Quasi-Topological Ricci Polynomial Gravities

Quasi-topological terms in gravity can be viewed as those that give no contribution to the equations of motion for a special subclass of metric ans\"atze. They therefore play no r\^ole in constructing these solutions, but can affect the general perturbations. We consider Einstein gravity extended with Ricci tensor polynomial invariants, which admits Einstein metrics with appropriate effective cosmological constants as its vacuum solutions. We construct three types of quasi-topological gravities. The first type is for the most general static metrics with spherical, toroidal or hyperbolic isometries. The second type is for the special static metrics where $g_{tt} g_{rr}$ is constant. The third type is the linearized quasi-topological gravities on the Einstein metrics. We construct and classify results that are either dependent on or independent of dimensions, up to the tenth order. We then consider a subset of these three types and obtain Lovelock-like quasi-topological gravities, that are independent of the dimensions. The linearized gravities on Einstein metrics on all dimensions are simply Einstein and hence ghost free. The theories become quasi-topological on static metrics in one specific dimension, but non-trivial in others. We also focus on the quasi-topological Ricci cubic invariant in four dimensions as a specific example to study its effect on holography, including shear viscosity, thermoelectric DC conductivities and butterfly velocity. In particular, we find that the holographic diffusivity bounds can be violated by the quasi-topological terms, which can induce an extra massive mode that yields a butterfly velocity unbound above.Comment: Latex, 56 pages, discussion on shear viscosity revise

The Progress, Challenges, and Perspectives of Directed Greybox Fuzzing

Most greybox fuzzing tools are coverage-guided as code coverage is strongly correlated with bug coverage. However, since most covered codes may not contain bugs, blindly extending code coverage is less efficient, especially for corner cases. Unlike coverage-guided greybox fuzzers who extend code coverage in an undirected manner, a directed greybox fuzzer spends most of its time allocation on reaching specific targets (e.g., the bug-prone zone) without wasting resources stressing unrelated parts. Thus, directed greybox fuzzing (DGF) is particularly suitable for scenarios such as patch testing, bug reproduction, and specialist bug hunting. This paper studies DGF from a broader view, which takes into account not only the location-directed type that targets specific code parts, but also the behaviour-directed type that aims to expose abnormal program behaviours. Herein, the first in-depth study of DGF is made based on the investigation of 32 state-of-the-art fuzzers (78% were published after 2019) that are closely related to DGF. A thorough assessment of the collected tools is conducted so as to systemise recent progress in this field. Finally, it summarises the challenges and provides perspectives for future research.Comment: 16 pages, 4 figure

The flavor-changing rare top decays t→cVVt\to c V V in topcolor-assisted technicolor theory

In the framework of topcolor-assisted technicolor (TC2) theory, we calculate the contributions of the scalars(the neutral top-pion $\pi_{t}^{0}$ and the top-Higgs $h_{t}^{0}$) to the flavor-changing rare top decays $t\to c V V$(V= W, g, $\gamma$ or Z). Our results show that $h_{t}^{0}$ can enhance the standard model $B_{r}^{SM}(t\longrightarrow cWW)$ by several orders of magnitude for most of the parameter space. The peak of the branching ratio resonance emerges when the top-Higgs mass is between $2m_{W}$ and $m_{t}$. The branching ratio $B_{r}(t\to c W W)$ can reach $10^{-3}$ in the narrow range.Comment: Latex file, 11pages, 2 eps figure

EDEN: A Plug-in Equivariant Distance Encoding to Beyond the 1-WL Test

The message-passing scheme is the core of graph representation learning. While most existing message-passing graph neural networks (MPNNs) are permutation-invariant in graph-level representation learning and permutation-equivariant in node- and edge-level representation learning, their expressive power is commonly limited by the 1-Weisfeiler-Lehman (1-WL) graph isomorphism test. Recently proposed expressive graph neural networks (GNNs) with specially designed complex message-passing mechanisms are not practical. To bridge the gap, we propose a plug-in Equivariant Distance ENcoding (EDEN) for MPNNs. EDEN is derived from a series of interpretable transformations on the graph's distance matrix. We theoretically prove that EDEN is permutation-equivariant for all level graph representation learning, and we empirically illustrate that EDEN's expressive power can reach up to the 3-WL test. Extensive experiments on real-world datasets show that combining EDEN with conventional GNNs surpasses recent advanced GNNs