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Abstract We propose a new greedy Kaczmarz algorithm for the solution of very large systems of linear equations. In our proposed algorithm, control sequence is determined by a greedy rule, and relaxation parameters are determined adaptively. Convergence of our proposed algorithm is proved. Numerical results show that the proposed algorithm is feasible and has faster convergence rate than the greedy randomized Kaczmarz algorithm. [ABSTRACT FROM AUTHOR]

Abstract In the present paper, we consider the discrete nonlinear Schrödinger equation − Δ u n + v n u n − ω u n = γ g n (u n) + h n , n ∈ Z , where v n , h n are real valued sequences, ω ∈ R , γ = ± 1 , and g n is a function sequence. We study this non-periodic discrete nonlinear Schrödinger equation with infinitely growing potential. Under some suitable conditions, the existence of multiple solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory. It is the first time to investigate the nonhomogeneous discrete nonlinear Schrödinger equation. [ABSTRACT FROM AUTHOR]

Abstract We study the weighted star discrepancy of the Halton sequence. In particular, we show that the Halton sequence achieves strong polynomial tractability for the weighted star discrepancy for product weights (γ j) j ≥ 1 under the mildest condition on the weight sequence known so far for explicitly constructive sequences. The condition requires sup d ≥ 1 max 0̸ ≠ u ⊆ [ d ] ∏ j ∈ u (j γ j) < ∞. The same result holds for Niederreiter sequences and for other types of digital sequences. Our results are true also for the weighted unanchored discrepancy. [ABSTRACT FROM AUTHOR]

Abstract We study a facility location problem motivated by requirements pertaining to the distribution of charging stations for electric vehicles: Place a minimum number of battery charging stations at a subset of nodes of a network, so that battery-powered electric vehicles will be able to move between destinations using " t -spanning" routes, of lengths within a factor t > 1 of the length of a shortest path, while having sufficient charging stations along the way. We give constant-factor approximation algorithms for minimizing the number of charging stations, subject to the t -spanning constraint. We study two versions of the problem, one in which the stations are required to support a single ride (to a single destination), and one in which the stations are to support multiple rides through a sequence of destinations, where the destinations are revealed one at a time. [ABSTRACT FROM AUTHOR]

Abstract This paper presents an efficient method for constructing 2 2 n − 2 cyclic different de Bruijn sequences of order 2 n from the feedback function of a de Bruijn sequence of order n. This is done by extending an n -stage nonlinear feedback shift register (NFSR) to a 2 n -stage NFSR, and then recursively joining all cycles of the 2 n -stage NFSR to form a full cycle. [ABSTRACT FROM AUTHOR]

Abstract On the basis of the order in which twinning occurs, twins are termed primary, secondary, and tertiary. In HCP materials, compression twins (CT) and extension twins (ET) are observed to form alternatively during sequential twinning. However, selections of twinning systems and variants are not yet fully understood. Both ET→CT→ET and CT→ET→CT sequences have been reported in literatures. Here we conduct a systematic and statistical study on the evolutions of twinning sequences and variants during cryogenic rolling of Ti. Both twinning sequences are observed in the same sample. Current statistical results indicate the selections of the twinning sequence and variants are governed by the following criteria: (1) the twinning sequence in an individual grain depends on its initial orientation; (2) the twin variant selection is mainly governed by the Schmid's law, although a few non-Schmid twins are observed along the short axis of the parent grains. These criteria are thought applicable to other HCP metallic materials. Highlights • Both ET→CT→ET and CT→ET→CT twining sequences were found in a LNT-rolled Ti sample. • Grain orientation dominates twinning systems variation in twinning sequence. • Schmid law can primarily explain the twin variant selection in twinning sequence. • The formation of low Schmid factor twin could be attributed to the low twinning free path. [ABSTRACT FROM AUTHOR]

