Various means (the arithmetic mean, the geometric mean, the harmonic mean, the power means) are often used as central tendency statistics. A new statistic of such type is offered for a sample from a distribution on the positive semi-axis, the gamma-weighted geometric mean. This statistic is a certain weighted geometric mean with adaptive weights.

The scope of this study was twofold: first, to introduce a new method in examining measurement invariance, especially with large-scale studies where a large number of group comparisons are involved: the alignment approach, where only configural invariance is necessary to achieve measurement invariance. Second, to evaluate the psychometric robustness of this approach using real-life data. Particularly, we applied this approach to examine whether the factor structure of a cognitive ability test (PGAT) exhibits measurement invariance across the 26 universities of the Kingdom of Saudi Arabia. The sample consisted of 9,849 graduate students from 26 universities around the Kingdom. The results indicated a robust configural model suggesting that the P-GAT subscales were invariant across the 26 universities. Finally, the aligned factor mean values were estimated, and factor mean comparisons of every group’s mean with all other group means were conducted for both cognitive domains (Verbal and Quantitative). In both domains, King Saud University had the highest mean score among all universities. Moreover, its mean factor score was significantly higher than any other university besides Dammam University. On the other hand, several universities allocated at the northern and Southern borders of the country exhibited the lowest factor mean scores.

Taiwan developing offshore wind power to promote green energy and self-electricity production. In this study, a Light Detection and Ranging (Lidar) was set up at Chang-Hua development zone one on the sea and 10km away from the seashore. At Lidar location, WRF (3.33km & 2km grid lengths) model and WAsP were used to simulate the wind speed at various elevations. Three days mean wind speed of simulated results were compared with Lidar data. From the four wind data sets, developed five different comparisons to find an error% and R-Squared values. Comparison between WAsP and Floating Lidar was shown good consistency. Lukang meteorological station 10 years wind observations at 5m height were used for wind farm energy predictions. The yearly variation of energy predictions of traditional and TGC wind farm layouts are compared under purely neutral and stable condition. The one-year cycle average surface heat flux over the Taiwan Strait is negative (-72.5 (W/m2) and 157.13 STD), which represents stable condition. At stable condition TGC (92.39%) and 600(92.44%), wind farms were shown higher efficiency. The Fuhai met mast wind data was used to estimate roughness length and power law exponent. The average roughness lengths are very small and unstable atmosphere.

I want to find an extension of the Hausdorff Measure and Fractal Measure which allows me to compute a unique, satisfying average for functions defined on non-fractal, measurable sets in the sense of Carathedory which has no gauge function.

Accurate forecasting of icing thickness has a great significance for ensuring the security and stability of power grid. In order to improve the forecasting accuracy, this paper proposes an icing forecasting system based on fireworks algorithm and weighted least square support vector machine (W-LSSVM). The method of fireworks algorithm is employed to select the proper input features with the purpose of eliminating the redundant influence. In addition, the aim of W-LSSVM model is to train and test the historical data-set with the selected features. The capability of this proposed icing forecasting model and framework is tested through the simulation experiments using real-world icing data from monitoring center of key laboratory of anti-ice disaster, Hunan, South China. The results show that the proposed W-LSSVM-FA method has a higher prediction accuracy and it may be a promising alternative for icing thickness forecasting.

This paper propose a kernel geometric mean metric learning (KGMML) algorithm. The basic idea is to obtain the closed-form solution of the geometric mean metric learning (GMML) algorithm in the high-dimensional feature space determined by the kernel function. Then, the solution is generalized as a form of kernel matrix by using the integral representation of the weighted geometric mean and the Woodbury matrix in this new feature space. Experimental results on 15 datasets show that the proposed algorithm can effectively improve the accuracy of the GMML algorithm and other metric algorithms.

Background: Fold change is widely used in biomedical research to quantify the magnitude of group differences in omics variables. However, the exact calculation method is often not reported, leading to inconsistent results. This study re-evaluates different fold-change calculation methods and provides a clear preference. Methods: Data scenarios with different distributions of treatment/test and reference data were created to challenge the assumption of interchangeable calculation methods. The main difference lies in the definition of the expected values of the groups used to calculate the log ratio, which is the basis of the fold change calculation. In addition, a multi-omics biomedical dataset was analyzed. Results: Using the arithmetic mean as the expected value for the treatment and reference groups resulted in incorrect fold change values more frequently than other methods, especially when the standard deviations between subgroups differed widely. Conclusions: The inferior arithmetic mean method is often perceived as the standard, although mathematically different equations are possible that differ mainly in the estimation of the expected value. Alternatives that define expectation by median, geometric mean, or paired fold change combinations are less susceptible to violations of equal variances or similar treatment/reference distributions.

This study explores students’ understanding of one measure of central tendency, the mean. A teaching experiment was conducted to understand how sixth-grade students made sense of this concept. Findings suggest that the students know how to solve mathematical problems related to mean using procedural understanding and lack of conceptual understanding.

Clustering, or otherwise known as cluster analysis, is a learning problem that takes place without any human supervision. This technique has often been utilized, much efficiently, in data analysis, and serves for observing and identifying interesting, useful, or desired patterns in the said data. The clustering technique functions by performing a structured division of the data involved, in similar objects based on the characteristics that it identifies. This process results in the formation of groups, and each group that is formed, is called a cluster. A single said cluster consists of objects from the data, that have similarities among other objects found in the same cluster, and resemble differences when compared to objects identified from the data that now exist in other clusters. The process of clustering is very significant in various aspects of data analysis, as it determines and presents the intrinsic grouping of objects present in the data, based on their attributes, in a batch of unlabeled raw data. A textbook or otherwise said, good criteria, does not exist in this method of cluster analysis. That is because this process is so different and so customizable for every user, that needs it in his/her various and different needs. There is no outright best clustering algorithm, as it massively depends on the user’s scenario and needs. This paper is intended to compare and study two different clustering algorithms. The algorithms under investigation are k-mean and mean shift. These algorithms are compared according to the following factors: time complexity, training, prediction performance and accuracy of the clustering algorithms.

In the paper, the authors survey integral representations (including the Lévy--Khintchine representations) and applications of some bivariate means (including the logarithmic mean, the identric mean, Stolarsky's mean, the harmonic mean, the (weighted) geometric means and their reciprocals, and the Toader--Qi mean) and the multivariate (weighted) geometric means and their reciprocals, derive integral representations of bivariate complex geometric mean and its reciprocal, and apply these newly-derived integral representations to establish integral representations of Heronian mean of power 2 and its reciprocal.

In recent times, there has been a growing interest in the use of control charts as a feedback process monitoring technique. Particularly, CUSUM schemes have been proven to be efficient for monitoring processes where the magnitude of the sustained mean shifts is small or moderate. However, because of the constant control limits, the detection ability of CUSUM schemes becomes slow at the initial set-up of the process. The fast initial response FIR feature has often been used to enhance it at the process startup. Meanwhile, the dynamism of real-life problems has always encouraged a more sensitive CUSUM scheme capable of detecting process shifts more rapidly. In this paper, an improved CUSUM scheme for monitoring process mean is proposed. This scheme will be substantial for monitoring processes whose observations are obtained at a distant time interval for example hourly, daily or weekly and where the sustained shifts are assumed to be small or moderate. To demonstrate the practical applications of the proposed scheme, we present its real-life application using datasets from a bottling company and petroleum refinery laboratory.

In the paper, by virtue of a Lévy–Khintchine representation and an alternative integral representation for the weighted geometric mean, the authors establish a Lévy–Khintchine representation and an alternative integral representation for the Toader–Qi mean. Moreover, the authors also collect an probabilistic interpretation and applications in engineering of the Toader–Qi mean.

Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2},\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.

Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2}% ,\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.

Ranked Set Sampling (RSS) is a useful technique for improving the estimator of population mean when the sampling units in a study can be easily ranked than the actual measurement. RSS performs better than simple random sampling (SRS) when the mean of units corresponding to each rank is used. The performance of RSS can be increased further by assigning weights to the ranked observations. In this paper, we propose weighted RSS procedures to estimate the population mean of positively skew distributions. It is shown that the gain in the relative precisions of the population mean for chosen distributions are uniformly higher than those based on RSS. The gains in relative precisions are substantially high. Further, the relative precisions of our estimator are slightly higher than the ones based on Neyman’s optimal allocation model for small sample sizes. Moreover, it is shown that, the performance of the proposed estimator increases as the skewness increases by using the example of lognormal family of distributions.

In this paper, we introduce the notion of weighted generalized group inverse in a Banach algebra with proper involution. This is a natural generalization of weighted weak group inverse for a complex matrix and Hilbert space operator. We present several characterizations and representations of this generalized inverse. In addition, a new partial order on elements in a Banach *-algebra is investigated by using the weighted generalized group inverse and some known results are thus generalized.

In this paper, we study the weighted reproducing kernels. We introduce a generalization of weighted reproducing property and extend it to relative reproducing property on Banach spaces. This generalization will develop the parallel computing and it can be used as a base of parallel learning for machines especially in the case that there are non-homogenous weighted hypothesis. This methods formulate learning and estimation problems in a relative reproducing kernel Banach space (RRKBS) of functions defined on the data domain, expanded in terms of a kernel.

In this paper we establish some weighted integral inequalities of Ostrowski, Čebyšev and Lupaş type. Applications for continuous probability density functions supported on infinite intervals with two examples are also given.

The heterogeneous structure implies that a few nodes may be crucial in maintaining network structural and functional properties. Identifying these crucial nodes correctly and quickly is a primary issue as contemporarily may face the mushrooming of large-scale datasets. Besides, the ‘weight issue’ is always ignored in this field which edge weight may play a positive/negative role in contributing to the node importance in different weighted networks. This paper provides a novel algorithm, Weighted Expectation Algorithm (WEA), which aims to ensure accuracy and speed of computation by taking advantage of dynamic programming to better handle the task of large-scale networks. Additionally, the weight issue that edge weights may contribute differently is addressed by a simply quantitative definition. Two standard experiments show WEA can maintain the network structure in connectivity well (by the lowest average robustness 0.192) and identify the node importance better in the spreading function test of spreading dynamics (by the highest average Kendall’s tau-b 0.678). In addition, the time complexities of different algo-rithms are evaluated, and their time-consuming are tested, proving that WEA consumes a rela-tively short time.

We have estimated the level of Risk Weighted Assets among 30 countries in Europe, in 30 trimesters, using data of the European Banking Authority-EBA of 139 variables. We perform an econometric model using Pooled OLS, Panel Data with Fixed Effects, Panel Data with Random Effects, Weighted Least Squares. We found that Risk Weighted Assets is negatively associated, among others, to the level of NFC loans in mining and quarrying, in public administration and defence, and in financial and insurance activities and positively associated, among others to distribution of NFC loans in human health services and social work activities, in education and the level of net fee and commission income. Furthermore, we apply a cluster analysis with the k-Means algorithm, and we find the presence of two clusters. A comparison was then made between eight different machine learning algorithms for predicting the value of the RWAs and we found that the best predictor is the linear regression. The RWA value is predicted to increase by 1.5%.

