On single processor scheduling problems with learning dependent on the number of processed jobs

The importance of the role that learning plays in manufacturing, industry and computer systems is undeniable as well as the profit that can be increased if this phenomenon is taken into consideration for short- and long-term optimization. In this paper, we focus on scheduling jobs on a single processor, where its effectiveness can increase with the number of processed jobs, to minimize one of the following objectives: the maximum completion time with the release dates, the maximum lateness and the number of late jobs. It is proved that these well known polynomially solvable problems become at least NP-hard with the considered learning models. To solve them we provide some elimination procedures that are used to construct a branch and bound algorithm. Furthermore, we propose some fast heuristics for the problem of minimizing the number of late jobs with the general model of the learning effect.     

Outsourcing and scheduling for two-machine ordered flow shop scheduling problems

This paper considers a two-machine ordered flow shop problem, where each job is processed through the in-house system or outsourced to a subcontractor. For in-house jobs, a schedule is constructed and its performance is measured by the makespan. Jobs processed by subcontractors require paying an outsourcing cost. The objective is to minimize the sum of the makespan and the total outsourcing cost. Since this problem is NP-hard, we present an approximation algorithm. Furthermore, we consider three special cases in which job j has a processing time requirement p_j, and machine i a characteristic q_i. The first case assumes the time job j occupies machine i is equal to the processing requirement divided by a characteristic value of machine i, that is, p_j/q_i. The second (third) case assumes that the time job j occupies machine i is equal to the maximum (minimum) of its processing requirement and a characteristic value of the machine, that is, max{p_j, q_i} (min{p_j, q_i}). We show that the first and the second cases are NP-hard and the third case is polynomially solvable.     

Computation of the random arrival rule for bankruptcy problems

Bankruptcy problems are a fundamental class of fair division problems in microeconomics. Among the various solution concepts proposed for the problem, the random arrival rule is one of the most prominent. In this paper, we conduct a computational analysis of the rule. It is shown that the allocation returned by the rule is #P-complete to compute. The general complexity result is complemented by a pseudo-polynomial-time dynamic programming algorithm for the random arrival rule.     

An Infeasible Mizuno–Todd–Ye Type Algorithm for Convex Quadratic Programming with Polynomial Complexity

Infeasible interior point methods have been very popular and effective. In this paper, we propose a predictor–corrector infeasible interior point algorithm for convex quadratic programming, and we prove its convergence and analyze its complexity. The algorithm has the polynomial numerical complexity with O(nL)-iteration.     

Using the Renormalization Group to Classify Boolean Functions

This paper argues that the renormalization group technique used to characterize phase transitions in condensed matter systems can be used to classify Boolean functions. A renormalization group transformation is presented that maps an arbitrary Boolean function of N Boolean variables to one of N−1 variables. Applying this transformation to a generic Boolean function (one whose output for each input is chosen randomly and independently to be one or zero with equal probability) yields another generic Boolean function. Moreover, applying the transformation to some other functions known to be non-generic, such as Boolean functions that can be written as polynomials of degree ξ with ξ ≪ N and functions that depend on composite variables such as the arithmetic sum of the inputs, yields non-generic results. One can thus define different phases of Boolean functions as classes of functions with different types of behavior upon repeated application of the renormalization transformation. Possible relationships between different phases of Boolean functions and computational complexity classes studied in computer science are discussed.     

Interpreting non-random signatures in biomedical signals with Lempel-Ziv complexity

Lempel-Ziv complexity (LZ) [J. Ziv, A. Lempel, On the complexity of finite sequences, IEEE Trans. Inform. Theory 22 (1976) 75-81] and its variants have been used widely to identify non-random patterns in biomedical signals obtained across distinct physiological states. Non-random signatures of the complexity measure can occur under nonlinear deterministic as well as non-deterministic settings. Surrogate data testing have also been encouraged in the past in conjunction with complexity estimates to make a finer distinction between various classes of processes. In this brief letter, we make two important observations (1) Non-Gaussian noise at the dynamical level can elude existing surrogate algorithms namely: Phase-randomized surrogates (FT) amplitude-adjusted Fourier transform (AAFT) and iterated amplitude-adjusted Fourier transform (IAAFT). Thus any inference nonlinear determinism as an explanation for the non-randomness is incomplete (2) Decrease in complexity can be observed even across two linear processes with identical auto-correlation functions. The results are illustrated with a second-order auto-regressive process with Gaussian and non-Gaussian innovations. AR(2) processes have been used widely to model several physiological phenomena, hence their choice. The results presented encourage cautious interpretation of non-random signatures in experimental signals using complexity measures.     

TD-ERCS离散混沌伪随机序列的复杂性分析

采用相空间直接观察法和行为复杂性算法,系统地分析了新型TD-ERCS离散混沌系统产生的伪随机序列的复杂性,得出了其复杂性变化规律.在Kolmogorov复杂性基础上,应用经典的Limpel-Ziv算法,ApEn算法和PE算法,从一维时间序列到多维相空间重构两方面计算了TD-ERCS离散混沌伪随机序列的复杂度大小.计算结果表明,TD-ERCS系统的行为复杂性高,而且该系统的复杂性大小随系统参数改变的变化范围小,是一个复杂性非常稳定的全域性离散混沌系统,其产生的混沌伪随机序列适合于信息加密或扩频通信. 关键词： 混沌 混沌伪随机序列 TD-ERCS系统 复杂度     

Infinite family of transmission irregular trees of even order

Distance between two vertices is the number of edges in a shortest path connecting them in a connected graph $G$. The transmission of a vertex $v$ is the sum of distances from $v$ to all the other vertices of $G$. If transmissions of all vertices are mutually distinct, then $G$ is a transmission irregular graph. It is known that almost no graphs are transmission irregular. Infinite families of transmission irregular trees of odd order were presented in Alizadeh and Klav?ar (2018). The following problem was posed in Alizadeh and Klav?ar (2018): do there exist infinite families of transmission irregular trees of even order? In this article, such a family is constructed.     

Consecutive Supramolecular Polymerization of a Rylene-Based Twistacene

The synthesis and self-assembling features of twistacene 1 are reported. The supramolecular polymerization of 1 displays a consecutive pathway to afford slipped ( AggI ) and rotationally displaced ( AggII ) aggregates conditioned by the formation of intramolecularly H-bonded pseudocycles. In methylcyclohexane, both AggI and AggII are highly stable and the interconversion of the kinetically controlled AggI into the thermodynamically controlled AggII takes several weeks to occur. The utilization of toluene as solvent changes the energetic level for both aggregates and favors a faster conversion of AggI into AggII within a period of minutes. This conversion can be accelerated by the addition of seeds. Furthermore, concentration dependent kinetic studies demonstrate the consecutive character of the supramolecular polymerization of 1 .