Abstract We adapt and generalize to conservative systems the analysis of a model in Tartar (1989), a sequence of differential equations which in the limit gives an effective equation with a memory effect: our result is obtained under more realistic assumptions concerning the oscillations of the initial data and the coefficients. [ABSTRACT FROM AUTHOR]

The uncertainty sources of the intermittent generation and load demand as well as transmission line unavailability threaten the security of power systems. In this paper, to treat these uncertainties, a new stochastic optimal power flow considering the security constraints is proposed. A scenario generation method is also presented to model the uncertainties of wind generations and load demands considering their correlations. In the proposed model, the uncertainties are coped with through combination of optimal here-and-now and wait-and-see decisions. The effectiveness of the proposed model is shown on the well-known IEEE 24-bus test system. Higher effectiveness of the proposed model compared with four deterministic methods and one other stochastic method to determine procured reserve and ‘after-the-fact’ conditions is numerically illustrated. Additionally, the impact of the number of scenarios on the performance of the proposed model is evaluated by means of a sensitivity analysis. It has also been shown that the scenarios generated considering correlations have more smooth variations and can more effectively capture the uncertain behavior of load. [ABSTRACT FROM AUTHOR]

This paper addresses the challenge to design an effective method for managers to efficiently process hazardous states via recorded historical data by developing a stochastic state sequence model to predict discrete safety states – represent the hazardous level of a project or individual person over a period of time through a Real-Time Location System (RTLS) on construction sites. This involves a mathematical model for state prediction that is suitable for the big-data environment of modern complex construction projects. Firstly, an algorithm is constructed for extracting incidents from pre-analysis of the walk-paths of site workers based on RTLS. The algorithm builds three categories of hazardous region distribution – certain static, uncertain static and uncertain dynamic – and employs a frequency and duration filter to remove noise and misreads. Key regions are identified as either ‘hazardous’, ‘risky’, ‘admonitory’ or ‘safe’ depending on the extent of the hazard zone from the object’s boundary, and state recognition is established by measuring incidents occurring per day and classifies personal and project states into ‘normal’, ‘incident’, ‘near-miss’ and ‘accident’. A Discrete-Time Markov Chain (DTMC) mathematical model, focusing on the interrelationship between states, is developed to predict states on construction sites. Finally, a case study is provided to demonstrate how the system can assist in monitoring discrete states and which indicates it is feasible for the construction industry. [ABSTRACT FROM AUTHOR]

Stochastic computing utilizes compact arithmetic circuits that can potentially lower the implementation cost in silicon area. In addition, stochastic computing provides inherent fault tolerance at the cost of a less efficient signal encoding. Finite impulse response (FIR) filters are key elements in digital signal processing (DSP) due to their linear phase-frequency response. In this article, we consider the problem of implementing FIR filters using the stochastic approach. Novel stochastic FIR filter designs based on multiplexers are proposed and compared to conventional binary designs implemented using Synopsys tools with a 28-nm cell library. Silicon area, power and maximum clock frequency are obtained to evaluate the throughput per area (TPA) and the energy per operation (EPO). For equivalent filtering performance, the stochastic FIR filters underperform in terms of TPA and EPO compared to the conventional binary design, although the stochastic design shows more graceful degradation in performance with a significant reduction in energy consumption. A detailed analysis is performed to evaluate the accuracy of stochastic FIR filters and to determine the required stochastic sequence length. The fault-tolerance of the stochastic design is compared with that of the binary circuit enhanced with triple modular redundancy (TMR). The stochastic designs are more reliable than the conventional binary design and its TMR implementation with unreliable voters, but they are less reliable than the binary TMR implementation when the voters are fault-free. [ABSTRACT FROM AUTHOR]

