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Modern artificial intelligence (AI) systems are powered by foundation models. This paper presents a new set of foundation models, called Llama 3. It is a herd of language models that natively support multilinguality, coding, reasoning, and tool usage. Our largest model is a dense Transformer with 405B parameters and a context window of up to 128K tokens. This paper presents an extensive empirical evaluation of Llama 3. We find that Llama 3 delivers comparable quality to leading language models such as GPT-4 on a plethora of tasks. We publicly release Llama 3, including pre-trained and post-trained versions of the 405B parameter language model and our Llama Guard 3 model for input and output safety. The paper also presents the results of experiments in which we integrate image, video, and speech capabilities into Llama 3 via a compositional approach. We observe this approach performs competitively with the state-of-the-art on image, video, and speech recognition tasks. The resulting models are not yet being broadly released as they are still under development.

In the paper, we present an accelerating cosmological model in $f(R,\mathcal{L}_{m})$ gravity with the parameter constrained through the cosmological data sets. At the beginning, we have employed a functional form of $f(R,\mathcal{L}_{m}) =\frac{R}{2}+\alpha R^2+\mathcal{L}_{m}^\beta$, where $\alpha$ and $\beta$ are model parameters. This model is well motivated from the Starobinsky model in $f(R)$ gravity and the power law form of $f(\mathcal{L}_{m})$. The Hubble parameter has been derived with some algebraic manipulation and constrained by Hubble data and Pantheon$^{+}$ data. With the constraint parameters, present value of deceleration parameter has been obtained to as $q_{0}\approx-0.63$ with the transition at $z_{t}\approx0.7$. It shows the early deceleration and late time acceleration behaviour. The present value of other geometric parameters such as the jerk and snap parameter are obtained to be $j_{0}\approx0.78$ and $s_{0}\approx 0.1$ respectively. The state finder diagnostic test gives the quintessence behaviour at present and converging to $\Lambda$CDM at late times. Moreover the $Om(z)$ diagnostics gives negative slope which shows that the model favours the state finder diagnostic result. Also the current age of Universe has been obtained as, $t_{0} = 13.64~~Gyrs$. The equation of state parameter also shows the quintessence behaviour. Based on the present analysis, it indicates that the $f(R,\mathcal{L}_{m})$ gravitational theory may be another alternative to study the dark energy models., Comment: 12 pages, 10 figures

We performed an analysis of the extreme-ultraviolet (EUV) wave event on 2022 March 31. The event originated from active region (AR) 12975 located at N13W52 in the field of view of the Atmospheric imaging Assembly (AIA) and exactly at the west limb viewed by the EUV Imager (EUVI) of the Solar Terrestrial Relations Observatory-Ahead (STEREO-A) satellite. The EUV wave was associated with an M9.6 class flare. The event was also well observed by MLSO and COR1 coronagraphs. We revealed here evident coexistence of two components of EUV waves in AIA as well as in EUVI images i.e., a fast-mode wave and a nonwave, which was predicted by the EUV wave hybrid model. The speeds of the fast-mode and non wave EUV wave components in AIA varies from ~430 to 658 km/s and ~157 to 205 km/s, respectively. The computed speeds in STEREO-A for the fast-mode wave and nonwave components are ~520 and ~152 km/s, respectively. Another wave emanated from the source AR and interacted with ambient coronal loops, showing evident reflection in the EUV images above the solar limb. The speed of the reflected wave in the plane of the sky is ~175 km/s. With the precise alignments, we found that the fast-mode EUV wave is just ahead of the coronal mass ejection (CME) and the nonwave component is cospatial with the frontal loop of the accompanied CME. The event also showed stationary fronts., Comment: 6 figures, 16 pages

Given a (proper) vertex coloring $f$ of a graph $G$, say $f\colon V(G)\to \mathbb{N}$, the difference edge labelling induced by $f$ is a function $h\colon E(G)\to \mathbb{N}$ defined as $h(uv)=|f(u)-f(v)|$ for every edge $uv$ of $G$. A graceful coloring of $G$ is a vertex coloring $f$ of $G$ such that the difference edge labelling $h$ induced by $f$ is a (proper) edge coloring of $G$. A graceful coloring with range $\{1,2,\dots,k\}$ is called a graceful $k$-coloring. The least integer $k$ such that $G$ admits a graceful $k$-coloring is called the graceful chromatic number of $G$, denoted by $\chi_g(G)$. We prove that $\chi(G^2)\leq \chi_g(G)\leq a(\chi(G^2))$ for every graph $G$, where $a(n)$ denotes the $n$th term of the integer sequence A065825 in OEIS. We also prove that graceful coloring problem is NP-hard for planar bipartite graphs, regular graphs and 2-degenerate graphs. In particular, we show that for each $k\geq 5$, it is NP-complete to check whether a planar bipartite graph of maximum degree $k-2$ is graceful $k$-colorable. The complexity of checking whether a planar graph is graceful 4-colorable remains open.

