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LECTURE NOTES ON THE AKS SORTING NETWORK
"... For the basics of sorting networks, see Chapter 28 of Cormen, Leiserson, and Rivest (1990). A perfect halver is a comparator network with output wires split into blocks BL,BR of equal sizes in such a way that, given any input consisting of a distinct keys, the network ..."
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For the basics of sorting networks, see Chapter 28 of Cormen, Leiserson, and Rivest (1990). A perfect halver is a comparator network with output wires split into blocks BL,BR of equal sizes in such a way that, given any input consisting of a distinct keys, the network
Cognitive theories of early gender development
 Psychological Bulletin
, 2002
"... The contribution of cognitive perspectives (cognitive–developmental theory and gender schema theory) to a contemporary understanding of gender development is evaluated. Recent critiques of cognitive approaches are discussed and empirical evidence is presented to counter these critiques. Because of t ..."
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Cited by 47 (1 self)
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The contribution of cognitive perspectives (cognitive–developmental theory and gender schema theory) to a contemporary understanding of gender development is evaluated. Recent critiques of cognitive approaches are discussed and empirical evidence is presented to counter these critiques. Because of the centrality of early gender development to the cognitive perspective, the latest research is reviewed on how infants and toddlers discriminate the sexes and learn the attributes correlated with sex. The essence of cognitive approaches—emphasis on motivational consequences of gender concepts; the active, selfinitiated view of development; and focus on developmental patterns—is highlighted and contrasted with social–cognitive views. The value of cognitive theories to the field is illustrated, and recommendations are made concerning how to construct comprehensive, integrative perspectives of gender development. How individuals develop a “gendered ” self and gendertyped differentiation has intrigued researchers of human behavior for as long as social development has been a field of empirical study. Initially, observations of clear gender typing in children as young as 5 years old led researchers to examine how socialization pro
A sorting network in bounded arithmetic
, 2008
"... We formalize the construction of Paterson’s variant of the Ajtai–Komlós–Szemerédi sorting network of logarithmic depth in the bounded arithmetical theory VNC¹∗ (an extension of VNC¹), under the assumption of existence of suitable expander graphs. We derive a conditional psimulation of the propositi ..."
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Cited by 1 (0 self)
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We formalize the construction of Paterson’s variant of the Ajtai–Komlós–Szemerédi sorting network of logarithmic depth in the bounded arithmetical theory VNC¹∗ (an extension of VNC¹), under the assumption of existence of suitable expander graphs. We derive a conditional p
Fault Tolerant Circuits and Probabilistically Checkable Proofs
 IN PROCEEDINGS OF THE 10TH ANNUAL STRUCTURE IN COMPLEXITY THEORY
, 1995
"... We introduce a new model of fault tolerant Boolean circuits. We allow an adversary to choose some gates to be faulty, unlike the model considered by von Neumann and Pippenger where the errors are randomly distributed. Our model also differs from previous models that considered nonrandom faults. Our ..."
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Cited by 7 (1 self)
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We introduce a new model of fault tolerant Boolean circuits. We allow an adversary to choose some gates to be faulty, unlike the model considered by von Neumann and Pippenger where the errors are randomly distributed. Our model also differs from previous models that considered nonrandom faults. Our main result is that every symmetric function has a small (size O(n), depth O(logn)) fault tolerant circuit that will compute the function adequately, even if a small constant fraction of the gates is modified by an adversary. We also show a perhaps unexpected relation between our model and probabilistically checkable proofs.
Fish models for environmental carcinogenesis: The rainbow trout. Environmental Health Perspectives 104
, 1996
"... Progress over the past 30 years has revealed many strengths of the rainbow trout as an alternative model for environmental carcinogenesis research. These include low rearing costs, an early lifestage ultrasensitive bioassay, sensitivity to many classes of carcinogen, a welldescribed tumor patholog ..."
