In this article, we have proved the Darboux's theorem. This theorem is important to prove the Riemann integrability. We can replace an upper bound and a lower bound of a function which is the definition of Riemann integration with convergence of sequence by Darboux's theorem. We adopt the following rules: x, y are real numbers, i, j, k are natural numbers, and p, q are finite sequences of eleme...

This paper proposes an ultra-low power CMOS random number generator (RNG), which is based on an oscillator-sampling architecture. The noisy oscillator consists of a dual-drain MOS transistor, a noise generator and a voltage control oscillator. The dual-drain MOS transistor can bring extra-noise to the drain current or the output voltage so that the jitter of the oscillator is much larger than t...

Random number generation (RNG) requires executive control. A novel paradigm using the eight drum pads of an electronic drum set as an input device was used to test 15 healthy subjects who engaged in random or ordered number generation (ONG). Brain potentials time-locked to the drum-beats revealed a more negative response during RNG compared to ONG which had a left frontal distribution. Source a...

We propose methods for constructing high-quality pseudorandom number generators (RNGs) based on an ensemble of hyperbolic automorphisms of the unit two-dimensional torus (Sinai-Arnold map or cat map) while keeping a part of the information hidden. The single cat map provides the random properties expected from a good RNG and is hence an appropriate building block for an RNG, although unnecessar...

The problem of efficiently disseminating data from a mobile stimulus (source) to multiple mobile users (sinks) in a large-scale sensor network has been challenging. We address this problem by proposing a minimum-energy tree-based data dissemination scheme, Dynamic Localized Minimum-Energy Agent Tree-Based Scheme (DLATS). We exploit the fact that sensor nodes are stationary and location-aware. I...

Introduction: Random number generation is indispensable in cryptography, scientific computing and stochastic computing. In cryptography, the quality of randomness of the generator is critical for security [1]. The pseudo-RNG generates sequences using a deterministic algorithm, so the sequence inevitably repeats and becomes predictable. A true RNG is nondeterministic and unpredictable, often rel...

Neurophysiological and functional imaging studies have demonstrated that frontal regions of the brain are particularly responsive to homeostatic sleep pressure. Previous neuropsychological studies indicate that sleep deprivation causes impairments in prefrontal cortical function. Random number generation (RNG) is thought to provide a sensitive index of executive functions that rely on the prefr...

We provide the first provable-security analysis of the Intel Secure Key hardware RNG (ISK-RNG), versions of which have appeared in Intel processors since late 2011. To model the ISKRNG, we generalize the PRNG-with-inputs primitive, introduced by Dodis et al. at CCS’13 for their /dev/[u]random analysis. The concrete security bounds we uncover tell a mixed story. We find that ISKRNG lacks backwar...

trajectory using genetic algorithms (GA) is presented. The efficiency of the proposed approach, without loss of generality, is demonstrated through a simulation carried out on a planar 6-DOF robot manipulator. The approach benefits from two key features. First, the method of data representation which guarantees the satisfaction of joints angle limits, and second the conversion of considered mod...