The Common Multiples of are multiples that a set of numbers have in common. So, the common multiples of 3 and 4 are 12, 24, 36, 48, ... The Least CommonMultiple (abbreviated L.C.M.) is the smallest multiple the numbers have in common. Thus, the L.C.M. of 3 and 4 is 12. The Least Common Denominator (L.C.D.) is the L.C.M. of the denominators of a set of fractions.
In this paper a numerical method for the computation of the approximate least commonmultiple (ALCM) of a set of several univariate real polynomials is presented. The most important characteristic of the proposed method is that it avoids root finding procedures and computations involving the greatest common divisor (GCD). Conversely, it is based on the algebraic construction of a special matrix which contains key data from the original set of polynomials and leads to the formulation of a linear system which provides the degree and the coefficients of the ALCM using low-rank approximation techniques and numerical optimization tools particularly in the presence of inaccurate data. The numerical stability and complexity of the method is analysed and a comparison with other methods is provided.
linguistic set (HFLS) [ 18 ] was obtained based on combining a linguistic term (LT) set with a HFS so as to satisfy the hesitant linguistic evaluation requirements [ 19 , 20 ] of DMs. After that, an interval-valued HFLS [ 21 ] was presented as an extension form by combining an interval-valued LT set with a HFS. Recently, Ye [ 22 ] proposed the hesitant neutrosophic linguistic number (HNLN) to carry out hesitant decision-making problems with the neutrosophic linguistic number that contains partial determinacy and partial indeterminacy. However, there is no definition or decision-making method for the hesitant sets of LNNs in the existing literature. Additionally, in the hesitant linguistic expressions of DMs, the components between two hesitant sets generally have difference in their length sizes, and thus it is difficult to directly perform measure calculations between hesitant sets. Thus, several researchers have proposed some extension methods to extend the shorter items in the two hesitant sets by adding the minimum values, maximum values, or any values [ 23 , 24 ] to reach their identical length. However, these extension methods depend too much on the subjective preferences and interests of the DMs. To solve this problem, we have already introduced the least commonmultiple cardinality (LCMC) to extend the hesitant fuzzy elements in our previous research works [ 22 , 25 ], which become more objective for the decision-making calculation of HFSs.
Any multiple of 84 must contain the primes of 84, thus any multiple of 84 must contain the primes 2 • 2 • 3 • 7 . Similarly, any multiple of 120 must contain the primes of 120, thus it must contain the primes 2 • 2 • 2 • 3 • 5 . Since the LCM must be common to both list, it must contain both sets of primes. What is the smallest number possible? It must have three 2’s (from the second list), a 3, a 5, and a 7, so it is 2 • 2 • 2 • 3 • 5 • 7 = 840 . Thus the LCM of 84 and 120 is 840. The procedure is the same using three numbers. Suppose we want to find the LCM of 48, 60, and 150. Using the prime factorizations of the three numbers:
Single genetic variants discovered so far have been only weakly associated with melanoma. This study aims to use multiple single nucleotide polymorphisms (SNPs) jointly to obtain a larger genetic effect and to improve the predictive value of a conventional phenotypic model. We analyzed 11 SNPs that were associated with melanoma risk in previous studies and were genotyped in MD Anderson Cancer Center (MDACC) and Harvard Medical School investigations. Participants with ≥15 risk alleles were 5-fold more likely to have melanoma compared to those carrying ≤6. Compared to a model using the most significant single variant rs12913832, the increase in predictive value for the model using a polygenic risk score (PRS) comprised of 11 SNPs was 0.07(95% CI, 0.05-0.07). The overall predictive value of the PRS together with conventional phenotypic factors in the MDACC population was 0.69 (95% CI, 0.64-0.69). PRS significantly improved the risk prediction and reclassification in melanoma as compared with the conventional model. Our study suggests that a polygenic profile can improve the predictive value of an individual gene polymorphism and may be able to significantly improve the predictive value beyond conventional phenotypic melanoma risk factors.
