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Lower bounds on twoterminal network reliability
, 1985
"... One measure of twoterminal network reliability, termed probabilistic connectedness, is the probability that two specified communication centers can communicate. A standard model of a network is a graph in which nodes represent communications centers and edges represent links between communication c ..."
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One measure of twoterminal network reliability, termed probabilistic connectedness, is the probability that two specified communication centers can communicate. A standard model of a network is a graph in which nodes represent communications centers and edges represent links between communication centers. Edges are assumed to have statistically independent probabilities of failing and nodes are assumed to be perfectly reliable. Exact calculation of twoterminal reliability for general networks has been shown to be #Pcomplete. As a result is desirable to compute upper and lower bounds that avoid the exponential computation likely required by exact algorithms. Two methods are considered for computing lower bounds on twoterminal reliability
Fault Tolerance in Wireless Sensor Networks,” Book chapter
 in Handbook of Sensor Networks, I. Mahgoub and M. Ilyas
"... Abstract: In this Chapter, we address fault tolerance in wireless sensor networks. In order to make the presentation selfcontained, we start by providing a short summary of sensor networks and classical fault tolerance techniques. After that, we discuss the three phases of fault tolerance (fault mo ..."
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Abstract: In this Chapter, we address fault tolerance in wireless sensor networks. In order to make the presentation selfcontained, we start by providing a short summary of sensor networks and classical fault tolerance techniques. After that, we discuss the three phases of fault tolerance (fault models, fault detection and identification and resiliency mechanisms) at four levels of abstractions (hardware, system software, middleware, and applications) and four scopes (components of individual node, individual node, network, and the distributed system). The technical cores of the chapter are two casestudies on heterogeneous fault tolerance and discrepancy minimizationbased fault detection and correction. We conclude the chapter with a brief survey of the future directions for fault tolerance research in wireless sensor networks.
Amplification and Percolation
, 1992
"... Moore and Shannon had shown that relays with arbitrarily high reliability can be built from relays with arbitrarily poor reliability. Valiant used similar methods to construct monotone readonce formulae of size O(n ff+2 ) (where ff = log p 5\Gamma1 2 ' 3:27) that amplify (/ \Gamma 1 n ..."
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Moore and Shannon had shown that relays with arbitrarily high reliability can be built from relays with arbitrarily poor reliability. Valiant used similar methods to construct monotone readonce formulae of size O(n ff+2 ) (where ff = log p 5\Gamma1 2 ' 3:27) that amplify (/ \Gamma 1 n ; / + 1 n ) (where / = p 5\Gamma1 2 ' 0:62) to (2 \Gamman ; 1 \Gamma 2 \Gamman ) and deduced as a consequence the existence of monotone formulae of the same size that compute the majority of n bits. Boppana had shown that any monotone readonce formula that amplifies (p \Gamma 1 n ; p + 1 n ) to ( 1 4 ; 3 4 ) (where 0 ! p ! 1 is constant) has size of at least\Omega\Gamma n ff ) and that any monotone, not necessarily readonce, contact network (and in particular any monotone formula) that amplifies ( 1 4 ; 3 4 ) to (2 \Gamman ; 1 \Gamma 2 \Gamman ) has size of at least \Omega\Gamma n 2 ). We extend Boppana's results in two ways. We first show that his two lower bounds...
An Insecurity Flow Model
 Proc. Workshop on New Security Paradigms, Langdale, Cumbria, United Kingdom
, 1997
"... We examine a new way of looking at security violations, called insecurity flow. We express our new paradigm via a formal mathematical model that combines elements of graph theory and discrete probability. Prior work by Moore and Shannon on building reliable circuits out of unreliable components, and ..."
