New setting is introduced to study “closing numbers” and “super-closing numbers” as optimal-super-resolving number, optimal-super-coloring number and optimal-super-dominating number. In this way, some approaches are applied to get some sets from (Neutrosophic)n-SuperHyperGraph and after that, some ideas are applied to get different types of super-closing numbers which are called by optimal-super-resolving number, optimal-super-coloring number and optimal-super-dominating number. The notion of dual is another new idea which is covered by these notions and results. In the setting of dual, the set of super-vertices is exchanged with the set of super-edges. Thus these results and definitions hold in the setting of dual. Setting of neutrosophic n-SuperHyperGraph is used to get some examples and solutions for two applications which are proposed. Both setting of SuperHyperGraph and neutrosophic n-SuperHyperGraph are simultaneously studied but the results are about the setting of n-SuperHyperGraphs. Setting of neutrosophic n-SuperHyperGraph get some examples where neutrosophic hypergraphs as special case of neutrosophic n-SuperHyperGraph are used. The clarifications use neutrosophic n-SuperHyperGraph and theoretical study is to use n-SuperHyperGraph but these results are also applicable into neutrosophic n-SuperHyperGraph. Special usage from different attributes of neutrosophic n-SuperHyperGraph are appropriate to have open ways to pursue this study. Different types of procedures including optimal-super-set, and optimal-super-number alongside study on the family of (neutrosophic)n-SuperHyperGraph are proposed in this way, some results are obtained. General classes of (neutrosophic)n-SuperHyperGraph are used to obtains these closing numbers and super-closing numbers and the representatives of the optimal-super-coloring sets, optimal-super-dominating sets and optimal-super-resolving sets. Using colors to assign to the super-vertices of n-SuperHyperGraph and characterizing optimal-super-resolving sets and optimal-super-dominating sets are applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on n-SuperHyperGraph to get new results about closing numbers and super-closing numbers alongside sets in the way that some closing numbers super-closing numbers get understandable perspective. Family of n-SuperHyperGraph are studied to investigate about the notions, super-resolving and super-coloring alongside super-dominating in n-SuperHyperGraph. In this way, sets of representatives of optimal-super-colors, optimal-super-resolving sets and optimal-super-dominating sets have key role. Optimal-super sets and optimal-super numbers have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal-super ones. Simultaneously, three notions are applied into (neutrosophic)n-SuperHyperGraph to get sensible results about their structures. Basic familiarities with n-SuperHyperGraph theory and neutrosophic n-SuperHyperGraph theory are proposed for this article.

Introduction: Polycystic Ovary Syndrome (PCOS) is an endocrinologic disorder that affects 5-15 % of women of their reproductive age and is a frequent cause of infertility. Major symptoms include hyperandrogenism, ovulatory dysfunction, a characteristic multi-follicular morphology of the ovary, an elevated ratio of LH/FSH, and often obesity and/or insulin resistance. PCOS also represents a state of chronic low-grade inflammation that is closely interlinked with the metabolic features. Inflammatory processes consist of the acute inflammatory response and resolution processes initiated concomitantly. "Classical" pro-inflammatory lipid mediators like prostaglandins (PG), leukotrienes (LT), or thromboxanes (TX) are derived from arachidonic acid (AA) and are crucial for the initial response. Resolution processes are driven by four families of so-called specialized pro-resolving mediators (SPMs): resolvins, maresins, lipoxins, and protectins. SPM biosynthesis starts from the essential polyunsaturated fatty acids DHA, DPA, or EPA via certain hydroxylated intermediates (18-HEPE, 17-HDHA, 14-HDHA). The present study aimed to establish lipid mediator profiles of PCOS patients compared to healthy women to identify differences in their resolutive and pro-inflammatory lipid parameters. Material and Methods: Blood samples were taken (20 ml), separated into plasma and serum, and analyzed by HPLC/MS-QQQ. Fifteen female patients (18-45 years) were diagnosed with PCOS according to Rotterdam criteria, and five healthy women, as comparator group, were recruited for the study. The main outcome measures were: Pro-inflammatory lipid mediators (PG, LT, TX) and their precursor AA; SPMs (Resolvins, Maresins, Protectins, Lipoxins), their precursors EPA, DHA, DPA, and their active biosynthesis pathway intermediates (18-HEPE, 17-HDHA, 14-HDHA). Ratio [(sum of pro-inflammatory molecules)/sum of SPMs]. Results: The level of pro-inflammatory parameters in serum was significantly higher in PCOS-affected women. The ratio [(sum of pro-inflammatory molecules) / (sum of SPMs plus hydroxylated intermediates)] reflecting the inflammatory state was significantly lower in the group of healthy women. Conclusion: There is a strong pro-inflammatory state in PCOS patients. Further research will clarify whether supplementation with SPMs or their precursors may improve this state.

