On the period length of generalized inversive pseudorandom number generators

Eichenauer and Lehn's inversive congruential pseudorandom number generator is generalized for arbitrary composite moduli. The maximal period is determined and simple constructive methods are given to find parameters for these generators.     

On the Distribution of Pseudorandom Numbers and Vectors Generated by Inversive Methods

Inversive methods provide an attractive alternative to linear methods for pseudorandom number and vector generation. We present the first nontrivial results on the distribution of sequences of digital inversive pseudorandom numbers and inversive pseudorandom vectors in parts of the period. The proofs are based on a new bound for certain exponential sums over finite fields. Received: March 19, 1999     

P-RnaPredict--a parallel evolutionary algorithm for RNA folding: effects of pseudorandom number quality

This paper presents a fully parallel version of RnaPredict, a genetic algorithm (GA) for RNA secondary structure prediction. The research presented here builds on previous work and examines the impact of three different pseudorandom number generators (PRNGs) on the GA's performance. The three generators tested are the C standard library PRNG RAND, a parallelized multiplicative congruential generator (MCG), and a parallelized Mersenne Twister (MT). A fully parallel version of RnaPredict using the Message Passing Interface (MPI) was implemented on a 128-node Beowulf cluster. The PRNG comparison tests were performed with known structures whose sequences are 118, 122, 468, 543, and 556 nucleotides in length. The effects of the PRNGs are investigated and the predicted structures are compared to known structures. Results indicate that P-RnaPredict demonstrated good prediction accuracy, particularly so for shorter sequences.     

Sampling Boolean Functions over Abelian Groups and Applications

We obtain efficient sampling methods for recovering or compressing functions over finite Abelian groups with few Fourier coefficients, i.e., functions that are (approximable by) linear combinations of few, possibly unknown Fourier basis functions or characters. Furthermore, our emphasis is on efficiently and deterministically finding small, uniform sample sets, which can be used for sampling all functions in natural approximation classes of Boolean functions. Due to this requirement, even the simplest versions of this problem (say, when the set of approximating characters is known) require somewhat different techniques from the character theory of finite Abelian groups that are commonly used in other discrete Fourier transform applications. We briefly discuss applications of our efficient, uniform sampling methods in computational learning theory, efficient generation of pseudorandom strings, and testing linearity; we also state highly related open problems that are not only applicable in these contexts, but are also of independent mathematical interest. Received: December 14, 1998; revised version: October 20, 1999     

Optimization of random number generators: efficient search for high-quality LCGs

In this work we will discuss how to optimize multipliers for prime-modulus linear congruential pseudo-random number generators with respect to the spectral test. The optimization efficiency has shown itself to be strongly dependent on the encoding strategy for the multipliers within the random search process. The optimal encoding technique will be demonstrated to be a representation in terms of powers of a primitive root. A sample distributed large-scale parameter search for subsequence stable LCGs will be conducted using the developed concepts.     

On the Lattice Structure of Pseudorandom Numbers Generated over Arbitrary Finite Fields

Marsaglia's lattice test for congruential pseudorandom number generators modulo a prime is extended to a test for generators over arbitrary finite fields. A congruential generator η₀,η₁,…, generated by η _n =g(n), n = 0, 1,…, passes Marsaglia's s-dimensional lattice test if and only if s≤ deg(g). It is investigated how far this conditin holds true for polynomials over arbitrary finite fields F _q , particularly for polynomials of the form g _d (x)=α(x+β) ^d +γ, α, β, γ∈F _q , α≠ 0, 1 ≤d≤q− 1. Received: December 13, 1999; revised version: November 17, 2000     

Lattice Structure and Linear Complexity of Nonlinear Pseudorandom Numbers

 It is shown that a q-periodic sequence over the finite field F _q passes an extended version of Marsaglia's lattice test for high dimensions if and only if its linear complexity is large. The consequences of this result for nonlinear and inversive pseudorandom number generators are worked out. Received: October 2, 2001 Keywords: Pseudorandom number generator, Nonlinear method, Inversive method, Linear complexity, Marsaglia's lattice test.     

Integrating order acceptance decisions with flexible due dates in a production planning model with load-dependent lead times

We consider a tactical planning problem, which integrates production planning decisions together with order acceptance decisions, while taking into account the dependency between workload and lead times. The proposed model determines which orders to accept and in which period they should be produced, so that they can be delivered to the customer within the acceptable flexible due dates. When the number of accepted orders increases, the workload and production lead time also increase, and this may result in the possibility of missing customer due dates. This problem is formulated as a mixed integer linear programme for which two relax-and-fix heuristic solution methods are proposed. The first one decomposes the problem based on time periods, while the second decomposes it based on orders. The performances of these heuristics are compared with that of a state-of-the-art commercial solver. Our results show that the time-based relax-and-fix heuristic outperforms the order-based relax-and-fix heuristic, and the solver solution as it yields better integrality gaps for much less CPU effort.     

