Deterministic Sequences Research Articles

An approximate dynamic programming approach for the vehicle routing problem with stochastic demands

This paper examines approximate dynamic programming algorithms for the single-vehicle routing problem with stochastic demands from a dynamic or reoptimization perspective. The methods extend the rollout algorithm by implementing different base sequences (i.e. a priori solutions), look-ahead policies, and pruning schemes. The paper also considers computing the cost-to-go with Monte Carlo simulation in addition to direct approaches. The best new method found is a two-step lookahead rollout started with a stochastic base sequence. The routing cost is about 4.8% less than the one-step rollout algorithm started with a deterministic sequence. Results also show that Monte Carlo cost-to-go estimation reduces computation time 65% in large instances with little or no loss in solution quality. Moreover, the paper compares results to the perfect information case from solving exact a posteriori solutions for sampled vehicle routing problems. The confidence interval for the overall mean difference is (3.56%, 4.11%).

Growth and environmental quality: Testing the double convergence hypothesis

This paper discusses the double convergence hypothesis (DCH) that the uncritical analysis of the so-called environmental Kuznets curve (EKC) implicitly implies. According to the EKC, empirical evidence would support the hypothesis that economic growth, through a deterministic sequence of phases, would produce cross-country convergence in per capita output and, as a by-product, convergence in (the demand for) environmental quality. However, factual analysis seems to reject the general hypothesis of convergence in per capita output, limiting the validity of such an assessment to the case of homogeneous groups of countries. This is why, to test the DCH, the paper focuses on the original group of OECD countries for which the economic convergence turned out to be true. This allows us to verify whether “green” β and σ convergence follows as a consequence of economic convergence. The paper also tests for a more equitable distribution of protection policies among countries. Unlike other studies, which do not make the DCH explicit and have focused on pollutant emissions, this research explicitly tests for the double convergence using, as a proxy for the demand for environmental quality, the territory set aside for protected areas. The results confirm that, for the selected homogenous group of countries, growth has accompanied the demand for environmental quality. This happens both in terms of conditional and stochastic convergence.

Logic Built-In Self-Test for Core-Based Designs on System-on-a-Chip

A system-on-a-chip (SoC) built with embedded intellectual property (IP) cores offers attractive methodology design reuse, reconfigurability, and customizability. However, the integration of the design-for-testability (DfT) structures of the IP cores in these complex SoCs presents daunting challenges to designers and ultimately affects the time-to-market goals. In this paper, we introduce a design methodology to reduce the time to market by taking core test data from the design environment and automatically generating DfT structures that can easily be integrated into the SoC. A novel automated synthesis methodology to generate an SoC built-in self-test (BIST) to test the IP and custom logic cores is proposed. The proposed technique, i.e., NonExclusive Xor Test of 2D linear feedback shift register (NEXT 2D LFSR), is modeled after the principle of configurable 2D LFSR design, which generates a deterministic sequence of test vectors for random-vector-resistant faults and then random test vectors for random-vector-detectable faults. The basis of this method is to explore the design solution space for optimal 2D LFSR while embedding the test patterns by nonexclusively considering xor gates as the conventional LFSR does but including a simple logic solution for minimal hardware optimization. Moreover, the proposed approach is capable of optimizing the 2D LFSRs with consideration of the don't-care bits in the incompletely specified test patterns.

Quasi-random sampling for signal recovery

The problem of reconstruction of band-limited signals from nonuniformly sampled and and noisy observations is studied. It is proposed to sample a signal at quasi-random points that form a deterministic sequence, with properties resembling a random variable, being uniformly distributed. Such quasi-random points can be easily and efficiently generated. The reconstruction method based on the modified Whittaker–Shannon cardinal expansion is proposed and its asymptotical properties are examined. In particular, the sufficient conditions for the convergence of the mean integrated squared error are found. The key difference between the proposed reconstruction algorithm and the classical Whittaker–Shannon scheme is in treating the sampling rate and the reconstruction rate differently. This distinction is necessary to ensure consistency of the reconstruction algorithm in the presence of noise.