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We examine a new way of looking at security violations, called insecurity flow. We express our new paradigm via a formal mathematical model that combines elements of graph theory and discrete probability. Prior work by Moore and Shannon on building reliable circuits out of unreliable components, and the physics community’s interest in dynamical systems, especially percolation theory, motivates our work. 1. A New Paradigm We wish to analyze how insecurity may spread throughout composed protection schemes. System (information) insecurity can be investigated in many different ways. Previous work on this area has been concerned with information flow; by looking at the capacity of a covert channel [Mi], or investigating which variants of noninterference hold upon system composition [MC]. This previous work is limited to multilevel security. The concept of illicit information flow is certainly important and well documented. However, we wish to investigate the concept of insecurity flow, not information flow. Thus, we put forth a new paradigm dealing with the abstract notion of an “invader ” penetrating through “security holes ” of various protective security domains. We present a formal model of this new paradigm of insecurity flow by using graph and discrete probability theory. Prior work exists using graph theory and/or probability theory [Dl], [D2], [0], [Le], [LB] to model system reliability. However, those probabilistic models analyze how the probability of “breaking in ” varies with time. Our paradigm views a “break in ” as a O/l proposition. The breach either happens or does not happen. It does not, like the reliabilitybased work, happen asymptotically
The boolean functions computed by random boolean formulas or how to grow the right function. Random Structures and Algorithms
, 2005
"... Among their many uses, growth processes (probabilistic amplification), were used for constructing reliable networks from unreliable components, and deriving complexity bounds of various classes of functions. Hence, determining the initial conditions for such processes is an important and challenging ..."
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Among their many uses, growth processes (probabilistic amplification), were used for constructing reliable networks from unreliable components, and deriving complexity bounds of various classes of functions. Hence, determining the initial conditions for such processes is an important and challenging problem. In this paper we characterize growth processes by their initial conditions and derive conditions under which results such as Valiant’s[Val84] hold. First, we completely characterize growth processes that use linear connectives. Second, by extending Savick´y’s [Sav90] analysis, via “Restriction Lemmas”, we characterize growth processes that use monotone connectives, and show that our technique is applicable to growth processes that use other connectives as well. Additionally, we obtain explicit bounds on the convergence rates of several growth processes, including the growth process studied by Savick´y (1990).
Organizational Structure as a Determinant of Performance: Evidence From Mutual Funds
, 2008
"... This paper develops and tests a model of how organizational structure influences organizational performance. Organizational structure, conceptualized as the decisionmaking structure among a group of individuals, is shown to affect the number of initiatives pursued by organizations, and the omission ..."
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This paper develops and tests a model of how organizational structure influences organizational performance. Organizational structure, conceptualized as the decisionmaking structure among a group of individuals, is shown to affect the number of initiatives pursued by organizations, and the omission and commission errors (Type I and II errors, respectively) made by organizations. The empirical setting are over 150,000 stockpicking decisions made by 609 mutual funds. Mutual funds offer an ideal and rare setting to test the theory, as detailed records exist on the projects they face, the decisions they make, and the outcomes of these decisions. The independent variable of the study, organizational structure, is coded from fund management descriptions made by Morningstar, and the estimates of the omission and commission errors are computed by a novel technique that uses bootstrapping to create measures which are comparable across funds. The findings suggest that organizational structure has relevant and predictable effects on a wide range of
On Boolean Decision Trees with Faulty Nodes
 In Random Structures and Algorithms
, 1994
"... We consider the problem of computing with faulty components in the context of the Boolean decision tree model, in which cost is measured by the number of input bits queried and the responses to queries are faulty with a fixed probability. We show that if f can be represented in kDNF form and in jC ..."
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We consider the problem of computing with faulty components in the context of the Boolean decision tree model, in which cost is measured by the number of input bits queried and the responses to queries are faulty with a fixed probability. We show that if f can be represented in kDNF form and in jCNF form, then O(n log(min(k; j)=q)) queries suffice to compute f with error probability less than q, where n is the number of input bits. 1 Introduction In this paper, we describe a method for performing reliable computation despite the presence of faulty components. This problem has been well studied in various contexts. The model we consider here is the noisy Boolean decision tree. In a Boolean decision tree, the value of a function on n bits is computed as follows: Each step consists of a query of an input bit, where the choice of the query may depend on the outcome of the previous queries. The cost Current address: LIP ENSLyon, 46 All'ee d'Italie, 69364 Lyon Cedex 07, France. Part...
Network Reliability and Fault Tolerance
, 1999
"... this article, we will use the term network reliability in a broad sense and cover several subtopics. We will start with network availability and performability, and then discuss survivable network design, followed by fault detection, isolation, and restoration as well as preplanning. We will conclud ..."
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this article, we will use the term network reliability in a broad sense and cover several subtopics. We will start with network availability and performability, and then discuss survivable network design, followed by fault detection, isolation, and restoration as well as preplanning. We will conclude with a short discussion on recent issues and literature.