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We study the topological order that arises from chiral states with ${\rm SU}(N)$ or ${\rm SO}(N)$ edge-state symmetry. This extends our previous study of topological orders that descend from the bosonic $E_8$ quantum Hall state. We use exactly solvable models of coupled electron wires to construct states with ${\rm SU}(m)_n$, ${\rm SO}(m)_n$, or ${\rm Sp}(m)_n$ topological order for various levels $n$. We use our constructions to write down string operators for various non-Abelian anyons. We thereby provide a systematic, microscopic understanding of quantum Hall states, topological superconductors, and spin liquids with emergent non-Abelian quasiparticle excitations, including those of Ising, metaplectic, and Fibonacci type., Comment: 32 pages, 2 figures

In recent years, Natural Language Processing (NLP) has played a significant role in various Artificial Intelligence (AI) applications such as chatbots, text generation, and language translation. The emergence of large language models (LLMs) has greatly improved the performance of these applications, showing astonishing results in language understanding and generation. However, they still show some disadvantages, such as hallucinations and lack of domain-specific knowledge, that affect their performance in real-world tasks. These issues can be effectively mitigated by incorporating knowledge graphs (KGs), which organise information in structured formats that capture relationships between entities in a versatile and interpretable fashion. Likewise, the construction and validation of KGs present challenges that LLMs can help resolve. The complementary relationship between LLMs and KGs has led to a trend that combines these technologies to achieve trustworthy results. This work collected 28 papers outlining methods for KG-powered LLMs, LLM-based KGs, and LLM-KG hybrid approaches. We systematically analysed and compared these approaches to provide a comprehensive overview highlighting key trends, innovative techniques, and common challenges. This synthesis will benefit researchers new to the field and those seeking to deepen their understanding of how KGs and LLMs can be effectively combined to enhance AI applications capabilities.

Transformers achieve state-of-the-art accuracy and robustness across many tasks, but an understanding of the inductive biases that they have and how those biases are different from other neural network architectures remains elusive. Various neural network architectures such as fully connected networks have been found to have a simplicity bias towards simple functions of the data; one version of this simplicity bias is a spectral bias to learn simple functions in the Fourier space. In this work, we identify the notion of sensitivity of the model to random changes in the input as a notion of simplicity bias which provides a unified metric to explain the simplicity and spectral bias of transformers across different data modalities. We show that transformers have lower sensitivity than alternative architectures, such as LSTMs, MLPs and CNNs, across both vision and language tasks. We also show that low-sensitivity bias correlates with improved robustness; furthermore, it can also be used as an efficient intervention to further improve the robustness of transformers., Comment: 24 pages, 19 figures, 3 tables

Two way ranging data for spacecraft tracking of China's first Martian mission Tianwen-I is analysed. Shortly before the spacecraft entered the Mars parking orbit, the two way coherent microwave link between the spacecraft and the Earth resembles a long arm gravitational wave interferometer, with both the spacecraft and the Earth regarded as in an approximate free falling state. By carefully selecting and analysing data segments of the time series of the two way ranging data during this time span, a parametric statistical model is built for the data segments and an upper limit for the stochastic gravitational waves background (SGWB) is then estimated within the frequency window 0.1Hz to 0.1 mHz. The upper bound improves considerably on those obtained before. In particular, around the deci-Hz band, there is a three orders improvement on the bound obtained previously by the two way ranging data of the Chang e 3 mission. Scientific applications of the upper bound is then considered and a weak upper bound is worked out for axions which is a promising candidate for ultra light dark matter., Comment: 10 pages, 8 figures

In an attempt to understand the Penrose inequality for black holes with angular momentum, an axisymmetric, vacuum, asymptotically Euclidean initial data set subject to certain quasi stationary conditions is considered for a case study. A new geometric definition of angular velocity of a rotating black hole is defined in terms of the momentum constraint, without any reference to a stationary Killing vector field. The momentum constraint is then shown to be equivalent to a Beltrami equation for compressible fluid flow. In terms of spinors, a generalised first law for rotating black holes (possibly with multi-connected horizon located along the symmetry axis) is then proven and may be regarded as a Penrose type inequality for black holes with angular momentum., Comment: 24 pages, 4 figures

A certain class of exact solutions of Einstein Maxwell spacetime in general relativity is discussed which demonstrates at the level of theory that, when certain parametric resonance condition is met, the interaction of electromagnetic field with a gravitational wave will display certain Liapounov instability and lead to exponential amplification of a gravitational wave train described by certain Newman-Penrose component of the Weyl curvature. In some way akin to a free electron laser in electromagnetic theory, by the conversion of electromagnetic energy into gravitational energy in a coherent way, the feasibility of generating a pulsed laser like intense beam of gravitational wave is displayed., Comment: 12 pages, 7 figures

