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.

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 wireless sensor networks (WSNs), each sensor node can estimate the global parameter from the local data in distributed manner. This paper proposed a robust diffusion estimation algorithm based on minimum error entropy criterion with self-adjusting step-size, which are referred to as diffusion MEE-SAS (DMEE-SAS) algorithm. The DMEE-SAS algorithm has fast speed of convergence and is robust against non-Gaussian noise in the measurements. The detailed performance analysis of the DMEE-SAS algorithm is performed. By combining the DMEE-SAS with diffusion minimum error entropy (DMEE) algorithms, an Improving DMEE-SAS algorithm is proposed, in non-stationary environment where tracking is very important. The Improving DMEE-SAS algorithm can avoid insensitivity of the DMEE-SAS algorithm due to the small effective step-size near the optimal estimator, and obtain a fast convergence speed. Numerical simulations are given to verify the effectiveness and advantages of these proposed algorithms.

Chemotherapy for lung cancer has made remarkable progress, and its selection has been subdivided by genetic analysis. Although response evaluation criteria in solid tumors (RECIST) is a simple and highly objective evaluation method, it has been pointed out that it has the disadvantage of not being able to accurately evaluate the therapeutic effect of molecularly targeted drugs and immune checkpoint inhibitors. The purpose of this study is to determine whether quantitative evaluation of DWIBS is useful in determining the effectiveness of treatment for lung cancer. There were 31 patients with lung cancer and 56 patterns were obtained. First, the determination of treatment effect (PD, SD, PR) based on RECIST was performed on CT. Second, tDV and ADC (median) were measured using BD score from DWI images taken at the same time, and the rate of change was calculated. Then, we compared and examined the correlation between RECIST and the rate of change in tDV. There were correlations between RECIST and the rate of change in tDV in PD and PR cases respectively. Compared RECIST on CT, DWIBS using BD score would be more accurate for response evaluation of treatment. There was a tendency that tDV decreased with increasing ADC values, but some of the cases had a dissociated response with increasing ADC values and increasing tDV. Thus, since the color display of ADC values allows us to infer their contents, it would be useful for the evaluation of cases such as dissociated response and pseudoprogression, which are suspected to be atypical responses that are difficult to evaluate with RECIST and other methods.

This study aimed to identify the utility of diffusion-weighted magnetic resonance (MR) imaging with an apparent diffusion coefficient (ADC) map as a predictor of the intrahepatic response of hepatocellular carcinoma (HCC) to cisplatin-based hepatic arterial infusion chemotherapy (HAIC). We retrospectively evaluated 113 consecutive patients with HCC who underwent gadoxetic acid-enhanced and diffusion-weighted MR imaging. The appropriate cutoff for the tumor-to-liver ADC ratio was determined to be 0.741. Of the 113 patients, 51 (45%) presented with a tumor-to-liver ADC ratio < 0.741. Evaluation of the intrahepatic treatment response after 2-3 cycles of HAIC in these 51 patients revealed that 20 patients (39%) experienced an objective response to HAIC. On the other hand, only 10 of the 62 patients with a tumor-to-liver ADC ratio ≥ 0.741 (16%) experienced an objective response. Thus, the objective response rate was significantly higher in patients with a tumor-to-liver ADC ratio < 0.741 than in those with a tumor-to-liver ADC ratio ≥ 0.741 (P = 0.006). Multivariate logistic regression analysis using parameters including perfusion alteration, percentage of a non-enhancing portion, and tumor-to-liver ADC ratio revealed that a tumor-to-liver ADC ratio < 0.741 (odds ratio 3.03; P = 0.015) is the sole predictor of an objective response to HAIC. Overall survival rates were significantly higher in patients with objective responses to HAIC than in those without objective responses (P = 0.001 by log-rank test). In conclusion, patients with unresectable HCC with a tumor-to-liver ADC ratio < 0.741 showed a favorable intrahepatic response to HAIC. Therefore, diffusion-weighted MR imaging can play a critical role as a predictor of response to cisplatin-based HAIC in unresectable HCC.

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.

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.

Colorectal liver metastases (CRLM) patients combined with hepatic lymph node metastases was a negative prognostic factor associated with outcomes. Up to now, there was still lack of a reliable method to identify the status of hepatic lymph nodes. The aim of this study was to investigate the predictive ability of mono-exponential, bi-exponential, and stretched-exponential diffusion-weighted imaging (DWI) models to distinguish between benign and malignant hepatic lymph nodes in CRLM patients who underwent neoadjuvant chemotherapy prior to surgery. In total, 97 CRLM patients with pathologically proved hepatic lymph node status were included. Various quantitative parameters, including the apparent diffusion coefficient (ADC) from mono-exponential model, D, D*, and f derived from intravoxel incoherent motion (IVIM) model, as well as DDC and α from stretched-exponential model (SEM), were measured. Multivariate analysis revealed that the pre- treatment DDC value and the short diameter of the largest lymph node after treatment were independent predictors of metastatic hepatic lymph nodes. A nomogram combining these two factors demonstrated excellent performance in distinguishing between benign and malignant lymph nodes in CRLM patients, with an area under the curve (AUC) of 0.873. Therefore, the nomogram can serve as a preoperative assessment tool for determining the status of hepatic lymph nodes and aiding in the decision-making process for surgical treatment in CRLM patients.

The generation and maintenance of membrane potential is a fundamental part of Membrane Pump Theory. One of the key points of this hypothesis is based on a natural or facilitated molecular diffusion through several types of ion channels and pumps like the Na/K ATPase. Chemistry, physics and especially electrochemistry, however, bring strong contradictions to this theoretical assumption. By respecting the principles of chemistry and electrostatics, it becomes obvious that this theoretical hypothesis cannot work. The ionic diffusion that would be at the origin of this potential cannot take place. Indeed, the topology and the forces involved definitively exclude the current model, which must absolutely be revised according to the current state of our knowledge and allow an advance in the understanding of the phenomena and open new research perspectives.

