In this paper, an analytical form of Rump Function is presented. This seminal function constitutes a fundamental concept of digital signal processing theory and is also involved in many other areas of applied mathematics. In particular, Rump Function is performed in a simple manner as the limit of a sequence of real functions letting ? tend to infinity. This limit is zero for strictly negative values of the real variable ? whereas it coincides with the independent variable ? for strictly positive values of the variable ?. The novelty of this work compared to other research studies concerning analytical expressions of the Ramp Function, is that the proposed formula is not exhibited in terms of miscellaneous special functions, e.g. Gamma Function, Biexponential Function or any other special functions such as Error Function, Hyperbolic Function, Orthogonal polynomials etc. Hence, this formula may be much more practical, flexible and useful in the computational procedures which are inserted into digital signal processing techniques and other engineering practices.

Neptunea cumingii is an economically important marine shellfish found in the Yellow Sea and Bohai Sea areas of China. However, due to environmental factors, such as global warming, Neptunea cumingii resources are in decline along the coast of China. In this study, samples of Neptunea cumingii were collected in Zhangzidao and Yantai during spring, summer， autumn, and winter to clarify the gene expression patterns and regulatory mechanisms in the gills in different seasons. Transcriptome analysis was conducted using Neptunea cumingii gill tissues and genes with significantly different expression levels were extracted for functional verification. The most genes with differences in expression（DEGs） were found in comparisons of the winter and summer samples. Gene enrichment analysis based on Gene Ontology and Kyoto Encyclopedia of Genes and Genomes terms showed that these DEGs were mainly involved in immune and metabolic pathways, and they had significant effects on oxidative stress, body metabolism, and protein synthesis in Neptunea cumingii. Further screening of DEGs identified 34 genes related to temperature regulation comprising 13 genes with roles in innate immunity in shellfish, 12 genes related to oxidative stress, and nine genes related to protein synthesis and energy metabolism. Eleven DEGs were randomly selected for qPCR verification and the results were consistent with the transcriptome analysis results. In summary, the transcriptome results differed significantly between seasons in the gill tissues of Neptunea cumingii. The expression levels of immune regulatory genes could be promoted in Neptunea cumingii during the high temperature season, whereas the expression of these genes may be inhibited in the low temperature season. The results obtained in this study provide insights into the molecular defense mechanisms that might allow Neptunea cumingii to adapt to climate change.

: Extra- and intra-cellular activity occurs under the direction of numerous inter-molecular interactions, and in any tissue or cell, molecules are densely packed, thus promoting those molecular interactions. Galectins and chemokines, the focus of this review, are small, protein effector molecules that mediate various cellular functions, in particular cell adhesion and migration, as well as cell signaling/activation. In the past, researchers have reported that combinations of these (and other) effector molecules act separately, yet sometimes in concert, but nevertheless physically apart and via their individual cell receptors. This view that each effector molecule functions independently of the other limits our thinking about functional versatility and cooperation, and, in turn, ignores the prospect of physiologically important inter-molecular interactions, especially when both molecules are present or co-expressed in the same cellular environment. This review is focused on such protein-protein interactions with chemokines and galectins, their homo- and hetero-oligomeric structures that they can form, and the functional consequences of those paired interactions.

Mathematical models across the applied sciences often utilize a standard methodological representation called a state variable formulation more commonly referred to as state space form. Recent research in unmanned underwater vehicle motor turbine blade thermal modeling for fatigue-life is generalized here permitting the proposed novel state space from to be applied to electrodynamics, motion mechanics, and many other disciplines. Proposed here is a very compact form inherently representing time variance, with a convenient presentation of dynamic variables applicable to all proper transfer functions, where all the distinct, real poles, zeros and gain of the transfer function appear as explicit components in the state space. The resulting manifestation simplifies utilization of the state space methods broadly across the applied sciences.

We study the propagation of a particular field that we call Gaussian-top-hat that presents self-focusing and maintains its shape for some propagation distances.

Semantic segmentation is a very popular topic in modern computer vision and it has applications to many fields. Researchers proposed a variety of architectures over time, but the most common ones exploit an encoder-decoder structure that aims to capture the semantics of the image and it low level features. The encoder uses convolutional layers, in general with a stride larger than one, to extract the features, while the decoder recreates the image by upsampling an using skip connections with the first layers. In this work, we use DeepLab as architecture to test the effectiveness of creating an ensemble of networks by randomly changing the activation functions inside the network multiple times. We also use different backbone networks in our DeepLab to validate our findings. We manage to reach a dice coefficient of 0.888, and a mean Intersection over Union (mIoU) of 0.825, in the competitive Kvasir-SEG dataset. Results in skin detection also confirm the performance of the proposed ensemble, which is ranked first with respect to other state-of-the-art approaches (including HardNet) in a large set of testing datasets. The developed code will be available at https://github.com/LorisNanni.

