Born-Infeld Type Extension of (Non-)Critical Gravity

We consider the Born-Infeld type extension of (non-)critical gravity which is higher curvature gravity on Anti de-Sitter space with specific combinations of scalar curvature and Ricci tensor. This theory may also be viewed as a natural extension of three-dimensional Born-Infeld new massive gravity to arbitrary dimensions. We show that this extension is consistent with holographic $c$-theorem and scalar graviton modes are absent in this theory. After showing that ghost modes in the theory can be truncated consistently by appropriate boundary conditions, we argue that the theory is classically equivalent to Einstein gravity at the non-linear level. Black hole solutions are discussed in the view point of the full non-linear classical equivalence between the theory and Einstein gravity. Holographic entanglement entropy in the theory is also briefly commented on.Comment: 1+13 pages, improvements in presentation, references added, accepted to PR

Cd diffused mesa-substrate buried heterostructure InGaAsP/InP laser

A new type of buried heterostructure InGaAsP/InP lasers grown by a single-step liquid phase epitaxy on Cd diffused mesa substrate is described. These lasers exhibit excellent current and optical confinement. Threshold currents as low as 15 mA are achieved for a laser with a 2-µm-wide active region

Meromorphic open-string vertex algebras

A notion of meromorphic open-string vertex algebra is introduced. A meromorphic open-string vertex algebra is an open-string vertex algebra in the sense of Kong and the author satisfying additional rationality (or meromorphicity) conditions for vertex operators. The vertex operator map for a meromorphic open-string vertex algebra satisfies rationality and associativity but in general does not satisfy the Jacobi identity, commutativity, the commutator formula, the skew-symmetry or even the associator formula. Given a vector space \mathfrak{h}, we construct a meromorphic open-string vertex algebra structure on the tensor algebra of the negative part of the affinization of \mathfrak{h} such that the vertex algebra struture on the symmetric algebra of the negative part of the Heisenberg algebra associated to \mathfrak{h} is a quotient of this meromorphic open-string vertex algebra. We also introduce the notion of left module for a meromorphic open-string vertex algebra and construct left modules for the meromorphic open-string vertex algebra above.Comment: 43 pape

Cost-efficient Cooperative Video Caching Over Edge Networks

Cooperative caching has emerged as an efficient way to alleviate backhaul traffic and enhance user experience by proactively prefetching popular videos at the network edge. However, it is challenging to achieve the optimal design of video caching, sharing, and delivery within storage-limited edge networks due to the growing diversity of videos, unpredictable video requirements, and dynamic user preferences. To address this challenge, this work explores cost-efficient cooperative video caching via video compression techniques while considering unknown video popularity. Firstly, we formulate the joint video caching, sharing, and delivery problem to capture a balance between user delay and system operative cost under unknown time-varying video popularity. To solve this problem, we develop a two-layer decentralized reinforcement learning algorithm, which effectively reduces the action space and tackles the coupling among video caching, sharing, and delivery decisions compared to the conventional algorithms. Specifically, the outer layer produces the optimal decisions for video caching and communication resource allocation by employing a multi-agent deep deterministic policy gradient algorithm. Meanwhile, the optimal video sharing and computation resource allocation are determined in each agent’s inner layer using the alternating optimization algorithm. Numerical results show that the proposed algorithm outperforms benchmarks in terms of the cache hit rate, delay of users and system operative cost, and effectively strikes a trade-off between system operative cost and users’ delay

Operadic formulation of topological vertex algebras and Gerstenhaber or Batalin-Vilkovisky algebras

We give the operadic formulation of (weak, strong) topological vertex algebras, which are variants of topological vertex operator algebras studied recently by Lian and Zuckerman. As an application, we obtain a conceptual and geometric construction of the Batalin-Vilkovisky algebraic structure (or the Gerstenhaber algebra structure) on the cohomology of a topological vertex algebra (or of a weak topological vertex algebra) by combining this operadic formulation with a theorem of Getzler (or of Cohen) which formulates Batalin-Vilkovisky algebras (or Gerstenhaber algebras) in terms of the homology of the framed little disk operad (or of the little disk operad).Comment: 42 page

Geometry of Reduced Supersymmetric 4D Yang-Mills Integrals

We study numerically the geometric properties of reduced supersymmetric non-compact SU(N) Yang-Mills integrals in D=4 dimensions, for N = 2,3, ..., 8. We show that in the range of large eigenvalues of the matrices A^mu, the original D-dimensional rotational symmetry is spontaneously broken and the dominating field configurations become one-dimensional, as anticipated by studies of the underlying surface theory. We also discuss possible implications of our results for the IKKT model.Comment: 14 pages, Latex + 3 eps fig., a comment added to the conclusion

Extending the first-order post-Newtonian scheme in multiple systems to the second-order contributions to light propagation

In this paper, we extend the first-order post-Newtonian scheme in multiple systems presented by Damour-Soffel-Xu to the second-order contribution to light propagation without changing the virtueof the scheme on the linear partial differential equations of the potential and vector potential. The spatial components of the metric are extended to second order level both in a global coordinates ($q_{ij}/ c^4$) and a local coordinates ($Q_{ab}/ c^4$). The equations of $q_{ij}$ (or $Q_{ab}$) are obtained from the field equations.The relationship between $q_{ij}$ and $Q_{ab}$ are presented in this paper also. In special case of the solar system (isotropic condition is applied ($q_{ij} = \delta_{ij} q$)), we obtain the solution of $q$. Finally, a further extension of the second-order contributions in the parametrized post-Newtonian formalism is discussed.Comment: Latex2e; 6 pages PS fil

On tree amplitudes with gluons coupled to gravitons

In this paper, we study the tree amplitudes with gluons coupled to gravitons. We first study the relations among the mixed amplitudes. With BCFW on-shell recursion relation, we will show the color-order reversed relation, $U(1)$-decoupling relation and KK relation hold for tree amplitudes with gluons coupled to gravitons. We then study the disk relation which expresses mixed amplitudes by pure gluon amplitudes. More specifically we will prove the disk relation for mixed amplitudes with gluons coupled to one graviton. Using the disk relation and the properties of pure gluon amplitudes, the color-order reversed relation, $U(1)$-decoupling relation and KK relation for mixed amplitudes can also be proved. Finally, we give some brief discussions on BCJ-like relation for mixed amplitudes.Comment: 33pages,no figur