For the past few decades, researchers have been intrigued with glassy polymers, which have applications ranging from gas separations to corrosion protection to drug delivery systems. The techniques employed to examine the sorption and diffusion of small molecules in glassy polymers are the subject of this review. Diffusion models in glassy polymers are regulated by Fickian and non-Fickian diffusion, with non-Fickian diffusion being more prevalent. The characteristics of glassy polymers are determined by sorption isotherms, and different models have been proposed in the literature to explain sorption in glassy polymers during the last few years. This review also includes the applications of glassy polymer. Despite having so many applications, current researchers still have difficulty in implementing coating challenges due to issues like as physical ageing, which is briefly discussed in the review.

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.

The diffusion coefficient (D) is a key parameter characterizing gas transport in coal seams. Usually, the D is calculated from the desorption curve of particle coal, which cannot accurately reflect the diffusion characteristics under the stress constraint conditions of in-situ coal seams. In this paper, based on Fick's law of counter diffusion, different metamorphic deformed coals of medium and high coal rank are taken as the research object. The change laws of D under different confining pressure, gas pressure, and temperature conditions are tested and analyzed, and the influencing mechanisms on the D are discussed. The results show that the D of different metamorphic deformed coals decreases exponentially with the increase of confining pressure, and increases exponentially with the increase of gas pressure and temperature. There is a limit diffusion coefficient. The influence of confining pressure on the D is essentially determined by the change of effective stress, and the D has a negative effect of effective stress similar to permeability. The effect of gas pressure on the D involves two mechanisms, namely, mechanical and adsorption effects, which are jointly restricted by effective stress and coal particle shrinkage and expansion deformation. The effect of temperature on the D is mainly achieved by changing the root mean square speed and average free path of gas molecules. Under the same temperature and pressure conditions, the D increases first and then decreases with the increase of deformation degree, and the D of fragmented coal is the largest. Under similar deformation conditions, the D of high-rank anthracite is greater than that of medium-rank fat coal. It is considered that porosity is the key factor affecting the change of D in different metamorphic deformed coals.

An interesting anomaly of the diffusion process with an apparently negative diffusion coefficient defined through the mean-square displacement in a one-dimensional quantum molecular chain model is shown. Nevertheless, the system satisfies the H-theorem, so that the second law of thermodynamics is satisfied. The reason why the “diffusion constant” becomes negative is due to the effect of the phase mixing process, which is a characteristic result of the one-dimensionality of the system. We illustrate the situation where this negative “diffusion constant” appears.

Diffusion bonding is often used on pre-machined parts to generate internal cavities, e.g. for cooling injection molding tools close to the mold cavity. Only then, the workpieces are finished to their final dimensions. In the case of micro-process devices, however, it is essential to precisely control the deformation, as otherwise uncontrollable pressure losses will occur with channel cross-sections in the sub-millimeter range. Post-processing is not possible. The most important process parameters for diffusion bonding are temperature, dwell time and contact pressure, with the bonding temperature and contact pressure acting in opposite directions and showing a strong non-linear dependence on deformation. In addition, the deformation is influenced by a number of other factors such as the absolute size of the cross-section and the aspect ratio of the parts, the dimensions and distribution of the internal cross sections and the overall percentage of the cross-section to be bonded. In micro process engineering, small material cross-sections in the range of the materials microstructure can facilitate additional deformation mechanisms such as grain boundary sliding, which are not relevant at all for larger structures. For parts consisting of multiple layers, tolerances in thickness and roughness of multiple surfaces must be levelled, contributing to the percentaged deformation. This makes it difficult, especially in micro process engineering and in single or small series production, to determine suitable joining parameters in advance, which on the one hand do not cause unforeseen large deformations, but on the other hand reliably produce highly vacuum-tight components. Hence, a definition of a fixed percentaged deformation does not work for all kinds of components. This makes it difficult to specify parameters for surely obtain high-vacuum tight parts. For successful diffusion bonding, atoms must diffuse over the bonding planes, forming a monolithic part in which the original layers are no longer visible. Only then, mechanical properties identical to those of the base material, which has been subjected to identical heat treatment, can be achieved. In this paper, the impacts of different material cross section widths as well as of the aspect ratio on deformation were investigated. By accident, it was found that also accuracy of the temperature measurement may have a serious impact in terms of deformation.

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

It is shown by numerical modelling that anisotropic diffusion can compensate and even overcome diffusion broadening - the main limiting factor of devices working at atmospheric pressure. The thickness of ion clouds coming out of the ionisation chamber is reduced ~ 1000 times in the ADMA inlet increasing the resolution. This finding has a great potential that enables construction of a device with resolution close to that of currently available desktop ion separation devices – high pressure mass spectrometers, but with much lower cost of manufacture and with smaller dimensions. Comprehensive numerical modelling along with mathematical analysis of physical concepts enables reduction of the footprint and manufacturing costs. Modelling determined that the resolving power (RP) potential of the ADMA is greater than the RP of currently available on the market devices for the airport security market. The ADMA technology enables very fast detection of threats; at least 100 times faster than currently used in Ion Mobility Spectrometers (IMS). This potentially allows an increase in passenger throughput in airports.

A set of programs for the numerical simulation of the diffusion decomposition processes was developed by using simulation methods, kinetic and particle method. The complex has been validated on the model system Ni-Al by the growth of -phase separations. The results on the evolution of the distribution function and other characteristics of the ensemble, which in the zero volume fraction approximation are asymptotically in good agreement with the theory and the experiment, have been obtained. The peculiarity of the created program complex is the possibility of its adaptation to the description of the decomposition of multicomponent multiphase systems. Fig. 6, list of references - 19 titles.