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Cited by 21 (8 self)
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Progress over the past 30 years has revealed many strengths of the rainbow trout as an alternative model for environmental carcinogenesis research. These include low rearing costs, an early lifestage ultrasensitive bioassay, sensitivity to many classes of carcinogen, a welldescribed tumor pathology, responsiveness to tumor promoters and inhibitors, and a mechanistically informative nonmammalian comparative status. Lowcost husbandry, for example, has permitted statistically challenging tumor study designs with up to 10,000 trout to investigate the quantitative interrelationships among carcinogen dose, anticarcinogen dose, DNA adduct formation, and final tumor outcome. The basic elements of the trout carcinogen bioassay include multiple exposure routes, carcinogen response, husbandry requirements, and pathology. The principal known neoplasms occur in liver (mixed hepatocellular/cholangiocellular adenoma and carcinoma, hepatocellular carcinoma), kidney (nephroblastoma), swim bladder (adenopapilloma), and stomach (adenopapilloma). Trout possess a complex but incompletely characterized array of cytochromes P450, transferases, and other enzymic systems for phase and phase 11 procarcinogen metabolism. In general, trout exhibit only limited capacity for DNA repair, especially for removal of bulky DNA adducts. This factor, together with a high capacity for P450 bioactivation and negligible
Periodic Constant Depth Sorting Networks
 In Proc. 11th STACS
, 1994
"... . Comparator networks of constant depth can be used for sorting in the following way. The computation consists of a number of iterations, say t, each iteration being a single run through the comparator network. The output of a round j (j ! t) is used as the input for the round j + 1. The output of t ..."
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Cited by 12 (5 self)
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. Comparator networks of constant depth can be used for sorting in the following way. The computation consists of a number of iterations, say t, each iteration being a single run through the comparator network. The output of a round j (j ! t) is used as the input for the round j + 1. The output of the round t is the output of the computation. In such a way, it is possible to apply a network with a small number of comparators for sorting long input sequences. However, it is not clear how to make such a computation fast. OddEven Transposition Sort gives a periodic sorting network of depth 2, that sorts n numbers in n=2 iterations. The network of depth 8 proposed by Schwiegelshohn [8] sorts n numbers in O( p n log n) iterations. Krammer [5] modified the algorithm and obtained a network of depth 6 sorting in O( p n log n) iterations. For a fixed but arbitrary k 2 N , we present a periodic sorting network of depth O(k) that sorts n input numbers in O(k 2 \Delta n 1=k ) steps. 1 In...
Matching Nuts and Bolts Optimally
, 1995
"... The nuts and bolts problem is the following: Given a collection of n nuts of distinct sizes and n bolts of distinct sizes such that for each nut there is exactly one matching bolt, find for each nut its corresponding bolt subject to the restriction that we can only compare nuts to bolts. That is we ..."
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show the existence of this algorithm by showing the existence of certain expanderbased comparator networks. Our algorithm is asymptotically optimal in terms of the number of nutandbolt comparisons it does. Another view of this result is that we show the existence of a decision tree with depth O(n lg
The Convergence of Bird Flocking
, 2009
"... We bound the time it takes for a group of birds to reach steady state in a standard flocking model. We prove that (i) within single exponential time fragmentation ceases and each bird settles on a fixed flying direction; (ii) the flocking network converges only after a number of steps that is an ite ..."
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Cited by 14 (6 self)
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We bound the time it takes for a group of birds to reach steady state in a standard flocking model. We prove that (i) within single exponential time fragmentation ceases and each bird settles on a fixed flying direction; (ii) the flocking network converges only after a number of steps that is an iterated exponential of height logarithmic in the number of birds. We also prove the highly surprising result that this bound is optimal. The model directs the birds to adjust their velocities repeatedly by averaging them with their neighbors within a fixed radius. The model is deterministic, but we show that it can tolerate a reasonable amount of stochastic or even adversarial noise. Our methods are highly general and we speculate that the results extend to a wider class of models based on undirected flocking networks, whether defined metrically or topologically. This work introduces new techniques of broader interest, including the flight net, the iterated spectral shift, and a certain residueclearing argument in circuit complexity.
Results 1  10
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156