The longest common subsequence (LCS) problem is a prominent NP–hard optimization problem where, given an arbitrary set of input strings, the aim is to find a longest subsequence, which is common to all input strings. This problem has a variety of applications in bioinformatics, molecular biology and file plagiarism checking, among others. All previous approaches from the literature are dedicated to solving LCS instances sampled from uniform or near-to-uniform probability distributions of letters in the input strings. In this paper, we introduce an approach that is able to effectively deal with more general cases, where the occurrence of letters in the input strings follows a non-uniform distribution such as a multinomial distribution. The proposed approach makes use of a time-restricted beam search, guided by a novel heuristic named Gmpsum. This heuristic combines two complementary scoring functions in the form of a convex combination. Furthermore, apart from the close-to-uniform benchmark sets from the related literature, we introduce three new benchmark sets that differ in terms of their statistical properties. One of these sets concerns a case study in the context of text analysis. We provide a comprehensive empirical evaluation in two distinctive settings: (1) short-time execution with fixed beam size in order to evaluate the guidance abilities of the compared search heuristics; and (2) long-time executions with fixed target duration times in order to obtain high-quality solutions. In both settings, the newly proposed approach performs comparably to state-of-the-art techniques in the context of close-to-uniform instances and outperforms state-of-the-art approaches for non-uniform instances.

In this paper we study the Roman domination number of some classes of planar graphs - convex polytopes: An, Rn and Tn. We establish the exact values of Roman domination number for: An, R3k, R3k+1, T8k, T8k+2, T8k+3, T8k+5 and T8k+6. For R3k+2, T8k+1, T8k+4 and T8k-1 we propose new upper and lower bounds, proving that the gap between the bounds is 1 for all cases except for the case of T8k+4, where the gap is 2.

In a network, a k-plex represents a subset of n vertices where the degree of each vertex in the subnetwork induced by this subset is at least n − k. The maximum edge-weight k-plex partitioning problem (Max-EkPP) is to find the k-plex partitioning in edge-weighted network, such that the sum of edge weights is maximal. The Max-EkPP has an important role in discovering new information in large sparse biological networks. We propose a variable neighborhood search (VNS) algorithm for solving Max-EkPP. The VNS implements a local search based on the 1-swap first improvement strategy and the objective function that takes into account the degree of every vertex in each partition. The objective function favors feasible solutions, also enabling a gradual increase in terms of objective function value when moving from slightly infeasible to barely feasible solutions.A comprehensive experimental computation is performed on real metabolic networks and other benchmark instances from literature. Comparing to the integer linear programming method from literature, our approach succeeds to find all known optimal solutions. For all other instances, the VNS either reaches previous best known solution or improves it. The proposed VNS is also tested on a large-scaled dataset which was not previously considered in literature.

The coronavirus COVID-19 has been affected all the countries and territories in 2020. In this study we cluster European countries according to the cumulative relative number of European COVID-19 patients. The clustering is based on publicly available data published at European Centre for Disease Prevention and Control website and performed by three clustering methods: K-means, agglomerative and BIRCH clustering. Clustering performance, evaluated by Silhouette Coefficient value, shows satisfying accuracy of the obtained clusters. The results presented in this study can be useful to public health officers and practitioners to easier deal with COVID-19 challenges.

We live in a digital world when people rely more on smart devices and dedicate their time to searching information online. According to some research, 85% of users now compare and check reviews of products or services prior to their selection, and Google states that as many as 77% of patients search the Internet before they are make decision. That is why more and more health organizations recognize the need for online presence and the use of digital channels to attract new clients. The age group of 15-35 which trusts social media and easier forms of communication when it comes to important decisions. This gives healthcare professionals a platform to engage with such an interactive audience easily. Benefits - Health organization can either easily promote a product or service to the target group, as it is possible to determine who you want to target for preventive campaigns and services. In the digital world, you can easily measure and optimize results and gain accurate data as much as the range of activities. Reach, Engagement, CPC? Reach shows how many users have seen the posting, and what is higher, it is spreading more widely. Engagement is the interaction you achieve with your target group. How can you determine that you have paid off and that you have achieved your goal? One of the real indicators of many parameters is certainly the CPC (Cost per Click). In digital marketing, CPC is an advertising payment model according to which an advertiser pays each time a user clicks on a link. Conclusions The Healthcare industry remains behind other industries in the scope of digital marketing efforts. In 2017, only 50% of the survey respondents reported using a CRM system, while significantly more (65%) report using a CRM in 2018. Use of a marketing tool has doubled from last year’s survey, from 23% to 48%. Advanced or emerging digital activities, such as wearables or beacon technology, are still not being used much by healthcare organizations. Key messages Social networks empowers health clients. Majority people between the age group 18-24 (90%) trust information shared on social media.