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- Nicholas Pippenger
- 20th Annual Symposium on Foundations of Computer…
- 1979

It is well known that time bounds for machines correspond closely to size bounds for networks, and that space bounds correspond to depth bounds. It is not known whether simultaneous time and space bounds correspond to simultaneous size and depth bounds. It is shown here that simultaneous time and "reversal" bounds correspond to simultaneous size and depth… (More)

- Nicholas Pippenger
- 17th Annual Symposium on Foundations of Computer…
- 1976

2. the sum of two (not necessarily distinct) previously computed vectors is available at a cost of one "step". (which can be regarded as integers); if we have no MULTIPLY instruction in our machine, we must simulate scalar multiplication by addition. (This problem would be more realistic if we allowed negative coefficients, subtractions, and short shifts.… (More)

- Adi Livnat, Nicholas Pippenger
- Journal of theoretical biology
- 2008

Systematic mistakes can be distinguished from other types of mistakes in that they are repeatable and predictable within a given organism, and are not due to uncertainty or lack of information. Here we provide a mathematical definition for the concept of systematic mistakes, which captures the way this concept has been used in the behavioral sciences. We… (More)

- Adi Livnat, Nicholas Pippenger
- Proceedings of the National Academy of Sciences…
- 2006

Many behaviors have been attributed to internal conflict within the animal and human mind. However, internal conflict has not been reconciled with evolutionary principles, in that it appears maladaptive relative to a seamless decision-making process. We study this problem through a mathematical analysis of decision-making structures. We find that, under… (More)

- Adi Livnat, Christos Papadimitriou, Nicholas Pippenger, Marcus W. Feldman
- Proceedings of the National Academy of Sciences…
- 2010

The assumption that different genetic elements can make separate contributions to the same quantitative trait was originally made in order to reconcile biometry and Mendelism and ever since has been used in population genetics, specifically for the trait of fitness. Here we show that sex is responsible for the existence of separate genetic effects on… (More)

- Nicholas Pippenger
- 20th Annual Symposium on Foundations of Computer…
- 1979

The problem solved in this paper is the following. Let x I' xn be indeterminates; let [I' ... , rk be simple radicals, by which is meant let rl' ... , rk be the square roots of rational functions of x I' ... , xn ; and let f I' , fm be simple algebraic Junctions, by which is meant let f I' , fm be rational functions of rl' ... , rk and xI' ... , x(l" What… (More)

A classic puzzle asks for the resistance between vertices at the ends of a long diagonal when the edges of a cube are replaced by 1-ohm resistors. The solution relies on the observation that for each of the endpoints, the three adjacent vertices are at the same potential, by the symmetry of the cube under a 120 rotation about the long diagonal. The network… (More)

e _ 2'/z 2 4 4 6 6 8 1 / 8 2 () (33) 1/4 ( 5577) which is proved as follows . For v > 2, the Pth factor is [2' '. . 2P/(2p'+ 1) . (2 1)]'áz [(2"-'-1)!!z2"!!z/2 .2v-'!!z(2v-1)!!z]'/z where n!!=n(n-2) . . .4.2 if n is even, n(n-2) . . .3 .1 if n is odd. Since 2°!!=2 z " '2° '1 and (2°-1)!!=2°! /2°!!=2°!/2z" '2°'!, this expression becomes [2z"2°-'16/2 .2… (More)

- R . Fagin, Jürg Nievergelt, Nicholas Pippenger, H. R. Strong, Extendible Hashing
- 1992

typedef struct { int owner; slock_t sem } Node; shared Node treee2*n-1]; shared T baggn], *result; shared int weighttn]; /* n>1 */ void process(pid) int pid; { int partner, son, node; node = pid; son = pid; while (node > 0) { son = node; node = (son) / 2; S_LOCK(&(treeenode].sem)); S_LOCK(&(treeeson].sem)); if (treeeson].owner != pid) { /* the son has… (More)

We examine the problem of finding an optimalpolicy in routing single-connection calls between a client and a server on simple models of connection networks. We study the graphs , and with respect to possible configurationsof vertices, edges and directed edges within our client-server model. The many different configurations of the system are reduced to a… (More)