Evidence supports an association between low magnesium (Mg) intake and coronary heart disease and between Mg intake and endothelial function. The aim of this study was to assess the effect of one week of Mg supplementation on endothelial function, assessed by flow mediated dilatation (FMD). Nineteen healthy men and women completed this cross-over pilot study in which participants were randomised to take an over-the-counter magnesium supplement for one week or to follow their usual diet. Weight, FMD and blood pressure (BP) were taken on completion of each intervention and 24hour urine collections and blood samples were taken to assess compliance. Baseline serum Mg was within normal range for all participants. Urinary Mg and urinary magnesium-creatinine ratio (Mg/Cr) significantly increased between interventions, (p = 0.03, p = 0.005 respectively). No significant differences in FMD or BP were found between the interventions. A significant negative correlation was seen between age and FMD (r = -0.496, p = 0.031). When adjusted for age, saturated fat was negatively associated with FMD (p = 0.045). One week of Mg supplementation did not improve FMD in a healthy population.

Development and engineering of protein crystals regarding mechanical stability and crystallizability occurs on a small scale. Later in the process chain of industrial production however, filtration properties are important to separate the crystals from mother liquor. Many protein crystals are sensitive to mechanical stress which is why it is important to know the filtration behavior early on. In this study we analyze settling and filtration behavior of isometric, rod-like and needle shaped lysozyme and rod-like alcohol dehydrogenase (ADH) crystals on a small scale using an optical analytical centrifuge. Needle shaped lysozyme and rod-like ADH crystals show compressible material behavior. With the results from settling and filtration experiments the flux density function is calculated and modeled which can be used to describe the whole settling and permeation process in dependency of the solids volume fraction. This is also an issue for simulations of industrial processes.

Evidence supports an association between low magnesium (Mg) intake and coronary heart disease and between Mg intake and endothelial function. The aim of this study was to assess the effect of one week of Mg supplementation on endothelial function, assessed by flow mediated dilatation (FMD). Nineteen healthy men and women completed this cross-over pilot study in which participants were randomised to take an over-the-counter magnesium supplement for one week or to follow their usual diet. Weight, FMD and blood pressure (BP) were taken on completion of each intervention and 24hour urine collections and blood samples were taken to assess compliance. Baseline serum Mg was within normal range for all participants. Urinary Mg and urinary magnesium-creatinine ratio (Mg/Cr) significantly increased between interventions, (p = 0.03, p = 0.005 respectively). No significant differences in FMD or BP were found between the interventions. A significant negative correlation was seen between age and FMD (r = -0.496, p = 0.031). When adjusted for age, saturated fat was negatively associated with FMD (p = 0.045). One week of Mg supplementation did not improve FMD in a healthy population.

In this article, we set up some adequate conditions for analytic functions associated with cosine hyperbolic function. We determine conditions on α such that 1+α (ϰ^(2+P(j-1) ) g^' (ϰ))/(Pg^j (ϰ)),for each j=0,1,2,3 are subordinated by Janowski function, then (g(ϰ))/ϰ^P <cosℏ⁡(ϰ),(ϰ∈C). By choosing specific values of functions g we get some adequate conditions for multivalent starlike function related with cosine hyperbolic.

Magnesium (Mg) deficiency may be a catalyst in the process of endothelial dysfunction, an early event in the pathogenesis of atherosclerosis. The aim was to determine the acute effect of an oral Mg supplement compared to control on endothelieal function assessed by flow-mediated-dilatation (FMD). Nineteen participants (39 years, body mass index (BMI) 22.9kg/m2) completed this randomised cross-over study. Blood pressure (BP) and FMD were measured and blood samples taken before participants drank 200ml water with or without an over the counter Mg supplement (450mg and 300mg for men and women). Measurements were repeated at 60 and 120 minutes. There was a statistically significant two-way interaction between treatment and time on serum Mg (p = .037). A difference of -0.085mm in FMD was observed 60 minutes post drink in the control group compared to baseline FMD, and no difference was observed in the supplement group compared to baseline. Despite the non-significant interaction between treatment and time on FMD, the difference seen in the control group and the lack of change in the supplement group at 60 minutes post-drink suggests that Mg may attenuate the reduction in FMD post-prandially.

Background: obese pre-diabetics have altered expression of cytokines, and sirtuin-1, that might influence myocardial function via microRNAs (miRs) expression. Objectives: to evaluate inflammatory/oxidative stress, miRs’ expression and cardiovascular function in obese pre-diabetics randomly assigned to metformin therapy vs. placebo vs. normo-glycemics at 12 months of follow-up. Materials and methods: eighty-three obese patients enrolled for abdominoplastic surgery, were divided in pre-diabetics (n 55), normo-glycemics (n 28), and assigned to hypocaloric diet. Pre-diabetics were randomly assigned to metformin (n 23) or to placebo (n 22) plus hypocaloric diet. Results: at enrollment, pre-diabetics obese vs. normo-glycemic presented higher values of glucose, insulin resistance (HOMA-IR), inflammatory/oxidative stress markers, miR-195 and miR-27, and lower values of sirtuin-1 (p<0.05). At 12 months of follow up, obese pre-diabetics with metformin vs. placebo experienced significant reduction of glucose values, HOMA-IR, and inflammatory/oxidative stress markers, with significant reduction of intima-media thickness (IMT), septum and posterior wall thickness, and left ventricle mass (LVM), (p <0.05). At 12 months of follow-up, obese pre-diabetics with placebo vs. normo-glycemics had higher values of inflammatory/oxidative stress markers, higher values of IMT, septum and posterior wall thickness, LVM, and myocardial performance index (MPI), (p<0.05). Obese pre-diabetics in metformin vs. placebo, and obese pre-diabetics with placebo vs. normoglycemics, had significant differences about IMT, MPI, and LVM (p<0.05). Obese pre-diabetics in metformin vs. placebo showed significant reduction of serum miR-195 and miR-27 (p<0.05). Obese pre-diabetics in metformin vs. normoglycemics showed higher expression of serum miR-195 and miR-27 ( p<0.05). Finally, we found inverse relation between IMT and insulin (R -0.351), HOMA-IR (R -0.340), miR-195 (R -0.355), miR-27 (R -0.181); between LVEF and Insulin (R -0.332), HOMA-IR (R -0.142), miR-195 (R -0.297) and miR-27 (R -0.163). We found inverse correlation between LVM and sirtuin-1 (R -0.272), Insulin (R -0.810), HOMA-IR (R-0.183), miR-195 (R -0.446) and miR-27 (R-0.433), and direct correlation with interleukin-6 (R 0.195). MPI inversely linked to miR-195 (R -0.260) and miR-27 (R -0.591). Conclusion: in obese pre-diabetics metformin therapy significantly reduces inflammation/oxidative stress, circulating miR-195 and miR-27, causing reduction of LVM, IMT and amelioration of cardiac performance.

