two stacked honeycomb lattices which can be related via four different types of non-Hermitian time-reversal symmetry. Implementing the correct time-reversal symmetry provides us with either two counterpropagating edge states in a real gap, or a single edge state in an imaginary gap. The counterpropagating edge states allow for either helical or chiral transport along the lattice perimeter. In stark contrast, we find that the edge state in the imaginary gap does not propagate. Instead, it remains spatially localized while its amplitude continuously increases. Our model is well-suited for realizing these edge states in photonic waveguide lattices.
We report on a novel spin-charge fluctuation in the all-in-all-out pyrochlore magnet Cd$_2$Os$_2$O$_7$, where the spin fluctuation is driven by the conduction of thermally excited electrons/holes and associated fluctuation of Os valence. The fluctuation exhibits an activation energy significantly greater than the spin-charge excitation gap and a peculiar frequency range of $10^{6}$--$10^{10}$ s$^{-1}$. These features are attributed to the hopping motion of carriers as small polarons in the insulating phase, where the polaron state is presumably induced by the magnetoelastic coupling via the strong spin-orbit interaction. Such a coupled spin-charge-phonon fluctuation manifests as a part of the metal-insulator transition that is extended over a wide temperature range due to the modest electron correlation comparable with other interactions characteristic for 5$d$-subshell systems.
The $e^+e^- \rightarrow ZH$ process is the dominant process for the Higgs boson production at the future Higgs factory. In order to match the analysis on the Higgs properties with the highly precise experiment data, it will be crucial to include the theoretical prediction to the full next-to-next-to-leading order electroweak effect in the production rate $\sigma(e^+e^-\rightarrow ZH)$. In this inspiring work, we categorize the two-loop Feynman diagrams of the $\mathcal O(\alpha^2)$ correction to $e^+e^- \rightarrow ZH$ into 6 categories according to the relevant topological structures. Although 25377 diagrams contribute to the $\mathcal O(\alpha^2)$ correction in total, the number of the most challenging diagrams with seven denominators is 2250, which contain only 312 non-planar diagrams with 155 independent types. This categorization could be a valuable reference for the complete calculation in the future.
Connection of the Four Color Theorem (FCT) with some operations on trees is described. L.H. Kauffman's theorem about FCT and vector cross product is discussed. Operation of transplantation on trees linked with the move of brackets according to the associative law is used to formulate a conjecture. When map is represented as a tying of the trees this conjecture proposes the existence of special coloring of this map. This coloring makes possible successive transplantations such that one of these trees is transformed to another, and all the intermediate maps are colored properly. It means (in terms of L.H. Kauffman) that not only for two different positions of brackets in a product of n factors the associative law works (on special values of factors) but also there is a way of moving brackets that for all intermediate positioning of brackets the associative law is obeyed. Some classes of trees for which the conjecture is proved are presented.
The advent of two-dimensional (2D) crystals has led to numerous scientific breakthroughs. Conventional 2D systems have in-plane covalent bonds and a weak out-of-plane van-der-Waals bond. Here we report a new type of 2D material composed of discrete magnetic molecules, where anisotropic van-der-Waals interactions bond the molecules into a 2D packing. Through mechanical exfoliation, we can obtain single-crystalline molecular monolayers, which can be readily integrated into other 2D systems. Optical spectroscopy suggests the few-layered molecules preserve the temperature-induced spin-crossover switching observed in the bulk form but show a drastic increase in thermal hysteresis unique to these thin 2D molecule assemblies. The trapping of spin bistability with decreasing layer number can arise from domain wall dynamics in reduced dimensions. Our results establish molecular solids with strong anisotropy of intermolecular interactions as precursors to a novel class of 2D materials, affording new possibilities to control functionalities through substrate and interlayer interactions.
Let $G=(V,E)$ be a finite simple graph. The Sombor index $SO(G)$ of $G$ is defined as $\sum_{uv\in E(G)}\sqrt{d_u^2+d_v^2}$, where $d_u$ is the degree of vertex $u$ in $G$. Let $G$ be a connected graph constructed from pairwise disjoint connected graphs $G_1,\ldots ,G_k$ by selecting a vertex of $G_1$, a vertex of $G_2$, and identifying these two vertices. Then continue in this manner inductively. We say that $G$ is a polymer graph, obtained by point-attaching from monomer units $G_1,...,G_k$. In this paper, we consider some particular cases of these graphs that are of importance in chemistry and study their Sombor index.
The AdS/CFT correspondence relates deformations of the CFT by "multi-trace operators" to "non-local string theories". The deformed theories seem to have non-local interactions in the compact directions of space-time; in the gravity approximation the deformed theories involve modified boundary conditions on the fields which are explicitly non-local in the compact directions. In this note we exhibit a particular non-local property of the resulting space-time theory. We show that in the usual backgrounds appearing in the AdS/CFT correspondence, the commutator of two bulk scalar fields at points with a large enough distance between them in the compact directions and a small enough time-like distance between them in AdS vanishes, but this is not always true in the deformed theories. We discuss how this is consistent with causality.
We have considered a general 5D warped model with SM fields propagating in the bulk and computed explicit expressions for oblique and non-oblique electroweak observables as well as for flavor and CP violating effective four-fermion operators. We have compared the resulting lower bounds on the Kaluza-Klein (KK) scale in the RS model and a recently proposed model with a metric modified towards the IR brane, which is consistent with oblique parameters without the need for a custodial symmetry. We have randomly generated 40,000 sets of O(1) 5D Yukawa couplings and made a fit of the quark masses and CKM matrix elements in both models. This method allows to identify the percentage of points consistent with a given KK mass, which in turn provides us with a measure for the required fine-tuning. Comparison with current experimental data on Rb, FCNC and CP violating operators exhibits an improved behavior of our model with respect to the RS model. In particular, allowing 10% fine-tuning the combined results point towards upper bounds on the KK gauge boson masses around 3.3 TeV in our model as compared with 13 TeV in the RS model. One reason for this improvement is that fermions in our model are shifted, with respect to fermions in the RS model, towards the UV brane thus decreasing the strength of the modifications of electroweak observables.
Gamma-ray searches for new physics such as dark matter are often driven by investigating the composition of the extragalactic gamma-ray background (EGB). Classic approaches to EGB decomposition manifest in resolving individual point sources and dissecting the intensity spectrum of the remaining unresolved component. Furthermore, statistical methods have recently been proven to outperform the sensitivity of classic source detection algorithms in finding point-source populations in the unresolved flux regime. In this article, we employ the 1-point photon count statistics of eight years of Fermi-LAT data to resolve the population of extragalactic point sources and to decompose the diffuse isotropic background contribution for Galactic latitudes |b|>30 deg. We use three adjacent energy bins between 1 and 10 GeV. For the first time, we extend the analysis to incorporate a potential contribution from annihilating dark matter smoothly distributed in the Galaxy. We investigate the sensitivity reach of 1-point statistics for constraining the thermally-averaged self-annihilation cross section <\sigma v> of dark matter, using different template models for the Galactic foreground emission. Given the official Fermi-LAT interstellar emission model, we set upper bounds on the DM self-annihilation cross section <\sigma v> that are comparable with the constraints obtained by other indirect detection methods, in particular by the stacking analysis of several dwarf spheroidal galaxies.