The Digital Tent Map: Performance Analysis and Optimized Design as a Low-Complexity Source of Pseudorandom Bits

In this paper, the discretized Tent map is analyzed as a source of pseudorandom bits. To evaluate the performance of the proposed pseudorandom bit generators (PRBGs), different issues were considered, such as the period length, the statistical characteristics of the generated bit sequences, and the hardware complexity required in digital circuit implementations. The results show that, under proper design conditions, the Tent-map-based PRBGs represent a suitable alternative to other traditional low-complexity PRBGs such as the linear feedback shift registers.     

Methods for the physical and chemical characterisation of surfaces of titanium implants

At present, one is still searching for physical and chemical methods which are suitable for the characterisation of biocompatibility of implant surfaces. In this paper, we analysed differently structured titanium surfaces (the roughness average of the various structures differs by four orders of magnitude) with a number of electrochemical and physical methods such as electrochemical impedance spectroscopy, chronoamperometry, linear sweep voltammetry, surface profiling and scanning electron microscopy. The aim of the work is to compare the specific methods regarding their significance, and to correlate the results. Beside the extraction of physical and electrochemical parameters which are typical for the above-mentioned methods, the possibility of the determination of the fractal dimension of the surface structures is also examined. Cell biological examinations concerning the mechanism of cell adhesion were used to verify the ability of the parameters measured by the referred methods to describe the biocompatibility of the analysed surfaces.     

Analysis of (k 0 ,k 1 ) clock-controlled sequences

Cryptographic sequence generators are discussed in which a linear feedback shift register (LFSR) is clock controlled in a pseudorandom manner by another register. A model of clock-controlled sequences is proposed. The necessary and sufficient condition guaranteeing the maximal linear complexity and the maximal period of such sequences is given. Two kinds of improved models having better statistical properties are given. In order to study the security of this model, three types of algebraic attacking algorithms are proposed. If the length of the second LFSR in such a model is large, the model can resist our algebraic attacks.     

Pseudorandom Number Assignment in Quadratic Response Surface Designs

This paper examines three general strategies for the assignment of pseudorandom number streams to simulation experiments in quadratic response surface designs. Comparisons of these variance-reduction schemes are presented for four design criteria that collectively address the two goals of response surface methodology: prediction and optimization.     

Improved-fidelity error diffusion through blending with pseudorandom encoding

Error diffusion (ED) and pseudorandom encoding (PRE) methods of designing Fourier transform holograms are compared in terms of their properties and the optical performance of the resulting far-field diffraction patterns. Although both methods produce a diffuse noise pattern due to the error between the desired fully complex pattern and the encoded modulation, the PRE errors reconstruct uniformly over the nonredundant band-width of the discrete-pixel spatial light modulator, while the ED errors reconstruct outside the window of the designed diffraction pattern. Combining the two encoding methods produces higher-fidelity diffraction patterns than either method produces individually. For some designs the fidelity of the ED-PRE algorithm is even higher over the entire nonredundant bandwidth than for the previously reported [J. Opt. Soc. Am. A 16, 2425 (1999)] minimum-distance-PRE algorithm.     

An effectively modified direct Trefftz method for 2D potential problems considering the domain''s characteristic length

The present paper proposes a new modification of the direct Trefftz method by taking the characteristic length of the problem domain into account, whose inclusion into the T-complete bases ensures that the modified direct Trefftz method is stable, because the condition number of the resulting linear equations system can be greatly reduced over 12 orders. Then, the boundary element method and the Fourier series method are used to derive the linear equations system to determine the unknown coefficients, which can be employed to solve the mixed-boundary value 2D potential problems. We use numerical examples to explore why the conventional direct Trefftz method is unstable and the modified one is stable and workable. The direct Trefftz method is applicable to the case where the problem size is smaller or with its maximum length near to 1 and using suitable elements number or bases number. Under this condition, the modified method still has a great advantage to improve the accuracy up to two or three orders.     

Comparison and evaluation of lot-to-order matching policies for a semiconductor assembly and test facility

This paper is motivated by the problem of assigning semiconductor fabrication wafer lots to customer orders of various sizes. The goal of this research is to develop a method for deciding, on a given day, which orders to fill and the assignment of available lots to orders. This problem can be formulated as an integer program with a non-linear objective and non-linear constraints. Because of the complexity of this formulation, the problem is decomposed into two integer linear programs and solved in sequence by heuristic methods. In this paper, heuristic solutions are selected for the two subproblems and the performances of these heuristics are analysed in an experimental design using a representative data set. Based on this analysis, it is shown that the greedy heuristics selected perform significantly better than current practice. Finally, future research is discussed.     