House is the haven that keeps people from natural and human conditions, it gives them trust, safety, and steadiness. It is one of the most basic human needs this became a serious function which cities offer, and became one of the most important aspects which caught urban researchers interest, they take into consideration a wide range of architectural, social, and economic indicators. The study aims to provide an overall conception of Rwandz residential functions, using a collection of parameters and some GIS and statistical techniques, to help establish plans and future projects to improve the growth of this city and other towns and cities in that area. The study found that the old parts of Rwandz city which are located in the core, differ from the outer parts which are relatively newer in many properties, generally, the core is more densely populated than the outer, bigger family size, more illiteracy, and unemployment, few incomes, older houses, smaller houses, in the opposite of the outer parts. Besides, the study tested the correlation coefficient between the criteria; it found some strong statistical relationships between them, which reflected some real-life properties of the residential function. Lastly, the study designed a regression model to predict the main residential function criteria.

In this paper we introduce the Umbrella function and its recurrence relations. Also we provide the integral representation for the this newly defined function.

BACKGROUND: Knee osteoarthritis (OA) commonly causes increase in the patients’ disability and reduce their function because it causes pain, limitation in knee range of motion and decrease in muscle power.AIM: This study investigated the effect of three different physical therapy programs on knee range of motion , pain level, muscle strength and functional condition in patients with knee OA. DESIGN: Randomized comparative study.SETTING: Outpatient Rehabilitation clinic of Tongji Hospital (Wuhan, China).POPULATION: Seventy-two patients of Knee OA (aged 40-70) enrolled and randomly allocated into three groups. Group A (n=24) received physical agents and isometric quadriceps exercises, group B (n=24) received same physical agents as group A in addition to open kinetic chain exercises and group C (n=24) received physical agents as group A in addition to closed kinetic chain exercises.METHODS: knee range of motion (by electro goniometer), knee pain level (by VAS), quadriceps muscle strength (by isokinetic dynamometer) and functional condition (by WOMAC) were assessed before and after 5 weeks of treatment.RESULTS: In between group analysis, there were significant differences (P<0.05) between the three groups for all outcome measure. In within-group analysis, group C was the only group that showed significant differences (P<0.05) in all the outcomes. Group A and B showed significant differences (P<0.05) in quadriceps muscle strength and knee pain and no significant differences (P>0.05) in knee ROM and functional condition.CONCLUSIONS: After the study, our solid conclusion is that in physical therapy programs or protocols, closed kinematic chain exercise is very effective, it improves knee ROM, and help in reducing knee pain, muscle strength, function and disability for patients with knee osteoarthritis.CLINICAL REHABILITATION IMPACT: Comparison between different physical therapy programs provides the rehabilitation team with the best treatment intervention that is more effective in treating the problems associated with knee osteoarthritis.

Background and Aim: Zinc plays a pivotal role in various zinc enzymes, resulting in the maintenance of liver function. Patients with chronic liver diseases (CLDs) usually have lower concentrations of zinc, which decrease further as liver fibrosis progresses. It remains unknown whether long-term zinc supplementation improves liver function and reduces the risk of hepatocellular carcinoma (HCC) development. Patients and Methods: Two hundred sixty-seven patients with CLDs who received a zinc preparation (Zn-group; 196 patients), or who did not receive zinc (no Zn-treatment group; 71 patients) were retrospectively analyzed in this study. The Zn-group was divided into 4 groups according to their serum Zn concentrations at 6 months after the start of Zn treatment. Results: Liver function significantly deteriorated in the no Zn-treatment group, while no notable change was observed in the Zn-group. The cumulative incidence rates of events and HCC at 3 years were lower in the Zn-group (9.5%, 7.6%) than in the no Zn-treatment group (24.9%, 19.2%) (p<0.001). According to the serum Zn concentrations, the cumulative incidence rates of events and HCC were significantly decreased in patients with Zn concentrations ≥ 70 µg/dl (p<0.001). Conclusion: Zinc supplementation appears to be effective at maintaining liver function and suppressing events and HCC development, especially among patients whose Zn concentration is greater than 70 µg/dl.