For a significant fraction of the systems in our sample the origin of the emission from the secondary star is not known, and for the vast majority of the PCEBs with multiple emission sources we still do not have any information on the mechanism behind that phenomenon. In fact, so far the origin of both com- ponents has been firmly established only for LTT 560 (Tappert et al. 2011). The present work should therefore encourage more detailed studies, since it is clear that the presence of multiple emission components in PCEBs is not an isolated, but rather a common phenomenon. On the basis of the currently present data we can conclude that the best place to look for it are short-period PCEBs (P orb < 4 h) with a white dwarf primary that is not too
15. Julstrom, B.A., and Hinkemeyer, B.: Starting from scratch: Growing longest common subsequences with evolution In: Proceedings of the 9th In-ternational Conference on Parallel Problem Solving From Nature (PPSN IX), Lecture Notes in Computer Science 4193, Springer Berlin / Hei-delberg, pp. 930-938 (2006.) 16. Needleman, D.B., and Wunsch, C.D.: A general method applicable to the search for similarities in the
Convolutional Neural Networks (CNN) based approaches to recognition tasks have recently been evaluated and com- parisons of different such deep architectures have been made on a common ground . Among various observations made in this recent survey work, it identified aspects of deep and shallow methods that can be successfully shared. A major bottleneck of learning CNNs for a given task is the requirement of a very large number of annotated image samples in order to estimate millions of its parameters. This has prevented applica- tion of CNNs to problems having only limited labelled training samples. However, in a recent work of object recognition , the authors have successfully shown that image representations learned with CNNs on large-scale annotated datasets could be transferred to other visual recognition tasks having only a limited amount of training data. Similar to our present study on document analysis tasks, the authors of  have shown that despite major differences in image characteristics and tasks in the two datasets, the transferred representation could lead to significantly improved results in a classification problem, outperforming the corresponding state of the art classifiers.
Macronutrients, such as lipids are vital components of both neurons and glial cells and their profile (saturated or un- saturated) has been proposed to play a huge role in brain function . Furthermore, the brain has a very high energy demand and as such utilises a large proportion of the dietary intake of carbohydrates in order to function effec- tively. However, it is less obvious how other dietary- derived nutrients or non-nutrient components may impact on the functioning of the brain. Despite this, a large number of dietary intervention studies in humans and animals, in particular those using foods and beverages derived from Vitis vinifera (grape), Camellia sinensis (tea), Theobroma cacao (cocoa) and Vaccinium spp. (blueberry) have dem- onstrated beneficial effects on human vascular function and on improving memory and learning [15, 16, 32, 60, 69, 76, 80]. While such foods and beverages differ greatly in chemical composition, macro- and micronutrient content and caloric load per serving, they have in common that they are amongst the major dietary sources of a group of phytochemicals called flavonoids.
In conclusion, Wigwams, a novel method developed to discover statistically significant genes that potentially share a common regulatory mechanism over multiple conditions, is capable of re-discovering known examples of co-expression, thus validating this method. Extensive research has been completed on metabolic pathways in Arabidopsis, and how these pathways differ in their function under certain conditions. Much experimental work and effort has been devoted to dis- covering how they differ, which has required substantial amounts of time. Wigwams was able to correctly uncover known examples of co-expression and co-regulation in a short space of time. This highlights the potential for uncovering new relationships between genes in stress conditions quickly, with the added bonus that experiments can be directed specifically at a small number of genes in specific conditions, rather than using large-scale reverse genetics approaches, which are time consuming and inefficient, as a means of discovering gene regulatory elements.
Quality Assurance is a very important aspect of a large projects lifespan, especially when de- veloping and troubleshooting software products originating from many institutions, each producing many components using various bug/feature trackers. Acquiring reliable and consistent data sets across multiple institutions provides the only mechanism to produce meaningful metrics and key perform indicators (KPIs) (see Linda Westfall).
After studying the pathway involved, it should that different genes had some common pathway, including neuroactive ligand-receptor interaction, retinol metabolism, drug metabolism, steroid hormone biosynthesis and so forth. The fully list is not shown here. It is quite interesting because there seemed no common patterns among these genes. They were independently correlated with expression levels of all genes and their mutation did not show co-occurrence.
This paper studies a single-supplier, multiple-retailer supply chain for a single commodity. The demand of the commodity occurs only at the retailers with constant rates, and the supplier is responsible for replenishing all the retailers’ requests to satisfy their demands. The supplier is the leader of the supply chain, and it provides a sequence of prescheduled epochs for all the retailers to choose their order replenishment timings. The cost disadvantages of the retailers for joining the replenishment timings shall be compensated by the supplier through quantity discounts. In addition, the costs considered in the supply chain include setup and delivery costs of the supplier, as well as holding and ordering setup costs of the retailers. The objective of the supply chain is to minimize the total cost of the supplier.
