40,111 research outputs found
EFFICIENT COMPUTER SEARCH FOR MULTIPLE RECURSIVE GENERATORS
Pseudo-random numbers (PRNs) are the basis for almost any statistical simulation and thisdepends largely on the quality of the pseudo-random number generator(PRNG) used. In this study, we used some results from number theory to propose an efficient method to accelerate the computer search of super-order maximum period multiple recursive generators (MRGs). We conduct efficient computer searches and successfully found prime modulus p, and the associated order k; (k = 40751; k = 50551; k = 50873) such that R(k; p) is a prime. Using these values of ks, together with the generalized Mersenne prime algorithm, we found and listed many efficient, portable, and super-order MRGs with period lengths of approximately 10e 380278.1;10e 471730.6; and 10e 474729.3. In other words, using the generalized Mersenne prime algorithm, we extended some known results of some efficient, portable, and maximum period MRGs. In particular, the DX/DL/DS/DT large order generators are extended to super-order generators.For r k, super-order generators in MRG(k,p) are quite close to an ideal generator. Forr \u3e k; the r-dimensional points lie on a relatively small family of equidistant parallel hyperplanesin a high dimensional space. The goodness of these generators depend largely on the distance between these hyperplanes. For LCGs, MRGs, and other generators with lattice structures, the spectral test, which is a theoretical test that gives some measure of uniformity greater than the order k of the MRG, is the most perfect figure of merit. A drawback of the spectral test is its computational complexity. We used a simple and intuitive method that employs the LLL algorithm, to calculate the spectral test. Using this method, we extended the search for better DX-k-s-t farther than the known value of k = 25013: In particular, we searched and listed better super-order DX-k-s-t generators for k = 40751; k = 50551, and k = 50873.Finally, we examined, another special class of MRGs with many nonzero terms known as the DW-k generator. The DW-k generators iteration can be implemented efficiently and in parallel, using a k-th order matrix congruential generator (MCG) sharing the same characteristic polynomial. We extended some known results, by searching for super-order DW-k generators, using our super large k values that we obtained in this study. Using extensive computer searches, we found and listed some super-order, maximum period DW(k; A, B, C, p = 2e 31 - v) generators
Implementation of a RANLUX Based Pseudo-Random Number Generator in FPGA Using VHDL and Impulse C
Monte Carlo simulations are widely used e.g. in the field of physics and molecular modelling. The main role played in these is by the high performance random number generators, such as RANLUX or MERSSENE TWISTER. In this paper the authors introduce the world's first implementation of the RANLUX algorithm on an FPGA platform for high performance computing purposes. A significant speed-up of one generator instance over 60 times, compared with a graphic card based solution, can be noticed. Comparisons with concurrent solutions were made and are also presented. The proposed solution has an extremely low power demand, consuming less than 2.5 Watts per RANLUX core, which makes it perfect for use in environment friendly and energy-efficient supercomputing solutions and embedded systems
Cluster Hybrid Monte Carlo Simulation Algorithms
We show that addition of Metropolis single spin-flips to the Wolff cluster
flipping Monte Carlo procedure leads to a dramatic {\bf increase} in
performance for the spin-1/2 Ising model. We also show that adding Wolff
cluster flipping to the Metropolis or heat bath algorithms in systems where
just cluster flipping is not immediately obvious (such as the spin-3/2 Ising
model) can substantially {\bf reduce} the statistical errors of the
simulations. A further advantage of these methods is that systematic errors
introduced by the use of imperfect random number generation may be largely
healed by hybridizing single spin-flips with cluster flipping.Comment: 16 pages, 10 figure
Guaranteeing the diversity of number generators
A major problem in using iterative number generators of the form
x_i=f(x_{i-1}) is that they can enter unexpectedly short cycles. This is hard
to analyze when the generator is designed, hard to detect in real time when the
generator is used, and can have devastating cryptanalytic implications. In this
paper we define a measure of security, called_sequence_diversity_, which
generalizes the notion of cycle-length for non-iterative generators. We then
introduce the class of counter assisted generators, and show how to turn any
iterative generator (even a bad one designed or seeded by an adversary) into a
counter assisted generator with a provably high diversity, without reducing the
quality of generators which are already cryptographically strong.Comment: Small update
On the design of state-of-the-art pseudorandom number generators by means of genetic programming
Congress on Evolutionary Computation. Portland, EEUU, 19-23 June 2004The design of pseudorandom number generators by means of evolutionary computation is a classical problem. Today, it has been mostly and better accomplished by means of cellular automata and not many proposals, inside or outside this paradigm could claim to be both robust (passing all the statistical tests, including the most demanding ones) and fast, as is the case of the proposal we present here. Furthermore, for obtaining these generators, we use a radical approach, where our fitness function is not at all based in any measure of randomness, as is frequently the case in the literature, but of nonlinearity. Efficiency is assured by using only very efficient operators (both in hardware and software) and by limiting the number of terminals in the genetic programming implementation
When Can Limited Randomness Be Used in Repeated Games?
The central result of classical game theory states that every finite normal
form game has a Nash equilibrium, provided that players are allowed to use
randomized (mixed) strategies. However, in practice, humans are known to be bad
at generating random-like sequences, and true random bits may be unavailable.
Even if the players have access to enough random bits for a single instance of
the game their randomness might be insufficient if the game is played many
times.
In this work, we ask whether randomness is necessary for equilibria to exist
in finitely repeated games. We show that for a large class of games containing
arbitrary two-player zero-sum games, approximate Nash equilibria of the
-stage repeated version of the game exist if and only if both players have
random bits. In contrast, we show that there exists a class of
games for which no equilibrium exists in pure strategies, yet the -stage
repeated version of the game has an exact Nash equilibrium in which each player
uses only a constant number of random bits.
When the players are assumed to be computationally bounded, if cryptographic
pseudorandom generators (or, equivalently, one-way functions) exist, then the
players can base their strategies on "random-like" sequences derived from only
a small number of truly random bits. We show that, in contrast, in repeated
two-player zero-sum games, if pseudorandom generators \emph{do not} exist, then
random bits remain necessary for equilibria to exist
Improved Heat Demand Prediction of Individual Households
One of the options to increase the energy efficiency of current electricity network is the use of a Virtual Power Plant. By using multiple small (micro)generators distributed over the country, electricity can be produced more efficiently since these small generators are more efficient and located where the energy is needed. In this paper we focus on micro Combined Heat and Power generators. For such generators, the production capacity is determined and limited by the heat demand. To keep the global electricity network stable, information about the production capacity of the heat-driven generators is required in advance. In this paper we present methods to perform heat demand prediction of individual households based on neural network techniques. Using different input sets and a so called sliding window, the quality of the predictions can be improved significantly. Simulations show that these improvements have a positive impact on controlling the distributed microgenerators
Communicating over adversarial quantum channels using quantum list codes
We study quantum communication in the presence of adversarial noise. In this
setting, communicating with perfect fidelity requires using a quantum code of
bounded minimum distance, for which the best known rates are given by the
quantum Gilbert-Varshamov (QGV) bound. By asking only for arbitrarily high
fidelity and allowing the sender and reciever to use a secret key with length
logarithmic in the number of qubits sent, we achieve a dramatic improvement
over the QGV rates. In fact, we find protocols that achieve arbitrarily high
fidelity at noise levels for which perfect fidelity is impossible. To achieve
such communication rates, we introduce fully quantum list codes, which may be
of independent interest.Comment: 6 pages. Discussion expanded and more details provided in proofs. Far
less unclear than previous versio
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