Aiming at the defects of low precision and time cumulative error, an external wireless signal weighted centroid localization algorithm aided inertial positioning method is designed in this paper. According to the signal strength of each anchor node received at the test point, the distance between the anchor node and the anchor node is obtained by using the attenuation model of the wireless signal. Three anchor nodes are used to measure the distance between the anchor node and the measured point. We can obtain the area to be measured according to the actual situation, the position of the measured point is obtained by the weighted centroid localization algorithm and a combined model of wireless signal aided inertial navigation system is established. The simulation results show that the method can greatly improve the positioning accuracy and restrain the divergence of the longitude error and latitude error.

In this study, we investigate the behavior of randomly moving particles with a defined average energy, focusing on their biased motion around a specific point. These particles' velocity magnitudes follow a Maxwell distribution with a specific scale parameter. Our analysis derives the stochastic rotation rules for these particles and introduces the Ito equation conditions for biased stochastic rotation at a given curl value. We also consider the special relativistic-like effects in this context. The findings are validated through a representative example.

In this paper, we investigate the effects of mean stress, multiaxial loading, and residual stresses on the fatigue life of springs. We study the fatigue life of a homogeneously stressed material subjected to cyclic loading with nonzero mean stress. Traditional methods for estimating fatigue life are based on Goodman and HAIGH diagrams. The formal analytical descriptions, namely "stress-life" and "strain-life" approaches, are found to be more suitable for the numerical methods. The fatigue analysis method described above, which describes crack growth per cycle, is extended. The extensions allow consideration of the mean stress of a load cycle. Closed-form expressions for crack length versus number of cycles are derived. The complementary effects on the fatigue life of springs, which ultimately have a significant influence on the fatigue life of springs, are summarized. For the proposed unified fatigue life functions, the ranges for the stress loading factor are extended by introducing the effective stress intensity. The solution leads to the factor range for the effective stress intensity, the effective mean value of the stress intensity factor and the effective stress ratio. The developed method assumes the homogeneous stress state in the whole spring element. For the non-homogeneously loaded structural elements, the weak-link concept is applied to account for fatigue.

In document forensic, Ink mismatch relays very important information about forgeries in this way we can find out the authenticity of documents. Finding out and distinguishing these unique inks from the multispectral document is very challenging task. In this paper we proposed the method to identify the inks using clustering. We used K-Mean clustering instead of widely known Fuzzy C-Means Clustering (FCM) and successfully identity the number of inks. For the purpose of optimizing and improving our results we used two optimization techniques such as Elbow and silhouette optimization techniques.

Background and Objectives To compare navigator-gated three-dimensional T1-weighted gradient-echo sequences (NG-3D T1W-GRE) with standard breath-hold T1W-GRE (BH T1W-GRE) for the detection of HCC nodules in patients with chronic viral hepatitis which undergo at magnetic resonance imaging (MRI) using gadoxetic acid. Methods and materials We evaluated 58 patients with hepatic nodules at least 1 cm in diameter detected by ultrasound who underwent liver MRI including NG-3D T1W-GRE sequences and breath hold T1-weighted gradient-echo sequences with different flip angles(FA) at 10-25-40° after contrast administration of gadoxetic acid at magnetic scanner operating at1.5 Tesla. Image quality and relative hepatic and nodular enhancement were evaluated by three blinded reviewers. Results In these patients, image quality of NG-3D T1W-GRE was assessed significantly better than quality of BHT1W- GRE (P < 0.005) and relative enhancement was significantly higher than that of BH- T1W-GRE ( P

In the radar system, detection represents a basic and important stage in the receiver side. The detection process is based on the thresholding criteria; two philosophies of this criteria, constant and adaptive threshold. The constant threshold is simple in design, but it has a mis-detection and does not control the false alarm rate. As for the adaptive threshold, it is powerful in target detection, and better control of the false alarm rate, where it is called Constant False Alarm Rate (CFAR). Lots of research in the CFAR design, but the gap in the previous works is that there is no CFAR algorithm can be working with all or most environmental fields and all or most target situations.In this paper, The CFAR, which can work with the most environment and most of the target situations, has been presented. The producing the design and implementation of the new practical CFAR processor is presented. Where, the new CFAR is a combination of the properties of three different CFAR algorithm (CA, OSGO, and OSSO), and from two different families; averaging and statistical. Where it has overperformed of it's is 97.25% for simulation and 96.25% for the implementable version for different target situations. The simulation analysis is made by using Matlab 2015, while the implementation is done by using Xilinx Spartan 700 3a.

Containing hundreds of spectral bands (features), hyperspectral images (HSIs) have high ability in discrimination of land cover classes. Traditional HSIs data processing methods consider the same importance for all bands in the original feature space (OFS), while different spectral bands play different roles in identification of samples of different classes. In order to explore the relative importance of each feature, we learn a weighting matrix and obtain the relative weighted feature space (RWFS) as an enriched feature space for HSIs data analysis in this paper. To overcome the difficulty of limited labeled samples which is common case in HSIs data analysis, we extend our method to semisupervised framework. To transfer available knowledge to unlabeled samples, we employ graph based clustering where low rank representation (LRR) is used to define the similarity function for graph. After construction the RWFS, any arbitrary dimension reduction method and classification algorithm can be employed in RWFS. The experimental results on two well-known HSIs data set show that some dimension reduction algorithms have better performance in the new weighted feature space.

In this short communication, following a brief introduction, we undertake a comprehensive analytical study of the weighted Simpson index. Our primary emphasis concerns the precise determination of the optimal point (minimizer) coordinates and of the minimum value of the index, a differentiable convex function, which is related to the harmonic mean concept. Furthermore, we address and solve the inversion problem and show the tight connection between both approaches. Last, we give some insights and final remarks on this subject.

Weighted Student Funding (WSF) systems have been implemented in various countries to give schools more autonomy over how to allocate their funding. School principals use funding to maintain school operations and foster innovation for achieving educational goals. However, despite the importance of this process, scholarly research has largely overlooked how principals make decisions about their financial resources. Accordingly, this study seeks to provide practical insights into the strategies used by one school by highlighting their staff’s perceptions about using their WSF to maintain school operations and spur innovation. Using a case study approach, we investigated a principal who effectively used a school’s WSF to transform a failing school into an innovative one. The findings revealed that the principal strategically implemented financial management mechanisms in a way that inspired teachers to deeply consider how a school's WSF can help achieve educational goals. The principal fostered consensus on the school's direction, encouraged innovation through hands-on experiential learning and strategic planning, and facilitated funding for innovative teachers by guiding proposal development. Insights into the shifting cultural and practical landscape of financial resource utilization within schools are discussed.

In this paper we provide amongst others some simple error bounds in approximating the weighted Riemann-Stieltjes integral $\int_{a}^{b}f\left(t\right) g\left(t\right) dv\left(t\right) $ by the use of three points formula \begin{equation*} f\left(b\right) \int_{c}^{b}g\left(s\right) dv\left(s\right) +f\left(a\right) \int_{a}^{d}g\left( s\right) dv\left( s\right) -f\left(x\right) \int_{c}^{d}g\left(t\right) dv\left(t\right) \end{equation*} where $x,$ $c,$ $d\in \left[a,b\right],$ $g,$ $v:\left[a,b\right] \rightarrow \mathbb{C}$ under bounded variation and Lipschitzian assumptions for the function $f$ and such that the involved Riemann-Stieltjes integrals exist.

This study introduces a new discrete distribution which is a weighted version of Poisson-Lindley distribution. The weighted distribution is obtained using the negative binomial weight function and can be fitted to count data with over-dispersion. The p.m.f., p.g.f. and simulation procedure of the new weighted distribution, namely weighted negative binomial Poisson-Lindley (WNBPL), are provided. The maximum likelihood method for parameter estimation is also presented. The WNBPL distribution is fitted to several insurance datasets, and is compared to the Poisson and negative binomial distributions in terms of several statistical tests.

This paper employs the two-step procedure developed by Cheung and Ng (1996) to analyze the causality-in-mean and causality-in-variance between the housing and stock markets of the UK. The empirical findings make two key contributions. First, although previous studies have indicated a one-way causal relation from the housing market to the stock market in the UK, this paper discovered a two-way causal relation between them. Second, a causality-in-variance as well as a causality-in-mean was detected from the housing market to the stock market.

In a particle swarm with a fixed kinetic energy, the constituent particles move randomly and their velocity magnitudes follow a Maxwell distribution characterized by specific parameters. Within a certain time frame, particles in a sub-swarm may exhibit a bias in their movement direction. Thus, the particles may exhibit a special characteristic (biased random motion), where the group velocity in a particular direction remains constant u. For this biased particle swarm, composed of randomly moving particles with a fixed average speed c, particles have a higher probability of moving in a specific direction. Conversely, their likelihood of moving in all other directions is equally reduced. This study starts from the perspective of biased random walks and using Mathematica software proves that the diffusion rate of particles (in the reference frame R_u observed from R₀) in all directions is slower than that of an unbiased particle swarm with the same average speed c. Specifically, the degree of reduction is determined by the Lorentz-like factor. Lastly, we present the Ito equation for this biased random motion and provide associated verification examples. This study aims to serve as a reference for comprehending the underlying principles of the special relativity effect.

Measurement uncertainty is typically expressed in terms of a symmetric interval , where denotes the measurement result and the expanded uncertainty. However, in the case of heteroscedasticity, symmetric uncertainty intervals can be misleading. In this paper, a different approach for the calculation of uncertainty intervals is introduced. This approach is applicable when a validation study has been conducted with samples with known concentrations. It will be shown how, under certain circumstances, asymmetric uncertainty intervals arise quite naturally and lead to more reliable uncertainty intervals.

Functional Data Analysis (FDA) is a relatively new field of statistics dealing with data expressed in the form of functions. FDA methodologies can be easily extended to the study of imaging data, an application proposed in Wang et al. (2020), where the authors settle the mathematical groundwork and properties of the proposed estimators. This methodology allows for the estimation of mean functions and simultaneous confidence corridors (SCC), also known as simultaneous confidence bands, for imaging data and for the difference between two groups of images. This is especially relevant for the field of medical imaging, as one of the most extended research setups consists on the comparison between two groups of images, a pathological set against a control set. FDA applied to medical imaging presents at least two advantages compared to previous methodologies: it avoids loss of information in complex data structures and avoids the multiple comparison problem arising from traditional pixel-to-pixel comparisons. Nonetheless, computing times for this technique have only been explored in reduced and simulated setups (Arias-López et al., 2021). In the present article, we apply this procedure to a practical case with data extracted from open neuroimaging databases and then measure computing times for the construction of Delaunay triangulations, and for the computation of mean function and SCC for one-group and two-group approaches. The results suggest that previous researcher has been too conservative in its parameter selection and that computing times for this methodology are reasonable, confirming that this method should be further studied and applied to the field of medical imaging.