This study was undertaken in Hope Hospital, a 900 bed- ded University Hospital in Salford, Greater Manchester, UK. The study was designed to record the atopic status for mold and non-mold allergens of asthma patients at every level of severity from very mild to very severe (defined as multiple hospital admissions despite intensive asthma medication). We studied patients with severe asthma dur- ing hospital admissions or at subsequent visits to the hos- pital chest clinic. Patients were recruited opportunistically during hospital admissions or during routine consulta- tions with the Respiratory Nurse Specialist (RNS) in the hospital Chest Clinic. Recruitment was evenly spread over 30 months from January 1996 to June 1998. During this period, the Respiratory Nurse service was under develop- ment with only one part-time RNS available to serve a large population of hospital in-patients and ambulatory care patients at chest clinics. Ward-based doctors and nurses referred patients with acute asthma to the RNS on an opportunistic basis based on availability of the part-
LB is the most common tick-transmitted disease in the northern hemisphere  and in Sweden . In this study a total of 186 patients had Borrelia infection, i.e. EM or serological evidence of a current Borrelia infec- tion. In accordance with other studies, , only 43% of the 174 patients with EM had serological evidence of B. burgdorferi infection. It has been reported that unspecific symptoms are common in LB and that they can be presented without a typical EM . However, most of our patients were recruited by the inclusion criteria EM with or without other symptoms, making it difficult to draw any general conclusions concerning the prevalence of unspecific symptoms in LB patients.
We have developed a modified meta-analysis counting method and applied it to the comparison of primary tumors versus metastases in various tumor types. We identified a list of 78 down-regulated genes and 1 up- regulated gene in metastases compared to primary tumors with a False Discovery Proportion of less than 0.1. Many of these genes are involved in pathways asso- ciated with metastasis. After comparing the list of genes generated by our analysis with six independent datasets testing primaries versus metastases, we found that four of the datasets demonstrated that these genes were dys- regulated than would be expected by chance alone (i.e. LS-statistic p-value < 0.05). We believe that the identifi- cation of this common metastatic signature could facili- tate further research in metastasis, such as outcome prediction, drug discovery, and other functional studies.
Pollen from a wide variety of sunflowers reduced counts of the bumblebee gut pathogen C. bombi when compared to buckwheat pollen and wildflower mixed pollen. Bees fed Solidago spp. and Helianthus spp. pollens had 80 –90% lower C. bombi cells compared to those that consumed buckwheat pollen. These results provide a much wider range of options for using sunflower pollen as a food supplement for managed bumblebees. Giacomini et al.  found that the intensity of C. bombi infection was lower in wild-caught workers when agricultural lands had more sunflower acreage. This study indicates that multiple sunflower cultivars or wild species could be used for pollen supplements or grown in pollinator-friendly plantings to help manage bee disease.
tests of cognitive function and memory in previous GWA studies (Need et al. 2009; Cirulli et al. 2010, 2012; Luciano et al. 2011; De Jager et al. 2012). In particular, RPS6KA5, which encodes ribosomal protein S6 kinase alpha-5, is part of a pathway involved in brain-derived neurotrophic factor (BDNF)/neurotrophin signaling; BDNF and other neurotro- phins are important in neural development, learning, and memory and are implicated in neurodegenerative diseases such as Huntington’s, Alzheimer’s and Parkinson’s (Tang et al. 2011). RPS6KA5 is also thought to be a part of the upstream pathway involved in learning-dependent chroma- tin remodeling, which is important in long-term memory for- mation (Peixoto and Abel 2013). In addition, the gene PDLIM1 has been found to have strong maternal transmission in trios where the child is affected with ADHD, and PDLIM1 has been shown to play a role in Alzheimer’s disease (Wang et al. 2012). A linkage study for intellectual disability found mutations in the ST3GAL3 gene (Hu et al. 2011), and muta- tions in the ACTG1 gene cause Baraitser–Winter syndrome, a developmental disorder affecting the face and brain (Rivière et al. 2012). Taken together, multiple studies suggest that genes in this subnetwork we identiﬁed using PEGASUS and HotNet2 are involved in regulatory processes that affect neu- ral development, learning, and memory.