This research was aimed to study the chickpea (Cicer arietinum L.) production among smallholder farmers in Damot Gale and Humbo Woredas. A multi-stage sampling technique was used in order to determine the sample respondents. By using simple random sampling techniques four sample Kebeles were selected. Cross sectional data were collected from 182 farmer households who were chickpea producers in 2016 production season. Primary data were collected from sample households using structured questionnaire. Descriptive statistics and econometric model were employed to analyze the data. To identify the production function of chickpea crops Cobbe-Douglas production function was employed. The study suggest interventions such as intensification strategies which increase yields through proper management and use of inputs, rural infrastructure improvement increases the likelihood of production of chickpea.

In this paper, we generalize the concept of I-statistical convergence, which is a recently introduced summability method, with an infinite matrix of complex numbers and a modulus function. Lacunary sequences will also be included in our definitions. The name of our new method will be A^{I}-lacunary statistical convergence with respect to a sequence of modulus functions. We also define strongly A^{I}-lacunary convergence and we give some inclusion relations between these methods.

The statistical bundle is the set of couples $(Q,W)$ of a probability density Q and a random variable W such that $\mathbb{E}$_Q [W] = 0. On a finite state space, we assume Q to be a probability density with respect to the uniform probability and give an affine atlas of charts such that the resulting manifold is a model for Information Geometry. Velocity and accelleration of a one-dimensional statistical model are computed in this set up. The Euler-Lagrange equations are derived from the Lagrange action integral. An example of Lagrangian using minus the entropy as potential energy is briefly discussed.

In this work, we introduce the class of h-MN-convex functions by generalizing the concept of MN-convexity and combining it with h-convexity. Namely, let M : [0, 1] → [a, b] be a Mean function given by M (t) = M (t; a, b); where by M (t; a, b) we mean one of the following functions: A_t (a, b) := (1 − t) a + tb, G_t (a, b) = a^1−tb^t and H_t (a, b) := $\frac{ab}{ta+\left(1-t\right)b}=\frac{1}{A_t\left(\frac{1}{a},\frac{1}{b}\right)}$ with the property that M (0; a, b) = a and M (1; a, b) = b. Let I, J be two intervals subset of (0, ∞) such that (0, 1) ⊆ J and [a, b] ⊆ I. Consider a non-negative function h : J → (0, ∞), a function f : I → (0, ∞) is said to be h-MN-convex (concave) if the inequality f (M (t; x, y)) ≤ (≥) N (h(t); f (x), f (y)), holds for all x, y ∈ I and t ∈ [0, 1]. In this way, nine classes of h-MN-convex functions are established, and therefore some analytic properties for each class of functions are explored and investigated. Characterizations of each type are given. Various Jensen’s type inequalities and their converses are proved.

In this work, several inequalities of Popoviciu type for h-MN-convex functions are proved, where M and N are denote to Arithmetic, Geometric and Harmonic means and h is a non-negative superadditive or subadditive function.

A simple approach was developed to predict corn yields using the MoDerate Resolution Imaging Spectroradiometer (MODIS) data product from two geographically separate major corn crop production regions: Illinois, USA and Heilongjiang, China. The MOD09A1 data product, which are 8-day interval surface reflectance data, were obtained from day of the year (DOY) 89 to 337 to calculate the leaf area index (LAI). The sum of the LAI from early in the season to a given date in the season [end of DOY (EOD)] was well fitted to a logistic function and represented seasonal changes in leaf area duration (LAD). A simple phenology model was derived to estimate the dates of emergence and maturity using the logistic function parameters b1 and b2, which represented the rate of increase in LAI and the date of maximum LAI, respectively. The phenology model predicted emergence and maturity dates fairly well, with root mean square error (RMSE) values of 6.3 and 4.9 days for the validation dataset, respectively. Two simple linear regression models (YP and YF) were established using LAD as the variable to predict corn yield; the yield model (YP) used LAD from predicted emergence to maturity, and the yield model (YF) used LAD for a predetermined period from DOY 89 to a particular EOD. When state/province corn yields for the validation dataset were predicted at DOY 321, near completion of the corn harvest, the YP model performed much better than the YF model, with RMSE values of 0.68 t/ha and 0.66 t/ha for Illinois and Heilongjiang, respectively. The YP model showed a similar or better performance, even for the much earlier yield prediction at DOY 257, compared to that of the YF model. In conclusion, the phenology and yield models were developed based only on logistic changes in remote sensing-derived LAD, and predicted phenological dates and corn yields with considerable accuracy and precision for the two regions selected for this study. However, these models must be examined for spatial portability in more diverse agro-climatic regions.

Transformation formula under the action of a general linear fractional transformation for generalized Dedekind eta-function has been a subject of intensive study, Rademacher, Dieter, Meyer et al. However, the (Hecke) modular relation structure has not been recognized until the work of Goldstein-de la Torre, and streamlining the classical proofs in the modular relation will reveal the meaning hidden in those works. Our main aim is to elucidate the works of these researchers in the context of modular relations.