This study evaluates the historical mean surface temperature (hereafter T2m) and examines how T2m changes over East Africa (EA) in the 21^st century using CMIP6 models. An evaluation was conducted based on mean state, trends, and statistical metrics (Bias, Correlation Coefficient, Root Mean Square Difference, and Taylor skill score). For future projections over EA, five best performing CMIP6 models (based on their performance ranking in historical mean temperature simulations) under the shared socioeconomic pathways SSP2-4.5 and SSP5-8.5 scenarios were employed. The historical simulations reveal an overestimation of the mean annual T2m cycle over the study region with fewer models depicting underestimations. Further, CMIP6 models reproduce the spatial and temporal trends within the observed range proximity. Overall, the best performing models are as follows: FGOALS-g3, HadGEM-GC31-LL, MPI-ESM2-LR, CNRM-CM6-1, and IPSL-CM6A-LR. During the three-time slice under consideration, the Multi Model Ensemble (MME) project many changes during the late period (2080 – 2100) with expected mean changes at 2.4 °C for SSP2-4.5 and 4.4 °C for the SSP5-8.5 scenario. The magnitude of change based on Sen’s slope estimator and Mann-Kendall test reveal significant increasing tendencies with projections of 0.24°C decade-1 (0.65°C decade-1) under SSP2-4.5 (SSP5-8.5) scenarios. The findings from this study illustrate higher warming in the latest model outputs of CMIP6 relative to its predecessor, despite identical instantaneous radiative forcing.

Hamacher operation which is generalization of the Algebraic and Einstein operation, can widely provide a large number of arithmetical operation with respect to uncertainty information, and Heronian mean can deal with correlations of the input arguments or different criteria and don’t make calculation redundancy, meanwhile, the normal intuitionistic fuzzy numbers (NIFNs) can depict distinctively normal distribution information in practical decision making. In this paper, a multi-criteria group decision-making (MCGDM) problem is researched under the NIFNs environment, and a new MCGDM approach is introduced on the basis of the Hamacher operation. Firstly, according to Hamacher t-conorm and t-norm, some operational laws of NIFNs are presented. Secondly, it is noticed that Heronian mean can’t only once take into account mutual relation between attribute values once, but also consider the correlation between input argument and itself. Therefore, we develop some operators and study their properties in order to aggregate normal intuitionistic fuzzy numbers information, these operators include Hamacher Heronian mean (NIFHHM), Hamacher weighted Heronian mean (NIFHWHM), Hamacher geometric Heronian mean (NIFHGHM) and Hamacher weighted geometric Heronian mean (NIFHWGHM). Furthermore, we apply the proposed operators to the MCGDM problem and present a new method. The main characteristics of this new method involve that: (1) it is suitable to make decision under the normal intuitionistic fuzzy numbers environment and more reliable and reasonable to aggregate the normal distribution information. (2) it utilizes Hamacher operation which can provide more reliable and flexible decision-making results and offer an effective and powerful mathematic tool for the MAGDM under uncertainty. (3) it uses the Heronian mean operator which can considers relationships between the input arguments or the attributes and don’t brings subsequently about redundancy. Lastly, an application is given for showing the feasibility and effectiveness of the presented method in this paper.

We consider a Mean Field Games model where the dynamics of the agents is given by a controlled Langevin equation and the cost is quadratic. A change of variables, introduced in [13], transforms the Mean Field Games system into a system of two coupled kinetic Fokker-Planck equations. We prove an existence result for the latter system, obtaining consequently existence of a solution for the Mean Field Games system.

We show that the implementation of the 1/c² transverse current-current interaction between electrons into the standard self-consistent electron BCS model in bulk under thermal equilibrium ensures in the stable superconductive phase the full compensation of a constant external magnetic field by the internal magnetic field created by the electrons i.e. one has an ideal diamagnet. However, no proof of the phenomenological London equation emerges within the bulk approach.

Prostate cancer (PCa) is the most diagnosed non-cutaneous cancer in men. Despite therapies such as radical prostatectomy, which is considered curative, distant metastases may form resulting in biochemical recurrence (BCR). This study used radiomic features calculated from multi-parametric magnetic resonance imaging (MP-MRI) to evaluate their ability to predict BCR and PCa presence. Data from a total of 279 patients, of which 46 experienced BCR, undergoing MP-MRI prior to surgery were assessed for this study. After surgery, the prostate was sectioned using patient-specific 3D-printed slicing jigs modeled using the T2-weighted imaging (T2WI). Sectioned tissue was stained, digitized, and annotated by a GU-fellowship trained pathologist for cancer presence. Digitized slides and annotations were co-registered to the T2WI and radiomic features were calculated across the whole prostate and cancerous lesions. A tree regression model was fitted to assess the ability of radiomic features to predict BCR, and a tree classification model was fitted with the same radiomic features to classify regions of cancer. We found that 10 radiomic features predict eventual BCR with an AUC of 0.97 and classifying cancer at an accuracy of 89.9%. This study showcases the application for a radiomics-based tool to screen for the presence of prostate cancer and assess patient prognosis, as determined by biochemical recurrence.

Power law relationships, which describe scaling relationships of data, are powerful information theoretic descriptive tools in many empirical contexts, including that of music. Zipf’s law (pink noise) describes the optimum case of a power law relation where observations are exactly inversely proportional to their rank. Descriptions that approximate a pink noise signature can be said to maximize the amount of information in a signal, and is thus suggestive of a richness of an understanding. This information density of pink noise signatures is not, however, necessarily a desirable quality for explanations in general, which, by definition, “flattens out” some data while highlighting others, ideally those most relevant to an interpretation. The privileging of data most relevant to comprehension corresponds to a red noise relationship, as opposed to the pink noise of Zipf’s law or the white noise of a description that highlights nothing in particular. Here, I explore and evaluate this concept of red noise explanations in the form of analyses of three comparable short piano works: Robert Schumann’s “Von fremden Ländern und Menschen” (no.1 from Kinderszenen op. 15, 1838), Frédéric Chopin’s Prelude op. 28 no. 20 (1838-9), and Felix Mendelssohn’s “Venetianisches Gondellied” (no. 6 from Lieder ohne Worte op. 19b, 1829-30).

This study examines the improvement in coupled intercomparison project phase six (CMIP6) models against the predecessor CMIP5 in simulating mean and extreme precipitation over the East Africa region. The study compares the climatology of the precipitation indices simulated by the CMIP models with the CHIRPS dataset using robust statistical techniques for 1981 – 2005. The results display the varying performance of the general circulation models (GCMs) in the simulation of annual and seasonal precipitation climatology over the study domain. CMIP6-MME shows improved performance in the local annual mean cycle simulation with a better representation of two peaks, especially the MAM rainfall relative to its predecessor. Moreover, simulation of extreme indices is well captured in CMIP6 models relative to its predecessor. The CMIP6-MME performed better than the CMIP5-MME with lesser biases in simulating SDII, CDD, and R20mm over East Africa. Remarkably, most CMIP6 models are unable to simulate extremely wet days (R95p). A few CMIP6 models (e.g., NorESM2-MM and CNRM-CM6-1) depicts robust performance in reproducing the observed indices across all analyses. Conversely, OND season shows the overestimation of some indices (i.e., R95p, PRCPTOT), except for SDII, CDD, and R20mm. Consistent with other studies, the mean ensemble performance for both CMIP5/6 shows better performance due to the cancellation of some systematic errors in the individual models. Generally, the CMIP6 depicts improved performance in the simulation of MAM season akin CMIP5 models. However, the new model generation is still marred with uncertainty, thereby depicting substandard performance over the East Africa domain. This calls for further investigation of attribution studies into the sources of persistent systematic biases and a prerequisite for identifying individual models with robust features that can accurately simulate observed patterns for future usage.

Background and Objectives: The existing recommendations for female pelvic magnetic susceptibility weighted imaging MRI (FP-SWI) have not been optimized to capture the disease characteristics of the female pelvis. Therefore, it is imperative to explore acquisition parameters before conducting larger-scale studies. To establish optimized flip angle (FA) for acquiring FP-SWI to improve the image quality of female pelvic lesion sites. Materials and Methods: To evaluate signal quality and lesion conspicuity, regions of interest (ROIs) were manually drawn within the lesion on SWI sequences. Signal intensity was measured within the ROIs. Additionally, signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) were calculated for SWI sequences acquired at three FA: 10°, 15°, and 20°. Finally, a qualitative assessment of anatomical detail visualization, geometric distortion extent, artifacts, and lesion clarity was performed using a four-point scale. The Wilcoxon rank sum test was employed to compare the qualitative evaluation parameters. The intra-class correlation coefficient (ICC) was calculated to determine the consistency of subjective ratings between two observers. Results: FA=10° showed significantly higher SNR than FA=15° and 20° in most anatomical regions (P&lt;0.05), while the CNR was significantly higher than FA=15° and 20° (P&lt;0.05). Compared with FA=15° and 20°, the image quality of FA=10° was significantly higher, with less distortion and ghosting, and better image contrast (P&lt;0.05). Lesions with FA=10° exhibited higher clarity compared to FA=15° and 20° (P&lt;0.05). Conclusions: The image quality of FP-SWI images at FA=10° exceeds that at FA=15° and 20°. We recommend that when conducting SWI examination of the female pelvic cavity, the FA value should be set at 10° to stabilize the SWI sequence and improve image quality.

We investigate \texorpdfstring{$L_2$}{}-approximation problems in the worst case setting in the weighted Hilbert spaces \texorpdfstring{$H(K_{R_{d,\a,\g}})$}{} with weights \texorpdfstring{$R_{d,\a,{\bm \ga}}$}{} under parameters \texorpdfstring{$1\ge \ga_1\ge \ga_2\ge \cdots\ge 0$ and $1<\az_1\le \az_2\le \cdots$}{}. Several interesting weighted Hilbert spaces \texorpdfstring{$H(K_{R_{d,\a,\g}})$}{} appear in this paper. We consider the worst case error of algorithms that use finitely many arbitrary continuous linear functionals. Multivariate approximation; information complexity; tractability; weighted Hilbert spacesWe discuss tractability of \texorpdfstring{$L_2$}{}-approximation problems for the involved Hilbert spaces, which describes how the information complexity depends on \texorpdfstring{$d$}{} and \texorpdfstring{$\va^{-1}$}{}. As a consequence we study the strongly polynomial tractability (SPT), polynomial tractability (PT), weak tractability (WT), and \texorpdfstring{$(t_1,t_2)$}{}-weak tractability (\texorpdfstring{$(t_1,t_2)$}{}-WT) for all \texorpdfstring{$t_1>1$}{} and \texorpdfstring{$t_2>0$}{} in terms of the introduced weights under the absolute error criterion or the normalized error criterion.

Noise reduction in medical images is a perplexing undertaking for the researchers in digital image processing. Noise generates maximum critical disturbances as well as touches the medical images quality, ultrasound images in the field of biomedical imaging. The image is normally considered as gathering of data and existence of noises degradation the image quality. It ought to be vital to reestablish the original image noises for accomplishing maximum data from images. Medical images are debased through noise through its transmission and procurement. Image with noise reduce the image contrast and resolution, thereby decreasing the diagnostic values of the medical image. This paper mainly focuses on Gaussian noise, Pepper noise, Uniform noise, Salt and Speckle noise. Different filtering techniques can be adapted for noise declining to improve the visual quality as well as reorganization of images. Here four types of noises have been undertaken and applied on medical images. Besides numerous filtering methods like Gaussian, median, mean and Weiner applied for noise reduction as well as estimate the performance of filter through the parameters like mean square error (MSE), peak signal to noise ratio (PSNR), Average difference value (AD) and Maximum difference value (MD) to diminish the noises without corrupting the medical image data.

