Slack Due-Window Assignment Scheduling Problem with Deterioration Effects and a Deteriorating Maintenance Activity

This paper studies the slack due-window assignment scheduling problem with deterioration effects and a deterioration maintenance activity on a single-machine. The machine deteriorates during the machining process, and at a certain moment performs a deterioration maintenance activity, that is, the duration time of the maintenance activity is a linear function of the maintenance starting time. It is needed to make a decision on when to schedule the deteriorating maintenance activity, the optimal common flow allowances and the sequence of jobs to minimize the weighted penalties for the sum of earliness and tardiness, weighted number of early and delayed, and weighted due-window starting time and size. This paper proposes a polynomial time algorithm to solve this problem.

Multiple Error Correction in Redundant Residue Number Systems: A Modified Modular Projection Method with Maximum Likelihood Decoding

Error detection and correction codes based on redundant residue number systems are powerful tools to control and correct arithmetic processing and data transmission errors. Decoding the magnitude and location of a multiple error is a complex computational problem: it requires verifying a huge number of different possible combinations of erroneous residual digit positions in the error localization stage. This paper proposes a modified correcting method based on calculating the approximate weighted characteristics of modular projections. The new procedure for correcting errors and restoring numbers in a weighted number system involves the Chinese Remainder Theorem with fractions. This approach calculates the rank of each modular projection efficiently. The ranks are used to calculate the Hamming distances. The new method speeds up the procedure for correcting multiple errors and restoring numbers in weighted form by an average of 18% compared to state-of-the-art analogs.

Optimally rescheduling jobs with a Last-In-First-Out buffer

This paper considers single-machine scheduling problems in which a given solution, i.e., an ordered set of jobs, has to be improved as much as possible by re-sequencing the jobs. The need for rescheduling may arise in different contexts, e.g., due to changes in the job data or because of the local objective in a stage of a supply chain that is not aligned with the given sequence. A common production setting entails the movement of jobs (or parts) on a conveyor. This is reflected in our model by facilitating the re-sequencing of jobs via a buffer of limited capacity accessible by a LIFO policy. We consider the classical objective functions of total weighted completion time, maximum lateness and (weighted) number of late jobs and study their complexity. For three of these problems, we present strictly polynomial-time dynamic programming algorithms, while for the case of minimizing the weighted number of late jobs NP-hardness is proven and a pseudo-polynomial algorithm is given.

The influence of transport offer on passenger traffic in the railway transport system in a post-socialist country: case study of Poland

The study examines factors influencing the number of rail passengers in Poland. The subjects of observation were 62 cities with poviat rights. The main factors influencing demand are the number of connections and the speed of trains. Therefore, we developed an original indicator – weighted number of connections, which takes into account the number of rail connections and the speed of trains. The article can be divided into two main parts: an assessment of the diversification of transport offer and transport demand in spatial terms, and an evaluation of the relationship between the variables. Poland has a large spatial diversity in terms of public rail transport offer and passenger traffic. There are three levels of city hierarchy according to the passenger number indicator: [1] Warsaw, [2] the largest agglomerations [3] other regional cities. Transport offer was found to have a statistically significant impact on transport demand.

Alexander polynomial and spanning trees

Inspired by the combinatorial constructions in earlier work of the authors that generalized the classical Alexander polynomial to a large class of spatial graphs with a balanced weight on edges, we show that the value of the Alexander polynomial evaluated at [Formula: see text] gives the weighted number of the spanning trees of the graph.

Co-occurrence of thyroid and breast cancer is associated with an increased oncogenic SNP burden

Background Epidemiological evidence suggests that synchronous or metachronous presentation of breast and thyroid cancers exceeds that predicted by chance alone. The following potential explanations have been hypothesized: common environmental or hormonal factors, oncogenic effect of the treatment for the first cancer, closer follow-up of cancer survivors, shared underlying genetic risk factors. While some cases were found to be related to monogenic disorders with autosomal inheritance, the genetic background of most cases of co-occurring breast and thyroid cancer is thought to be polygenic. Methods In this retrospective case-control study we compared the genetic profile of patients with a history of breast cancer (n = 15) to patients with co-occurring breast and thyroid cancer (n = 19) using next generation sequencing of 112 hereditary cancer risk genes. Identified variants were categorized based on their known association with breast cancer and oncogenesis in general. Results No difference between patients with breast and double cancers was observed in clinical and pathological characteristics or the number of neutral SNPs. The unweighted and weighted number of SNPs with an established or potential association with breast cancer was significantly lower in the group with breast cancer only (mean difference − 0.58, BCa 95% CI [− 1.09, − 0.06], p = 0.029, and mean difference − 0.36, BCa 95% CI [− 0.70, − 0.02], p = 0.039, respectively). The difference was also significant when we compared the number of SNPs with potential or known association with any malignancy (mean difference − 1.19, BCa 95% CI [− 2.27, − 0.11], p = 0.032 for unweighted, and mean difference − 0.73, BCa 95% CI [− 1.32, − 0.14], p = 0.017 for weighted scores). Conclusion Our findings are compatible with the hypothesis of genetic predisposition in the co-occurrence of breast and thyroid cancer. Further exploration of the underlying genetic mechanisms may help in the identification of patients with an elevated risk for a second cancer at the diagnosis of the first cancer.

High Precision Multiplier for RNS {2n−1,2n,2n+1}

The Residue Number System (RNS) is a non-weighted number system. Benefiting from its inherent parallelism, RNS has been widely studied and used in Digital Signal Processing (DSP) systems and cryptography. However, since the dynamic range in RNS has been fixed by its moduli set, it is hard to solve the overflow problem, which can be easily solved in Two’s Complement System (TCS) by expanding the bit-width of it. For the multiplication in RNS, the traditional way to deal with overflow is to scale down the inputs so that the result can fall in its dynamic range. However, it leads to a loss of precision. In this paper, we propose a high-precision RNS multiplier for three-moduli set 2n−1,2n,2n+1, which is the most used moduli set. The proposed multiplier effectively improves the calculation precision by adding several compensatory items to the result. The compensatory items can be obtained directly from preceding scalers with little extra effort. To the best of our knowledge, we are the first one to propose a high-precision RNS multiplier for the moduli set 2n−1,2n,2n+1. Simulation results show that the proposed RNS multiplier can get almost the same calculation precision as the TCS multiplier with respect to Mean Square Error (MSE) and Signal-to-Noise Ratio(SNR), which outperforms the basic scaling RNS multiplier about 2.6–3 times with respect to SNR.