爆炸冲击波超压加载伪随机网壳的分布规律研究

采用缩比模型爆炸试验与数值仿真相结合的方法,开展了爆炸冲击波超压加载伪随机网壳的分布规律研究。首先,选取具有代表性的某伪随机140面体网壳结构,开展了缩比模型爆炸试验,获得了表面特征测点的冲击波超压数据;之后,对比分析了试验与仿真结果的误差及原因,以试验数据为基础,建立了爆炸冲击波与某伪随机140面体网壳结构相互作用的数值仿真模型,并对空中爆炸和地面爆炸的3种不同距离共6种工况下,网壳结构的特征表面超压作用过程进行了计算和分析,拓展了试验结果;最后,对伪随机网壳表面冲击波超压分布规律进行了研究,并提出了增强网壳结构安全性的防护措施,为伪随机网壳结构抗冲击安全设计提供了参考。结果表明:与传统对称网壳结构相比,伪随机网壳在超压峰值分布规律和作用机制等方面都更为复杂,受到结构伪随机特性的影响,在相似位置表面,超压峰值也有明显差异;网壳迎爆面底部和中部超压峰值与其他部位相比,一般较高;在网壳外一定距离构筑防爆墙和加固网壳中部及底部节点的方法,可提升伪随机网壳结构的抗冲击安全性。     

Statistical treatment of photon/electron counting: extending the linear dynamic range from the dark count rate to saturation

An experimentally simple photon counting method is demonstrated providing 7 orders of magnitude in linear dynamic range (LDR) for a single photomultiplier tube (PMT) detector. In conventional photon/electron counting methods, the linear range is dictated by the agreement between the binomially distributed measurement of counted events and the underlying Poisson distribution of photons/electrons. By explicitly considering the log-normal probability distribution in voltage transients as a function of the number of photons present and the Poisson distribution of photons, observed counts for a given threshold can be related to the mean number of photons well beyond the conventional limit. Analytical expressions are derived relating counts and photons that extend the linear range to an average of ～11 photons arriving simultaneously with a single threshold. These expressions can be evaluated numerically for multiple thresholds extending the linear range to the saturation point of the PMT. The peak voltage distributions are experimentally shown to follow a Poisson weighted sum of log-normal distributions that can all be derived from the single photoelectron voltage peak-height distribution. The LDR that results from this method is compared to conventional single photon counting (SPC) and to signal averaging by analog to digital conversion (ADC).     

Modelling and performance evaluation of explosive storage policies in internet fulfilment warehouses

Internet Fulfilment Warehouses (IFWs) are designed to exclusively process online retail orders. An observational study reveals that IFW operating and design attributes are significantly different from traditional warehouses in their storage and fulfilment policies. Specifically, we identify six IFW differentiators: explosive storage, very large number of beehive storage locations, bins with commingled SKUs, immediate fulfilment, short picking routes with single unit picks and high transactions with total digital control. Explosive storage of incoming bulk allows for faster fulfilment of customer orders often within a few hours. A new IFW control model is developed. This describes the associated receiving and fulfilment flows. Two decision algorithms for generating (i) a stocking list and (ii) an order picking list are presented. A simulation model was built to evaluate the fulfilment performance of the explosive policy. Experimental runs on a problem with 400 SKUs, 3240 bins and 22,000 customer orders over nine days are reported. Results show that increasing levels of explosion reduce the linear fulfilment time by as much as 16%, confirming the IFW storage policy is advantageous. The results also show that fulfilment time behaviour is convex as a function of the maximum number of stops allowed by the picking algorithm parameter.     

Stream cipher based on pseudorandom number generation with optical affine transformation

We propose a new, to our knowledge, stream cipher technique for two-dimensional (2-D) image data that can be implemented by iterative optical transformation. The stream cipher uses a pseudorandom number generator (PRNG) to generate a pseudorandom bit sequence. The proposed method for the PRNG is composed of the iterative operation of 2-D affine transformation achieved by optical components and by modulo-n addition of the transformed images. We expect efficient execution of the method by optical parallel processing. We verify the performance of the proposed method in terms of security strength and clarify problems on optical implementation by the optical fractal synthesizer.     

Comparison of Spectral and Wavelet Estimators of Transfer Function for Linear Systems

We compare spectral and wavelet estimators of the response amplitude operator (RAO) of a linear system, with various input signals and added noise scenarios. The comparison is based on a model of a heaving buoy wave energy device (HBWED), which oscillates vertically as a single mode of vibration linear system. HBWEDs and other single degree of freedom wave energy devices such as oscillating wave surge convertors (OWSC) are currently deployed in the ocean, making such devices important systems to both model and analyse in some detail. The results of the comparison relate to any linear system. It was found that the wavelet estimator of the RAO offers no advantage over the spectral estimators if both input and response time series data are noise free and long time series are available. If there is noise on only the response time series, only the wavelet estimator or the spectral estimator that uses the cross-spectrum of the input and response signals in the numerator should be used. For the case of noise on only the input time series, only the spectral estimator that uses the cross-spectrum in the denominator gives a sensible estimate of the RAO. If both the input and response signals are corrupted with noise, a modification to both the input and response spectrum estimates can provide a good estimator of the RAO. A combination of wavelet and spectral methods is introduced as an alternative RAO estimator. The conclusions apply for autoregressive emulators of sea surface elevation, impulse, and pseudorandom binary sequences (PRBS) inputs. However, a wavelet estimator is needed in the special case of a chirp input where the signal has a continuously varying frequency.