An approach to the assessment of probabilistic inference is described which quantifies the performance on the probability scale. From both information and Bayesian theory, the central tendency of an inference is proven to be the geometric mean of the probabilities reported for the actual outcome and is referred to as the “Accuracy.” Upper and lower error bars on the accuracy are provided by the arithmetic mean and the -2/3 mean. The arithmetic is called the “Decisiveness” due to its similarity with the cost of a decision and the -2/3 mean is called the “Robustness”, due to its sensitivity to outlier errors. Visualization of inference performance is facilitated by plotting the reported model probabilities versus the histogram calculated source probabilities. The visualization of the calibration between model and source is summarized on both axes by the arithmetic, geometric, and -2/3 means. From information theory, the performance of the inference is related to the cross-entropy between the model and source distribution. Just as cross-entropy is the sum of the entropy and the divergence; the accuracy of a model can be decomposed into a component due to the source uncertainty and the divergence between the source and model. Translated to the probability domain these quantities are plotted as the average model probability versus the average source probability. The divergence probability is the average model probability divided by the average source probability. When an inference is over/under-confident, the arithmetic mean of the model increases/decreases, while the -2/3 mean decreases/increases, respectively.

This paper presents a new discrete counterpart of the mixture exponential distribution by utilizing the survival discretization method. The moment-generating function and associated moment measures are discussed. The distribution’s hazard rate function can assume increasing or decreasing forms, making it adaptable for diverse fields requiring count data modelling. The paper explores four distinct parameter estimation methods and assesses their performance through Monte Carlo simulations. The applicability of this distribution extends to time series analysis, particularly within the framework of the first-order integer-valued autoregressive process. Additionally, the paper explores quality control applications, addressing serial dependence challenges in count data encountered in production and market management. The performance of two distinct control charts, the cumulative sum chart and the exponentially weighted moving average chart, is evaluated for their effectiveness in detecting shifts in the process means under various models. A bivariate Markov chain approach is used to estimate the average run lengths of these charts, offering valuable insights for implementation. Design recommendations for achieving robustness in-control chart applications are provided. The effectiveness of the proposed models and charts is illustrated using a real data, demonstrating their practical superiority.

Using a theorem of Ulam and Hyers, we will prove the Hyers-Ulam stability of two-dimensional Lagrange's mean value points $(\eta, \xi)$ which satisfy the equation, $f(u, v) - f(p, q) = (u-p) f_x(\eta, \xi) + (v-q) f_y(\eta, \xi)$, where $(p, q)$ and $(u, v)$ are distinct points in the plane. Moreover, we introduce an efficient algorithm for applying our main result in practical use.

Background. To describe the characteristics of anterior mediastinal masses on conventional magnetic resonance imaging (MRI) and to assess the role of the Apparent Diffusion Coefficient (ADC) value in distinguishing benign from malignant mediastinal lesions. Methods. We conducted a retrospective cross-sectional study on 55 patients with anterior mediastinal mass who performed MRI before treatment. Biopsy and histopathological assessments were done after that. A radiologist evaluates the changes of signal intensity on these sequences: T1- weighted VIBE DIXON pre and post-contrast with Gadolinium, T2 HASTE, T2 TIRM, DWI/ADC, to determine the size, margin of the lesion, the presence of fat, cystic in it. ADCs values were calculated from the ADC maps which were constructed from b = 0 and b = 2000 Results. The study was composed of 55 patients, with 5 benign lesions and 50 malignant lesions. The ADCmean, ADCmedian, ADC10, and ADC90 in the histogram-based approach and hot-spot-ROI-based mean ADC for the malignant lesions was significantly lower than those found in benign lesions (P-value <0.05). The hot-spot-ROI-based mean ADC had the highest value in differentiation between benign and malignant mediastinal lesions, between group A (benign lesions, thymoma A, AB, B1) and group B (thymoma B2, B3 and other malignant lesions). The cut-off point of the ADC value differentiating malignant from benign mediastinal lesions was 1,17x10-3mm2/s with sensitivity of 80%, and specificity of 80%. The cut off point of the ADC value differentiating group A from group B was 0.99 x10-3mm2/s with sensitivity of 78,4%, and specificity of 88.9%. The cut-off point of the ADC value differentiating lymphoma from other malignant lesions was 0,91 x10-3mm2/s with sensitivity of 100%, and specificity of 60.5%. Conclusion. Diffusion-weighted MRI and measurement of ADC value in histogram-based approach and hot-spot-ROI-based mean ADC are very helpful in the differentiation between benign and malignant anterior mediastinal lesions.

Background: Many clinical conditions are affected by meteorological factors and climate changes. Psychiatric disorders are large contributors to the global disease burden, but the literature on the impact of climate changes on mental health is limited. The aim of this study is to investigate the correlation between rising temperatures and admissions for acute exacerbations of psychiatric disorders. Methods: Data were collected for summer months of years 2013 to 2022. Mean monthly tempera-tures were obtained from the meteorological station of the Department of Physics of the Universi-ty of Turin. Data on patients admitted to the acute psychiatric unit of San Luigi Gonzaga Univer-sity Hospital (Turin, Italy) were extracted from the hospital registry. Linear regression analyses were used to investigate the correlation between temperature and number of admissions. Results: A total of 1600 admissions to our psychiatric ward were recorded. Mean monthly temper-ature and monthly number of admissions were directly correlated (P = 0.0020). The correlation between temperature and admissions was significant for the subgroup of admissions due to Bipo-lar Disorders (BD) (P=0.0011), but not for Schizophrenia (P=0.6070) (SCZ) or Major Depressive Disorder (MDD) (P=0.0588). Conclusions: These results confirm the impact of meteorological factors on mental disorders, and in particular on the course of BD. This provides new insights into etiopathological mechanisms and can contribute to improved follow up and relapse prevention.

In order to better understand the extent to which global climate variability is linked to the frequency and intensity of heat waves and overall changes in temperature throughout the United States (US), correlations between long-term monthly mean, minimum, and maximum temperatures measured at sites throughout the contiguous US and low-frequency variability of multiple climate indices (CIs) are analyzed over the period 1948 to 2018 using correlation analysis. The Pearson’s correlation coefficient is used to assess correlation strength, while Leave-One-Out Cross-Validation and a bootstrapping technique (p-value) are used to address potential serial and spurious correlation and assess the significance of each correlation. Three parameters defined the sliding windows over which surface temperature and CI values were averaged: window size, lag time between the temperature and CI windows, and the beginning month of the temperature window. A 60-month sliding window size and 0 lag time resulted in the strongest correlations overall; beginning months were optimized on an individual site basis. Strong (r &gt;= 0.60) and significant (p-value &lt;= 0.05) correlations were identified. The Western Hemisphere Warm Pool (WHWP) and El Niño/Southern Oscillation (ENSO) exhibited the strongest links to temperatures in the western US, tropical Atlantic sea surface temperatures to temperatures in the central US, the WHWP to temperatures throughout much of the eastern US, and atmospheric patterns over the northern Atlantic to temperatures in the Northeast and Southeast. The final results were compared to results from previous studies focused on precipitation and coastal sea levels. Regional consistency was found regarding links between the northern Atlantic and overall weather and coastal sea levels in the Northeast and Southeast as well as on weather in the upper Midwest. Though the MJO and WHWP revealed dominant links with precipitation and temperature, respectively, throughout the West, ENSO revealed consistent links to sea levels and surface temperatures along the West Coast. These results help focus future research regarding specific mechanisms of climate variability that appear the exhibit strong links to US regional weather and sea level variability and prediction.

Artistic image completion is fundamental for the preservation and restoration of invaluable art paintings and it has experienced significant progress through the implementation of deep learning methodologies. Despite these advancements, challenges persist, even with sophisticated approaches like Generative Adversarial Networks (GANs), particularly in achieving optimal results for high-resolution paintings. Small-scale texture synthesis and the inference of missing information from distant contexts present persistent issues, leading to distortions in lines and unnatural colors, especially in art paintings with complicated structures and textures. Concurrently, patch-based image synthesis has evolved by incorporating global optimization on the image pyramid to enhance structural coherence and details. However, methods relying on gradient-based synthesis encounter obstacles related to directionality, inconsistency, and the heavy computational burdens associated with solving the Poisson equation in non-integrable gradient fields. This paper introduces a groundbreaking approach, integrating Weighted Similarity-Confidence Laplacian Synthesis, to comprehensively address these challenges and advance the field of artistic image completion. This proposal addresses challenges not only in high-resolution artistic image completion but also makes a significant contribution to the broader field of patch-based synthesis by utilizing the Laplacian pyramid for enhanced edge-aware correspondence search. Experimental result confirms the effectiveness of our approach, offering promising outcomes for the preservation and restoration of art paintings with complicated details and irregular missing regions.

One of the most important applications in the wireless sensor networks (WSN) is to classify mobile targets in the monitoring area. In this paper, a multi-DBN weighted voting classification algorithm is proposed on the basis of the Deep Belief Network (DBN) classifier and combined with the idea of voting method, which is implemented on the nodes of the WSN monitoring system by means of "upper training, lower transplantation" appraoch. The performance of the algorithm is verified by using real-world experimental data, and the results show that the proposed method has a higher accuracy in classifying the target signal features, achieving an average classification accuracy of 84.63% across four different types of moving targets. The experiment reveals that the multi-DBN weighted voting algorithm enhances the target classification accuracy by approximately 5% in comparison to the single DBN classifier, but the memory and computation time required for the algorithm to run are also increased at the same time. Compared to the FFNN classifier, which exhibited the highest classification accuracy among the four selected methods, the algorithm achieves an improvement of approximately 8.8% in classification accuracy. However, it incurs greater time overhead to run.

The assessment outcomes of regional susceptibility to geological disasters can directly indicate the extent and intensity of risks within the study area, thus, providing targeted guidance for disaster management efforts. This study selects eight evaluation indicators, namely elevation, gradient, terrain relief, lithology of strata, normalized difference vegetation index, distance from the fault, distance from road, and distance from the river. The study focuses on Huize County in Yunnan Province as the research area, utilizing the certainty factor (CF) and random forest (RF) models for evaluating the susceptibility to geological disasters. The non-geological disaster points in the study area are determined using the deterministic coefficient prior model, and the deterministic coefficient values for each evaluation factor serve as the classification data for the random forest model. The optimal parameters for the random forest are selected through iterative calculations of bag error in PyCharm, while the weight of the evaluation factor is determined based on the ran-dom forest model with the optimal parameters. The results of geological disaster susceptibility zoning in Huize County are obtained by overlaying the weighted deterministic coefficients of each evaluation factor. The accuracy of the evaluation results is verified using zoning statistics and ROC curves with a test sample of 30% of the points. The results demonstrate the high accuracy of the model in evaluating the susceptibility to geological disasters in Huize County. Compared to the single deterministic coefficient model, this approach offers advantages in terms of reliability and accuracy. The evaluation results can serve as a scientific reference for related work in Huize County.

