17,969 research outputs found
A one line factoring algorithm
We describe a variant of Fermat’s factoring algorithm which is competitive with SQUFOF in practice but has heuristic run time complexity O(n1/3) as a general factoring algorithm. We also describe a sparse class of integers for which the algorithm is particularly effective. We provide speed comparisons between an optimised implementation of the algorithm described and the tuned assortment of factoring algorithms in the Pari/GP computer algebra package
An experimental exploration of Marsaglia's xorshift generators, scrambled
Marsaglia proposed recently xorshift generators as a class of very fast,
good-quality pseudorandom number generators. Subsequent analysis by Panneton
and L'Ecuyer has lowered the expectations raised by Marsaglia's paper, showing
several weaknesses of such generators, verified experimentally using the
TestU01 suite. Nonetheless, many of the weaknesses of xorshift generators fade
away if their result is scrambled by a non-linear operation (as originally
suggested by Marsaglia). In this paper we explore the space of possible
generators obtained by multiplying the result of a xorshift generator by a
suitable constant. We sample generators at 100 equispaced points of their state
space and obtain detailed statistics that lead us to choices of parameters that
improve on the current ones. We then explore for the first time the space of
high-dimensional xorshift generators, following another suggestion in
Marsaglia's paper, finding choices of parameters providing periods of length
and . The resulting generators are of extremely
high quality, faster than current similar alternatives, and generate
long-period sequences passing strong statistical tests using only eight logical
operations, one addition and one multiplication by a constant
Probabilistic computing with future deep sub-micrometer devices: a modelling approach
An approach is described that investigates the potential of probabilistic "neural" architectures for computation with deep sub-micrometer (DSM) MOSFETs. Initially, noisy MOSFET models are based upon those for a 0.35 /spl mu/m MOS technology with an exaggerated 1/f characteristic. We explore the manifestation of the 1/f characteristic at the output of a 2-quadrant multiplier when the key n-channel MOSFETs are replaced by "noisy" MOSFETs. The stochastic behavior of this noisy multiplier has been mapped on to a software (Matlab) model of a continuous restricted Boltzmann machine (CRBM) - an analogue-input stochastic computing structure. Simulation of this DSM CRBM implementation shows little degradation from that of a "perfect" CRBM. This paper thus introduces a methodology for a form of "technology-downstreaming" and highlights the potential of probabilistic architectures for DSM computation
Peer Effects, Fast Food Consumption and Adolescent Weight Gain
This paper aims at opening the black box of peer effects in adolescent weight gain. Using Add Health data on secondary schools in the U.S., we investigate whether these effects partly flow through the eating habits channel. Adolescents are assumed to interact through a friendship social network. We first propose a social interaction model of fast food consumption using a generalized spatial autoregressive approach. We exploit results by Bramoullé, Djebbari and Fortin (2009) which show that intransitive links within a network (i.e., a friend of one of my friends is not my friend) help identify peer effects. The model is estimated using maximum likelihood and generalized 2SLS strategies. We also estimate a panel dynamic weight gain production function relating an adolescent’s Body Mass Index (BMI) to his current fast food consumption and his lagged BMI level. Results show that there are positive significant peer effects in fast food consumption among adolescents belonging to a same friendship school network. The estimated social multiplier is 1.59. Our results also suggest that, at the network level, an extra day of weekly fast food restaurant visits increases BMI by 2.4%, when peer effects are taken into account.Obesity, overweight, peer effects, social interactions, fast food, spatial models
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