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.

The conformity assessment of products or a measured value with the given standards is carried out based on the global risk of producers and consumers calculation. A product may conform to specifications but be falsely rejected as non-conforming. This is about the producer's risk. If a product doesn't meet the requirements but is falsely accepted as conforming, that poses a risk to the consumer. The conventional approach to risk assessment, which yields only a single numerical value for the global risk of producers and consumers, is naturally extended, and utilized for assessing risk in measurement models with linear regression. The outcomes of the two-dimensional extension, along a moderate scale, are the parabolas with an opening upwards. Risk surfaces were obtained through three-dimensional extension over the area limited by the moderate scale and guard band axes. Four models with different ranges of tolerance intervals were used to test this innovative method of risk assessment in linear regression. The corresponding standard measurement uncertainties are determined by applying a simplified measurement model with the use of comprehensive data on the measurement performance and by determining measurement uncertainty derived from consideration of the functional relationship obtained by linear regression analysis. Models that utilize information from linear regression analysis to determine measurement uncertainty are biased towards risks at the edges of the moderate scale. Testing the model's performances with metrics related to the confusion matrix, such as the F1 score, further substantiated this assertion. The diagnostic odds ratio has been proven to be extremely effective in identifying the curve along the guard band axis, along which the global risks of producers and consumers are at their lowest.

Multiple Gateways (GWs) provide network connectivity to Internet of Things (IoT) sensors in a Wide Area Network (WAN). The End Nodes (ENs) can connect to any GW by discovering and acquiring its periodic beacons. This provides GW diversity and hence improves coverage. If the GWs are within vicinity to each other, and they keep sending periodic beacons to be discovered, the result is interference and collisions. In this study, the impact of such intra-network interference is analyzed to determine the maximum number of GWs that can co-exist within a given urban neighborhood. The paper shows the relationship between beacon collisions and the resulting packet loss rates in a given urban environment. The expected collision rates are calculated for the Medium Access Control (MAC) layer. The eventual packet loss rates are calculated with the MAC and Physical (PHY) layers combined. For this purpose, a new co-channel interference model is presented. The model calculates the average Carrier to Interference ratio (C/I) averaged across all the colliding events. It takes into account the partial overlap durations and the relative power of each colliding signal. The model shows that a collision does not always cause a packet loss. Packet losses occur if there is a collision and if the C/I is below a threshold. The performance evaluation is presented using a combination of analytical and simulation methods. The analytical methods provide the theoretical foundation, and have been used to validate the simulation results. Furthermore, the system models are developed from experimental data obtained from measurements with real hardware. Numerical results are provided with a low bit rate Gaussian Frequency Shift Keying (GFSK) modulation at the PHY layer, which is derived from the IEEE 802.15.4 standard specification. This paper provides guidance on selecting the right GFSK modulation parameters for such low bit-rate and narrow bandwidth IoT applications. The analysis and simulation results show that larger beacon intervals help in reducing beacon loss rates, at the cost of larger beacon acquisition latency. On the flip side, the gateway discovery latency reduces with increasing GW density thanks to abundance of beacons.

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.

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.

IMPORTANCE: On December 10, 2021, the FDA published a Determination Letter, along with a Statistical Review and Evaluation Report, and concluded that under the non-informative prior, the local Bayesian optimal interval design (BOIN) design, in its revised form, can be designated fit-for-purpose for identifying the maximum tolerated dose of a new drug, assuming that dose-toxicity relationship is monotonically increasing. Although setting the BOIN design parameter p.tox = 1.4 * target.DLT.rate is recommended in almost all BOIN methodology articles and is the default value in the R package BOIN, it's unclear if the choice of p.tox should only depend on the target DLT rate and if certain range of p.tox could produce the same BOIN boundary table. DESIGN: In this simulation study, following parameters were varied one at a time, using R package BOIN, to explore their effects on the equivalence intervals of p.saf and p.tox: 1) target DLT rate, 2) n.earlystop, 3) cutoff.eli, 4) cohortsize, and 5) ncohort. And a simple 3+3 design was used as an example to explore equivalent sets of BOIN design parameters that can generate the same boundary table. RESULTS: When the early stopping parameter n.earlystop is relatively small or the cohortsize value is not optimized via simulation, it might be better to use p.tox < 1.4 * target.DLT.rate, or try out different cohort sizes, or increase n.earlystop, whichever is both feasible and provides better operating characteristics. This is because if the cohortsize was not optimized via simulation, even when n.earlystop = 12 and cohortsize > 3, the BOIN escalation/de-escalation rules generated using p.tox = 1.4 * target.DLT.rate could be exactly the same as those calculated using p.tox > 3 * target.DLT.rate, which might not be acceptable for some pediatric trials targeting 10% DLT rate. The traditional 3+3 design stops the dose finding process when 3 patients have been treated at the current dose level, 0 DLT has been observed, and the next higher dose has already been eliminated. If additional 3 patients were required to be treated at the current dose in the situation described above, the decision rules of this commonly used 3+3 design could be generated using BOIN design with target DLT rates ranging from 18% to 29%, p.saf ranging from 8% to 26%, and different p.tox values ranging from 39% to 99%. These BOIN parameters also need to satisfy a set of conditions. Meaning: This study demonstrates the importance of interpreting BOIN design parameter p.tox as an interval of toxicity rates that are considered too toxic, rather than one prespecified value that corresponds to the lowest toxicity probability that is deemed overly toxic. When designing a dose-finding trial using BOIN, it is important to perform simulation studies to identify equivalent sets of BOIN design parameters that can generate the same boundary table so that we can better compare the safety properties of different boundary tables.

The classical joint economic lot-sizing (JELS) policy in a single-vendor single-buyer system generates an equal production quantity in all cycles, where the input parameters remain static indefinitely. In this paper, a new two-echelon supply chain inventory model is developed involving a hybrid production system that simultaneously focuses on green and regular production methods with optimal allocation fraction of green and regular productions. Unlike the classical mathematical formulation, each cycle is independent from the previous one, and consequently, the input parameters can be adjusted to be responsive to the dynamic nature of demand rate and price fluctuation. A rigorous heuristic approach is used to derive a global optimal solution for a joint hybrid production system. The model accounts for carbon emissions from production and storage activities related to green and regular produced items along with transportation activity under a multi-level emission-taxing scheme. The results emphasize the significant impact of green production on emissions. That is, the higher the allocation fraction of green production the lower the total amount of emissions generated by the system, i.e., the system becoming more sustainable. Adopting a hybrid production method not only decreases the greenhouse gas (GHG) emissions dramatically, but also reduces the per unit time total cost when compared with regular production. One of the main findings is that the total system cost generated by the base closed-form formula of the proposed model is considerably lower than that of the existing literature i.e., 33.59% (16.13%) lower in the first cycle (subsequent cycles) when the regular production method is assumed. Moreover, the optimal production rate generated by the proposed model is the one that minimizes the emissions production function. Illustrative examples and special cases that reflect different realistic situations are compared to outline managerial insights.

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.

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.

(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&lt;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&lt;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.