In this study, we first discover some new concept coordinated UD-convex mappings with fuzzy-number values. After that, we look into Hermite-Hadamard type inequalities via fuzzy-number-valued coordinated UD-convex fuzzy-number-valued mapping (coordinated UD-convex FNVM). In the case of coordinated UD-convex FNVM, novel conclusions are derived by making particular decisions in recently proven inequalities. Additionally, it is demonstrated that the recently discovered inequalities are expansions of comparable findings in the literature. It is important to note that the main outcomes are validated by nontrivial examples.

This article is devoted to methods of processing random processes. Of particular relevance is the task of processing broadband non-stationary random processes. The processing of random processes is usually related to the assessment of their probabilistic characteristics. Very often, a non-stationary broadband random process is represented by a single implementation in a priori uncertainty about the type of distribution function. Such random processes occur in information and measuring communication systems in which information is transmitted at a real time pace (for example, radio telemetry systems of spacecraft). The use of methods of traditional mathematical statistics, for example, maximum likelihood methods to determine probability characteristics, in this case is not possible. The article discusses a method of processing non-stationary broadband random processes based on the use of non-parametric methods of decision theory. An algorithm for dividing the observation interval into stationary intervals using non-parametric Kendall statistics is considered, as well as methods for estimating probabilistic characteristics on the stationary interval using ordinal statistics. The article presents the results of statistical modeling using the Mathcad program.

Colorectal cancer is the third most diagnosed cancer in males and in females, representing 8% of estimated new cases and the third cause of cancer-related death in both sexes, accounting for 9% of cancer deaths in men and 8% in women. About 20% of patients diagnosed with CRC present metastatic disease. Although lung metachronous or synchronous metastatic spread without other involved sites has been reported in only a small proportion of patients, considering that this tumor is frequently diagnosed, the clinical approach to CRC pulmonary metastases represents a major issue for thoracic surgeons and CRC oncologists. Among patients diagnosed with pulmonary metastases from CRC, about 9 – 12% are eligible for local treatments with radical intent, including surgical resection, SBRT and ablation therapy. Due to the lack of randomized controlled trials among different local strategies, there is no definitive evidence about the optimal approach, although surgical resection is considered the most effective therapeutic option in this clinical scenario. Oncological achievement of primary radical resection, the biology of primary tumor and metastatic sites, disease free interval and or progression free survival are independent prognostic factors which make it possible to define a cohort of patients which might significantly benefit from pulmonary metastasectomy.

The present article seeks to study whether there is any relationship between the equation of the rhythmic figures (Lugos Abarca, 2023) and cardiac auscultation using Field's method, which consists of representing cardiac sounds by means of musical notation (Field, 2010). A new meaning is given to the equation, concluding a mathematical equality between the equation of the rhythmic figures and the formula for calculating the RR Interval.

This paper presents a novel algorithm, the multi-objective nonlinear interval PageRank (MONIPR) Algorithm. This algorithm extends the conventional PageRank (PR) algorithm, integrating nonlinear interval computation and multi-objective considerations into the computation process. The MONIPR algorithm bridges a research gap in integrating nonlinear interval approaches and multi-objective problems into the PR algorithm, which were traditionally treated separately. In addition, this research adopts the constrained interval arithmetic proposed to address the limitations of the conventional PR algorithm, which tends to overlook uncertainties and results in deterministic outcomes. In addition, we use a numerical example to demonstrate the proposed algorithm, contrasting it with the conventional approaches. A numerical example demonstrates the algorithm's performance by comparing the rank intervals obtained with the traditional crisp Markov chain and PR algorithm. The results highlight the ability of the proposed algorithm to provide a range of possible rank intervals, considering both uncertainty and multi-objectives. The findings suggest potential applications in decision-making, uncertainty quantification, and systems analysis.

We introduce and discuss a generalization of the classical multi-objective optimization to pairs of functions. This procedure is referred to as bi-multi-objective optimization. A justification of this general optimization procedure is presented, related both to multi-objective optimization under ambiguity concerning individual preferences and to Pareto optimality for a family of preferences with nontransitive indifference. Incidentally, the binary relation naturally associated to a bi-multi-objective optimization problem is represented by a finite bi-multi-utility, which generalizes to the nontransitive case the classical finite multi-utility representation. An important application is presented to Markowitz portfolio selection under ambiguity concerning both the vector of returns and the covariance matrix.

Due to the intermittency and fluctuation of photovoltaic (PV) output power, a high proportion of grid-connected PV power generation systems has a significant impact on power systems. Accurate PV power forecasting can alleviate the uncertainty of the PV power and is of great significance for the stable operation and scheduling of the power systems. Therefore, in this study, a feature rise-dimensional (FRD) two-layer ensemble learning (TLEL) model for short-term PV power deterministic forecasting and probability forecasting is proposed. First， based on the eXtreme Gradient Boosting (XGBoost), Random Forest (RF), CatBoost, and Long-short-term memory (LSTM) models, a TLEL model is constructed utilizing the ensemble learning algorithm. Meanwhile, the FRD method is introduced to construct the FRD-XGBoost-LSTM (R-XGBL), FRD-RF-LSTM(R-RFL), and FRD- CatBoost - LSTM (R-CatBL) models. Subsequently, the above models are combined to construct the FRD-TLEL model for deterministic forecasting, and perform probability interval forecasting based on quantile regression(QR). Finally, the performance of the proposed model is demonstrated with a real-world dataset. By comparing with other models, the proposed model displays better forecasting accuracy for deterministic forecasting and reliable forecasting intervals for probability forecasting, and good generalization ability in the datasets of different seasons and weather types.