Constrained stability and instability of polynomial difference equations with state-dependent noise

We examine the stability and instability of solutions of a polynomial difference equation with state-dependent Gaussian perturbations, and describe a phenomenon that can only occur in discrete time. For a particular set of initial values, we find that solutions approach equilibrium asymptotically in a highly regulated fashion: monotonically and bounded above by a deterministic sequence. We observe this behaviour with a probability that can be made arbitrarily high by choosing the initial value sufficiently small.<br> &nbsp;&nbsp;&nbsp;However, for any fixed initial value, the probability of instability is nonzero, and in fact we can show that as the magnitude of the initial value increases, the probability of instability approaches $1$.

Discrete asymptotic deterministic randomness for the generation of pseudorandom bits

The deterministic randomness not only can become a dominant approach in exploring the relationship between chaos and randomness, but also can be associated with some famous number theoretical concepts and open problems in number theory. Compared with chaotic sequences, asymptotic deterministic randomness sequences have the characteristic of multi-value correspondence, which makes those sequences unpredictable in short steps. In this Letter, we will propose the definition of the discrete asymptotic deterministic randomness, and then analyze the dynamical characteristics such as maximum-period and multi-value correspondence. Referring to the NIST800-22 statistical test suite, we will present and discuss two examples of PRBGs based on DADR, from the point of view of FPGA design and randomness quality.

A 440-nA True Random Number Generator for Passive RFID Tags

This paper describes a 440-nA true random number (RN) generator for passive ultrahigh frequency radio frequency identification (RFID) tags that operate in the 900-MHz band. Since passive tags derive their power supply through the rectification of the incoming RF signal, limited power is available, and hence, a typical total IC current budget is less than a few microamperes. An RN is generated by a passive RFID tag on the fly, and it is used by the reader to identify the tag uniquely and communicate with it in a field consisting of many tags. The RN in this paper consists of a 16-bit-long deterministic binary sequence to which a 3-bit true RN is added. Without the 3-bit true RN, if two tags happen to have the same deterministic 16-bit sequence, a collision occurs, and there is no way to resolve it. In this paper, we propose a power efficient way of generating the 3-bit true RN using the jitter-sampled carrier technique. This technique subsamples the already present 900-MHz RF carrier using a jittered (noisy) clock. The design challenges of sampling a high-frequency signal that swings above and below ground are described. In addition, the generation of a jitter of adequate magnitude with adequate high-frequency spectral content to ensure that the number is truly random is also described. Measurement results on a silicon prototype implemented in a 130-nm analog CMOS process are provided.

Implicit sequence learning in a search task

This study investigated the effects of selection demands on implicit sequence learning. Participants in a search condition looked for a target among seven distractors and responded on the target identity. The responses followed a deterministic sequence, and sequence learning was compared to that found in two control conditions in which the targets were presented alone, either at a central location or over a series of unpredictable locations. Sequence learning was obtained in all conditions, and it was equivalent for the two variable location conditions, regardless of the perceptual demands. Larger effects of learning were observed in the central location, both on the indirect measures and on the measures taken from a cued-generation task. The expression of learning decreased selectively in this condition when the sequence validity was reduced over a test block. These results are consistent with the claims that implicit and explicit learning are mixed in this central condition and that implicit learning is not affected by selection difficulty.

What is the impact of the explicit knowledge of sequence regularities on both deterministic and probabilistic serial reaction time task performance?

The aim of this study was to explore the role of prior explicit sequence knowledge by comparing its influence on serial reaction time (SRT) performance with either a deterministic or a probabilistic sequence. The results confirm that, with a deterministic sequence, preliminary explicit learning improves SRT performance. On the other hand, with a probabilistic sequence, the results show no advantage for SRT performance in explicit-learning conditions. In addition, by using the process dissociation procedure (Jacoby, 1991), we show that performance on a subsequent generation task was more sustained by controlled processes for participants in the explicit-learning conditions than for those in the incidental condition. On the whole, these results, showing that the influence of explicit knowledge can be suppressed in certain specific conditions, are consistent with the intervention of both implicit and explicit mechanisms in SRT tasks, and the results also show that their relative influence can be modulated by the particular demands of the task.