The airport ground handling services (AGHS) equipment supplier selection problem involves a safety guarantee on the part of the AGHS company that carries out the daily work. AGHS company can prevent aircraft damage and delays in airlines schedules, and ensure reliable and high-quality ground handling service. In our research, we developed an AGHS equipment supplier selection model based on the analytic hierarchy process and an AHP weighted fuzzy linear programming approach, and we solved the AGHS equipment supplier’s selection problem. The main objective of this article is to create an AHP and AHP-FLP decision model in order to help the AGHS company authorities select the best AGHS equipment supplier. The practical application in AGHS equipment supplier selection decisions can be interpreted as demonstrating that the proposed model provides knowledge and practical value for the AGHS industry.

Tail-biting convolutional codes extend the classical zero-termination convolutional codes: Both encoding schemes force the equality of start and end states, but under the tail-biting each state is a valid termination. This paper proposes a machine-learning approach to improve the state-of-the-art decoding of tail-biting codes, focusing on the widely employed short length regime as in the LTE standard. This standard also includes a CRC code. First, we parameterize the circular Viterbi algorithm, a baseline decoder that exploits the circular nature of the underlying trellis. An ensemble combines multiple such weighted decoders, each decoder specializes in decoding words from a specific region of the channel words' distribution. A region corresponds to a subset of termination states; the ensemble covers the entire states space. A non-learnable gating satisfies two goals: it filters easily decoded words and mitigates the overhead of executing multiple weighted decoders. The CRC criterion is employed to choose only a subset of experts for decoding purpose. Our method achieves FER improvement of up to 0.75dB over the CVA in the waterfall region for multiple code lengths, adding negligible computational complexity compared to the circular Viterbi algorithm in high SNRs.

In this paper, we introduce deboost, a Python library devoted to weighted distance ensembling of predictions for regression and classification tasks. Its backbone resides on the scikit-learn library for default models and data preprocessing functions. It offers flexible choices of models for the ensemble as long as they contain the predict method, like the models available from scikit-learn. deboost is released under the MIT open-source license and can be downloaded from the Python Package Index (PyPI) at https://pypi.org/project/deboost. The source scripts are also available on a GitHub repository at https://github.com/weihao94/DEBoost.

Assume that $f:C\rightarrow \mathbb{R}$ is subadditive (superadditive) and hemi-Lebesgue integrable on $C,$ a cone in the linear space $X$ with $0\in C. $ Then for all $x,$ $y\in C$ and a symmetric Lebesgue integrable and nonnegative function $p:\left[ 0,1\right] \rightarrow \lbrack 0,\infty ),$ \begin{align*} \frac{1}{2}f\left( x+y\right) \int_{0}^{1}p\left( t\right) dt& \leq \left( \geq \right) \int_{0}^{1}p\left( t\right) f\left( \left( 1-t\right) x+ty\right) dt \\ & \leq \left( \geq \right) \int_{0}^{1}p\left( t\right) f\left( tx\right) dt+\int_{0}^{1}p\left( t\right) f\left( ty\right) dt. \end{align*} In particular, for $p\equiv 1,$ we have \begin{equation*} \frac{1}{2}f\left( x+y\right) \leq \left( \geq \right) \int_{0}^{1}f\left( \left( 1-t\right) x+ty\right) dt\leq \left( \geq \right) \int_{0}^{1}f\left( tx\right) dt+\int_{0}^{1}f\left( ty\right) dt. \end{equation*} Some particular inequalities related to Jensen's dicrete inequality for convex functions are also given.

Cellular automata are mathematical models that represent systems with complex behavior through simple interactions between their individual elements. These models can be used to study unconventional computational systems and complexity. One notable aspect of cellular automata is their ability to create structures known as gliders, which move in a regular pattern to represent the manipulation of information. This paper introduces the modification of mean-field theory applied to cellular automata, using random perturbations based on the system’s evolution rule. The original aspect of this approach is that the perturbation factor is tailored to the nature of the rule, altering the behavior of the mean-field polynomials. By combining the properties of both the original and perturbed polynomials, it is possible to detect when a cellular automaton is more likely to generate gliders without having to run evolutions of the system.This methodology is a useful approach to finding more examples of cellular automata that exhibit complex behavior. We start by examining elementary cellular automata, then move on to examples of automata that can generate gliders with more states. To illustrate the results of this methodology, we provide evolution examples of the detected automata.

The Oxford English Dictionary includes 17 definitions for the word “model” as a noun and other 11 as a verb. Therefore, context is necessary to understand the meaning of the word model. For in-stance, “model railways” refer to replicas of railways and trains at a smaller scale and a “model student” refers to an exemplar individual. In some cases, a specific context, like cancer research, may not be sufficient to provide one specific meaning of a model. Even if the context is narrowed, specifically to the research related to the tumour microenvironment, a “model” can be understood in a wide variety of ways, from an animal model, to a mathematical expression. This paper presents a review of the different “models” of the tumour microenvironment grouped by the different def-initions of the word into four categories: model organisms, in vitro models, mathematical models, and computational models. Then, the frequency of different meanings of the word “model” related to the tumour microenvironment is measured from the number of entries in the MEDLINE database of the United States National Library of Medicine at the National Institutes of Health. The frequency of the main components of the microenvironment and the organ-related cancers modelled are also assessed quantitatively with specific keywords. Whilst animal models, in particular xenografts and mouse models are the most common used “models”, the number of entries have been slowly de-creasing. Mathematical models, prognostic and risk models follow in frequency and these have been growing in use.

The concept of neutrosophic number is a significant mathematical tool to deal with real scientific problems because it can tackle indeterminate and incomplete information which exists generally in real problems. In this article, we use neutrosophic numbers (a + bI), where a and bI denote determinate component and indeterminate component respectively. We explore the situations in which the input information is needed to express in terms of neutrosophic numbers. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine unknown criteria weights. We define neutrosophic number harmonic mean operators and proved their basic properties. Then, we develop two novel MCGDM strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility and effectiveness of the proposed two strategies. Sensitivity analysis with variation of “I” on neutrosophic numbers is performed to demonstrate how the preference ranking order of alternatives is sensitive to the change of “I”. The efficiency of the developed strategies is ascertained by comparing the obtained results from the proposed strategies with the existing strategies in the literature.

The administration of regional neuraxial analgesia for pain relief during labor is widely recognized as a safe and effective method involving medication delivery into the epidural or subarachnoid space in the lower back. This study proposes an innovative semantic image segmentation methodology emphasizing enhanced interpretability using convolutional Random Fourier Features and layer-wise weighted class-activation maps tailored explicitly for foot segmentation in regional analgesia monitoring. Namely, our contribution is twofold: i) a novel Random Fourier Features layer is introduced to deal with image data to enhance three well-known architectures (FCN, UNet, and ResUNet); ii) three novel quantitive measures are presented to evaluate the interpretability of a given deep learning model devoted to segmentation tasks. Our approach is rigorously evaluated on a demanding dataset of foot thermal images from pregnant women who received epidural anesthesia. Its small size and considerable variability characterize the dataset. Our validation results demonstrate that the proposed methodology not only achieves competitive foot segmentation performance but also significantly enhances the explainability of the process, rendering it well-suited for applications such as epidural insertion during labor.

Background The Delta Neutrophil Index (DNI), a prodiagnostic marker for sepsis, utilizes leukocyte count. Platelet activation, similar to leukocytes, plays a crucial role in host defence against pathogens and may serve as a predictor of sepsis outcome. However, the combined evaluation of Mean Platelet Component (MPC) and DNI in assessing sepsis has been rarely used. Methods To assess the prodiagnostic validity of simultaneous utilization of DNI and MPC in cases of human febrile sepsis, we conducted measurements of cellular indices, including DNI and MPC, as well as molecular biomarkers such as procalcitonin (PCT) and C-reactive protein (CRP). This study was carried out on patients admitted to the emergency department with suspected sepsis. Results Using a cutoff value of 2.65%, the sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) of DNI in sepsis were found to be 69%, 73.9%, 77.9%, and 64.1%, respectively. Furthermore, significant differences in DNI and MPC levels were observed between the sepsis and non-sepsis groups (6.7±7.8% versus 2.1±2.2%, P=0.000 and 26.0±1.9 g/dl versus 26.8±1.4 g/dl, P=0.002), respectively. Notably, there was a negative correlation between DNI and MPC, with the strength of the correlation varying based on the cause of sepsis. By setting the cutoff value for DNI at 6.2%, the sensitivity, specificity, and NPV improved to 100%, 80.3%, and 100%, respectively, although the PPV remained at 10.6%. Importantly, the DNI≥6.2 group exhibited a higher incidence of death (10.9%, 5/46) and multiorgan failure (19.6%, 9/46) compared to the DNI<6.2 group (0.0%, 0/46 and 0.0%, 0/167, respectively) (P=0.000 and P=0.000, respectively). Conclusions In our study, DNI demonstrates superior effectiveness compared to other molecular biomarkers such as CRP and procalcitonin in distinguishing febrile septic patients from febrile nonseptic patients and predicting prognosis. Additionally, there exists a negative correlation between MPC and DNI, making MPC a valuable marker for differentiating the etiology of sepsis. These findings hold significant clinical implications as DNI/MPC is a cost-effective and readily applicable approach in various impending sepsis scenarios. Notably, this study represents the first examination of the prodiagnostic validity of simultaneously employing DNI and MPC in human cases of febrile sepsis.

We study L_2-approximation problems in the weighted Hilbert spaces in the worst case setting. Three interesting weighted Hilbert spaces appear in this paper, whose weights are equipped with two positive parameters $\ga_j$ and $\az_j$ for $j=1,\,2,\dots,\,d$. We consider the worst case error of algorithms that use finitely many arbitrary continuous linear functionals. We discuss the exponential convergence-(t,s)-weak tractability (EC-(t,s)-WT) of these L_2-approximation problems under the absolute or normalized error criterion. In particular, we obtain the sufficient and necessary conditions for EC-(1,1)-WT and EC-(t,1)-WT with t

This study delves into the realm of heuristic evaluation within usability testing, focusing on refining and applying a tailored algorithm that simplifies the implementation of the Analytic Hierarchy Process for heuristic prioritization. Addressing the prevalent challenge of disparate evaluation methodologies and the absence of a standardized process in usability testing, our research introduces a novel method that leverages the Analytic Hierarchy Process alongside a bespoke algorithm. This algorithm utilizes transitive properties for pairwise comparisons, significantly reducing the evaluative workload. This innovative approach facilitates the estimation of heuristic relevance irrespective of the number of items per heuristic or the item scale and streamlines the overall evaluation process. In addition to rigorous simulation testing of the tailored algorithm, we applied our method in a practical scenario, engaging seven usability experts in evaluating a web interface. This empirical application underscored our method’s capacity to diminish the requisite comparison count and spotlight areas of improvement for critically weighted yet underperforming heuristics. The outcomes of this study underscore the efficacy of our approach in enhancing the efficiency and organization of heuristic evaluations, paving the way for more structured and effective usability testing methodologies in future research endeavors.