The iterative learning control is constructed for the discrete-time networked nonlinear systems with random measurement losses and unknown control direction, which have not been studied simultaneously in literature. Differing from the conventional Bernoulli random variable model, the random packet loss is modeled by an arbitrary stochastic sequence with bounded length requirement, which is a new model of realistic packet losses. A novel regulating approach based on truncations is introduced to make the proposed algorithm find the correct control direction adaptively, and then guarantee the almost sure convergence property. Therefore, this paper has three major innovations compared with reported studies, namely, the stochastic sequence model of packet loss, the novel control direction regulation method, and the almost sure convergence property of the proposed algorithm. An illustrative example shows the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: Gravitational search algorithm (GSA) is the one of the newest developed nature-inspired heuristics for optimization problem. It is designed based on the Newtonian gravity and has shown excellent search abilities when applying it to optimization problems. Nevertheless, GSA still has some disadvantages such as slow convergence speed and local optima trapping problems. To alleviate these inherent drawbacks and enhance the performance of GSA, chaos, which is of ergodicity and stochasticity, is incorporated into GSA by two kinds of methods. One method uses chaos to generate chaotic sequences to substitute random sequences, while another one uses chaos to act as a local search approach. The resultant hybrid algorithms, called chaotic gravitation search algorithms (CGSA1 and CGSA2), thus reasonably have advantages of both GSA and chaos. Eight widely used benchmark numerical optimization problems are chosen from the literature as the test suit. Experimental results demonstrate that both CGSA1 and CGSA2 perform better than GSA and other five chaotic particle swarm optimization. [Copyright &y& Elsevier]

Abstract: Truth of sentences in infinity is discussed in the framework of Rudolf Carnapʼs inductive logic, which uses finite state descriptions and an asymptotic limit approach for defining probabilities in infinity. This means that Carnapʼs approach suits well for a semantics which is based on finite observability. However, a proper link between asymptotic probability and truth in infinity is missing from Carnapʼs treatment. A novel notion of truth in infinity is introduced and referred to as the extended truth. The idea is that the truth of the sentence S is extended by a particular sequence of state descriptions (where the larger one contains all of the smaller ones) iff S is true in each state description of the sequence. The corresponding notion of extended probability is introduced. Some important results are proved for extended truth and extended probability. [Copyright &y& Elsevier]

Abstract: A simplification of probability based approaches on safety assessments and predictions of structural members is discussed. The modelling of time-dependent survival probabilities and reliability indexes of particular and single members is defined in a simple and easy perceptible manner using uniformed correlation factors of their conventional sequences. These factors of safety margin processes are analyzed and demonstrated by numerical example. [Copyright &y& Elsevier]

Abstract: This paper presents a 3D parametric fault representation for modeling the displacement field associated with faults in accordance with their geometry. The displacements are modeled in a canonical fault space where the near-field displacement is defined by a small set of parameters consisting of the maximum displacement amplitude and the profiles of attenuation in the surrounding space. The particular geometry and the orientation of the slip of each fault are then taken into account by mapping the actual fault onto its canonical representation. This mapping is obtained with the help of a curvilinear frame aligned both on the fault surface and slip direction. This formulation helps us to include more geological concepts in quantitative subsurface models during 3D structural modeling tasks. Its applicability is demonstrated in the framework of forward modeling and stochastic sequential fault simulations, and the results of our model are compared to observations of natural objects described in the literature. [Copyright &y& Elsevier]

Abstract: A flexible flow shop is a generalized flow shop with multiple machines in some stages. This system is fairly common in flexible manufacturing and in process industry. In most practical environments, scheduling is an ongoing reactive process where the presence of real time information continually forces reconsideration of pre-established schedules. This paper studies a flexible flow shop system considering non-deterministic and dynamic arrival of jobs and also sequence dependent setup times. The problem objective is to determine a schedule that minimizes average tardiness of jobs. Since the problem class is NP-hard, a novel dispatching rule and hybrid genetic algorithm have been developed to solve the problem approximately. Moreover, a discrete event simulation model of the problem is developed for the purpose of experimentation. The most commonly used dispatching rules from the literature and two new methods presented in this paper are incorporated in the simulation model. Simulation experiments have been conducted under various experimental conditions characterized by factors such as shop utilization, setup time level and number of stages. The results indicate that methods proposed in this study are much better than the traditional dispatching rules. [Copyright &y& Elsevier]