This article is devoted to Feller's diffusion equation which arises naturally in probabilities and physics (e.g. wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion coefficient is practically unbounded and most of its solutions are weakly divergent at the origin. In order to overcome these difficulties we reformulate this equation using some ideas from the Lagrangian fluid mechanics. This allows us to obtain a numerical scheme with a rather generous stability condition. Finally, the algorithm admits an elegant implementation and the corresponding Matlab code is provided with this article under an open source license.

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.

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).

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.

An algorithm for the treatment of images affected by both blurring and salt&pepper noise is proposed with a cost only proportional to the number of pixels. The methodology uses a discretization scheme for the Laplace operator multiplied by a suitable nonlinear term depending on the gradient. Even if this approach resembles a diffusion type algorithm, only one step of the procedure is applied, leading to significant time savings. The procedure is successfully tested on some standard black&white natural images.

Pulsed-field gradient (PFG) diffusion experiments can be used to measure anomalous diffusion in many polymer or biological systems. However, it is still complicated to analyze PFG anomalous diffusion, particularly the finite gradient pulse width (FGPW) effect. In practical applications, the FGPW effect may not be neglected such as in clinical diffusion magnetic resonance imaging (MRI). Here, two significantly different methods are proposed to analyze PFG anomalous diffusion: the effective phase shift diffusion equation (EPSDE) method and an observing the signal intensity at the origin method. The EPSDE method describes the phase evolution in virtual phase space, while the method to observe the signal intensity at the origin describes the magnetization evolution in real space. However, these two approaches give the same general PFG signal attenuation including FGPW effect, which can be numerically evaluated by a direct integration method. The direct integration method is fast and without overflow. It is a convenient numerical evaluation method for Mittag-Leffler function type PFG signal attenuation. The methods here provide a clear view of spin evolution under field gradient, and their results will help the analysis of PFG anomalous diffusion.

: Oscillation synchronization through diffusion-based communication of active materials can lead to emergence of diverse patterns and collective behaviors. A detailed general description of the formation process of synchronization or resynchronization dynamics is a challenging task. We employ a photosensitive Belousov-Zhabotinsky reaction-diffusion model (within a gel media) to investigate the recovery process of oscillation synchronization between a pair of gel patches. The recovery time for oscillation resynchronization can be modulated by patch-distance, species of signaling molecules, intensity and duration of illumination. Analysis reveals that the “switch effect” of the gel-distance and the “promotion effect” from illumination on the oscillation resynchronization originate from the competition between processes of photo-promotion of oscillation, diffusion of signaling molecules (HBrO2 and Br-) and disproportionation of HBrO2. These results will benefit studies on bio-inspired active materials and soft motors.

The focus of this paper is on analyzing the role and the choice of parameters in sociophysics diffusion models, by leveraging the potentialities of sociophysics from a mathematical programming perspective. We first present a generalised version of Galam’s opinion diffusion model (see, e.g. , ). For a given selection of the coefficients in our model, this proposal yields the original Galam’s model. The generalised model suggests guidelines for possible alternative selection of its parameters that allow to foster diffusion. Examples of the parameters selection process as steered by numerical optimisation, taking into account various objectives, are provided.

Dynamics of human populations can be affected by various socio-economic factors through their influence on the natality and mortality rates, and on the migration intensity and directions. In this work we study an economic-demographic model which takes into account the dependence of the wealth production rate on the available resources. In the case of nonlocal consumption of resources the homogeneous in space wealth-population distribution is replaced by a periodic in space distribution for which the total wealth increases. For the global consumption of resources, if the wealth redistribution is small enough, then the homogeneous distribution is replaced by a heterogeneous one with a single wealth accumulation center. Thus, economic and demographic characteristics of nonlocal and global economies can be quite different in comparison with the local economy.

Master equations define the dynamics that govern the time evolution of various physical processes on lattices. In the continuum limit, master equations lead to Fokker-Planck partial differential equations that represent the dynamics of physical systems in continuous spaces. Over the last few decades, nonlinear Fokker-Planck equations have become very popular in condensed matter physics and in statistical physics. Numerical solutions of these equations require the use of discretization schemes. However, the discrete evolution equation obtained by the discretization of a Fokker-Planck partial differential equation depends on the specific discretization scheme. In general, the discretized form is different from the master equation that has generated the respective Fokker-Planck equation in the continuum limit. Therefore, the knowledge of the master equation associated with a given Fokker-Planck equation is extremely important for the correct numerical integration of the latter, since it provides a unique, physically motivated discretization scheme. This paper shows that the Kinetic Interaction Principle (KIP) that governs the particle kinetics of many body systems, introduced in [G. Kaniadakis, Physica A 296, 405 (2001)], univocally defines a very simple master equation that in the continuum limit yields the nonlinear Fokker-Planck equation in its most general form.

Almost all modern inorganic light-emitting diode (LED) designs are based on double heterojunctions (DHJs) whose structure and current injection principle have remained essentially unchanged for decades. Although highly efficient devices based on the DHJ design have been developed and commercialized for energy-efficient general lighting, the conventional DHJ design requires burying the active region (AR) inside a pn-junction. This has hindered the development of emitters utilizing nanostructured ARs located close to device surfaces such as nanowires or surface quantum wells. Modern DHJ III-N LEDs also exhibit resistive losses which arise from the DHJ device geometry. The recently introduced diffusion-driven charge transport (DDCT) emitter design offers a novel way to transport charge carriers to unconventionally placed ARs. In a DDCT device, the AR is located apart from the pn-junction and the charge carriers are injected into the AR by bipolar diffusion. This device design allows the integration of surface ARs to semiconductor LEDs and offers a promising method to reduce resistive losses in high power devices. In this work, we present a review of the recent progress in gallium nitride (GaN) based DDCT devices, and an outlook of potential DDCT has for opto- and microelectronics.