In this work, we studied the Green’s functions of the second order differential operators with involution. Uniform equiconvergence of spectral expansions related to the second-order differential operators with involution is obtained. Basicity of eigenfunctions of the second-order differential operator operator with complex-valued coefficient is established.

GIGANTEA (GI) is a gene involved in multiple biological functions, which were analysed and are partially conserved in a series of mono- and dicotyledonous plant species. The identified biological functions include control over the circadian rhythm, light signalling, cold tolerance, hormone signalling and photoperiodic flowering. The latter function is a central role of GI, as it involves a multitude of pathways, both dependent and independent of the gene CONSTANS(CO) as well as on the basis of interaction with miRNA. The complexity of gene function of GI increases due to the existence of paralogs showing changes in genome structure as well as incidences of sub- and neofunctionalization. We present an updated report of the biological function of GI, integrating late insights into its role in floral initiation, flower development and flower volatile production.

In this study, we actually want to explore the time-fractional Phi-four equation via two methods, the exp _a function method and the hyperbolic function method. We transform a fractional order dierential equation into an ordinary differential equation using a wave transformation and the fractional derivative in conformable form. Then, the resulting equation has successfully been explored for new explicit exact solutions. The procured solutions are simply showed the effectiveness and plainness of the projected methods.

The owners of forests with water protection functions in Bulgaria do not receive compensation for their limited right to use wood and non-wood forest products from the forest areas they own. At the same time, the contribution derived from forests with water protection functions is received by water users and water consumers, whereas the costs of managing the forests are borne by their owners. The problem thus defined is not a forestry one, but an economic one, and the purpose of this paper ensues therefrom, namely to propose and test a methodology for valuating the produc-tion function of forest areas with water protection function in Bulgaria, allowing a fair distribu-tion of income between the forest owner and the user of forest ecosystem services. The methodol-ogy is based on the form of forest management and the analytical expression of the economic rela-tionship between a forest owner and a user of forest ecosystem services, constructed using Schen-rock’s formula. It has been tested with actual data on forest areas with water protection functions falling within the administrative and territorial scope of Velingrad municipality and based on the obtained results proposals have been made for the distribution of the contributions generated by forest ecosystems between the forest owner and the user of the forest ecosystem services.

Motivated for improving the efficiency and reliability of wind turbine energy conversion, this paper presents an advanced control design that enhances the power regulation efficiency and re-liability. The constrained behaviour of the wind turbine is taken into account, by using the barrier Lyapunov function in the analysis of the Lyapunov direct method. This, consequently, guarantees that the generated power remains within the desired bounds to satisfy the grid power demand. Moreover, a Nussbaum-type function is utilized in the control scheme, to cope with the unpre-dictable wind speed. This eliminates the need for accurate wind speed measurement or estimation. Furthermore, via properly designed adaptive laws, a robust actuator fault-tolerant capability is integrated into the scheme, handling the model uncertainty. Numerical simulations are performed on a high-fidelity wind turbine benchmark model, under different fault scenarios, to verify the effectiveness of the developed design. Also, a Monte-Carlo analysis is exploited for the evaluation of the reliability and robustness characteristics against the model-reality mismatch, measurement errors and disturbance effects.

As known all physical properties of solids are described well by the system of quantum linear harmonic oscillators. It is shown in the present paper that the system consisting of classical linear harmonic oscillators having temperature dependent masses or (and) frequencies has the same partition function as the system consisting of quantum linear harmonic oscillators having temperature independent masses and frequencies while the means of the square displacements of the positions of the oscillators from their mean positions for the system consisting of classical linear harmonic oscillators having: the temperature dependent masses; temperature dependent frequencies; and temperature dependent masses and frequencies differ from each other and from that of the system consisting of quantum linear harmonic oscillators, and hence, the system consisting of classical linear harmonic oscillators describes well the thermodynamic properties of the system consisting of quantum linear harmonic oscillators and solids.

Kim-Kim ([9]) studied some properties of the degenerate gamma and degenerate Laplace transformation and obtained their properties. In this paper, we define modified degenerate gamma and modified degenerate Laplace Transformation and investigate some properties and formulas related to them.

Euler’s product formula over the primes and Euler’s zeta function equate to enshrine the Fundamental Theorem of Arithmetic that every integer > 1 is the product of a unique set of primes. The product formula has no zero, and with a domain ≤1 Euler’s zeta diverges. Dirichlet’s eta function η(s), negates alternate terms of zeta, permitting convergence when s∈C and Re(s) < 1, and its non-trivial zeros {ρ}, have a deep relationship with the distribution of the primes. The Riemann Hypothesis is that all the non-trivial zeros have Re(ρ) = 1/2. This work examines the symmetries in a partial Euler’s zeta series with a complex domain equating it to the difference between two finite vector series whose matched terms have mirror-image arguments, but whose magnitudes differ when Re(s) ≠ 1/2. Analytical continuation generates a modified eta series η_l(s), in which every l^th term is multiplied by (1-l). If the integer l is appropriately determined by the Im(s), similar paired finite vector series have a difference that closely follows η_l (s) and their terminal vectors intersect in a unique way permitting zeros only when Re(s) = 1/2. Furthermore, those vectors tracking the derivatives of the series, have a special relationship permitting zeros of the differential only when Re(s) > 1/2.