The need to carry different items, which become an extra load, is a characteristic of trail running. The aim of this study is to determine physiological-metabolic changes produced by running with extra load. Four male well-trained trail runners completed three treadmill maximal metabolic tests carrying different loads (0% (L0), 5% (L5), and 10% (L10) of their body mass) in a weighted vest. Gasses exchange was monitored to assess ventilatory thresholds 1 (VT1), and 2 (VT2), zone of maximal fat oxidation, and peak oxygen consumption (VO2peak). Heart rate (HR), power and velocity (V) were tracked for comparing their behavior. A repeated measures ANOVA showed significant differences in V (p&lt;.001; ηp2= 0.910) as a limitation for reaching peak velocity (Vpeak) with L10 respect to L0 (p=0.001), and L5 (p=0.011). Power expression showed differences (p=0.068; ηp2= 0.592). It tended to be greater with L10 than L0 (p=0.057), despite achieving lower V. VT2 tended to occur at different %VO2peak (p=0.069; ηp2= 0.591). L5 VT2 was reached at higher %VO2peak than L0 (p=0.062), and L10 (p=0.071). ANOVA also showed a tendency to signification for V at this point (p= 0.098; ηp2= 0.538). In conclusion, L10 seems to limit Vpeak while L5 may delay VT2 expression.

The global rising demand for exploiting limited shared groundwater resources, coupled with significant water deficit, especially in arid and semi-arid regions, has led to escalating conflicts among stakeholders. As such, using Bankruptcy Theory methods can be an appropriate response to the reallocation of resources. This study introduces a novel approach to weighted Bankruptcy, where the relative importance of stakeholders is determined by their contributions to sustainable development, and the impact of their claims on the shared groundwater resources is considered. The framework is implemented in a two-level bankruptcy process including the plains and their beneficiaries (agriculture, drinking and industry). The proposed two-level weighted bankruptcy process applies to the Neyshabour-Ataiyeh-Sabzevar plains in Iran. The process is implemented for two scenarios including the Baseline scenario related to the present status of demands and the Future scenario associated with the estimated demands for the year 2041. To compare the weighted proposed method with the other weighted methods such as Proportional (WPRO), Constrained Equal Awards (WCEA), Pinile (WPIN), Talmud (WTAL), Constrained Equal Losses (WCEL), Modified Constrained Equal Losses (MWCEL), two categories including the deficit-based and resource-based approaches are considered. According to the stability analysis using the Bankruptcy Allocation Stability Index (BASI) method, among the deficit-based methods, the novel approach is chosen as the preferred method for the beneficiaries’ reallocation like the Sabzevar’s beneficiaries. Accordingly, it allocates 86.95%, 10.86% and 2.17% of the shared resource to the agricultural, drinking, and industrial demands, respectively. Among the resource-based methods, the WPIN method is selected for reallocation between the stakeholders and their beneficiaries in each level and scenario of reallocation. The novel approach offers a promising solution to the water resource reallocation problem, ensuring a more equitable and sustainable management of shared groundwater resources.

We study the efficient computation of power indices for weighted voting games with precoalitions amongst subsets of players (reflecting, e.g., ideological proximity) using the paradigm of dynamic programming. Starting from the state-of-the-art algorithms for computing the Banzhaf and Shapley-Shubik indices for weighted voting games we present a framework for fast algorithms for the three most common power indices with precoalitions, i.e. the Owen index, the Banzhaf-Owen index and the Symmetric Coalitional Banzhaf index, and point out why our new algorithms are applicable for large numbers of players. We discuss implementations of our algorithms for the three power indices with precoalitions in C++ and review computing times as well as storage requirements.

In this paper, using the discrete time model, we consider the average age of all files for a cached-files-updating system where a server generates N files and transmits them to a local cache. In order that the cached files are fresh, in each time slot the server updates files with certain probabilities. The age of one file or its age of information (AoI) is defined as the time the file stays in cache since it was last time sent to cache. Assume that each file in cache has corresponding request popularity. In this paper, we obtain the distribution function of the popularity-weighted average age over all files, which gives a complete description of this average age. For the random age of single file, both the mean and its distribution have been derived before by establishing a simple Markov chain. Using the same idea, we show that an N dimensional stochastic process can be constituted to characterize the changes of N file ages simultaneously. By solving the steady-state of the resulting process, we obtain the explicit expression of stationary probability for an arbitrary state-vector. Then, the distribution function of the popularity-weighted average age can be derived by mergering a proper set of stationary probabilities. For the possible applications, the distribution function can be utilized to calculate the probability that the average age violates certain statistical guarantee.

We propose an iterative scheme for feature-based positioning using a new weighted dissimilarity measure with the goal of reducing the impact of large errors among the measured or modeled features. The weights are computed from the location-dependent standard deviations of the features and stored as part of the reference fingerprint map (RFM). Spatial filtering and kernel smoothing of the kinematically collected raw data allow efficiently estimating the standard deviations during RFM generation. In the positioning stage, the weights control the contribution of each feature to the dissimilarity measure, which in turn quantifies the difference between the set of online measured features and the fingerprints stored in the RFM. Features with little variability contribute more to the estimated position than features with high variability. Iterations are necessary because the variability depends on the location, and the location is initially unknown when estimating the position. Using real WiFi signal strength data from extended test measurements with ground truth in an office building, we show that the standard deviations of these features vary considerably within the region of interest and are neither simple functions of the signal strength nor of the distances from the corresponding access points. This is the motivation to include the empirical standard deviations in the RFM. We then analyze the deviations of the estimated positions with and without the location-dependent weighting. In the present example the maximum radial positioning error from ground truth are reduced by 40% comparing to kNN without the weighted dissimilarity measure.

We prove a version of Ekeland Variational Principle (EkVP) in a weighted graph $G$ and its equivalence to Caristi fixed point theorem and to Takahashi minimization principle. The usual completeness and topological notions are replaced with some weaker versions expressed in terms of the graph $G$. The main tool used in the proof is the OSC property for sequences in a graph. Converse results, meaning the completeness of graphs for which one of these principles holds is also considered.

Motivated by important applications to the analysis of complex noise-induced phenomena, a problem of the constructive description of randomly forced equilibria for nonlinear systems with multiplicative noise is considered. Using apparatus of the first approximation systems, we construct an approximation of mean square deviations that explicitly takes into account the presence of multiplicative noise. This approximation is compared with the widely used approximation based on the stochastic sensitivity technique. The general mathematical results are illustrated with the example of the van der Pol oscillator with hard excitement.

In this paper, mean-field type games between two players with backward stochastic dynamics are defined and studied. They make up a class of non-zero-sum differential games where the players' state dynamics solve backward stochastic differential equations (BSDEs) that depend on the marginal distributions of player states. Players try to minimize their individual cost functionals, also depending on the marginal state distributions. Under some regularity conditions, we derive necessary and sufficient conditions for existence of Nash equilibria. Player behavior is illustrated by numerical examples, and is compared to a centrally planned solution where the social cost, the sum of player costs, is minimized. The inefficiency of a Nash equilibrium, compared to socially optimal behavior, is quantified by the so-called price of anarchy. Numerical simulations of the price of anarchy indicate how the improvement in social cost achievable by a central planner depends on problem parameters.

Among many research areas to which Ron Yager contributed are decision making under uncertainty (in particular, under interval and fuzzy uncertainty) and aggregation – where he proposed, analyzed, and utilized the use of Ordered Weighted Averaging (OWA). The OWA algorithm itself provides only a specific type of data aggregation. However, it turns out that if we allows several OWA stages one after another, we get a scheme with a universal approximation property – moreover, a scheme which is perfectly equivalent to deep neural networks. In this sense, Ron Yager can be viewed as a (grand)father of deep learning. We also show that the existing schemes for decision making under uncertainty are also naturally interpretable in OWA terms.

We will demonstrate how the CMB temperature simply can be predicted from what we will call geometric mean Planck gravitational potential energy in the universe. This falls nicely in line with the recent discovery that the CMB temperature also is a geometric mean of the minimum and maxium temerature in the Hubble sphere, and also that the CMB tem- perature can be derived from the Stefan-Boltzman law. Since the Coulomb force for Planck charges are identical to the Newton force for two Planck mass particles this also seems to give a potential connection between electrostatic force and the CMB temperature.

Humeral resurfacing arthroplasty (HRA) entails the substitution of the articular surface alone with a prosthetic cap without stem. It is a more conservative procedure which can be easily converted in a total arthroplasty if necessary. The present study aimed to evaluate the clinical and radiographical outcomes in a series of patients treated with HRA. 33 patients with a mean fol-low-up of 11 years were clinically (Constant score; Disability of the Arm, Shoulder and Hand score, DASH) and radiographically assessed before and after surgery. Constant and DASH score improved significantly after surgery, and only 2 cases needed revision surgery. HRA represents a valid therapeutic option in selected cases to improve the quality of life and delaying the need for more invasive procedures.

In recent years, researches on combining wavelet decomposition and convolutional neural network (CNN) together to classify hyperspectral images (HSI) have emerged, and some effective classification models have been proposed and achieved good classification results. However, there are two problems for most of the proposed models. One is the heavy training parameters and the other is that there is no distinction between the classification effectiveness of low frequency and high frequency features after wavelet decomposition. In this paper, a new light-weighted HSI classification model (LLFWCNN) is proposed, which performs multi-layer wavelet decomposition for HSI after dimensionality reduction, and only arranges the low frequency features in a specific stack mode, then classifies them through a well-designed convolutional neural network. Compared with other classification models, the number of parameters is only 2.5% of that of other models. And only the low frequency features after wavelet decomposition are used, while the high frequency features are abandoned. The results showed that compared with the state-of-the-art classification models, LLFWCNN could obtain the same or even better classification results with fewer network parameters and proved that the low frequency features after wavelet decomposition provide LLFWCNN with more favorable information for HSI classification as well.

In the literature, estimation of weighted extropy are least considered. In this paper some non parametric estimators of weighted extropy are given. The validation and comparison of the estimators are implemented with the help of simulation study and data illustration. The usefulness of the estimators are demonstrated using real data sets.

There has been considerable research on reconstructing 3D shapes from single-view images; however, preserving the detailed information of the input image remains difficult. In this paper, we propose the application of a gradient map to train a network, aimed at improving the visual quality of fine-grained details such as the thin and tiny components of generated shapes. Each gradient map was created from the original voxel data, and each value represented the amount of information per volume. Here, the gradient map was defined by several methods that mathematically quantify and represent the detailed structure of an object. By applying this map to the loss function in training, we could induce the network to intensively train partial details, such as thin and narrow parts. We demonstrated that the detailed information was well-recovered when a weight that is proportional to the gradient value was applied to the loss. Furthermore, it is expected that our method will contribute to the development of 3D technologies related to the construction of virtual space for simulation and new customer experience.