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.

A harmful impact of climate change and global warming has concerned various sectors of the international community. Numerous energy policies aiming at climate change mitigation have been implemented on a national and global scale. Renewable Energy Technologies (RET) play a critical role in enhancing sustainable solutions that significantly limit greenhouse gases (GHG) emissions. Such innovative technologies can facilitate energy transition through providing e.g. energy security, sustainable development, or effective usage of indigenous resources. However, the commercialization of RET becomes extremely challenging. The barriers can be of a different nature, although in this study the focus has been put on socio-economic and regulatory issues. In fact, there is ample evidence that energy policies play a central role in supporting renewables adoption. It is also claimed that RET require the whole ecosystem to support their successful diffusion. In this study, we explore multifarious barriers for a widespread RET diffusion in two European Union countries: Finland and Poland, indicating the most common barriers existing in the literature as well as analyzing major bottlenecks in the viewpoint of renewable energy companies’ executives. We also present statistics of the most commonly used RET in these countries in order to express the diffusion issues more appropriately. The outcomes of this study provide useful insight for the researchers in the energy transition field as well as practical managerial and regulatory implications aimed at overcoming these challenges.

A number of experiments suggest that the elementary particles are non-local entities. A dissipative self-organization, that treats particles as open systems may provide a better understanding of the underlying phenomena than conservative models. The proposed toy model is such an attempt. We found that self-gravitation (although accompanied by self-diffusion) may not only be compatible with the quantum phenomena but is perhaps the major reason for the existence of quantum fields. According to the proposed model, fields/particles (resemble those of the Standard Model) emerge from a dynamic self-organized medium (which we associate with vacuum dust) from competition between self-gravitation and self-diffusion. These forces produce turbulence in the form of vortices (which we call vacuum cells) that serve as the building blocks for fields and particles. Field/particle features and symmetries are based on their internal (intracellular) dynamics and vortex synchronization (intercellular dynamics). This model allows for rough estimations of relative field coupling strengths, the quantity of charges and flavors, the probabilities of quark transmutations, the dimensionality and the topologies of phase spaces, and other Standard Model parameters that came not from the theory but rather determined by experiment.

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.

This paper constituted an extension of two previous studies concerning the mathematical development of the grain boundary grooving in polycrystalline thins films in the cases of the evaporation/condensation and diffusion taken separately. The thermal grooving processes are deeply controlled by the various mass transfer mechanisms of evaporation–condensation, surface diffusion, lattice diffusion, and grain boundary diffusion. This study proposed a new original analytical solution to the mathematical problem governing the grain groove profile in the case of simultaneous effects of evaporation-condensation and diffusion in polycrystalline thin films submitted to thermal and mechanical stress, and fatigue effects; by resolving the corresponding fourth-order partial differential equation ∂y∂t=C∂2y∂x2-B∂4y∂x4 obtained from the approximation y'2≪1. The comparison of the new solution to that of diffusion alone proved an important effect of the coupling of evaporation and diffusion on the geometric characteristics of the groove profile. A second analytical solution based on the series development was also proposed. It was proved that change of the boundary conditions of the grain grooving profile largely affected the different geometric characteristics of the groove profile.

Polymer electrolyte was used as a medium for testing the performance of microband electrodes under conditions of linear diffusion. Cyclic voltammetry and chronoamperometry experiments were performed in such viscous medium, where diffusion rates are much slower than in fluid solutions. Confirmation of the existence of such conditions from the log i vs. log v or log i vs. log t relationships in the current equation always yielded values lower than the expected value of 0.5. This could indicate impure linear diffusion profile, i. e. some contribution from radial diffusion (edge effect). However, performing these tests in monomeric solvents of similar viscosities, such as glycerol or propylene glycol, gave the desired value of 0.5. These results lead to the conclusion that current equations which are based on Fick’s laws may not be applicable for polymer electrolytes, where various obstruction to diffusion make it a more complicated process than in monomeric solvents.

The presence of phase diffusion can lead to the loss of the advantages of quantum measurements. Squeezing is considered to be an effective method to reduce the detrimental effect of phase diffusion on the measurement. The Mach-Zehnder (MZ) interferometer has been exploited as a generic tool for precise phase measurement. Describing the reduction in quantum advantage caused by phase diffusion in an MZ interferometer that can be mitigated by squeezing is not easy to handle analytically, because the input state will change from a pure state to a mixed state after experiencing the diffusion noise in the MZ interferometer. We introduce a truncated MZ interferometer that can achieve the same potential phase sensitivity as the conventional MZ interferometer. This scheme can theoretically explain how phase diffusion reduces phase estimation and why squeezing counteracts in the presence of phase diffusion. Using the Gaussian property of the input state and the characteristic of Gaussian operation in the squeezing, the two orthogonal field quantities of the quantum state are squeezed and anti-squeezed to different degrees, and the analytic results are obtained. The truncated MZ interferometer is simpler to build and operate than the conventional MZ interferometer, and also mitigates the phase diffusion noise by the squeezing operation, thus making it useful for applications in precision metrology.