Introduction: Myasthenia gravis (MG), an immune disorder affecting nerve-muscle transmission, often necessitates tailored therapies to alleviative longitudinal symptom fluctuations. Here, we aimed to examine and compare the treatment cycle intervals and efficacy of efgartigimod in four patients. This case series mainly offers insights into personalized treatment cycle intervals and efficacy of efgartigimod for patients with MG in our facility in Japan. Methods: We retrospectively analyzed four patients with MG (2 patients with early-onset, 1 with late-onset, and 1 with seronegative MG, mainly managed with oral immunosuppressants as prior treatments) who completed four or more cycles of efgartigimod treatment from January 2022 to September 2023. We focused on changes in serum immunoglobulin (IgG) level, acetylcholine receptor antibody (AChR-Ab) titer, and quantitative MG (QMG) score. Results: Efgartigimod, administered at a median of 5.0 [IQR 5.0, 7.5] weeks between cycles, led to decreased serum IgG level in all patients and reduced AChR-Ab titers in seropositive patients. All patients showed sustained MG symptom improvement, with considerably reduced QMG scores before efgartigimod treatment. None of the patients required rescue medications or developed treatment-related adverse events. Conclusion: Customized efgartigimod administration intervals effectively enhanced clinical outcomes in patients with MG without notable symptom fluctuations, demonstrating the benefits of individualized treatment approaches and validating the safety of efgartigimod during the study period.

In this paper, we shall introduce the interval-valued spatial error model. Based on the idea of least square method of single-valued case, we give the parameter estimator for interval-valued spatial error model. The theoretical properties of the proposed estimator are proved. Finally, we give the numerical analysis and a real example.

(1) Background: In recent years, an innovative approach has emerged in the field of toxicology for managing acute intoxications caused by lipophilic substances: intravenous lipid emulsions (ILE). Through numerous experiments and case reports, the efficacy of lipid emulsions in counteracting toxicities induced by lipophilic agents, including a significant number of antiepileptic drugs (AE), has become increasingly evident. (2) Methods: Data spanning a 10-year period (2010-2020) was analyzed by searching through multiple scientific publication platforms like PubMed, Science Direct, Research Gate, and Springer Link. The study focused on reviewing relevant case reports detailing successful Intravenous lipid emulsion (ILE) administration in pa-tients with acute intoxications with antiepileptics, specifically examining the impact of fat emul-sions on neurological status, Glasgow Coma Scale (GCS) scores, and corrected QT interval con-cerning hemodynamic instability. (3) Results: The typical symptoms of antiepileptic toxicity in-clude central nervous system depression, ataxia, and nystagmus. Intravenous lipid emulsion ap-plication resulted in an increase in Glasgow Coma Scale scores and enhanced recovery from drug intoxication. (4) Conclusions: This study provides a comprehensive overview of the potential utility of ILE as a component to antidote therapy in cases of acute AE poisoning involving neurotropic drugs. The process involves the engagement of various mechanisms of antitoxic activity.

The responses of inflammatory cytokines and brain-derived neurotrophic factor (BDNF) to a high-intensity interval training (HIIT) session were compared between 7 postmenopausal (57±2 y) and 8 premenopausal females (44±3 y) during the luteal phase of their menstrual cycle, when estrogen and progesterone are highest, and. HIIT consisted of 10 x 1 min running intervals (90% maximum heart rate) separated by 1 min recovery intervals. Blood samples were collected at baseline (fasted), pre-exercise (postprandial), and 0, 30 and 90 min post-HIIT and analyzed for interleukin (IL-6) and 10 (IL-10), tumour necrosis factor-alpha (TNF-α) and BDNF. IL-6 significantly increased from pre-exercise to 0 min post-HIIT in postmenopausal (+40%, p=0.01) but 30 min post-HIIT in premenopausal females (+60%, p=0.02). IL-6 remained elevated at 90 min post-HIIT in premenopausal (+104%, p=0.05) and to a higher degree in postmenopausal (+385%, p<0.001). IL-10 showed no response. TNF-α increased from pre- to 0 min post-HIIT (+10%, p=0.05), then decreased to below pre-exercise at 30 min (-10%, p=0.02) and 90 min (-5%, p=0.04) in both groups. BDNF increased immediate post-HIIT in premenopausal (+60%, p<0.001) but not postmenopausal females. The differences in IL-6 and BDNF response to HIIT between pre and postmenopausal females provide evidence of the role of female reproductive hormones in the regulation of these exercise-induced responses.