Blockchain is a type of distributed ledger technology that consists of a growing list of records,called blocks,that are securely linked together using cryptography.Each blockchain-based solution deploys a specific con...Blockchain is a type of distributed ledger technology that consists of a growing list of records,called blocks,that are securely linked together using cryptography.Each blockchain-based solution deploys a specific consensus algorithm that guarantees the consistency of the ledger over time.The most famous,and yet claimed to be the most secure,is the Proof-of-Work(PoW)consensus algorithm.In this paper,we revisit the fundamental calculations and assumptions of this algorithm,originally presented in the Bitcoin white paper.We break down its claimed calculations in order to better understand the underlying assumptions of the proposal.We also propose a novel formalization model of the PoW mining problem using the Birthday paradox.We utilize this model to formalize and analyze partial pre-image attacks on PoW-based blockchains,with formal analysis that confirms the experimental results and the previously proposed implications.We build on those analyses and propose new concepts for benchmarking the security of PoW-based systems,including Critical Difficulty and Critical Difficulty per given portion.Our calculations result in several important findings,including the profitability of launching partial pre-image attacks on PoW-based blockchains,once the mining puzzle difficulty reaches a given threshold.Specifically,for any compromised portion of the network(q<0.5;honest majority assumption still holds),the attack is formally proven profitable once the PoW mining puzzle difficulty reaches 56 leading zeros.展开更多
In this paper we define the pre-image topological pressure for a sequence of subadditive continuous functions on the compact metric space. And we also give a subadditive pre-image variational principle under a very we...In this paper we define the pre-image topological pressure for a sequence of subadditive continuous functions on the compact metric space. And we also give a subadditive pre-image variational principle under a very weak condition.展开更多
The authors define and study topological pre-image entropy for the non-autonomous discrete dynamical systems given by a sequence {fi}i=1^∞ of continuous self-maps of a compact topological space. The basic properties ...The authors define and study topological pre-image entropy for the non-autonomous discrete dynamical systems given by a sequence {fi}i=1^∞ of continuous self-maps of a compact topological space. The basic properties and the invariant with respect to equiconjugacy of pre-image entropy for the non-autonomous discrete dynamical systems are obtained.展开更多
In this work, we analyzed the impact of interventions on populations which exhibit unimodal dynamics. The six landmarks that characterize the “shape” of the unimodal reproduction curve f ( x ) of the difference equa...In this work, we analyzed the impact of interventions on populations which exhibit unimodal dynamics. The six landmarks that characterize the “shape” of the unimodal reproduction curve f ( x ) of the difference equation, X n+1 = f ( X n )?, are defined and used in order to examine and determine the behavior of dynamics of populations. By using the Li-Yorke criterion for determination of chaos we propose a qualitative intervention rule that can be applied without any explicit population equation. This proposed strategy for intervention brings out many interesting behaviors in population dynamics. A qualitative decision rule can be applied with a straight edge without any population equation and therefore offers a robust strategy for the management of populations.展开更多
An important issue involved in kernel methods is the pre-image problem. However, it is an ill-posed problem, as the solution is usually nonexistent or not unique. In contrast to direct methods aimed at minimizing the ...An important issue involved in kernel methods is the pre-image problem. However, it is an ill-posed problem, as the solution is usually nonexistent or not unique. In contrast to direct methods aimed at minimizing the distance in feature space, indirect methods aimed at constructing approximate equivalent models have shown outstanding performance. In this paper, an indirect method for solving the pre-image problem is proposed. In the proposed algorithm, an inverse mapping process is constructed based on a novel framework that preserves local linearity. In this framework, a local nonlinear transformation is implicitly conducted by neighborhood subspace scaling transformation to preserve the local linearity between feature space and input space. By extending the inverse mapping process to test samples, we can obtain pre-images in input space. The proposed method is non-iterative,and can be used for any kernel functions. Experimental results based on image denoising using kernel principal component analysis(PCA) show that the proposed method outperforms the state-of-the-art methods for solving the pre-image problem.展开更多
基金funding from the National Research,Development and Innovation Office within the framework of the Artificial Intelligence National Laboratory Programme(MILAB),and from the national project TKP2021-NVA-09 implemented with the support provided by the Ministry of Innovation and Technol-ogy of Hungary from the National Research,Development and Innova-tion Fund.
