Limiting Weak Type Estimate for Capacitary Maximal Function

A capacitary analogue of the limiting weak type estimate of P. Janakiraman for the Hardy-Littlewood maximal function of an L1-function is discovered.Comment: 9 page

Isocapacity Estimates for Hessian Operators

Through a new powerful potential-theoretic analysis, this paper is devoted to discovering the geometrically equivalent isocapacity forms of Chou-Wang's Sobolev type inequality and Tian-Wang's Moser-Trudinger type inequality for the fully nonlinear $1\leq k\leq n/2$ Hessian operators.Comment: 23 pages, 5 figure

Poor man's holography: How far can it go?

One of the most exciting things in recent theoretical physics is the suspicion that gravity may be holographic, dual to some sort of quantum field theory living on the boundary with one less dimension. Such a suspicion has been supported mainly by a variety of specific examples from string theory. This paper is intended to purport the holographic gravity from a different perspective. Namely we propose that such a holography can actually be observed within the context of Einstein's gravity, where neither is spacetime required to be asymptotically AdS nor the boundary to be located at conformal infinity. We show that our holography works remarkably well at least at the level of thermodynamics and hydrodynamics. In particular, a perfect matching between the bulk gravity and boundary system is found not only for the equilibrium variation but also for the non-equilibrium entropy production, where a method of conserved current is seen to be efficient in relating the black hole perturbation in the bulk gravity and the non-equilibrium thermodynamics on the boundary.Comment: This essay received an honorable mention in the 2012 Essay Competition of the Gravity Research Foundation. 12 pages, revtex4; v2: slight improvement on presentation in section 3, typos fixed; v3: holographic derivation of the first law of thermodynamics in section 2 is clarified and strengthene

Generalized Kerr/CFT correspondence with electromagnetic field

The electrovac axisymmetric extreme isolated horizon/CFT correspondence is considered. By expansion techniques under the Bondi-like coordinates, it is proved that the near horizon geometry of electrovac axisymmetric extreme isolated horizon is unique. Furthermore, explicit coordinate transformation between the Bondi-like coordinates and the Poincare-type coordinates for the near horizon metric of the extreme Kerr-Newmann spacetime is found. Based on these analyses and the thermodynamics of the isolated horizon, then, the Kerr/CFT correspondence is generalized to nonstationary extreme black holes with electromagnetic fields.Comment: 14 page

Entropy of isolated horizon from surface term of gravitational action

Starting from the surface term of gravitational action, one can construct a Virasoro algebra with central extension, with which the horizon entropy can be derived by using Cardy formula. This approach gives a new routine to calculate and interpret the horizon entropy. In this paper, we generalize this approach to a more general case, the isolated horizon, which contains non-stationary spacetimes beyond stationary ones. By imposing appropriate boundary conditions near the horizon, the full set of diffeomorphism is restricted to a subset where the corresponding Noether charges form a Virasoro algebra with central extension. Then by using the Cardy formula, we can derive the entropy of the isolated horizon.Comment: 11 page

A Survey of Distributed Consensus Protocols for Blockchain Networks

Since the inception of Bitcoin, cryptocurrencies and the underlying blockchain technology have attracted an increasing interest from both academia and industry. Among various core components, consensus protocol is the defining technology behind the security and performance of blockchain. From incremental modifications of Nakamoto consensus protocol to innovative alternative consensus mechanisms, many consensus protocols have been proposed to improve the performance of the blockchain network itself or to accommodate other specific application needs. In this survey, we present a comprehensive review and analysis on the state-of-the-art blockchain consensus protocols. To facilitate the discussion of our analysis, we first introduce the key definitions and relevant results in the classic theory of fault tolerance which help to lay the foundation for further discussion. We identify five core components of a blockchain consensus protocol, namely, block proposal, block validation, information propagation, block finalization, and incentive mechanism. A wide spectrum of blockchain consensus protocols are then carefully reviewed accompanied by algorithmic abstractions and vulnerability analyses. The surveyed consensus protocols are analyzed using the five-component framework and compared with respect to different performance metrics. These analyses and comparisons provide us new insights in the fundamental differences of various proposals in terms of their suitable application scenarios, key assumptions, expected fault tolerance, scalability, drawbacks and trade-offs. We believe this survey will provide blockchain developers and researchers a comprehensive view on the state-of-the-art consensus protocols and facilitate the process of designing future protocols.Comment: Accepted by the IEEE Communications Surveys and Tutorials for publicatio

