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Given a graph $G$ with vertex set $V(G)$, a mapping $h : V(G) \rightarrow \lbrace 0, 1, 2, 3, 4, 5 \rbrace$ is called a quadruple Roman dominating function (4RDF) for $G$ if it holds the following. Every vertex $x$ such that $h(x)\in \{0,1,2, 3\}$ satisfies that $h(N[x]) = \sum_{v\in N[x]} h(v) \geq |\{y:y \in N(x) \; \text{and} \; h(y) \neq 0\}|+4$, where $N(x)$ and $N[x]$ stands for the open and closed neighborhood of $x$, respectively. The smallest possible weight $\sum_{x \in V(G)} h(x)$ among all possible 4RDFs $h$ for $G$ is the quadruple Roman domination number of $G$, denoted by $\gamma_{[4R]}(G)$. This work is focused on complexity aspects for the problem of computing the value of this parameter for several graph classes. Specifically, it is shown that the decision problem concerning $\gamma_{[4R]}(G)$ is NP-complete when restricted to star convex bipartite, comb convex bipartite, split and planar graphs. In contrast, it is also proved that such problem can be efficiently solved for threshold graphs where an exact solution is demonstrated, while for graphs having an efficient dominating set, tight upper and lower bounds in terms of the classical domination number are given. In addition, some approximation results to the problem are given. That is, we show that the problem cannot be approximated within $(1 - \epsilon) \ln |V|$ for any $\epsilon > 0$ unless $P=NP$. An approximation algorithm for it is proposed, and its APX-completeness proved, whether graphs of maximum degree four are considered. Finally, an integer linear programming formulation for our problem is presented., Comment: 14 pages

Star formation rates (SFRs), gas-phase metallicities, and stellar masses are crucial for studying galaxy evolution. The different relations resulting from these properties give insights into the complex interplay of gas inside galaxies and their evolutionary trajectory and current characteristics. We aim to characterize these relations at $z\sim 0.3$, corresponding to a 3-4 Gyr lookback time. We utilized optical integral field spectroscopy of 65 emission-line galaxies from the MAGPI survey at a redshift of $0.28

The demands on robotic manipulation skills to perform challenging tasks have drastically increased in recent times. To perform these tasks with dexterity, robots require perception tools to understand the scene and extract useful information that transforms to robot control inputs. To this end, recent research has introduced various object pose estimation and grasp pose detection methods that yield precise results. Assembly pose estimation is a secondary yet highly desirable skill in robotic assembling as it requires more detailed information on object placement as compared to bin picking and pick-and-place tasks. However, it has been often overlooked in research due to the complexity of integration in an agile framework. To address this issue, we propose an assembly pose estimation method with RGB-D input and 3D CAD models of the associated objects. The framework consists of semantic segmentation of the scene and registering point clouds of local surfaces against target point clouds derived from CAD models to estimate 6D poses. We show that our method can deliver sufficient accuracy for assembling object assemblies using evaluation metrics and demonstrations. The source code and dataset for the work can be found at: https://github.com/KulunuOS/6DAPose, Comment: 8 pages

We report a transport study on Pd$_3$In$_7$ which displays multiple Dirac type-II nodes in its electronic dispersion. Pd$_3$In$_7$ is characterized by low residual resistivities and high mobilities, which are consistent with Dirac-like quasiparticles. For an applied magnetic field $(\mu_{\text{0}} H)$ having a non-zero component along the electrical current, we find a large, positive, and linear in $\mu_{\text{0}} H$ longitudinal magnetoresistivity (LMR). The sign of the LMR and its linear dependence deviate from the behavior reported for the chiral-anomaly-driven LMR in Weyl semimetals. Interestingly, such anomalous LMR is consistent with predictions for the role of the anomaly in type-II Weyl semimetals. In contrast, the transverse or conventional magnetoresistivity (CMR for electric fields $\textbf{E} \bot \mu_{\text{0}} \textbf{H}$) is large and positive, increasing by $10^3-10^4$ \% as a function of $\mu_{\text{0}}H$ while following an anomalous, angle-dependent power law $\rho_{\text{xx}}\propto (\mu_{\text{0}}H)^n$ with $n(\theta) \leq 1$. The order of magnitude of the CMR, and its anomalous power-law, is explained in terms of uncompensated electron and hole-like Fermi surfaces characterized by anisotropic carrier scattering likely due to the lack of Lorentz invariance.