In this paper we present an efficient technique for the synthesis of very large sparse arrays, with arbitrary circularly symmetrical upper bounds for the pattern specifications. The algorithm, that is based on iterative smooth re-weighted L1 minimizations is very flexible, and is capable of achieving very good performances with respect to competitive algorithms. Furthermore, thanks to its efficiency, planar arrays of hundreds of wavelengths can be synthesized with limited computational effort.

Recreational and leisure areas play a special role. These areas mitigate or eliminate the disadvantages of living in large cities, and they enhance the quality of life in small towns. The aim of this study was to analyze the share of recreational and leisure areas in Polish counties in 2022. In Poland, recreational and leisure areas constitute a separate land-use category in cadastral registers. Annual cadastral data from the Land and Building Register at county level (in tabular form) were the main source of data for the study. The analysis revealed that the share of recreational and leisure areas was higher in counties situated in western and south-western Poland, as well as in cities. The spatially varied influence of socioeconomic factors on the share of recreational and leisure areas in Polish counties in 2002 was determined with the use of local Moran's I statistic and geographically weighted regression (GWR). The study confirmed that population density was significantly related to the share of recreational and leisure areas in Polish counties. The impact of the remaining socioeconomic factors associated with spatial and economic development varied across regions. The study also revealed that in addition to the current socioeconomic determinants, the share of recreational and leisure areas in Polish counties was also influenced by historical factors and the counties' development since their establishment.

Financial statements depict the condition of a company and need to be analyzed and evaluated to assess its performance. This research aims to analyze financial statements to describe the financial condition, measure business development over time, and evaluate the achievement of the com-pany's objectives. An optimization analysis of financial ratios is performed using the Weighted Goal Programming (WGP) model, which addresses multiple objectives by applying weights based on their priorities. The Analytical Hierarchy Process was used to determine the priority weights of deviation variables from each financial ratio target. Financial ratios were selected based on their impact on profit using factor analysis. The constructed WGP model aims to minimize deviations in Return on Assets, Operating Ratios, Operating Income Ratio, Total Assets Turnover, and Current Ratio. Computational calculations to solve the WGP model are per-formed using Python, with pseudocode provided. A case study on a company in the garment and textile sector was conducted and found that the Operating Ratio, Return on Assets, Operating Income Ratio, and Current Ratio still need improvement by developing strategies to achieve the targets. Sensitivity analysis was also employed to assess the resilience of the model in response to alterations in data.

This article presents a detailed examination of the methodology and modeling tools utilized to analyze gas flow in pipelines, rooted in the fundamental principles of gas dynamics. The methodology integrates numerical simulations with modern neural network techniques, particularly focusing on the Physics-Informed Neural Network (PINN) method. This innovative approach combines artificial neural networks (ANNs) with physical equations, offering a more efficient and accurate way to model various complex processes and phenomena. The proposed mathematical model, based on the Euler equation, has been meticulously implemented using the Python language. Verification with analytical solutions ensures the accuracy and reliability of the computations. In the research, a comprehensive comparative analysis was conducted between results obtained using the PINN method and those from conventional Computational Fluid Dynamics (CFD) approaches. The analysis highlighted the advantages of the PINN method, which produced smoother pressure and velocity fluctuation profiles while reducing computation time, demonstrating its potential as a transformative modeling tool. The data derived from this study are of paramount importance for ensuring ongoing energy supply reliability and can also be used to create predictive models related to gas behavior in pipelines. The application of modeling techniques for gas flow simulation has the potential to revolutionize the integrity of our energy infrastructure and utilization of gas resources. However, it is crucial to emphasize that the effectiveness of such models relies on continuous monitoring and frequent updates to ensure alignment with real-world conditions. This research not only contributes to a deeper understanding of compressible gas flows but also underscores the crucial role of advanced modeling methodologies in the sustainable management of gas resources for both current and future generations.

Quantifying an imaging modality’s ability to reproduce results is important for establishing its utility. In Magnetic Resonance Spectroscopic Imaging (MRSI), new acquisition protocols are regularly introduced, which improve upon their precursors with respect to signal-to-noise ratio (SNR), total acquisition duration, and nominal voxel resolution. This study has quantified the within-subject and between-subject reproducibility of one such new protocol (reduced-Field-of-View-Density-Weighted-Concentric-Ring-Trajectory (rFOV-DW-CRT) MRSI) by calculating the Coefficient of Variance of data acquired from a test-retest experiment. The Posterior Cingulate Cortex (PCC) and the Right Superior Corona Radiata (SCR) were selected as the Regions of Interest (ROIs) for Grey Matter (GM) and White Matter (WM), respectively. CVs for between-subject and within-subject are consistently around or below 15% for Glx, tCho, and Myo-Ins and below 5% for tNAA and tCr.

In this paper, we have established some new bounds of Fejér type Hermite-Hadamard inequality for k−fractional integrals involving r−times differentiable preinvex functions. It is noteworthy that in the past there was no weighted version of left and right sides of the Hermite-Hadamard inequality for k-fractional integrals for generalized convex functions available in literature.

Although automated Acute Lymphoblastic Leukemia (ALL) detection is essential, it is challenging due to the morphological correlation between malignant and normal cells. The traditional ALL classification strategy is arduous, time-consuming, often suffers inter-observer variations, and necessitates experienced pathologists. This article has automated the ALL detection task, employing deep Convolutional Neural Networks (CNNs). We explore the weighted ensemble of deep CNNs to recommend a better ALL cell classifier. The weights are estimated from ensemble candidates' corresponding metrics, such as accuracy, F1-score, AUC, and kappa values. Various data augmentations and pre-processing are incorporated for achieving a better generalization of the network. We train and evaluate the proposed model utilizing the publicly available C-NMC-2019 ALL dataset. Our proposed weighted ensemble model has outputted a weighted F1-score of 88.6%, a balanced accuracy of 86.2%, and an AUC of 0.941 in the preliminary test set. The qualitative results displaying the gradient class activation maps confirm that the introduced model has a concentrated learned region. In contrast, the ensemble candidate models, such as Xception, VGG-16, DenseNet-121, MobileNet, and InceptionResNet-V2, separately produce coarse and scatter learned areas for most example cases. Since the proposed ensemble yields a better result for the aimed task, it can experiment in other domains of medical diagnostic applications.

The aim of this study was to develop a novel nanostructured lipid carriers (NLCs) with hepatocytes targeting as carriers for the magnetic resonance imaging (MRI) contrast agent (i.e., magnetic nanostructured lipid carriers, MNLCs), and to evaluate the targeting ability of the MNLCs with T2-weighted MRI both in vitro and in vivo. Here, the galactose-octadecylamine (Gal-ODA) conjugates were synthesized by chemical coupling reaction between lactose acid (LA) and octadecylamine (ODA). Then the superparamagnetic iron oxide (SPIO) loaded nanostructured lipid carrier (conjugated by Gal-ODA, Gal-NLC-SPIO) was prepared by emulsification-ultrasonic method using monoglyceride as lipid materials. The Gal-NLC-SPIO with a diameter of about 50 nm could specifically internalize into LO2 (human hepatic cell line) cells. In vitro MRI results also proved the specific targeting ability of Gal-NLC-SPIO to LO2 cells. The in vivo MR imaging experiments using an orthotopic intrahepatic xenograft tumor model further validated the hepatocytes targeted effect of Gal-NLC-SPIO. The results of this study suggested that Gal-NLC-SPIO can be used as a contrast agent to aid in the diagnosis of hepatic diseases.

Abstract: — management of the Continuous Stirred Tank Reactor (CSTR) operation has proven to be a difficult undertaking due to the complex and ever-changing nature of its behavior, which is both nonlinear and dynamic, which is further compounded by its instability. Attempts have been made to use Proportional-Integral-Derivative (PID) controllers for such processes, but the performance is often poor due to the inherent limitations of the controllers. In contrast, heuristic algorithms have been employed to tune the controllers, but these methods can only provide optimal performance for a restricted range of parameter variations. This paper presents a novel approach that involves using a conventional gain scheduling PID controller in combination with a fuzzy gain scheduling (FGS) controller method to calibrate set-point weighted PID controllers for the CSTR process. The paper outlines the design of the controllers and evaluates their performance by subjecting them to varying input signals within the given bandwidth.

The main objective of this work was to evaluate the application of individual and ensemble machine learning models to classify malignant and benign breast masses using features from two-dimensional (2D) correlated spectroscopy spectra extracted from five-dimensional Echo Planar-Correlated Spectroscopic Imaging (5D EP-COSI) and Diffusion-weighted imaging (DWI). Twenty-four different metabolite and lipid ratios with respect to 2D diagonal peaks at 1.4ppm and 5.4ppm, and water from one-dimensional non-water-suppressed (NWS) spectra were used as the features. Additionally, water fraction, fat fraction and water-to-fat ratios from NWS spectra and apparent diffusion coefficients (ADC) from DWI were included. Nine most important features were identified using recursive feature elimination. XGBoost (AUC:93.0%, Accuracy:85.7%, F1-score:87.6%), GradientBoost (AUC:94.4%, Accuracy:87.0%, F1-score:89.4%), CatBoost (AUC:95.2%, Accuracy:86.9%, F1-score:88.4%) and RandomForest (AUC:92.2%, Accuracy:85.3%, F1-score:87.6%) were the best performing models. While the conventional biomarkers like choline, myo-Inositol, and glycine were statistically significant predictors, the key features contributing to the classification were ADC, 2D diagonal peaks at 0.9ppm, 2.1ppm and 2.3ppm, cross peaks between 1.4 and 0.9ppm, 4.3 and 4.1ppm, 2.1 and 1.4ppm and the triglyceryl-fat cross peak. The results highlight the contribution of the 2D spectral peaks to the model, and they demonstrate the potential of 5D EP-COSI for early breast cancer detection.

Objectives: To explore the potential of Radiomics alone and in combination with diffusion-weighted derived quantitative parameter namely apparent diffusion co-efficient (ADC) using supervised classification algorithms in predicting outcomes and prognosis. Materials and Methods: Retrospective evaluation of the imaging was done for a study cohort of uterine cervical cancer, candidates for radical treatment with chemo radiation. ADC values were calculated from the darkest part of the tumor, both before (labeled preADC) and post treatment (labeled postADC) with chemo radiation. Post extraction of 851 Radiomics features and feature selection by taking the union of the features which had Pearson correlation >0.35 for recurrence, >0.49 for lymph node and >0.40 for metastasis, analysis was done to predict clinical outcomes. Results: The study enrolled 52 patients who presented with variable FIGO stages and age range 28–79 (Median = 53 years) with median follow-up of 26.5 months (range, 7–76 months). Disease recurrence occurred in 12 patients (23%). Metastasis occurred in 15 patients (28%). A model generated with 24 radiomics features and preADC using a monotone multi-layer perceptron neural network to predict the recurrence yields AUC of 0.80 and kappa value as 0.55 and shows that addition of radiomics features on ADC values improves the statistical metrics by 40% approximately for AUC and 223% approximately for Kappa. Similarly, neural network model for prediction of metastasis re-turns AUC of 0.84 and kappa value as 0.65 over performs by 25% for AUC and 140% for Kappa approximately. There was a significant input of GLSZM features (SALGLE and LGLZE) and GLDM features (SDLGLE and DE) correlation with clinical outcomes of recurrence and metastasis. Conclusions: The study is an effort to bridge the unmet need of translational predictive biomarkers in stratification of uterine cervical cancer patients based on prognosis.