The basic idea is to expand the completed zeta function $\xi(s)$ in MacLaurin series (infinite polynomial), which can be further expressed as infinite product (Hadamard product) by conjugate complex roots. Finally, the functional equation $\xi(s)=\xi(1-s)$ leads to $(s-\alpha_i)^2 = (1-s-\alpha_i)^2, i \in \mathbb{N}$ with solution $\alpha_i= \frac{1}{2}, i \in \mathbb{N}$, where $\alpha_i$ are the real parts of the zeros of $\xi(s)$, i.e., $s_i =\alpha_i\pm j\beta_i, i\in \mathbb{N}$. Therefore, a proof of the Riemann Hypothesis is achieved.

Social surveys are conducted to determine how annoyed people are in a certain noise situation. The results are typically presented as exposure-response curves showing the percentage of the area population that are highly annoyed as a function of the noise exposure level. It is a well-known fact that the survey results are not only dependent on the accumulated noise exposure, DNL, DENL, or similar, but also on various other factors such as maximum levels, exposure patterns, noise spectra, etc. A re-analysis of previously reported surveys shows that the results are also to a large extent dependent on survey-specific factors like wording of the annoyance questions, how the questionnaires are presented, response scales, methods of scoring highly annoyed, etc. This paper discusses and quantifies the influence of such factors and suggests ways of comparing results from surveys that have been conducted according to different protocols and different analysis methods.

The purpose of this scoping review was to comprehensively clarify the methodology of Mental practice (MP) to date by systematically mapping studies that have performed MP on post-stroke paralytic upper extremity function. Specifically, (1) When is the most common timing of MP in-tervention after stroke onset? (2) What is the MP load (intervention time, number of interven-tion days, and intervention period)? (3) What are the most common methods of Motor Imagery (MI) recall and MI tasks during MP? (4) Is MP often used in conjunction with individual rehabili-tative therapies? (5) What is the paralyzed side's upper limb and cognitive function level at the start of MP intervention? Our scoping review was performed ac-cording to PRISMA-ScR to iden-tify research questions. Then, the PubMed, Scopus, Medline, and Cochrane Library databases were used to screen articles published by July 19, 2022. Eligible articles were selected all study designs were included, including studies involving the use of MP for post-stroke paralytic upper extremity function. Selection of eligible papers was done by two or more independent persons. Data were extracted from the eligible papers for items necessary to identify the research ques-tions. English-language articles identified for this study were 694, of which 62 were accepted. The most common intervention time was 30 minutes or less and the duration of the intervention was 5 times a week in MP. The most common method of recalling MI during MP was using an audio guide. In the future, it will be important to conduct accumulation of research to unify the varied widely MP methodologies identified in this study.

In this paper, it is shown that the bivariate beta statistical manifold of the first kind with three parameters has a gradient system Hamiltonian and is completely integrable. It is shown that this system admits a Lax pair representation. The question here is how to construct a gradient system and show that it is completely integrable while determining the integrable curves on the three-parameter bivariate beta manifold of the first kind admitting a potential function?To do this, we prove the existence of the potential on the manifold using ovidiu in Ovidiu, then using Amari's theorems in Amari, we show that this coordinate system admits a dual coordinate system. This will allow us to determine the Riemannian metric on the variety and to construct the gradient system. We linearise this system using Nakamura's method. We prove that it is Hamiltonian and completely integrable using the theorem in \cite{mama-proceeding}. It is shown that the Bivariate Beta of the first kind with three parameters, is an exponential function. The gradient system is linearizable. It is proven that the associate gradient system is Hamiltonian with $ \mathcal{H} $ which is in involution and satisfying $d\mathcal{H}=0.$ Therefore, the gradient system obtained is a sub-dynamical system of a $4$-dimensional system and is a completely integrable system. We show that the gradient system on the statistical model has the following Lax pair representation: $ \dot{L}= \left[L, N\right] $ where $L$ is a symmetric matrix and $N$ is the diagonal matrix. The gradient system defined by the Bivariate Beta family of the first kind with three parameters odd-dimensional manifold is a completely integrable Hamiltonian system.

The three-dimensional Ising model on the m$\times$n$\times$l cubic lattice with the screw boundary condition along the ${\bf X}$ direction and the periodic boundary conditions along both ${\bf Y}$ and ${\bf Z}$ directions is exactly solved by using the $2^{mn}$-dimensional representation of the rotation group in $2mn$-dimensions, similar to the Kaufman's spinor approach in two dimensions. The exact partition function is obtained from two sets of $2^{mn-1}$ eigenvalues of the $2^{mn}$-dimensional transfer matrix {\bf V} corresponding to the even and odd eigenvectors, respectively. Such the eigenvalues are determined by the angles of the 2mn-dimensional rotation associated with {\bf V}.

This work aims to introduce a novel concept: the Riesz-Dunkl fractional derivatives, within the context of Dunkl type operators. A particularly noteworthy revelation is that when a specific parameter $\kappa$ equals zero, the Riesz-Dunkl fractional derivative smoothly reduces to both the well-known Riesz fractional derivative and the fractional second-order derivative. Furthermore, we introduce a new concept: the fractional Sobolev space. This space is defined and characterized using the versatile framework of the Dunkl transform.

