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How big is too big? Critical Shocks for Systemic Failure Cascades Submitted (2012). How big is too big? Critical Shocks for Systemic Failure Cascades
"... External or internal shocks may lead to the collapse of a system consisting of many agents. If the shock hits only one agent initially and causes it to fail, this can induce a cascade of failures among neighboring agents. Several critical constellations determine whether this cascade remains finite ..."
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External or internal shocks may lead to the collapse of a system consisting of many agents. If the shock hits only one agent initially and causes it to fail, this can induce a cascade of failures among neighboring agents. Several critical constellations determine whether this cascade remains finite or reaches the size of the system, i.e. leads to systemic risk. We investigate the critical parameters for such cascades in a simple model, where agents are characterized by an individual threshold θi determining their capacity to handle a load αθi with 1 − α being their safety margin. If agents fail, they redistribute their load equally to K neighboring agents in a regular network. For three different threshold distributions P (θ), we derive analytical results for the size of the cascade, X(t), which is regarded as a measure of systemic risk, and the time when it stops. We focus on two different regimes, (i) EEE, an external extreme event where the size of the shock is of the order of the total capacity of the network, and (ii) RIE, a random internal event where the size of the shock is of the order of the capacity of an agent. We find that even for large extreme events that exceed the capacity of the network finite cascades are still possible, if a powerlaw threshold distribution is assumed. On the other hand, even small random fluctuations may lead to full cascades if critical conditions are met. Most importantly, we demonstrate that the size of the “big” shock is not the problem, as the systemic risk only varies slightly for changes of 10 to 50 percent of the external shock. Systemic risk depends much more on ingredients such as the network topology, the safety margin and the threshold distribution, which gives hints on how to reduce systemic risk. 1
Specifying a Timestampbased Protocol For Multistep Transactions Using LTL
"... Abstract—Most of the concurrent transactional protocols consider serializability as a correctness criterion of the transactions execution. Usually, the proof of the serializability relies on mathematical proofs for a fixed finite number of transactions. In this paper, we introduce a protocol to deal ..."
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Abstract—Most of the concurrent transactional protocols consider serializability as a correctness criterion of the transactions execution. Usually, the proof of the serializability relies on mathematical proofs for a fixed finite number of transactions. In this paper, we introduce a protocol to deal with an infinite number of transactions which are iterated infinitely often. We specify serializability of the transactions and the protocol using a specification language based on temporal logics. It is worthwhile using temporal logics such as LTL (Lineartime Temporal Logic) to specify transactions, to gain full automatic verification by using model checkers. Keywords—Multistep transactions, LTL specifications, Model Checking.
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"... Abstract. In a recent paper Iyama and Yoshino consider two interesting examples of isolated singularities over which it is possible to classify the indecomposable maximal CohenMacaulay modules in terms of linear algebra data. In this paper we present two new approaches to these examples. In the fir ..."
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Abstract. In a recent paper Iyama and Yoshino consider two interesting examples of isolated singularities over which it is possible to classify the indecomposable maximal CohenMacaulay modules in terms of linear algebra data. In this paper we present two new approaches to these examples. In the first approach we give a relation with cluster categories. In the second
Temporal Logics Specifications for Debit and Credit Transactions
"... Abstract — Recently, with the emergence of mobile technology and mobile banking, debit and credit transactions have been the most common transactions that are widely spreading, using such technologies. In this research, we specify the concurrent debit and credit transactions in temporal logics such ..."
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Abstract — Recently, with the emergence of mobile technology and mobile banking, debit and credit transactions have been the most common transactions that are widely spreading, using such technologies. In this research, we specify the concurrent debit and credit transactions in temporal logics such as CTL (Computational Tree Logic) and LTL (LinearTime Temporal Logic). These specifications describe the infinite histories that may be produced by the iterations of such concurrent transactions infinitely many times. We represent the infinite histories as a model of temporal logics formulae. Then, model checkers, such as NuSMV or SPIN, can carry out exhaustive checks of the correctness of the concurrent debit and credit transactions. Moreover, in this paper, we presume that the serializability condition is too strict. Therefore, a relaxed condition has been suggested to keep the database consistent. Moreover, the relaxed condition is easier to encode into temporal logics formulae.