A statistical study towards the high-mass BGPS clumps with the MALT90 survey

In this work, we perform a statistical investigation towards 50 high-mass clumps using the data from the Bolocam Galactic Plane Survey (BGPS) and the Millimetre Astronomy Legacy Team 90-GHz survey (MALT90). Eleven dense molecular lines (N$_2$H$^+$(1-0), HNC(1-0), HCO$^+$(1-0), HCN(1-0), HN$^{13}$C(1-0), H$^{13}$CO$^+$(1-0), C$_2$H(1-0), HC$_3$N(10-9), SiO(2-1), $^{13}$CS(2-1) and HNCO$(4_{4,0}-3_{0,3}))$ are detected. N$_2$H$^+$ and HNC are shown to be good tracers for clumps in virous evolutionary stages since they are detected in all the fields. And the detection rates of N-bearing molecules decrease as the clumps evolve, but those of O-bearing species increase with evolution. Furthermore, the abundance ratios [N$_2$H$^+$]/[HCO$^+$] and Log([HC$_3$N]/[HCO$^+$]) decline with Log([HCO$^+$]) as two linear functions, respectively. This suggests the transformation of N$_2$H$^+$ and HC$_3$N to HCO$^+$ as the clumps evolve. We also find that C$_2$H is the most abundant molecule with an order of $10^{-8}$. Besides, three new infall candidates G010.214-00.324, G011.121-00.128, and G012.215-00.118(a) are discovered to have large-scaled infall motions and infall rates in the magnitude of $10^{-3}$ M$_\odot$ yr$^{-1}$.Comment: 40 pages, 14 figures, 6 table

The Petrov-like boundary condition at finite cutoff surface in Gravity/Fluid duality

Previously it has been shown that imposing a Petrov-like boundary condition on a hypersurface may reduce the Einstein equation to the incompressible Navier-Stokes equation, but all these correspondences are established in the near horizon limit. In this note, we remark that this strategy can be extended to an arbitrary finite cutoff surface which is spatially flat, and the Navier-Stokes equation is obtained by employing a non-relativistic long-wavelength limit.Comment: 17 pages, no figures, published in PR

Improving Robustness of ML Classifiers against Realizable Evasion Attacks Using Conserved Features

Machine learning (ML) techniques are increasingly common in security applications, such as malware and intrusion detection. However, ML models are often susceptible to evasion attacks, in which an adversary makes changes to the input (such as malware) in order to avoid being detected. A conventional approach to evaluate ML robustness to such attacks, as well as to design robust ML, is by considering simplified feature-space models of attacks, where the attacker changes ML features directly to effect evasion, while minimizing or constraining the magnitude of this change. We investigate the effectiveness of this approach to designing robust ML in the face of attacks that can be realized in actual malware (realizable attacks). We demonstrate that in the context of structure-based PDF malware detection, such techniques appear to have limited effectiveness, but they are effective with content-based detectors. In either case, we show that augmenting the feature space models with conserved features (those that cannot be unilaterally modified without compromising malicious functionality) significantly improves performance. Finally, we show that feature space models enable generalized robustness when faced with a variety of realizable attacks, as compared to classifiers which are tuned to be robust to a specific realizable attack.Comment: 1. v5.0; 2. To appear at the 28th USENIX Security Symposium, 201

Sonic velocity in holographic fluids and its applications

Gravity/fluid correspondence becomes an important tool to investigate the strongly correlated fluids. We carefully investigate the holographic fluids at the finite cutoff surface by considering different boundary conditions in the scenario of gravity/fluid correspondence. We find that the sonic velocity of the boundary fluids at the finite cutoff surface is critical to clarify the superficial similarity between bulk viscosity and perturbation of the pressure for the holographic fluid, where we set a special boundary condition at the finite cutoff surface to explicitly express this superficial similarity. Moreover, we further take the sonic velocity into account to investigate a case with more general boundary condition. In this more general case, two parameters in the first order stress tensor of holographic fluid cannot be fixed, one can still extract the information of transport coefficients by considering the sonic velocity seriously.Comment: 13 pages; version accepted by Chinese Physics