Depression is one of the psychiatric disorders characterized by anxiety, pessimism, and suicidal tendencies, which seriously affect the quality of life of patients and their families. In this paper, we used polynomial-based kernel Granger causality values as network node connectivity indicators to construct brain networks for 5 depressed patients and 11 healthy individuals’ magnetoencephalogram(MEG) under positive, neutral, and negative emotional stimuli, respectively, and found that depressed patients had closer information exchange between frontal and occipital regions compared to healthy individuals and other brain regions, and fewer causal connections in parietal and central regions. Further analysis of the topological properties of the network revealed that depressed patients had higher mean degrees under negative stimuli (p=0.008)and lower mean clustering coefficients than healthy individuals(p=0.034). Comparing the mean degree and mean clustering coefficient of the same sample under different emotional stimuli, we found that depressed patients had the greater mean degree and mean clustering coefficient under negative stimuli than neutral and positive stimuli. We also found that patients’ feature path lengths under negative and neutral stimuli significantly deviated from small-world attributes. The results suggest that analysis of nuclear Granger causality-based brain networks can effectively characterize depression pathology.

Very poor oral health, common among older adults, is associated with cognitive decline.This study aimed to investigate the association between denture use, chewing ability, and cognitive function in Korean middle-aged adults using samples representing middle-aged people at the national level. This longitudinal study included 9,998 middle-aged adults via Korea Longitudinal Study of Aging 7th special survey data. Denture use, chewing ability, health-related factors, and general characteristics were assessed by the Computer Assisted Personal Interview. After controlling general characteristics using a generalized estimating equation model, the association of denture use and MMSE scores with chewing ability of those with or without dentures and MMSE scores were analysed. Twenty-four percent of participants wore dentures among them, 35.1% complained of difficulty chewing when wearing dentures. Among participants who did not wear dentures, 16.4% complained of difficulty chewing. MMSE scores were lower among denture-wearers than non-denture wearers (β = -0.026, p < 0.001). In both groups, MMSE scores decreased with chewing difficulty and were significantly reduced among non-denture wearers (p < 0.05). Chewing ability was closely associated with cognitive function. Given the negative effect of difficulty chewing on cognitive function, maintaining chewing ability should be of great concern.

Some p53 mutants lose their tumor suppressor activity and acquire new oncogenic functions, known as a gain of function. Recent studies have shown that p53 mutants can exert oncogenic effects through specific miRNAs. We identified the differentially expressed miRNA profiles of the three most frequent p53 mutants (p53R273C, p53R248Q, and p53R175H) in the Saos-2 cell line (null p53) transfected as compared with p53WT transfected cells. The association between these miRNAs and the signaling pathways in which they might participate was performed through the miRPath Software. QRT-PCR was employed to validate the miRNAs profiles. In addition, we explored if the induction of cell migration and invasion by the p53R48Q mutant was dependent on the miR-182-5p. We observed that p53 mutants have an overall negative effect on miRNA expression. Likewise, we found miRNAs differentially expressed associated with regulating Oncogenic signaling pathways. We found overexpression of miR-182-5p, which is associated with processes such as cell migration and invasion. Inhibition of mutant p53R248Q and miR-182-5p increased FOXF2-MTSS1 levels and decreased cell migration and invasion. Our results suggest that p53 mutants increase the expression of miR-182-5p, and this miRNA is also necessary to induce cell migration and invasion by the p53R248Q mutant in a cancer cell model.

The coastal zone, situated at the sensitive interface between land and sea, serves as a pivotal area of extensive human economic activities. As one of China's economic special zones, Xiamen exemplifies the comprehensive trajectory of coastal governance in China. This research adopts an interdisciplinary approach grounded in historical geography and political ecology, employing data collection methods encompassing historical literature, field surveys, and interviews. The research findings indicate that:(1) The year 1994 witnessed the pivotal role played by the United Nations Convention on the Law of the Sea (UNCLOS) in connecting Jimei Peninsula from a local context to the international arena, thus signifying a momentous turning point in the process of scale reconstruction. However, the subsequent implementation of the Coastal Exclusion Policy in 2002 had detrimental consequences, leading to the disintegration of the local scale, the erosion of maritime culture, and the disregard for the livelihood security of displaced coastal populations.(2)The Coastal Exclusion Policy serves as an instrumental tool for implementing scale politics, while its functional realignment has had profound implications for the coastal zone, encompassing economic transformation, ecological degradation, and the marginalization of the socio-cultural fabric that intertwines humans and the coastal environment.

Background: the aim of this study was to assess acute changes on left atrial (LA) function a during a progressive exercise in patients with heart failure with mid-range ejection fraction (HFmrEF) in comparison to healthy controls (HS). Methods: twenty patients with established HFmrEF were compared with 10 HS, age-matched controls. All subiects performed a stepwise exercise test on cyclette. Echocardiography was performed at baseline, during submaximal effort, at peak of exercise, and after 5 minutes of recovery. Results: HS obtained an higher value of METs at peak exercise than HFmrEF (7.4 vs 5.6; between group p 0.002). Heart rate and systolic blood pressure presented a greater increase in the HS group than in HFmrEF (between-groups p 0.006 and p 0.003 respectively). In the HFmrEF group peak atrial longitudinal strain (PALS), and conduit strain were both increased at submaximal exercise (p<0.05 for both versus baseline) and remained constant at peak exercise. Peak atrial contraction strain (PACS) did not show significant changes during the exercise. In the control group PALS and PACS increased significantly at submaximal level (p<0.05 for both versus baseline) but PALS returned near baseline values at peak exercise; conduit strain decreased progressively during the exercise in HS. Stroke volume (SV) increased in both groups at submaximal exercise; at peak exercise SV remained constant in the HFmrEF while it decreased in controls (between-groups p 0.002). Conclusions: Patient with HFmrEF, show a proper increase of LA reservoir function during incremental exercise that contributes to maintain SV throughout the exercise.