Symbol Error Rate Performance of QS-CDMA over Frequency Selective Time Non-Selective Multipath Generalized Gamma Fading Channels

Quasisynchronous (QS) Code Division Multiple Access (CDMA) is currently being considered for a variety of wireless applications and services because QS-CDMA enables information transmission with a good quality of service. In this paper, for M-ary signaling, the Symbol Error Rate (SER) performance of QS-CDMA communication system with a maximal ratio combiner (MRC) over frequency-selective, time-nonselective multipath Generalized Gamma (GG3) fading channels is derived not only for any deterministic spreading sequences but also for any chip-limited chip waveforms, and it is investigated for Rectangular, Half-Sine, and Raised-Cosine chip waveforms by means of numerical and simulation results. Numerical and simulation results show that the performance of QS-CDMA is as good as or slightly better than synchronous CDMA (S-CDMA) when the maximum quasisynchronous delays do not need to be less than some specific values depending on the path power scattering. With this flexibility of quasisynchronous delays, both the transmitter and receiver complexities are reduced as quasisynchronous communication is a challenging task for researchers. Additionally, since not only the spreading sequences but also the partial autocorrelation functions of the chip waveform are influential on the performance of multipath QS-CDMA, a measure, Partial Power Ratio (PPR) is defined based on these partial autocorrelation functions in order to select or design a chip waveform for quasisynchronous communication. Furthermore, results show that QS-CDMA using the chip waveform whose PPR is greater has better performance.

The Taming of the Shrew: Tailoring Freak Wave Sequences for Seakeeping Tests

If you want to build a ship, don't drum up people together to collect woodand don't assign them tasks and work but rather teach them to long for the endless immensity of the sea.___Antoine de Saint-Exupery (1900–1944)___The basic law of the seaway is the apparent lack of any law.___Lord Rayleigh___Based on the wave focusing technique for the generation of task-related wave packets, a new technique is proposed for the synthesization of tailored design wave sequences in extreme seas. The physical wave field is fitted to predetermined global and local target characteristics designed in terms of significant wave height, peak period, as well as wave height, crest height, and period of individual waves. The generation procedure is based on two steps: First, a linear approximation of the desired wave train is computed by a sequential quadratic programming method that optimizes an initially random phase spectrum for a given variance spectrum. The wave board motion derived from this initial guess serves as a starting point for directly fitting the physical wave train to the target parameters. The subplex method is applied to improve systematically a certain time frame of the wave board motion, which is responsible for the evolution of the response-related design wave sequence. The discrete wavelet transform is introduced to reduce significantly the number of free variables to be considered in the fitting process. Wavelet analysis allows the efficient localization of the relevant information on the electrical control signal of the wave maker in time and frequency domain. As the presented technique permits the deterministic generation of design rogue wave sequences in extreme seas, it is well suited for investigating the mechanism of arbitrary wave-structure interactions, including capsizing, slamming, and green water as well as other survivability design aspects. Even worst case wave sequences, such as the Draupner New Year wave, can be modeled in the wave tank to analyze the evolution of these events and to evaluate the response of offshore structures under abnormal conditions. This procedure is illustrated by investigations of an offshore lift operation, of the behavior of a semisubmersible and an FPSO in tailored freak waves as well as the analysis of ship capsizing in deterministic wave sequences at selected target positions.

Does implicit learning in non-demented Parkinson’s disease depend on the level of cognitive functioning?