We present a new mathematical model of disease spread reflecting specialties of covid-19 epidemic by elevating the role social clustering of population. The model can be used to explain slower approaching herd immunity in Sweden, than it was predicted by a variety of other mathematical models; see graphs Fig. \ref{GROWTH2}. The hierarchic structure of social clusters is mathematically modeled with ultrametric spaces having treelike geometry. To simplify mathematics, we consider homogeneous trees with $p$-branches leaving each vertex. Such trees are endowed with algebraic structure, the $p$-adic number fields. We apply theory of the $p$-adic diffusion equation to describe coronavirus' spread in hierarchically clustered population. This equation has applications to statistical physics and microbiology for modeling {\it dynamics on energy landscapes.} To move from one social cluster (valley) to another, the virus (its carrier) should cross a social barrier between them. The magnitude of a barrier depends on the number of social hierarchy's levels composing this barrier. As the most appropriate for the recent situation in Sweden, we consider {\it linearly increasing barriers.} This structure matches with mild regulations in Sweden. The virus spreads rather easily inside a social cluster (say working collective), but jumps to other clusters are constrained by social barriers. This behavior matches with the covid-19 epidemic, with its cluster spreading structure. Our model differs crucially from the standard mathematical models of spread of disease, such as the SIR-model. We present socio-medical specialties of the covid-19 epidemic supporting our purely diffusional model.

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.

It is known that ammonium has a higher permeability through anion-exchange and bipolar membranes compared to K+ cation that has the same mobility in water. However, the mechanism of this high permeability is not clear enough. We develop a mathematical model based of the Nernst-Planck and Poisson equations for diffusion of ammonium chloride through an anion-exchange membrane; proton exchange reactions between ammonium, water and ammonia are taken into account. It is assumed that ammonium, chloride and OH− ions can only pass through membrane hydrophilic pores, while ammonia can also dissolve in membrane matrix fragments not containing water and diffuse through these fragments. It is found that due to the Donnan exclusion of H+ ions as coions, the pH in the membrane internal solution increases when approaching the membrane side facing distilled water. Consequently, there is a change in the principal nitrogen-atom carrier in the membrane: in the part close to the side facing the feed NH4Cl solution (pH&lt;8.8), it is the NH4+ cation, and in the part close to distilled water, NH3 molecules. The concentration of NH4+ reaches almost zero at a point close to the middle of the membrane cross-section, which approximately halves the effective thickness of the diffusion layer for the transport of this ion. When NH3 takes over the nitrogen transport, it only needs to pass through the other half of the membrane. Leaving the membrane, it captures an H+ ion from water, and the released OH− goes towards the membrane side facing the feed solution to meet the NH4+ ions. The comparison of the simulation with experiment shows a satisfactory agreement.

Li₂MnO₃ is critical component in the well-studied Li-excess cathode materials xLi₂MnO₃•(1- x)LiMO₂ for achieving high lithium storage capacity. In this article, the diffusion of Li ions in Li₂MnO₃ is studied using molecular dynamics (MD) simulation with well-behaved empirical force fields obtained by fitting against the crystal structure from experiment and phonons calculated using Density Function Theory (DFT). We have found two possible tetrahedral hopping channels, 0-TM and 1-TM(Mn⁴⁺) channel, which are differentiated by the face sharing octahedral cations. Simulation results show that the 0-TM channel is active for Li hopping, while 1-TM(Mn4+) channel is inactive. During the delithiation process, the Li ions in the TM layered are firstly removed, then those in the Li layer. However, the Li ions will be trapped in the tetrahedral 0-TM channels as long as the four face sharing octahedral sites are cleared. Up to x=1.0 for Li₂-xMnO₃, almost all the Li ions are located at the tetrahedral sites, forming a regular array along a axis. The de-intercalation of tetrahedral Li ions requires a high voltage (>5.2 V vs. Li/Li+), limiting the practical capacities measured in lab. The diffusion of Mn ions into the Li layers is observed in a deeper delithiated structure (x=1.2 for Li₂-xMnO₃), indicating an initial phase transformation to a spinel-like structure. However, the Mn ions are mainly trapped in the tetrahedral sites in the Li layer, instead of the octahedral sites fin spinel-like structure. A few of Mn ions diffusing into the octahedral sites in Li layers have no face sharing tetrahedral Li ions, revealing a further Li de-intercalation is imperative for the complete phase transformation. Our model is not stable for x≥1.4 in Li₂-xMnO₃. Other charge compensation mechanism should be considered in this high delithiation stage, eg. oxygen release.

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.

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.

Hydrogel microneedles are a promising technology for the delivery of different types of medicines locally and painlessly, as well as ISF extraction. As the hydrogel microneedles are inserted into the tissue, they swell and release drugs. To improve the effectiveness of this technology in delivering medicine at controlled and desirable doses and intervals, a deep understanding of the mechanism of drug delivery inside the microneedles is required. In this work, drug diffusion inside a tapered microneedle is investigated using numerical simulation. The microneedle is divided into many small elements, and the mass transfer equation of meloxicam is solved in each element over time. The skin is simulated as the sink in the microneedle surface for drug absorption. Simulations are performed for different sizes of microneedles. For a microneedle with a height of 500 µm and a base diameter of 250 µm, the drug completely penetrates the skin within 3.2 seconds. The rate of drug diffusion from the tip of the microneedle is higher than diffusion from the side area near the microneedle base. The obtained data demonstrate that in addition to the height and the base diameter, the microneedle’s aspect ratio, h/d, also affects the time of drug diffusion. We present a nonlinear equation to predict the time of complete drug diffusion as a function of the microneedle geometrical parameter, including the height and base diameter. The proposed equation calculates the total drug diffusion time with an error of less than 7% for all studied cases. Predicting drug diffusion patterns inside microneedles can be helpful in the biomedical field, especially in the drug-controlled release system for the optimization of drug delivery.