文摘Blockchain is a type of distributed ledger technology that consists of a growing list of records,called blocks,that are securely linked together using cryptography.Each blockchain-based solution deploys a specific consensus algorithm that guarantees the consistency of the ledger over time.The most famous,and yet claimed to be the most secure,is the Proof-of-Work(PoW)consensus algorithm.In this paper,we revisit the fundamental calculations and assumptions of this algorithm,originally presented in the Bitcoin white paper.We break down its claimed calculations in order to better understand the underlying assumptions of the proposal.We also propose a novel formalization model of the PoW mining problem using the Birthday paradox.We utilize this model to formalize and analyze partial pre-image attacks on PoW-based blockchains,with formal analysis that confirms the experimental results and the previously proposed implications.We build on those analyses and propose new concepts for benchmarking the security of PoW-based systems,including Critical Difficulty and Critical Difficulty per given portion.Our calculations result in several important findings,including the profitability of launching partial pre-image attacks on PoW-based blockchains,once the mining puzzle difficulty reaches a given threshold.Specifically,for any compromised portion of the network(q<0.5;honest majority assumption still holds),the attack is formally proven profitable once the PoW mining puzzle difficulty reaches 56 leading zeros.
基金The first author is supported by a grant from Postdoctoral Science Research Program (0701049C) of Jiangsu Provincethe second author is partially supported by the NSF (10571086) of Chinathe National Basic Research Program-973 Program (2007CB814800) of China
文摘In this paper we define the pre-image topological pressure for a sequence of subadditive continuous functions on the compact metric space. And we also give a subadditive pre-image variational principle under a very weak condition.
基金the National Natural Science Foundation of China under Grant Nos.10661001 and 10761007Natural Science Foundation of Jiangxi under Grant No.2007GZS2398partly by Nanchang University Science Foundation under Grant No.Z-03713
文摘The authors define and study topological pre-image entropy for the non-autonomous discrete dynamical systems given by a sequence {fi}i=1^∞ of continuous self-maps of a compact topological space. The basic properties and the invariant with respect to equiconjugacy of pre-image entropy for the non-autonomous discrete dynamical systems are obtained.
文摘In this work, we analyzed the impact of interventions on populations which exhibit unimodal dynamics. The six landmarks that characterize the “shape” of the unimodal reproduction curve f ( x ) of the difference equation, X n+1 = f ( X n )?, are defined and used in order to examine and determine the behavior of dynamics of populations. By using the Li-Yorke criterion for determination of chaos we propose a qualitative intervention rule that can be applied without any explicit population equation. This proposed strategy for intervention brings out many interesting behaviors in population dynamics. A qualitative decision rule can be applied with a straight edge without any population equation and therefore offers a robust strategy for the management of populations.
基金Project supported by the National Science and Technology Major Project of China(No.2012EX01027001-002)the Fun-damental Research Funds for the Central Universities,China
文摘An important issue involved in kernel methods is the pre-image problem. However, it is an ill-posed problem, as the solution is usually nonexistent or not unique. In contrast to direct methods aimed at minimizing the distance in feature space, indirect methods aimed at constructing approximate equivalent models have shown outstanding performance. In this paper, an indirect method for solving the pre-image problem is proposed. In the proposed algorithm, an inverse mapping process is constructed based on a novel framework that preserves local linearity. In this framework, a local nonlinear transformation is implicitly conducted by neighborhood subspace scaling transformation to preserve the local linearity between feature space and input space. By extending the inverse mapping process to test samples, we can obtain pre-images in input space. The proposed method is non-iterative,and can be used for any kernel functions. Experimental results based on image denoising using kernel principal component analysis(PCA) show that the proposed method outperforms the state-of-the-art methods for solving the pre-image problem.
基金Supported by the National Natural Science Foundation of China under Grant No.90604036the National Basic Research Program of China under Grant No.2004CB318004the National High-Tech Research and Development Plan of China under Grant No.2007AA01Z470~~
