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Articles 1 - 6 of 6
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The Expected Capacity Of Concentrators, Nicholas Pippenger
The Expected Capacity Of Concentrators, Nicholas Pippenger
All HMC Faculty Publications and Research
The expected capacity of a class of sparse concentrators called modular concentrators is determined. In these concentrators, each input is connected to exactly two outputs, each output is connected to exactly three inputs, and the girth (the length of the shortest cycle in the connexion graph) is large. Two definitions of expected capacity are considered. For the first (which is due to Masson and Morris), it is assumed that a batch of customers arrive at a random set of inputs and that a maximum matching of these customers to servers at the outputs is found. The number of unsatisfied requests …
On A Lower Bound For The Redundancy Of Reliable Networks With Noisy Gates, Nicholas Pippenger
On A Lower Bound For The Redundancy Of Reliable Networks With Noisy Gates, Nicholas Pippenger
All HMC Faculty Publications and Research
A proof is provided that a logarithmic redundancy factor is necessary for the reliable computation of the parity function by means of a network with noisy gates. This result was first stated by R.L. Dobrushin and S.I. Ortyukov (1977). However, the authors believe that the analysis given by Dobrushin and Ortyukov is not entirely correct. The authors establish the result by following the same steps and by replacing the questionable part of their analysis with entirely new arguments.
Stochastic Orderings Induced By Star-Shaped Functions, Henry A. Krieger
Stochastic Orderings Induced By Star-Shaped Functions, Henry A. Krieger
All HMC Faculty Publications and Research
The non-decreasing functions whicl are star-shaped and supported above at each point of a non-empty closed proper subset of the real line induce an ordering, on the class of distribution functions with finite first moments, that is strictly weaker than first degree stochastic dominance and strictly stronger than second degree stochastic dominance. Several characterizations of this ordering are developed, both joint distribution criteria and those involving only marginals. The latter are deduced from a decomposition theorem, which reduces the problem to consideration of certain functions which are star-shaped on the complement of an open interval.
Selection Networks, Nicholas Pippenger
Selection Networks, Nicholas Pippenger
All HMC Faculty Publications and Research
An upper bound asymptotic to $2n\log _e n$ is established for the number of comparators required in a network that classifies $n$ values into two classes, each containing $n / 2$ values, with each value in one class less than or equal to each value in the other. (The best lower bound known for this problem is asymptotic to $(n / 2)\log _2 n$.)
When Is Every Order Ideal A Ring Ideal?, Melvin Henriksen, Suzanne Larson, Frank A. Smith
When Is Every Order Ideal A Ring Ideal?, Melvin Henriksen, Suzanne Larson, Frank A. Smith
All HMC Faculty Publications and Research
A lattice-ordered ring ℝ is called an OIRI-ring if each of its order ideals is a ring ideal. Generalizing earlier work of Basly and Triki, OIRI-rings are characterized as those f-rings ℝ such that ℝ/I is contained in an f-ring with an identity element that is a strong order unit for some nil l-ideal I of ℝ. In particular, if P(ℝ) denotes the set of nilpotent elements of the f-ring ℝ, then ℝ is an OIRI-ring if and only if ℝ/P(ℝ) is contained in an f-ring with an identity element that is a strong order unit.
Modulated, Frequency-Locked, And Chaotic Cross-Waves, William B. Underhill, Seth Lichter, Andrew J. Bernoff
Modulated, Frequency-Locked, And Chaotic Cross-Waves, William B. Underhill, Seth Lichter, Andrew J. Bernoff
All HMC Faculty Publications and Research
Measurements were made of the wave height of periodic, quasi-periodic, and chaotic parametrically forced cross-waves in a long rectangular channel. In general, three frequencies (and their harmonics) may be observed: the subharmonic frequency and two slow temporal modulations — a one-mode instability associated with streamwise variation and a sloshing motion associated with spanwise variation. Their interaction, as forcing frequency, f, and forcing amplitude, a, were varied, produced a pattern of Arnold tongues in which two or three frequencies were locked. The overall picture of frequency-locked and -unlocked regions is explained in terms of the Arnold tongues predicted by …