Objectives This study aimed to evaluate the eicosanoid and pro-resolutive parameters in Post Covid Syndrome (PCS) patients during 12 weeks of a supplementation with a marine oil enriched in SPMs. Patient and methods The study was conducted in 53 adult patients with a PCS. The subjects included must have had a positive COVID-19 test (PCR, fast antigen test, or serologic test) and persistent symptoms related to COVID-19 at least 12 weeks before their enrolment in the study. The following parameters were evaluated: Polyunsaturated fatty acids: EPA, DHA, ARA, DPA, Specialized Pro-resolving mediators (SPMs) 17-HDHA, 18-HEPE, 14-HDHA, resolvins, maresins, protectins, and lipoxins. The eicosanoids group included prostaglandins, thromboxanes, and leukotrienes. The development of the clinical symptoms of fatigue and dyspnea were evaluated using the Fatigue Severity Scale (FSS) and the Modified Medical Research Council (mMRC) Dyspnea Scale. Three groups with different amounts of intake were evaluated: daily use of 500mg, 1500mg, and 3000mg were compared to a control group without use of the product. Results In the serum from PCS patients, an increase of 17-HDHA, 18-HEPE, 14-HDHA could be observed. Also, a decrease in the ratio between the pro-inflammatory and pro-resolutive lipid mediators was detected. Both differences were significant (p < 0.05). There were no differences between the three treatment groups. Fatigue and dyspnoea showed a trend to improve after supplementation in all groups. Conclusions A clear enrichment in serum of the three monohydroxylated SPMs could be observed also at a dosage of 500 mg per day. In the same way, a clear improvement in fatigue and dyspnoea was observed with this dosage. Clinical Trial Registry: ISRCTN13270662.

The use of selective pro resolving mediators including the monohydroxylates are promising substances for the management of different acute and chronic diseases.In the field of obstetrics many clinical entities like uterine contractions or the occurrence of pre-eclampsia are still serious complications during pregnancy.The use of enriched marine oil nutritional’s may contribute to an attenuation of these diseases as the containing selective pro resolving mediators exhibit pro resolutive actions that can positively modulate inflammatory diseases and those leading to serious obstetrical complications.

Consider a robot that is navigating in a space modeled by a graph, and that wants to know its current location. It can send a signal to determine how far it is from each landmark among a set of fixed landmarks. We study the problem of computing the minimum required number of landmarks, and where they should be placed so that the robot can always determine its location. Since the problem is an NP-complete problem, the robot's responses to the actions are slow. To accelerate this response, we can use the parallel version of this problem. In this work, we introduce a new parallel implementation for determining the metric dimension of a given graph. We run the proposed algorithm on a symmetric multi-processing (SMP) cluster using C programming language and the Message Passing Interface (MPI) library. Finally, we run our implementation on four categories of graphs (the tracks in which the robot moves): a cycle graph Cn, a path graph Pn, a triangular snake graph and a ladder graph Ln. Preliminary computational results indicate that the metric dimension problem is an NP-complete problem and prove the ability of the proposed algorithm to achieve a speedup of 6 for 8 processors.

Obesity is associated with chronic low-grade inflammation. Polyunsaturated fatty ac-ids such as omega-3 (n-3), are essential in the pro-resolution of inflammation. An 8-week double-blind randomized clinical trial was conducted with a n-6:n-3, 5:1 ratio, along with daily 1.8 g of n-3 supplementation vs. placebo. A total of 40 subjects were included, 21 in omega 3 group and 19 in placebo group. The n-3 supplementation had a superior effect compared to placebo increasing levels of Resolvin D1 [129.3 (-90.1 - 193.5) vs. -16.8 (-237.8 - 92.5) pg/mL, p=0.041], IL-10 [1.4 (-0.7 - 4.6) vs. -2.0 (-5 - 0.05) pg/mL, p=0.001], and decreasing IL-6 [-0.67 (2.72 - -0.59) vs. 0.03 (-0.59 - 1.84) pg/mL p=0.015], and MCP-1 [-29.6 (-94.9 - 5.50) vs. 18.3 (-97.3 - 66.35) pg/mL, p=0.040]. In con-clusion, n-3 supplementation promoted resolution of inflammation by increasing sys-temic levels of Resolvin D1, IL-10, and decreasing IL-6 and MCP-1.