Abstract: Social interactions among individuals are commonly observed in both plants and animals, and may be partly genetically determined. The social effect of an individual does not affect the phenotype of the individual itself, but rather the phenotypes of all other individuals sharing the environment. As an alternative to traditional breeding schemes solely focusing on the direct breeding value affecting the phenotype of the individual itself, selection may be focused on total breeding values, including both direct and social effects. The latter may give a substantial increase in the rate of genetic gain of the population, given existence of significant social genetic effects. However, social effects are only identifiable when individuals are allocated in several groups. Previously, it has been suggested that an optimum design should include many small groups consisting of unrelated individuals, e.g., by randomly allocating individuals to each group (RAN). However, we hypothesize that a design with few (three) families per group (3FAM), and where each family is tested repeatedly in three different groups would be more advantageous. Using stochastic simulations, assuming a full-sib data structure typical for aquaculture breeding schemes, we compared the two designs with respect to accuracy of breeding values and their ability to produce accurate estimates of (co)variance components of direct and social effects. The results showed that the 3FAM design was clearly superior with respect to precision of estimated genetic (co)variance components of social effects and had substantially higher accuracy of both social and total breeding values, compared with the RAN design (16 to 105% increase). The advantage was particularly expressed at scenarios with zero or negative genetic correlation between direct and social genetic effects. [Copyright &y& Elsevier]

Abstract: The performance of Bayesian state estimators, such as the extended Kalman filter (EKF), is dependent on the accurate characterisation of the uncertainties in the state dynamics and in the measurements. The parameters of the noise densities associated with these uncertainties are, however, often treated as ‘tuning parameters’ and adjusted in an ad hoc manner while carrying out state and parameter estimation. In this work, two approaches are developed for constructing the maximum likelihood estimates (MLE) of the state and measurement noise covariance matrices from operating input–output data when the states and/or parameters are estimated using the EKF. The unmeasured disturbances affecting the process are either modelled as unstructured noise affecting all the states or as structured noise entering the process predominantly through known, but unmeasured inputs. The first approach is based on direct optimisation of the ML objective function constructed by using the innovation sequence generated from the EKF. The second approach – the extended EM algorithm – is a derivative-free method, that uses the joint likelihood function of the complete data, i.e. states and measurements, to compute the next iterate of the decision variables for the optimisation problem. The efficacy of the proposed approaches is demonstrated on a benchmark continuous fermenter system. The simulation results reveal that both the proposed approaches generate fairly accurate estimates of the noise covariances. Experimental studies on a benchmark laboratory scale heater-mixer setup demonstrate a marked improvement in the predictions of the EKF that uses the covariance estimates obtained from the proposed approaches. [Copyright &y& Elsevier]

Abstract: Patients with schizophrenia make decisions on the basis of less evidence when required to collect information to make an inference, a behavior often called jumping to conclusions. The underlying basis for this behavior remains controversial. We examined the cognitive processes underpinning this finding by testing subjects on the beads task, which has been used previously to elicit jumping to conclusions behavior, and a stochastic sequence learning task, with a similar decision theoretic structure. During the sequence learning task, subjects had to learn a sequence of button presses, while receiving a noisy feedback on their choices. We fit a Bayesian decision making model to the sequence task and compared model parameters to the choice behavior in the beads task in both patients and healthy subjects. We found that patients did show a jumping to conclusions style; and those who picked early in the beads task tended to learn less from positive feedback in the sequence task. This favours the likelihood of patients selecting early because they have a low threshold for making decisions, and that they make choices on the basis of relatively little evidence. [Copyright &y& Elsevier]

