scholarly journals Mapping Stochastic Devices to Probabilistic Algorithms.

2021 ◽  
Author(s):  
James Aimone ◽  
Alexander Safonov
Keyword(s):  
Probabilistic Algorithms

Probabilistic algorithms for polynomial absolute factorization

2010 ◽  
Vol 43 (3/4) ◽  
pp. 77-78
Author(s):  
C. Bertone ◽  
G. Chéze ◽  
A. Galligo
Keyword(s):  
Probabilistic Algorithms

Analyzing the Effect of Node Density on the Performance of the LAR-1P Algorithm

2012 ◽  
Vol 7 (2) ◽  
pp. 16-29
Author(s):  
Hussein Al-Bahadili ◽  
Ali Maqousi ◽  
Reyadh S. Naoum
Keyword(s):  
Network Performance ◽  
Ad Hoc ◽  
High Density ◽  
Low Density ◽  
Probabilistic Algorithms ◽  
Excellent Performance ◽  
Node Density ◽  
Simulation Results ◽  
Mobile Ad Hoc ◽  
Hoc Networks

The location-aided routing scheme 1 (LAR-1) and probabilistic algorithms are combined together into a new algorithm for route discovery in mobile ad hoc networks (MANETs) called LAR-1P. Simulation results demonstrated that the LAR-1P algorithm reduces the number of retransmissions as compared to LAR-1 without sacrificing network reachability. Furthermore, on a sub-network (zone) scale, the algorithm provides an excellent performance in high-density zones, while in low-density zones; it preserves the performance of LAR-1. This paper provides a detailed analysis of the performance of the LAR-1P algorithm through various simulations, where the actual numerical values for the number of retransmissions and reachability in high- and low-density zones were computed to demonstrate the effectiveness and significance of the algorithm and how it provides better performance than LAR-1 in high-density zones. In addition, the effect of the total number of nodes on the average network performance is also investigated.

Efficient Probabilistic Calculation of a Thermal Transient on a 3D FE Model With Variable Heat Exchange Coefficient

2013 ◽  
Author(s):  
Thibault Demol ◽  
Jean-Pierre Izard ◽  
Nicolas Tartare
Keyword(s):  
Transfer Functions ◽  
Physical Problem ◽  
Nuclear Industry ◽  
Fe Model ◽  
Probabilistic Algorithms ◽  
Heat Exchange Coefficient ◽  
Probabilistic Algorithm ◽  
Constant Heat ◽  
Element Analysis ◽  
Reactor Pressure

Probabilistic calculations are often used to evaluate reliability in nuclear industry. One of their main difficulties is that failure probabilities are, in this domain, very low and therefore their computations are very long. The speed of the calculations depends on the probabilistic algorithm and the complexity of the physical problem (usually modeled by a finite element analysis). The optimization of the probabilistic algorithms benefits from a wealth of literature but the physical problem is often very simplified by a lot of approximations. This paper develops a methodology to avoid some approximations. The geometry of the problem is often brought back to a 1D or 2D problem. Here, large 3D mesh can still be used thanks to transfer functions. This requires the linearity of the problem and especially a constant heat transfer coefficient for a thermo-elastic analysis. This limitation has been removed. This article’s focus is on methodology but qualitative results of a probabilistic brittle fracture application of a reactor pressure vessel (RPV) in ferritic steel are given. Other kinds of analysis can benefit from similar methodology.

scholarly journals Uniform derandomization from pathetic lower bounds

2012 ◽  
Vol 370 (1971) ◽  
pp. 3512-3535 ◽  
Author(s):  
Eric Allender ◽  
V. Arvind ◽  
Rahul Santhanam ◽  
Fengming Wang
Keyword(s):  
Word Problem ◽  
Lower Bounds ◽  
Black Box ◽  
Arithmetic Circuits ◽  
List Type ◽  
Probabilistic Algorithms ◽  
Constant Depth ◽  
Subexponential Time ◽  
Polynomial Size ◽  
Threshold Circuits

The notion of probabilistic computation dates back at least to Turing, who also wrestled with the practical problems of how to implement probabilistic algorithms on machines with, at best, very limited access to randomness. A more recent line of research, known as derandomization, studies the extent to which randomness is superfluous. A recurring theme in the literature on derandomization is that probabilistic algorithms can be simulated quickly by deterministic algorithms, if one can obtain impressive (i.e. superpolynomial, or even nearly exponential) circuit size lower bounds for certain problems. In contrast to what is needed for derandomization, existing lower bounds seem rather pathetic. Here, we present two instances where ‘pathetic’ lower bounds of the form n 1+ ϵ would suffice to derandomize interesting classes of probabilistic algorithms. We show the following: — If the word problem over S 5 requires constant-depth threshold circuits of size n 1+ ϵ for some ϵ >0, then any language accepted by uniform polynomial size probabilistic threshold circuits can be solved in subexponential time (and, more strongly, can be accepted by a uniform family of deterministic constant-depth threshold circuits of subexponential size). — If there are no constant-depth arithmetic circuits of size n 1+ ϵ for the problem of multiplying a sequence of n  3×3 matrices, then, for every constant d , black-box identity testing for depth- d arithmetic circuits with bounded individual degree can be performed in subexponential time (and even by a uniform family of deterministic constant-depth AC 0 circuits of subexponential size).

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