This paper studies the spatial joint evolution of cooperative behavior and a partially assortative matching institution that protects cooperators. We consider cooperation as characterized by a cultural trait transmitted via an endogenous socialization mechanism a la Bisin and Verdier (2001) and we assume that such trait can diffuse randomly in space due to some spatial noise in the socialization mechanism. Using mathematical techniques from reaction-diffusion equations theory, we show that, under some conditions, an initially localized domain of preferences for cooperation can invade the whole population and characterize the asymptotic speed of diffusion. We consider first thecase with exogenous assortativeness, and then endogeneize the degree of social segmentation in matching, assuming that it is collectively set at each point of time and space by the local community. We show how relatively low cost segmenting institutions can appear in new places thanks to the spatial random diffusion of cooperation, helping a localized cultural cluster of cooperation to invade the whole population. The endogenous assortative matching institution follows a life cycle process : appearing, growing and then disappearing once a culture of cooperation is suffciently established in the local population.

Using a nonclassical symmetry of nonlinear reaction-diffusion equations, some exact multi-dimensional time-dependent solutions are constructed for a fourth-order Allen-Cahn-Hilliard equation. This models a phase field that gives a phenomenological description of a two-phase system near the critical temperature. Solutions are given for the changing phase of a cylindrical or spherical inclusion, allowing for a 'mushy zone' with mixed state that is controlled by imposing a pure state at the boundary. The diffusion coefficients for transport of one phase through the mixture, depend on the phase field value, since the physical structure of the mixture depends on the relative proportions of the two phases. A source term promotes stability of both of the pure phases but this tendency may be controlled or even reversed through the boundary conditions.

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.

Additive manufacturing processes offer various options to fabricate metal parts, which show numerous ecological and technological advantages compared to formative and subtractive manufacturing methods. Due to quick availability and high accuracy, they are particularly suitable to produce complex prototypes. Metal fused deposition modeling is a relatively new material extrusion additive manufacturing technique based on the widely used fused filament deposition process. This study focuses on the Inconel 625 metal filament from Markforged Inc., it consists of a mixture of metal powder and a binder system, the latter being removed during washing and sintering. In this article, the mechanical properties of printed and sintered Inconel were investigated using tensile testing specimens with three different infill patterns, solid, triangular, and gyroid, printed in flatwise and upright direction. In addition, investigations into the dimensional accuracy of the printed specimens and the sintering shrinkage were carried out. The results showed that neither the dimensional accuracy nor the sintering shrinkage was significantly influenced by the printing orientation. In the context of lightweight engineering, the structures proofed beneficial especially within the elastic region. Generally, triangular infill patterns resulted in higher stiffness, while gyroids led to more ductile specimens. A mass-related evaluation of tensile testing elucidates that with aid of the infill structures weight savings of 40 % resulted in mechanical performance decreased by only 20 % on average.

The interplay between Diffuse Idiopathic Skeletal Hyperostosis (DISH) and the gut microbiota represents a compelling area of research, offering insights into the relationship between spinal degenerative diseases and the gut's microbial inhabitants. This comprehensive review seeks to unravel the complex connection, shedding light on its implications for human health and potential therapeutic avenues. A crucial section dives into the world of gut microbiota (GM), exploring its impact on human health, featuring its defining characteristics, and highlighting its role in metabolism, immunomodulation, host interaction, and how its composition changes over time. The subsequent portion delves into the relationship between microbiome composition and pathological bone development, including the link between Intervertebral Disc Degeneration (IDD) and gut inflammation, emphasizing how gut inflammation and GM dysbiosis play pivotal roles. Further dissecting the interconnections, various axes of influence, including the gut-spine axis, gut-bone axis, gut-joint axis, gut-disc axis (specific to DISH), gut-ligament axis, and gut-muscle axis, are discussed. Of particular interest is the section on the impact of GM on DISH-derived pain, addressing a critical aspect of the condition's manifestation. The review discusses the potential of GM modulation as a treatment for DISH, providing hope for therapeutic advancements. Additionally, it highlights the positive impact of lifestyle interventions, such as dietary modifications, sleep optimization, and exercise regimens, in mitigating GM dysbiosis and potentially improving DISH outcomes. Lastly, the intriguing prospect of fecal microbiome transplant and its implications for DISH management is examined, opening new avenues for research and therapeutic interventions. In conclusion, this comprehensive review underscores the intricate interplay between DISH and the gut microbiota, offering a fresh perspective on the impact of GM on spinal degenerative diseases. It emphasizes the potential for innovative treatments, such as GM modulation and lifestyle interventions, and presents fecal microbiome transplant as an exciting area for future exploration.

Carbon fibers (CFs) cannot be directly used for the preparation of CF paper because of their chemically inert nature. Herein, the surface of CF was modified via the spontaneous oxidative self-polymerization of dopamine. By taking full advantage of the spontaneous oxidation and self-polymerization properties of PD to maintain the maximum strength of CFs, a polydopamine-modified CF paper (PDA-CFP) with excellent performance was prepared using PD-modified CFs (PDA-CFs), which increased the proportion of hydrophilic functional groups on the surface of carbon fibers, increased the O/C ratio on the CF surface by 6 times, and improved the bond strength between the modified CF and the adhesive by making full use of the interaction force between polydopamine and PVA fibers. In this way, the primary properties of the CF paper was improved. Overall, the results showed that the dispersion of CF was considerably improved by the dopamine modification. In addition, the primary physical properties of PDA-CFP were better than those of virgin CF paper (CFP-0). PDA-CFP exhibited a maximum tensile strength of 2.04 kN/m2, a minimum resistivity of 0.06055 Ω·cm and a minimum porosity of 72.4%. The tightness could be increased by up to 12.1%.