Recently, chiral anomaly (CA) has been proposed to occur in spin-orbit coupled noncentrosymmetric metals (SOC-NCMs), motivating CA to be a Fermi surface property rather than a Weyl node property. Although the nature of the anomaly is similar in both SOC-NCMs and Weyl systems, here we point out significant fundamental differences between the two. We show that the different nature of the orbital magnetic moment (OMM) in the two systems leads to non-trivial consequences -- particularly the sign of the longitudinal magnetoconductance always remains positive in a SOC non-centrosymmetric metal, unlike a Weyl metal that displays either sign. Furthermore,we investigate the planar Hall effect and the geometrical contribution to the Hall effect in the two systems and point out significant differences in the two systems. We conduct our analysis for magnetic and non-magnetic impurities, making our study important in light of current and upcoming experiments in both SOC-NCMs and Weyl metals.

We present an observational study of the dark matter fraction in star-forming disk-like galaxies up to redshift $z \sim 2.5$, selected from publicly available integral field spectroscropic surveys: KMOS$^{\rm 3D}$, KGES, and KROSS. To model the $H\alpha$ kinematics of these galaxies, we employ 3D forward-modelling, which incorporates beam-smearing and inclination corrections, and yields rotation curves. Subsequently, these rotation curves are corrected for gas pressure gradients, resulting in circular velocity curves or `intrinsic' rotation curves. Our final sample comprises of 263 rotationally supported main sequence star-forming galaxies with redshifts ranging from $0.6 \leq z < 2.5$. We estimate the dark matter fraction of these galaxies by subtracting the baryonic mass from the total mass, where the total mass is derived from the intrinsic rotation curves. We provide novel observational evidence, suggesting that at a fixed redshift, the dark matter fraction gradually increases with radius such that the outskirts of galaxies are dark matter dominated, similarly to local star-forming disk galaxies. This observed dark matter fraction exhibits a decreasing trend with increasing redshift and, on average, the fraction within the effective radius (upto outskirts) remains above 50\%, similar to locals. We investigate the relationships between dark matter, baryon surface density, and circular velocity of galaxies. We observe that low stellar mass galaxies, with $\log(M_{\rm star}\ [\mathrm{M_\odot}]) \leq 10.0$, undergo a higher degree of evolution, which may be attributed to the hierarchical merging of galaxies. Most importantly, we discuss several sources of uncertainties and current limitations in the field, as well as their impact on the measurements of dark matter fraction and its trend across galactic scales and cosmic time., Comment: Comments are welcome

Quantum interference is studied in a three-band model of pseudospin-one fermions in the $\alpha-\mathcal{T}_3$ lattice. We derive a general formula for magnetoconductivity that predicts a rich crossover between weak localization (WL) and weak antilocalization (WAL) in various scenarios. Recovering the known results for graphene ($\alpha=0$), we remarkably discover that WAL is notably enhanced when one deviates slightly from the graphene lattice, i.e. when $\alpha>0$, even though Berry's phase is no longer $\pi$. This is attributed to the presence of multiple Cooperon channels. Upon further increasing $\alpha$, a crossover to WL occurs that is maximal for the case of the Dice lattice ($\alpha=1$). Our work distinctly underscores the role of non-trivial band topology in the localization properties of electrons confined to the two-dimensional $\alpha-\mathcal{T}_3$ lattice., Comment: 5pages + 23 pages Supplemental Information

The Planar Hall effect (PHE) in topological materials has been a subject of great interest in recent years. Generally, it is understood to originate from the chiral-anomaly (CA) induced charge pumping between doubly degenerate Weyl nodes. However, the occurrence of PHE in the materials with positive and anisotropic orbital magnetoresistance has raised questions about CA being the sole origin of this effect. Here, we report the PHE, magnetoresistance, and thermal transport properties (Seebeck and Nernst coefficients) on the Ag intercalated PdTe$_2$. We observe positive longitudinal magnetoresistance, the linear field dependence of the amplitude of PHE, and a prolate pattern in the parametric plots. The planar Hall resistivity and anisotropic magnetoresitance fits well with theoretical study of CA being the origin of PHE. So, our observations are consistent with Weyl physics dominating the PHE in PdTe$_2$, Cu$_{0.05}$PdTe$_2$, and Ag$_{0.05}$PdTe$_2$. We further support our data with a theoretical model that reproduces the qualitative experimental features. In addition, we have calculated the Seebeck ($\it{S}$) and Nernst ($\nu$) coefficients for PdTe$_2$ and Cu and Ag intercalated compounds. The estimated values of Fermi energy for the Cu and Ag intercalated compounds are respectively two times and three times larger than that of PdTe$_2$., Comment: 16 pages, 16 figures