Abstract: In this paper we address the problem of recognising embedded activities within continuous spatial sequences obtained from an online video tracking system. Traditionally, continuous data streams such as video tracking data are buffered with a sliding window applied to the buffered data stream for activity detection. We introduce an algorithm based on Smith–Waterman (SW) local alignment from the field of bioinformatics that can locate and accurately quantify embedded activities within a windowed sequence. The modified SW approach utilises dynamic programming with two dimensional spatial data to quantify sequence similarity and is capable of recognising sequences containing gaps and significant amounts of noise. A more efficient SW formulation for online recognition, called Online SW (OSW), is also developed. Through experimentation we show that the OSW algorithm can accurately and robustly recognise manually segmented activity sequences as well as embedded sequences from an online tracking system. To benchmark the classification performance of OSW we compare the approach to dynamic time warping (DTW) and the discrete hidden Markov model (HMM). Results demonstrate that OSW produces higher precision and recall than both DTW and the HMM in an online recognition context. With accurately segmented sequences the SW approach produces results comparable to DTW and superior to the HMM. Finally, we confirm the robust property of the SW approach by evaluating it with sequences containing artificially incorporated noise. [Copyright &y& Elsevier]

Abstract: In order to construct sequences with ideal correlation functions, we propose the concept of generalized difference sets and give their existence conditions. [Copyright &y& Elsevier]

Abstract: An infinite binary sequence is Kolmogorov–Loveland (or KL-) random if there is no computable non-monotonic betting strategy that succeeds on in the sense of having an unbounded gain in the limit while betting successively on bits of . A sequence is KL-stochastic if there is no computable non-monotonic selection rule that selects from an infinite, biased sequence. One of the major open problems in the field of effective randomness is whether Martin-Löf randomness is the same as KL-randomness. Our first main result states that KL-random sequences are close to Martin-Löf random sequences in so far as every KL-random sequence has arbitrarily dense subsequences that are Martin-Löf random. A key lemma in the proof of this result is that for every effective split of a KL-random sequence at least one of the halves is Martin-Löf random. However, this splitting property does not characterize KL-randomness; we construct a sequence that is not even computably random such that every effective split yields two subsequences that are 2-random. Furthermore, we show for any KL-random sequence that is computable in the halting problem that, first, for any effective split of both halves are Martin-Löf random and, second, for any computable, nondecreasing, and unbounded function and almost all , the prefix of of length has prefix-free Kolmogorov complexity at least . Again, the latter property does not characterize KL-randomness, even when restricted to left-r.e. sequences; we construct a left-r.e. sequence that has this property but is not KL-stochastic and, in fact, is not even Mises–Wald–Church stochastic. Turning our attention to KL-stochasticity, we construct a non-empty class of KL-stochastic sequences that are not weakly 1-random; by the usual basis theorems we obtain such sequences that in addition are left-r.e., are low, or are of hyperimmune-free degree. Our second main result asserts that every KL-stochastic sequence has effective dimension 1, or equivalently, a sequence cannot be KL-stochastic if it has infinitely many prefixes that can be compressed by a factor of . This improves on a result by Muchnik, who has shown that were they to exist, such compressible prefixes could not be found effectively. [Copyright &y& Elsevier]

We consider Markov chains {Γn} with transitions of the form Γn=f(Xn,Yn)Γn−1+g(Xn,Yn), where {Xn} and {Yn} are two independent i.i.d. sequences. For two copies {Γn} and {Γn′} of such a chain, it is well known that L(Γn)−L(Γn′)⇒0 provided E[log(f(Xn,Yn))]<0, where ⇒ is weak convergence. In this paper, we consider chains for which also ||Γn−Γn′||→0, where ||·|| is total variation distance. We consider in particular how to obtain sharp quantitative bounds on the total variation distance. Our method involves a new coupling construction, one-shot coupling, which waits until time n before attempting to couple. We apply our results to an auto-regressive Gibbs sampler, and to a Markov chain on the means of Dirichlet processes. [Copyright &y& Elsevier]