The Scalable Parallel Random Number Generators (SPRNG) library is widely used to generate random numbers in Monte Carlo simulations due to the good statistical properties of both its serial and parallel random number streams. In this paper, we suggest an efficient hardware architecture for the Parallel Additive Lagged-Fibonacci Generator (PALFG) provided by the SPRNG library. This design has be...

1. Robert P. Backstrom. "On the Determination of the Zeros of the Fibonacci Sequence." The Fibonacci Quarterly 4, No. 4 (1966):313-322. 2. R. D. Carmichael. "On the Numerical Factors of the Arithmetic Forms a + 3." Annals of Mathematics9 2nd Ser. 15 (1913):30-70. 3. John H. Halton. "On the Divisibility Properties of Fibonacci Numbers." The Fibonacci Quarterly 4, No. 3 (1966):217-240. 4. D.H. Le...

In the first part of this work we provide a formula for the number of edges of the Hasse diagram of the independent subsets of the hth power of a path ordered by inclusion. For h = 1 such a value is the number of edges of a Fibonacci cube. We show that, in general, the number of edges of the diagram is obtained by convolution of a Fibonacci-like sequence with itself. In the second part we consi...

There are several data structures which can calculate the prefix sums of an array efficiently, while handling point updates on the array, such as Segment Trees and Binary Indexed Trees (BIT). Both these data structures can handle the these two operations (query and update) in O(log n) time. In this paper, we present a data structure similar to the BIT, but with an even smaller constant. To do t...

Charge balance law based on conservation of charge is stated and employed to analyze on-chip linear, Fibonacci and exponential charge pumps. For micro-power on-chip implementations, both the positiveand the negativeplate parasitic capacitors have to be considered. Voltage conversion ratios and efficiencies can be obtained in closed form for singleand dual-branch linear charge pumps, but not for...

In decision diagrams (DDs) methods for circuit synthesis, it is possible to directly transfer a DD for a given function f into a network realizing f by the replacement of non-terminal nodes in the DD with the corresponding circuit modules. The chief bottleneck of mapping a DD into a network is the inherent feature that the depth of the network produced, is equal to the number of variables in f....

The random Fibonacci sequence is defined by t1 = t2 = 1 and tn = ±tn−1 + tn−2, for n > 3, where each ± sign is chosen at random with probability P (+) = P (−) = 12 . Viswanath has shown that almost all random Fibonacci sequences grow exponentially at the rate 1.13198824 . . . . We will consider what happens to random Fibonacci sequences when we remove the randomness; specifically, we will choos...

BACKGROUND In most phase I oncology trials, it is often stated that the dose increments follow a "modified-Fibonacci sequence". This term, however, is vague. METHODS To better characterize this sequence, we reviewed 81 phase I trials based on this concept. RESULTS Out of 198 phase I oncology trials, 81 (41%) are based on modified-Fibonacci series. Actual incremental ratios varied in a large...

In the language of mathematical chemistry, Fibonacci cubes can be defined as the resonance graphs of fibonacenes. Lucas cubes form a symmetrization of Fibonacci cubes and appear as resonance graphs of cyclic polyphenantrenes. In this paper it is proved that the Wiener index of Fibonacci cubes can be written as the sum of products of four Fibonacci numbers which in turn yields a closed formula f...

The Fibonacci dimension fdim(G) of a graph G was introduced in [7] as the smallest integer d such that G admits an isometric embedding into Qd, the d-dimensional Fibonacci cube. A somewhat new combinatorial characterization of the Fibonacci dimension is given, which enables more comfortable proofs of some previously known results. In the second part of the paper the Fibonacci dimension of the r...