Lipid mesophases are being intensively studied as potential candidates for drug-delivery purposes. Extensive experimental characterization has unveiled a wide palette of release features depending on the nature of the host lipids and of the guest molecule, as well as on the environmental conditions. However, only few simulation works have addressed the matter, which hampers a solid rationalization of the richness of outcomes observed in experiments. Particularly, to date there are no theoretical works addressing the impact of hydropathy on the transport of a molecule within lipid mesophases, despite the significant fraction of hydrophobic molecules among currently-available drugs. Similarly, the high heterogeneity of water mobility in the nanoscopic channels within lipid mesophases has also been neglected. To fill this gap, we introduce here a minimal model to account for these features in a lamellar geometry, and systematically study the role played by hydropathy and water-mobility heterogeneity by Brownian-dynamics simulations. We unveil a fine interplay between the presence of free-energy barriers, the affinity of the drug for the lipids, and the reduced mobility of water in determining the net molecular transport. More in general, our work is an instance of how multiscale simulations can be fruitfully employed to assist experiments in release systems based on lipid mesophases.

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.

Magnetic Nanoparticles (MNPs) is a promising technique to cure brain diseases. On the one hand, by serving as drug carriers, they can bypass the blood-brain barrier and deliver drug molecules to the brain parenchyma; on the other hand, their transport trajectory can be manipulated by applying an external magnetic field. However, due to the complex microstructure of brain tissues, e.g. the anisotropy of white matter (WM), how to achieve desired drug distribution patterns, e.g. uniform distribution, by tuning the drug delivery system is largely unknown. Here, in this study, by adopting a mathematical model capable of capturing the diffusion trajectories of MNPs in the microstructures, we systematically investigated the effects of key parameters in the MNPs delivery system on the equivalent diffusion coefficient of MNPs in the microenvironment of brain WM. The results show that uniform distribution of MNPs in anisotropic tissues can be achieved by adjusting the particle size and magnetic field. We have not only obtained a deeper understanding on how to optimise the MNPs delivery system, it can also be anticipated that an improved mathematical model could even help to achieve complex drug distribution patterns in the complicated brain environment by designing an appropriate combination of the key parameters.

We develop the process of discounting when underlying rates follow a jump-diffusion process, that is, when, in addition of diffusive behavior, rates suffer a series of finite discontinuities located at random Poissonian times. Jump amplitudes are also random and governed by an arbitrary density. Such a model may describe the economic evolution specially when extreme situations occur (pandemics, global wars, etc.). When between jumps the dynamical evolution is governed by an Ornstein-Uhlenbeck diffusion process, we obtain exact and explicit expressions for the discount function and the long-run discount rate and show that the presence of discontinuities may drastically reduce the discount rate, a fact that has significant consequences for environmental planning. We also discuss as a specific example the case when rates are described by the continous time random walk.

The work is devoted to the investigation of virus quasispecies evolution and diversification due to mutations, competition for host cells, and cross-reactive immune responses. The model consists of a nonlocal reaction-diffusion equation for the virus density depending on the genotype considered as a continuous variable and on time. This equation contains two integral terms corresponding to the nonlocal effects of virus interaction with host cells and with immune cells. In the model, a virus strain is represented by a localized solution concentrated around some given genotype. Emergence of new strains corresponds to a periodic wave propagating in the space of genotypes. The conditions of appearance of such waves and their dynamics are described.

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.

Abstract: The diffusion of competition under the coexistence of multi-generation products has become one of the important challenges faced by enterprises in their daily and sustainable operations. At the same time, the competition between different brands has intensified the difficulty and complexity of decision-making in the process of multi-generation product operation, Therefore, based on the Norton-Bass model diffusion process, this paper introduces two marketing variables, dynamic price and quality level, builds a multi-generation product diffusion model under the dual-brand competition, and analyzes the impact of the company's revenue on the launch time to market, pricing, quality or technical level. By using system dynamics (SD) method, From the perspective of strong brand and weak brand enterprises, the competition diffusion model is built and simulated. The simulation shows that: i) When enterprises have the same brand competitiveness, reducing the pricing level cannot obtain more revenue, but diminish the overall revenue of the industry; Raising the pricing level can get more revenue, but also improve the revenue of competitors. ii) When the competitive strength of enterprises is different, the strong brand tends to maintain a stable pricing on the basis of improving the quality level, or slightly raise the price. Weak brands tend to raise the pricing of new products significantly on the basis of improving the quality level. iii) The launch time to market decision of new product is influenced by the degree of product quality upgrade. Therefore, the frequency of releasing new products should trade-off against the degree of technological upgrading of product quality. This paper provides the theoretical basis and new insights for the new product launch and operation decision of enterprises.

Rapid solidification during metal additive manufacturing (AM) leads to non-equilibrium microsegregation, which can result in the formation of detrimental phases and cracking. Most of the microsegregation models, assume a Scheil-type solidification, where the solidification interface is planar and there exists local equilibrium at the interface along with either zero or infinite solute diffusion in the respective participating phases - solid and liquid. This assumption leads to errors in prediction. One has to account for finite solute diffusion and the curvature at the dendritic tip for more accurate predictions. In this work, we compare different microsegregation models that do and do not consider finite diffusion and dendrite tip kinetics against the experiments. We also propose a method to couple dendrite tip kinetics with the diffusion module (DICTRA®) implemented in Thermo-Calc®. The models which accounted for both finite diffusion and dendrite tip kinetics matched well with the experimental data.

We study an air-fluidized granular monolayer, composed in this case of plastic spheres, which roll on a metallic grid. The air current is adjusted so that the spheres never loose contact with the grid, so that the dynamics may be regarded as pseudo two-dimensional (or two-dimensional, if the effects of sphere rolling are not taken into account). We find two surprising continuous transitions, both of them displaying two coexisting phases. Moreover, in all cases, we found the coexisting phases display strong energy non-equipartition. In the first transition, at weak fludization, a glassy phase coexists with a disordered fluid-like phase. In the second transition, a hexagonal crystal coexists with the fluid phase. We analyze, for these two-phase systems, the specific diffusive properties of each phase, as well as the velocity correlations. Surprisingly, we find a glass phase at very low packing fraction and for a wide range of granular temperatures. Both phases are characterized also by a strong anti-correlated velocities upon collision. Thus, the dynamics observed for this quasi two-dimensional system unveils phase transitions with peculiar properties, very different from the predicted behavior in well know theories for their equilibrium counterparts.

