Evaporation induced traversability of the Einstein--Rosen wormhole

Suppose, the Universe comes into existence (as classical spacetime) already with an empty spherically symmetric macroscopic wormhole present in it. Classically the wormhole would evolve into a part of the Schwarzschild space and thus would not allow any signal to traverse it. I consider semiclassical corrections to that picture and build a model of an evaporating wormhole. The model is based on the assumption that the vacuum polarization and its backreaction on the geometry of the wormhole are weak. The lack of information about the era preceding the emergence of the wormhole results in appearance of three parameters which -- along with the initial mass -- determine the evolution of the wormhole. For some values of these parameters the wormhole turns out to be long-lived enough to be traversed and to transform into a time machine.Comment: v.2 A bit of discussion has been added and a few references v.3 Insignificant changes to match the published versio

Security, trust and cooperation in wireless sensor networks

Wireless sensor networks are a promising technology for many real-world applications such as critical infrastructure monitoring, scientific data gathering, smart buildings, etc.. However, given the typically unattended and potentially unsecured operation environment, there has been an increased number of security threats to sensor networks. In addition, sensor networks have very constrained resources, such as limited energy, memory, computational power, and communication bandwidth. These unique challenges call for new security mechanisms and algorithms. In this dissertation, we propose novel algorithms and models to address some important and challenging security problems in wireless sensor networks. The first part of the dissertation focuses on data trust in sensor networks. Since sensor networks are mainly deployed to monitor events and report data, the quality of received data must be ensured in order to make meaningful inferences from sensor data. We first study a false data injection attack in the distributed state estimation problem and propose a distributed Bayesian detection algorithm, which could maintain correct estimation results when less than one half of the sensors are compromised. To deal with the situation where more than one half of the sensors may be compromised, we introduce a special class of sensor nodes called \textit{trusted cores}. We then design a secure distributed trust aggregation algorithm that can utilize the trusted cores to improve network robustness. We show that as long as there exist some paths that can connect each regular node to one of these trusted cores, the network can not be subverted by attackers. The second part of the dissertation focuses on sensor network monitoring and anomaly detection. A sensor network may suffer from system failures due to loss of links and nodes, or malicious intrusions. Therefore, it is critical to continuously monitor the overall state of the network and locate performance anomalies. The network monitoring and probe selection problem is formulated as a budgeted coverage problem and a Markov decision process. Efficient probing strategies are designed to achieve a flexible tradeoff between inference accuracy and probing overhead. Based on the probing results on traffic measurements, anomaly detection can be conducted. To capture the highly dynamic network traffic, we develop a detection scheme based on multi-scale analysis of the traffic using wavelet transforms and hidden Markov models. The performance of the probing strategy and of the detection scheme are extensively evaluated in malicious scenarios using the NS-2 network simulator. Lastly, to better understand the role of trust in sensor networks, a game theoretic model is formulated to mathematically analyze the relation between trust and cooperation. Given the trust relations, the interactions among nodes are modeled as a network game on a trust-weighted graph. We then propose an efficient heuristic method that explores network heterogeneity to improve Nash equilibrium efficiency

Byzantine Vector Consensus in Complete Graphs

Consider a network of n processes each of which has a d-dimensional vector of reals as its input. Each process can communicate directly with all the processes in the system; thus the communication network is a complete graph. All the communication channels are reliable and FIFO (first-in-first-out). The problem of Byzantine vector consensus (BVC) requires agreement on a d-dimensional vector that is in the convex hull of the d-dimensional input vectors at the non-faulty processes. We obtain the following results for Byzantine vector consensus in complete graphs while tolerating up to f Byzantine failures: * We prove that in a synchronous system, n >= max(3f+1, (d+1)f+1) is necessary and sufficient for achieving Byzantine vector consensus. * In an asynchronous system, it is known that exact consensus is impossible in presence of faulty processes. For an asynchronous system, we prove that n >= (d+2)f+1 is necessary and sufficient to achieve approximate Byzantine vector consensus. Our sufficiency proofs are constructive. We show sufficiency by providing explicit algorithms that solve exact BVC in synchronous systems, and approximate BVC in asynchronous systems. We also obtain tight bounds on the number of processes for achieving BVC using algorithms that are restricted to a simpler communication pattern

HIGH ORDER BOUND-PRESERVING DISCONTINUOUS GALERKIN METHODS AND THEIR APPLICATIONS IN PETROLEUM ENGINEERING

This report contains researches in the theory of high-order bound-preserving (BP) discontinuous Galerkin (DG) method and their applications in petroleum engineering. It contains both theoretical analysis and numerical experiments. The compressible miscible displacements and wormhole propagation problem, arising in petroleum engineering, is used to describe the evolution of the pressure and concentrations of different components of fluid in porous media. The important physical features of concentration and porosity include their boundedness between 0 and 1, as well as the monotone increasing for porosity in wormhole propagation model. How to keep these properties in the simulation is crucial to the robustness of the numerical algorithm. In the first project, we develop high-order bound-preserving discontinuous Galerkin methods for the coupled system of compressible miscible displacements on triangular meshes. We consider the problem with multi-component fluid mixture and the (volumetric) concentration of the jth component,cj, should be between 0 and 1. The main idea is stated as follows. First, we apply the second-order positivity-preserving techniques to all concentrations c′ js and enforce P jcj= 1 simultaneously to obtain physically relevant boundedness for every components. Then, based on the second-order BP schemes, we use the second-order numerical fluxes as the lower order one to combine with high-order numerical fluxes to achieve the high-order accuracy. Finally, since the classical slope limiter cannot be applied to polynomial upper bounds, we introduce a new limiter to our algorithm. Numerical experiments are given to demonstrate the high-order accuracy and good performance of the numerical technique. In our second project, we propose high-order bound-preserving discontinuous Galerkin methods to keep the boundedness for the porosity and concentration of acid, as well as the monotone increasing for porosity. The main technique is to introduce a new variable r to replace the original acid concentration and use a consistent flux pair to deduce a ghost equation such that the positive-preserving technique can be applied on both original and deduced equations. A high-order slope limiter is used to keep a polynomial upper bound which changes over time for r. Moreover, the high-order accuracy is attained by the flux limiter. Numerical examples are given to demonstrate the high-order accuracy and bound-preserving property of the numerical technique

Asynchronous Byzantine Consensus with 2f+1 Processes (extended version)

Reviewed by Paulo J. SousaByzantine consensus in asynchronous message-passing systems has been shown to require at least $3f+1$ processes to be solvable in several system models (e.g., with failure detectors, partial synchrony or randomization). Recently a couple of solutions to implement Byzantine fault-tolerant state-machine replication using only $2f+1$ replicas have appeared. This reduction from $3f+1$ to $2f+1$ is possible with a hybrid system model, i.e., by extending the system model with trusted/trustworthy components that constrain the power of faulty processes to have certain behaviors. Despite these important results, the problem of solving Byzantine consensus with only $2f+1$ processes is still far from being well understood. In this paper we present a methodology to transform crash consensus algorithms into Byzantine consensus algorithms with different characteristics, with the assistance of a reliable broadcast primitive that requires trusted/trustworthy components to be implemented. We exemplify the methodology with two algorithms, one that uses failure detectors and one that is randomized. We also define a new flavor of consensus and use it to solve atomic broadcast with only $2f+1$ processes, showing the practical interest of the consensus algorithms presented