Background: Early identification and prevention of hypoxic ischemic encephalopathy (HIE) may reduce neonatal mortality and morbidity. Objective: We aimed to correlate between urinary Activin-A and MRI (conventional and Diffusion-weighted) and the severity of HIE in full-term neonates. Methods: Forty-five full-term neonates with HIE admitted to NICU and 15 normal neonates were enrolled into the study. The concentration of urinary Activin-A was determined using enzyme immunoassay kits and MRI were done. Correlations between urinary Activin-A and MRI with the degree of HIE were done. Results: Urinary Activin-A levels were significantly higher in neonates with HIE than controls (P<0.001). It was positively correlated with the clinical grading of HIE and a cutoff value of 0.08µg/l on day-1 after birth had a sensitivity of 98.6% and specificity of 97.1% for prediction of HIE. DW-MRI detected HIE with a high sensitivity (85%) compared to the low sensitivity of conventional MRI (35%). An ADC value of ≤ 0.8 was the best sensitivity-specificity cutoff point for detecting severe ischemic injury. DW-MRI imaging was positively correlated with Urinary Activin-A and both of them were positively correlated with the clinical grades of HIE (P < 0.001). Conclusions: DW-MRI imaging is correlated well with urinary Activin-A in full-term neonates with HIE and both of them are correlated with the degree of HIE. Early determination of urinary Activin-A combined with DW-MRI imaging can early detect HIE and its severity in full-term neonates with HIE.

In this paper we derive a unified perspective for Optimal Transport (OT) theory and Mean Field Control (MFC) theory to analyse the learning process for Neural Networks algorithms in a high-dimensional framework. We consider Mean Field Neural Networks in the context of MFC theory, specifically the mean field formulation of OT theory that allows the development of highly efficient algorithms while providing a powerful tool in the context of explainable Artificial Intelligence.

The increase in life expectancy, according to the World Health Organization, is a fact, and with it rises the incidence of age-related neurodegenerative diseases. The most recurrent symptoms are those associated with tremors resulting from Parkinson's Disease (PD) or Essential Tremors (ET). The main alternatives for the treatment of these patients are medication and surgical intervention, which sometimes have restrictions and side effects. Through computer simulations in Matlab software, this work investigates the performance of adaptive algorithms based on least mean squares (LMS) to suppress tremors in upper limbs, especially in the hands. The signals resulting from pathological hand tremors, related to PD, present components at frequencies that vary between 3~Hz and 6~Hz, with the more significant energy present in the fundamental and second harmonics, while physiological hand tremors, referred to as ET, vary between 4~Hz and 12~Hz. We simulated and used these signals as reference signals in adaptive algorithms, Filtered-x Least Mean Square (Fx-LMS), Filtered-x Normalized Least Mean Square (Fx-NLMS), and a hybrid Fx-LMS\&NLMS purpose. Our results showed that the vibration control provided by the Fx-LMS\&LMS algorithm is the most suitable for physiological tremors. For pathological tremors, we have used a proposed algorithm with a filtered sinusoidal input signal, Fsinx-LMS, which presented the best results in this specific case.

A novel compressible real gas 1D finite volume thermofluid network modelling methodology is proposed that can be applied in the analysis of supercritical CO₂ (sCO2) power cycles. It is applied to simulate centrifugal compressor performance via a mean line approach that directly solves the mass, energy, and momentum balance equations for the discretized flow channels within the machine along with the associated loss models, component characteristics, and applicable compressible real gas equation of state. This can be integrated seamlessly with the rest of the power cycle components like pipes, valves, heat exchangers, etc., thereby eliminating the need for static performance maps and the associated difficulties to ensure similarity over the whole range of operation. This direct simulation of the internal flows also makes it possible to do integrated cycle design optimization that includes the geometry of the compressors, and to simulate fast transients for dynamic analysis. The methodology was applied to simulate well-documented air and sCO2 centrifugal compressors and compared the generated results with that of conventional thermofluid network incompressible and compressible ideal gas approaches. The results indicate that the proposed compressible real gas approach can capture the stagnation pressure changes and isentropic efficiencies with good accuracy for both cases over the whole range of mass flow rates and shaft rotational speeds. In contrast, the conventional thermofluid network incompressible and compressible ideal gas approaches are only applicable in selected regions of the fluid property regime and suffer from discretization errors and inappropriate treatment of the relationship between stagnation and static pressures. Furthermore, comparative analyses between the newly proposed approach and the traditional mechanical energy balance method are performed, showing that the latter approach needs to be discretized more finely through the compression process to correctly capture the polytropic compression path shape, whereas the former more accurately captures the stagnation pressure changes through the analyzed compressors with only a single increment per compressor component.

This study focused on evaluating the potential of natural fermentation of pea flour (F) to improve the release of antioxidant compounds. Two fermentation conditions of F were performed: 1: 36.4% w/w, 24 h, 30°C (FF1); 2: 14.3% w/w, 24 h, 37°C (FF2); pH values decreased to 4.4-4.7, with a predominance of lactic acid bacteria. An increment of the proteolysis degree (TNBS method) (greater for FF2), polypeptides aggregation and decrease of solubility, increase of &lt; 2 kDa peptides, and increase in the ORAC potency of PBS-soluble fractions after fermentation was demonstrated. After simulated gastrointestinal digestion (SGID, COST-INFOGEST), FF1D and FF2D showed greater proteolysis degrees (63 and 53%) than F1D and F2D (45%), with differences in the molecular composition of the different digests. ORAC and HORAC potencies increased in all cases. FF2D presented the greater ORAC value, with higher activities for &gt; 4 kDa, some in the range 2 to 0.3 kDa. and &lt; 0.10 kDa fractions. Fermentation also increased the 60 % ethanol extracted phenolic compounds, mainly flavonoids, and the ORAC activity. After SGID, the flavan-3-ols disappeared but some phenolic acids increased respect to F. Fermentation in condition 2 was considered the most appropriate to obtain a functional antioxidant ingredient.

Background: Approximately 75% of all head and neck cancer patients are treated with radiotherapy (RT). RT to the oral cavity results in acute and late adverse events which can be severe and detrimental to a patient’s quality of life and function. The purpose of this study was to explore associations between RT dose to a defined oral cavity organ at risk (OAR) avoidance structure, provider and patient reported outcomes (PROs), opioid use, and hospitalization. Methods: This was a retrospective analysis of prospectively obtained outcomes using multivariable modeling. The study included 196 patients treated with RT involving the oral cavity for a head and neck tumor. A defined oral cavity OAR avoidance structure was used in all patients for RT treatment planning. Validated PROs were collected prospectively. Opioid use and hospitalization were abstracted electronically from medical records. Results: Multivariable modeling revealed the mean dose to the oral cavity OAR was significantly associated with opioid use (p=0.0082) and hospitalization (p=0.0356) during and within 30 days of completing RT. Conclusion: The findings of this study may be valuable in RT treatment planning for patients with tumors of the head and neck region to reduce the need for opioid use and hospitalization during treatment.

The use of several light-related variables, such as the Secchi disc depth, the euphotic depth, and in particular, the diffuse attenuation coefficient (Kd), is deeply rooted in phytoplankton research, but these are not the most appropriate indicators of the amount of light available for photosynthesis. We argue that the variable of interest for phytoplankton is the mean light intensity in the mixed layer (Im), which represents the mean light to which phytoplankton cells are exposed throughout their life cycle, while being continuously mixed in the mixed layer. We use empirical data collected in different coastal ecosystems in southern Portugal to demonstrate why Im should be the preferred metric instead of the deeply rooted Kd. We show that, although the relationship between Im and Kd is inversely proportional, it is not always strong or even significant. Different Im values can be associated to the same Kd, but distinct Im have different physiological effects of phytoplankton. Therefore, Kd does not capture the amount of light available for photosynthesis, given that, unlike Im, Kd calculation does not consider the depth of the mixed layer. Therefore, we urge phytoplankton researchers to consider the measurement and calculation of Im when evaluating light-related processes in phytoplankton ecology.

As 180-degree meanders are observed in abundance in nature, a meandering channel with two consecutive 180-degree bends was designed and constructed to investigate bed topography variations. These two 180-degree mild bends are located between two upstream and downstream straight paths. In this study, different mean velocity to critical velocity ratios have been tested at the upstream straight path to determine the meander's incipient motion. To this end, bed topography variations along the meander and the downstream straight path were addressed for different mean velocity to critical velocity ratios. In addition, the upstream bend's effect on the downstream bend has been investigated. Results indicated that the maximum scour depth at the downstream bend has increased as a result of changing the mean velocity to critical velocity ratio from 0.8 to 0.84, 0.86, 0.89, 0.92, 0.95, and 0.98 by respectively 1.5, 2.5, 5, 10, 12, and 26 times. Moreover, increasing the ratio increased the maximum sedimentary height by 3, 10, 23, 48, 49, and 56 times. The upstream bend's incipient motion was observed for the mean velocity to critical velocity ratio of 0.89, while the downstream bend was equal to 0.78.

Due to the highly nonlinear, multi-stage, and strongly time-varying marine lysozyme fermentation process, it is difficult to assure the stability and prediction accuracy of the traditional single global soft sensor model on a global scale. This study innovatively proposed a soft sensor model based on an improved seagull optimization algorithm (ISOA) combined with Gaussian process regression (GPR) weighted ensemble learning. First, the sample data set is divided into multiple local sample subsets by the improved density peak clustering algorithm (ADPC). Second, the Gaussian process regression model is optimally altered with an improved seagull optimization algorithm for the purpose of establishing the corresponding sub-prediction model. Finally, the prediction model's fusion strategy is ultimately determined depending on the degree of connection between the test samples and a subset of local pieces. Simulation results show that the proposed soft sensor model, which searches GPR based on ISOA and combines various sub-models, can predict the key biochemical parameters of the marine lysozyme fermentation process better with less prediction error under the condition of fewer training data, and it can be expanded to the soft sensor models of general nonlinear systems, according to simulation results.

Feature selection is a crucial step in machine learning, aiming to identify the most relevant features in high-dimensional data, in order to reduce the computational complexity of model development and improve its generalization performance. Ensemble feature ranking methods combine the results of several feature selection techniques to identify a subset of the most relevant features for a given task. In many cases, they produce a more comprehensive ranking of features than the individual methods used in them. This paper presents a novel approach to ensemble feature ranking, which uses a weighted average of the individual ranking scores calculated by the individual methods. The optimal weights are determined using a Taguchi-type design of experiments. The proposed methodology significantly improves classification performance on the CSE-CIC-IDS2018 dataset, particularly for attack types where traditional average-based feature ranking score combinations resulted in low classification metrics.