Nonlinear catastrophes caused by geological fluids are a fundamental issue in rock mechanics and the geoengineering hazard field. For the consideration of hydrodynamic force on red-bed mudstone softening damage, X-ray visualization test on the fissure flow in mudstone block failure under hydrodynamic force was performed in this study based on block scale and the physical phenomena of fissure seepage and nonlinear diffusion were further explored. A new method for evaluating the hydro-damage degrees of rocks using an X-ray image analysis was proposed, and the quantitative relation of diffusion coefficients of hydro-damage and seepage was established. The research results revealed that the hydrodynamic force promoted the fluid-filled fissure behavior in mudstone specimen failure. Also, the seepage and diffusion phenomena of fluid in rocks during failures were indicated using X-ray imaging. A dual mechanical behavior was presented in the nonlinear seepage and abnormal diffusion of a red mudstone geological body under hydrodynamic conditions. The damaged degree of mudstone was aggravated by the effect of hydrodynamic force, and the initial seepage–diffusion coefficient with respect to lower hydro-damage was larger than the final seepage–diffusion coefficient with respect to higher hydro-damage of rocks with a decreasing nonlinear trend.

We investigate entropy generation in unsteady three-dimensional axisymmetric MHD nanofluid flow over a non-linearly stretching sheet. The flow is subject to thermal radiation and a chemical reaction. The conservation equations were solved using the spectral quasi-linearization method. The novelty of the work is in the study of entropy generation in three-dimensional axisymmetric MHD nanofluid and the choice of the spectral quasilinearization method as the solution method. The effects of Brownian motion and thermophoresis are also taken into account when the nanofluid particle volume fraction on the boundary in passively controlled. The results show that as the Hartman number increases, both the Nusselt number and the Sherwood number decrease whereas the skin friction increases. It is further shown that an increase in the thermal radiation parameter corresponds to a decrease in the Nusselt number. Moreover, entropy generation increases with the physical parameters.

Cannabis is among the oldest human domesticates and has been subjected to intensive artificial (human-mediated) selection throughout history to create a wide array of varieties and biotypes for diverse uses, including fibre, food, biofuel, medicine and drugs. This paper briefly reviews the available literature on the taxonomy, evolutionary origin and domestication of this plant, as well as its worldwide dispersal, in both its wild and cultivated forms. Emphasis is placed on Europe and especially on the Iberian Peninsula. Today, it is accepted that Cannabis is a monospecific genus with two subspecies, C. sativa subsp. sativa and C. sativa subsp. indica, originating in Europe and Asia, respectively, by allopatric differentiation after geographic isolation fostered by Pleistocene glacial-interglacial cycles. Palynological and phylogeographic evidence situates the Cannabis ancestor on the NE Tibetan Plateau during the mid-Oligocene. The timing and place of domestication is still a matter of debate between contrasting views that defend single or multiple Neolithic domestication centres situated in different parts of the Eurasian supercontinent, notably central/southeastern China and the Caucasus region. Recent meta-analyses have suggested that wild Cannabis may have already been spread across Europe in the Pleistocene, and its domestication could have occurred during the European Copper/Bronze ages. According to the available reviews and meta-analyses, pre-anthropic dispersal of Cannabis into the Iberian Peninsula seems to have occurred only in postglacial times, and the earlier signs of cultivation date to the Early Medieval Ages. However, the palynological and archaeological evidence used to date is insufficient for a sound assessment, and the development of thorough Iberian databases to address further meta-analysis is essential for more robust conclusions. Some clues are provided for these achievements to be fulfilled.

This study aimed to evaluate potential posttreatment changes in ADC values within the tissue surrounding the enhancing lesion, particularly in areas not exhibiting MRI characteristics of in-volvement. Additionally, the objective was to investigate the correlation between ADC values, treatment response, and survival outcomes in individuals diagnosed with gliomas. This retrospective study included a total of 49 patients that underwent either stereotactic biopsy or maximal surgical resection. Histologically confirmed as Grade III or IV gliomas, all cases adhered to the 2016 and 2021 WHO classifications, with subsequent radio-chemotherapy administered post-surgery. Patients were divided into two groups: short and long survival group. Baseline and follow-up MRI scans were obtained on a 1.5T MRI scanner. Two ROI circles were positioned near the enhancing area, one ROI in the NAWM ipsilateral to the neoplasm and another symmetrically in the contralateral hemisphere on ADC maps. At follow-up there was a significant difference in both ipsilateral and contralateral NAWM be-tween the two groups, -0.0857 (p=0.004) and -0.0607 (p=0.037), respectively. There was a weak negative correlation between survival and ADC values in ipsilateral and contralateral NAWM at the baseline with the correlation coefficient -0.328 (p=0.02) and -0.302 (p=0.04), respectively. The correlation was stronger at the follow-up. The findings indicate that ADC values in normal appearing white matter (NAWM) may function as a prognostic biomarker in patients with diffuse gliomas.

In our latest studies with the help of the self-similar Ansatz we derived new type of 1 solutions for the regular diffusion equation which are much more complex than the well-known 2 Gaussian and error functions. These solutions contain additional Kummer’s M and Kummer’s U 3 functions with quadratic argument. In the present treaties we perform an analogous analysis for the 4 regular diffusion equation which has a complex diffusion coefficient. Formally, it is equivalent to 5 the free Schrödinger equation however it is far from being trivial how the solutions can be given 6 quantum mechanical interpretation. We investigate both the one dimensional Cartesian and the 7 spherical symmetric equations. We find solutions which fulfill the L2 integrability criteria therefore 8 might have quantum mechanical relevance in the future.