A graceful $l$-coloring of a graph $G$ is a proper vertex coloring with $l$ colors which induces a proper edge coloring with at most $l-1$ colors, where the color for an edge $ab$ is the absolute difference between the colors assigned to the vertices $a$ and $b$. The graceful chromatic number $\chi_g(G)$ is the smallest $l$ for which $G$ permits graceful $l$-coloring. The problem of computing the graceful chromatic number of regular graphs is still open, though the existence of the lower bound was proved in \cite{3}. Hence, we pay attention to the computation of the graceful chromatic number of a special class of regular graphs namely complete graphs using set theoretic approach. Also, a few characterization of graphs based on their graceful chromatic number were examined., Comment: 8 pages, 4 figures

Scalar non-standard interactions (NSI) presents an exciting pathway for probing potential new physics that extends beyond the Standard Model (BSM). The scalar coupling of neutrinos with matter can appear as a sub-dominant effect that can impact the neutrino oscillation probabilities. The uniqueness of these interactions is that it can directly affect the neutrino mass matrix. This makes oscillations sensitive to the absolute neutrino mass. The effects of scalar NSI scales linearly with matter density which motivates its exploration in long-baseline sector. The presence of scalar NSI can influence the key measurements in the field of neutrino physics, including the precise determination of the leptonic CP phase ($\delta_{CP}$), neutrino mass ordering and the octant of $\theta_{23}$. The precise determination of $\delta_{CP}$ is one of the major goals of DUNE, which is an upcoming long-baseline experiment. A better understanding of the impact of scalar NSI on CP measurement sensitivities is crucial for accurate interpretation of $\delta_{CP}$ phase. In this work, we have explored the impact of the complex off-diagonal scalar NSI elements $\eta_{\alpha\beta}$ and their associated phases $\phi_{\alpha\beta}$ on the CP-measurement sensitivities at DUNE. We have explored the impact of the neutrino mass scale on these sensitivities. We look for constraining these off-diagonal elements for different neutrino mass scales. We also explore their correlation with $\delta_{CP}$, investigating potential degeneracies that can arise due to additional phases. We also perform a correlation study among different scalar NSI elements. We show that the inclusion of the complex scalar NSI elements can significantly modify the CP phase measurements., Comment: 26 pages, 9 figures

Overcoming the challenge of limited data availability within materials science is crucial for the broad-based applicability of machine learning within materials science. One pathway to overcome this limited data availability is to use the framework of transfer learning (TL), where a pre-trained (PT) machine learning model (on a larger dataset) can be fine-tuned (FT) on a target (typically smaller) dataset. Our study systematically explores the effectiveness of various PT/FT strategies to learn and predict material properties with limited data. Specifically, we leverage graph neural networks (GNNs) to PT/FT on seven diverse curated materials datasets, encompassing sizes ranging from 941 to 132,752 datapoints. We consider datasets that cover a spectrum of material properties, ranging from band gaps (electronic) to formation energies (thermodynamic) and shear moduli (mechanical). We study the influence of PT and FT dataset sizes, strategies that can be employed for FT, and other hyperparameters on pair-wise TL among the datasets considered. We find our pair-wise PT-FT models to consistently outperform models trained from scratch on the target datasets. Importantly, we develop a GNN framework that is simultaneously PT on multiple properties (MPT), enabling the construction of generalized GNN models. Our MPT models outperform pair-wise PT-FT models on several datasets considered, and more significantly, on a 2D material band gap dataset that is completely out-of-distribution from the PT datasets. Finally, we expect our PT/FT and MPT frameworks to be generalizable to other GNNs and materials properties, which can accelerate materials design and discovery for various applications.

We demonstrate a sapphire machining process integrated with intermediate-scale quantum processors. The process allows through-substrate electrical connections, necessary for low-frequency mode-mitigation, as well as signal-routing, which are vital as quantum computers scale in qubit number, and thus dimension. High-coherence qubits are required to build fault-tolerant quantum computers and so material choices are an important consideration when developing a qubit technology platform. Sapphire, as a low-loss dielectric substrate, has shown to support high-coherence qubits. In addition, recent advances in material choices such as tantalum and titanium-nitride, both deposited on a sapphire substrate, have demonstrated qubit lifetimes exceeding 0.3 ms. However, the lack of any process equivalent of deep-silicon etching to create through-substrate-vias in sapphire, or to inductively shunt large dies, has limited sapphire to small-scale processors, or necessitates the use of chiplet architecture. Here, we present a sapphire machining process that is compatible with high-coherence qubits. This technique immediately provides a means to scale QPUs with integrated mode-mitigation, and provides a route toward the development of through-sapphire-vias, both of which allow the advantages of sapphire to be leveraged as well as facilitating the use of sapphire-compatible materials for large-scale QPUs., Comment: 9 pages, 6 figures

In this study, we investigate the spin dynamics of a frustrated Kagom\'e lattice system, focusing on the nonlinearity of spin oscillations induced by a harmonic magnetic field under varying strengths of Dzyaloshinskii-Moriya interaction (DMI), exchange field, and anisotropy energy. We have utilized Poincar\'e Surface Sections (PSS) and Power Spectra (PS) for different DMI and anisotropy energy to study the spin dynamics. Our findings reveal that when the DMI strength, external field, anisotropy, and applied magnetic field are weak, the oscillations are quasi-periodic, mostly dominated by the exchange field. With the increase in the DMI strength, the oscillation of the system becomes highly aperiodic. Strong anisotropy tends to induce periodic oscillations, but increasing DMI eventually leads to chaotic behaviour. Additionally, the external magnetic field destabilizes the periodicity of oscillations in systems with weak easy-axis anisotropy, but the systems with strong anisotropy, the oscillations remain unaffected by the external field's strength. Our analysis of magnon dispersion and magnetic resonance (MR) spectra reveals multiple resonance peaks at higher DMI strengths, indicating a complex interplay between spin wave excitation and system parameters. These results underscore the importance of understanding the inherent DMI and anisotropy in the Kagom\'e lattice during fabrication for various applications. Moreover, our comprehensive analysis of spin dynamics in a Kagom\'e lattice system demonstrates a clear transition from quasi-periodic to chaotic oscillations with the increase in DMI strength.