We investigated the influence of the level of cognitive functioning on sequence-specific learning in Parkinson’s disease (PD). This was done by examining the relationship between the scales for outcomes in Parkinson’s disease-cognition [SCOPA-COG, Marinus, J., Visser, M., Verwey, N. A., Verhey, F. R. J., Middelkoop, H. A. M.,Stiggelbout, A., et al. (2003). Assessment of cognition in Parkinson’s disease. Neurology, 61, 1222–1228] and the serial reaction time (SRT) task [Nissen, M. J., & Bullemer, P. T. (1987). Attentional requirements for learning: Evidence from performance measures. Cognitive Psychology, 19, 1–32] in a homogeneous sample, consisting of 25 PD patients diagnosed in Stage 3 of the Hoehn and Yahr [Hoehn, M. M., & Yahr, M. D. (1967). Parkinsonism: onset, progression, and mortality. Neurology, 17, 427–442] scale. Six patients in the low scoring cognitive group, 11 patients in the average scoring and eight patients in the high scoring group, conducted a SRT task with a deterministic sequence. Sequence-specific learning was assessed by inserting a random block to determine whether the acquisition of sequence movements differed between groups. Our results indicate an association between cognitive functioning in PD patients and sequence learning. These findings emphasize the use of assessing cognition in addition to the well-known motor aspects in PD.

Specifying and Executing Reactive Scenarios With Lutin

This paper presents the language Lutin and its operational semantics. This language specifically targets the domain of reactive systems, where an execution is a (virtually) infinite sequence of input/output reactions. More precisely, it is dedicated to the description and the execution of constrained random scenarios. Its first use is for test sequence specification and generation. It can also be useful for early simulation of huge systems, where Lutin programs can be used to describe and simulate modules that are not yet fully developed.The programming style mixes relational and imperative features. Basic statements are input/output relations, expressing constraints on a single reaction. Those constraints are then combined to describe non deterministic sequences of reactions. The language constructs are inspired by regular expressions, and process algebra (sequence, choice, loop, concurrency). Moreover, the set of statements can be enriched with user defined operators. A notion of stochastic directive is also provided, in order to finely influence the selection of a particular class of scenarios.

Motion Planning for Haptic Guidance

Haptic devices allow a user to feel either reaction forces from virtual interactions or reaction forces reflected from a remote site during a bilateral teleoperation task. Also, guiding forces can be exerted to train the user in the performance of a virtual task or to assist him/her to safely teleoperate a robot. The generation of guiding forces relies on the existence of a motion plan that provides the direction to be followed to reach the goal from any free configuration of the configuration space ( ${\mathcal C}$ -space). This paper proposes a method to obtain such a plan that interleaves a sampling-based exploration of ${\mathcal C}$ -space with an efficient computation of harmonic functions. A deterministic sampling sequence (with a bias based on harmonic function values) is used to obtain a hierarchical cell decomposition model of ${\mathcal C}$ -space. A harmonic function is iteratively computed over the partially known model using a novel approach. The harmonic function is the navigation function used as motion plan. The approach has been implemented in a planner (called the Kautham planner) that, given an initial and a goal configuration, provides: (a) a channel of cells connecting the cell that contains the initial configuration with the cell that contains the goal configuration; (b) two harmonic functions over the whole ${\mathcal C}$ -space, one that guides motions towards the channel and another that guides motions within the channel towards the goal; and (c) a path computed over a roadmap built with the free samples of the channel. The harmonic functions and the solution path are then used to generate the guiding forces for the haptic device. The planning approach is illustrated with examples on 2D and 3D workspaces.

Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays

In this paper we explore the potential of one-dimensional and two-dimensional deterministic aperiodic plasmonic arrays for the design of electromagnetic coupling and plasmon-enhanced, sub-wavelength optical fields on chip-scale devices. In particular, we investigate the spectral, far-field and near-field optical properties of metal nanoparticle arrays generated according to simple deterministic sequences characterized by fractal Fourier spectra. Additionally, we will consider the case of flat Fourier-transform sequences, which reproduce the behavior of purely random systems to an arbitrary degree of accuracy. Based on the coupled dipole approach (CDA) and finite difference time domain (FDTD) simulations, we study the radiative (long-range) and quasi-static (short-range) electromagnetic coupling in deterministic aperiodic plasmon arrays of metal nanoparticles. In addition, we investigate the local field enhancement and the enhancement scaling in periodic and aperiodic arrays with increasing degree of complexity. We believe that the accurate control of electromagnetic coupling and sub-wavelength field enhancement in deterministic aperiodic environments will enable novel nanodevice applications in areas such as field-enhanced nanosensors, engineered SERS substrates and optical nano-antenna arrays.