The complex interplay between dietary factors, inflammation, and macrophage polarization is pivotal in the pathogenesis and progression of chronic liver diseases (CLDs). Omega-3 fatty acids (FAs) have been attracted attention due to their potential to modulate inflammation and exert protective effects in various pathological conditions. This review explores the emerging role of omega-3 FAs and their specialized pro-resolving mediators (SPMs) in the context of macrophage polarization, with a focus on chronic liver diseases. Omega-3, eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA) have promising effects in mitigating inflammation and enhancing the resolution of inflammatory responses. They influence the M1/M2 macrophage phenotype balance, promoting a shift towards the M2 anti-inflammatory phenotype. SPMs, such as resolvins (Rvs), protectins (PDs), and maresins (MaRs), have emerged as potent regulators of inflammation and macrophage polarization. They show anti-inflammatory and pro-resolving properties. These mediators modulate the expression of cytokines, facilitate the phagocytosis of apoptotic cells, and promote tissue repair. MaR1, in particular, has demonstrated significant hepatoprotective effects by promoting M2 macrophage polarization, reducing oxidative stress, and inhibiting key inflammatory pathways such as NF-κB. In the context of CLD, such as nonalcoholic fatty liver disease (NAFLD) and cirrhosis, omega-3 and their SPMs have shown promise in attenuating liver injury, promoting tissue regeneration, and modulating macrophage phenotypes. However, the mechanisms underlying their effects and their interactions with other cell types within the liver microenvironment require further investigation. Understanding the intricate relationship among SPM and macrophage polarization holds unlimited potential for the development of novel therapeutic strategies for chronic liver diseases.

Inflammation is a conserved process that involve the activation of immune and non-immune cells aiming at protecting the host from bacteria, viruses, toxins and injury. However, unresolved inflammation and permanent release of pro-inflammatory mediators are responsible for the promotion of a condition called “low-grade systemic chronic inflammation”, characterized by tissue and organ damages, metabolic changes and increased susceptibility to non-communicable diseases. Several studies have demonstrated that different dietary components may influence modifiable risk factors for diverse chronic human pathologies. Marine n-3 polyunsaturated fatty acids (n-3 PUFAs), mainly eicosapentaenoic (EPA) and docosahexaenoic acid (DHA), are well recognized anti-inflammatory and immunomodulatory agents able to influence many aspects of the inflammatory process. The aim of this article is to review the recent literature that relates to the modulation of human disease, such as rheumatoid arthritis, by n-3 PUFAs.

Omega-3 polyunsaturated fatty acids (PUFA) play a pivotal role in health, wellbeing, and inflammatory diseases in humans. Lack of omega-3 consumption is associated with diseases. Specialized Pro-resolving Mediators (SPM) are produced from Omega-3-PUFAs and accelerate resolution of inflammation. They are classified as resolvins, maresins, protectins, and lipoxins. SPMs actions in resolution consist in limiting neutrophilic infiltration, promote the clearance of apoptotic cell and cellular debris, enhancing efferocytosis and phagocytosis, counter regulate the production of pro-inflammatory mediators such as chemokines and cytokines, and promote pro-resolving macrophage phenotype. We identified temporal plasma and serum increases of SPMs after 6 g of oral supplementation of SPM-enriched emulsion in ten healthy subjects. We also described temporal increases of omega-3, as well as pharmacokinetics fundamentals in plasma and serum using LC-MS/MS lipid profiling. These results provide evidence of temporal increases of SPMs that together support the idea that given oral supplementation is a good source of essential bioactive SPMs.

When separation to the parameters of interest appears below resolution limit of the estimator, the ambiguity arises whether two parameter estimates relate to one source emitted twice or two close sources emitted once. In the paper, novel Bayes technique aimed to identify one/two sources below resolution limit by the pair of Gaussian estimates of a source(s) planar location as parameter is developed. Prior probabilities of the hypotheses on one/two sources are available from the analysis of physical characteristics of the emissions, assuming that they can be equally probable. The identifier recalculates a posteriori these probabilities subject to a distance between sources. It is applied to distinguish two location estimates obtained in the planar time difference of arrival mobile communication network. The work of the identifier is studied in the domain of closely spaced network users where covariance matrices of estimates are sufficiently approximated by the constant. The application gives an example of how the identifier revises the prior probabilities and can change thereby the initial preference of a hypothesis with a distance between users in some cases.