We study bosonic topological phases constructed from electrons. In addition to a bulk excitation energy gap, these bosonic phases also have a fermion energy gap, below which all local excitations in the bulk and on the edge are even combinations of electrons. We focus on chiral phases, in which all low-energy edge excitations move in the same direction, that arise from the short-range entangled $E_8$ quantum Hall state, the bosonic analog of the filled lowest Landau level of electrons. The $E_8$ edge-state theory features an $E_8$ Kac-Moody symmetry that can be decomposed into ${\cal G}_A \times {\cal G}_B$ subalgebras, such as $SU(3) \times E_6$, $SO(M) \times SO(16-M)$, and $G_2 \times F_4$. (Here, $\{SO(M) \}$, $\{SU(N)\}$, and $\{E_8, G_2, F_4 \}$ denote orthogonal, unitary, and exceptional Lie algebras.) Using these symmetry decompositions, we construct exactly solvable coupled-wire model Hamiltonians for families of long-range entangled ${\cal G}_A$ or ${\cal G}_B$ bosonic fractional quantum Hall states that ``partially fill" the $E_8$ state and are pairwise related by a generalized particle-hole symmetry. These long-range entangled states feature either Abelian or non-Abelian topological order. Some support the emergence of non-local Dirac and Majorana fermions, Ising anyons, metaplectic anyons, Fibonacci anyons, as well as deconfined $\mathbb{Z}_2$ gauge fluxes and charges., Comment: 48 pages, 6 figures

We present Stanford Pupper, an easily-replicated open source quadruped robot designed specifically as a benchmark platform for legged robotics research. The robot features torque-controllable brushless motors with high specific power that enable testing of impedance and torque-based machine learning and optimization control approaches. Pupper can be built from the ground up in under 8 hours for a total cost under $2000, with all components either easily purchased or 3D printed. To rigorously compare control approaches, we introduce two benchmarks, Sprint and Scramble with a leader board maintained by Stanford Student Robotics. These benchmarks test high-speed dynamic locomotion capability, and robustness to unstructured terrain. We provide a reference controller with dynamic, omnidirectional gaits that serves as a baseline for comparison. Reproducibility is demonstrated across multiple institutions with robots made independently. All material is available at https://stanfordstudentrobotics.org/quadruped-benchmark.

We use the entanglement negativity, a bipartite measure of entanglement in mixed quantum states, to study how multipartite entanglement constrains the real-space structure of the ground state wavefunctions of $(2+1)$-dimensional topological phases. We focus on the (Abelian) Laughlin and (non-Abelian) Moore-Read states at filling fraction $\nu=1/m$. We show that a combination of entanglement negativities, calculated with respect to specific cylinder and torus geometries, determines a necessary condition for when a topological state can be disentangled, i.e., factorized into a tensor product of states defined on cylinder subregions. This condition, which requires the ground state to lie in a definite topological sector, is sufficient for the Laughlin state. On the other hand, we find that a general Moore-Read ground state cannot be disentangled even when the disentangling condition holds., Comment: 35 pages, 5 figures

Gravitational wave detection in space promises to open a new window in astronomy to study the strong field dynamics of gravitational physics in astrophysics and cosmology. The present article is an extract of a report on a feasibility study of gravitational wave detection in space, commissioned by the National Space Science Center, Chinese Academy of Sciences almost a decade ago. The objective of the study was to explore various possible mission options to detect gravitational waves in space alternative to that of the (e)LISA mission concept and look into the requirements on the technological fronts. On the basis of relative merits and balance between science and technological feasibility, a set of representative mission options were studied and in the end a mission design was recommended as the starting point for research and development in the Chinese Academy of Sciences. The mission design was eventually adopted by the current TAIJI mission as the baseline parameters for the project. Subject to technological constraints, the baseline parameters of the TAIJI mission were designed in such a way to optimise the capability of a spaceborne gravitational wave detector to probe high redshift light seed, intermediate mass black holes and thereby shed important light on the structure formation in early Universe., Comment: Two authors added to the preprint, to appear in "Handbook of Gravitational Wave Astronomy, Springer". arXiv admin note: text overlap with arXiv:1410.7296

Consider an asymptotically Euclidean initial data set with a smooth marginally trapped surface (possibly a union of future and past multi-connected components) as inner boundary. By a further development of the spinorial framework underlying the positive energy theorem, a refined Witten identity is worked out and in the maximal slicing case, a close connection of the identity with a conformal invariant of Yamabe type is revealed. A Kato-Yau inequality for the Sen-Witten operator is also proven from a conformal geometry perspective. Guided by the Hamiltonian picture underlying the spinorial framework, a Penrose type inequality is then proven to the effect that given the dominant energy condition, the ADM energy-momentum is, up to a non-zero constant less than unity, bounded by the areal radius of the marginally trapped surface. To establish the Penrose inequality in full generality, it is then sufficient to show that the norm of the Sen-Witten spinor, subject to the APS boundary condition imposed on a suitably defined outermost marginally trapped surface, is bounded below by that attained in the Schwarzschild metric.