Application of low-discrepancy sampling method in structural reliability analysis

This study introduces and investigates various low-discrepancy sequences and then develops a new procedure in which the low-discrepancy sequences are combined with the importance sampling technique to estimate the failure probability. This proposed low-discrepancy sampling method is based on the concept that the deterministic low-discrepancy sequences of points can significantly improve the accuracy of the classical Monte Carlo (MC) method over purely random sampling. Different benchmark examples verify that the proposed method is more accurate with the same number of samples and has a faster rate of convergence in order to achieve a given accuracy when compared with the MC method. Therefore, the low-discrepancy sampling method shows great potential for improving the accuracy and efficiency of the MC-based simulation method for structural reliability analysis.

Reliability–redundancy optimization by means of a chaotic differential evolution approach

The reliability design is related to the performance analysis of many engineering systems. The reliability–redundancy optimization problems involve selection of components with multiple choices and redundancy levels that produce maximum benefits, can be subject to the cost, weight, and volume constraints. Classical mathematical methods have failed in handling nonconvexities and nonsmoothness in optimization problems. As an alternative to the classical optimization approaches, the meta-heuristics have been given much attention by many researchers due to their ability to find an almost global optimal solution in reliability–redundancy optimization problems. Evolutionary algorithms (EAs) – paradigms of evolutionary computation field – are stochastic and robust meta-heuristics useful to solve reliability–redundancy optimization problems. EAs such as genetic algorithm, evolutionary programming, evolution strategies and differential evolution are being used to find global or near global optimal solution. A differential evolution approach based on chaotic sequences using Lozi’s map for reliability–redundancy optimization problems is proposed in this paper. The proposed method has a fast convergence rate but also maintains the diversity of the population so as to escape from local optima. An application example in reliability–redundancy optimization based on the overspeed protection system of a gas turbine is given to show its usefulness and efficiency. Simulation results show that the application of deterministic chaotic sequences instead of random sequences is a possible strategy to improve the performance of differential evolution.

Nonuniversal behavior for aperiodic interactions within a mean-field approximation

We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following one of two deterministic aperiodic sequences, the Fibonacci or period-doubling one. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponents beta, gamma, and delta . For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.

PROBABILISTIC ASPECTS OF EXTREME EVENTS GENERATED BY PERIODIC AND QUASIPERIODIC DETERMINISTIC DYNAMICS

We consider the distribution of the maximum for finite, deterministic, periodic and quasiperiodic sequences, and contrast the extreme value distributions in these cases with the classical results for iidrv's. A significant feature in the case of deterministic sequences is a multi-step structure for the distribution function. The extreme value distribution for the circle map with an irrational parameter is obtained in closed form with the help of the three-gap theorem for the map Xj+1 = (Xj + a) mod 1 where a ∈ (0,1) is an irrational number.

Deterministic Spreading Sequences for the Reverse Link of DS-CDMA With Noncoherent $M$-ary Orthogonal Modulation: Impact and Optimization

M-ary orthogonal modulation with noncoherent detection is an attractive scheme for the reverse link of direct-sequence code-division multiple access (DS-CDMA). The performance analysis of such DS-CDMA systems with random spreading sequences has been thoroughly studied. However, little satisfactory work has been done for systems with deterministic spreading sequences, regardless of their importance from the viewpoint of multiple-access interference reduction. To fill this void, we consider deterministic spreading sequences in this paper. We first present a detailed error performance analysis for the reverse link of DS-CDMA with -ary orthogonal modulation on both additive white Gaussian noise (AWGN) and multipath Rayleigh-fading channels. Then, we formulate the design of spreading sequences for the DS-CDMA system as a nonlinear discrete optimization problem. Two steps are taken to complete the task of sequence optimization: (1) A large code space is generated by permutating a single binary code matrix and imposing a Kronecker product structure on candidate code matrices, and (2) an evolutionary algorithm is applied to efficiently perform optimization. Numerical examples show that the optimized sequences considerably improve the system performance, especially when the number of users is relatively small or an AWGN channel is considered. In addition, our proposed approach can make a good tradeoff between code performance and search complexity.