MicroRNAs (miRNAs) regulate plant growth and development and their responses to biotic and abiotic stresses. Although extensive studies show that miR159 family members regulate leaf and flower development in Arabidopsis thaliana, the roles of miRNAs in soybean (Glycine max) are poorly understood. Here, we identified six MIR159 genes in soybean, MIR159aMIR159f, and investigate their expression patterns in plants under low-phosphorus (low-P), NaCl, or abscisic acid (ABA) treatments. In soybean leaves, MIR159e and MIR159f expression was induced by low-P treatment, while in roots, MIR159b, MIR159c, MIR159e, and MIR159f expression was upregulated. In flowers, low-P led to upregulation of MIR159a, MIR159b, MIR159c, and MIR159f, but downregulation of MIR159d and MIR159e. In soybean nodules, MIR159b was upregulated but MIR159a, MIR159c, and MIR159d was downregulated under P deficiency. NaCl treatment induced MIR159a, MIR159b, MIR159c, and MIR159e expression in leaves, and MIR159aMIR159f expression in roots. ABA treatment upregulated MIR159a, MIR159b, and MIR159c but downregulated MIR159d, MIR159e, and MIR159f in leaves. These results suggest that miR159 family members function in plant abiotic stress responses. Moreover, total P content in leaves was significantly lower in plants overexpressing MIR159e than in the wild type, suggesting that miR159e may regulate P absorption and transport in soybean.

In this compact and focused paper, we revisit the interplay between Bramble and Filter through the lens of a submodular partition function.

Loose Tangle is a concept in graph theory that has a dual relationship with branch-width which is well-known graph width parameter. Ultrafilter, a fundamental notion in mathematics, is similarly known to have a dual relationship with branch-width when extended to a connectivity system (X, f). In this compact paper, we revisit and contemplate the interplay between Loose Tangle and Filter through the lens of a submodular partition function.

This paper describes some neural representations that may be helpful for realising intelligence in the human brain. The ideas come from the author's own cognitive model, where a number of algorithms have been developed over time. Through developing and trying to implement the architecture, ideas like separating the data from the function have become architecturally appropriate and there have been several opportunities to make the system more orthogonal. Similarly for the human brain, neural structures may work in-sync with the neural functions, or may be slightly separate from them. Each section discusses one of the neural assemblies with a potential functional result, that cover ideas such as timing or scheduling, inherent intelligence and neural binding. Another aspect of self-representation or expression is interesting and may help the brain to realise higher-level functionality based on these lower-level processes.

Abstract Aim: The study aimed to evaluate the clinical laboratory features of moderate and severe COVID-19 patients among a cohort of the Egyptian population. The study also aimed to assess the accuracy—sensitivity, specificity, and area under the curve (AUC) of various detected parameters in predicting the severity of COVID-19 infection. Patients and methods: One hundred diagnosed COVID-19 patients and fifty healthy participants in total were involved in current study. COVID-19 patients were categorized based on how severe their symptoms into two groups. Estimates were made for serum levels of alanine aminotransferase (ALT), aspartate aminotransferase (AST), albumin, lactate dehydrogenase (LDH) and C-reactive protein (CRP) as well as white blood cells (WBCs) count, lymphocytes count, and hemoglobin content (Hb) content. Results: COVID-19 patients displayed increased serum levels of liver enzymes and CRP as well as WBCs count when compared to healthy individuals. On the other hand, Hb content, lymphocytes count, and albumin level fell in all COVID-19 patients. The severe group showed a statistically significant rise in liver enzymes, WBCs, and CRP levels, compared with moderate group. WBCs and lymphocytes counts were closely correlated with age, ALT, LDH, and CRP in all cases. WBCs and lymphocytes counts also had a negative correlation with albumin Level. Additionally, WBCs count, lymphocytes count, LDH activity and CRP level have higher AUC in severe than in moderate cases. WBCs count, LDH activity and CRP level have AUC above 0.80 in the severe group. Conclusion: The current investigation found a significant correlation between WBCs count, lymphocytes count, CRP level and liver injury in COVID-19 patients. WBCs count, lymphocytes count, LDH activity and CRP level were effective indicators for determining the severity of COVID-19.

The paper continues the study of efficient algorithms for the computation of zeta functions over the complex plane. We aim to apply the modifications of algorithms to the investigation of underlying fractal structures associated with the Riemann zeta function. We discuss the computational complexity and numerical aspects of the implemented algorithms based on series with binomial-like coefficients.

Executive functioning is a key component involved in many of the processes necessary for effective weight management behavior change (e.g., setting goals). Cognitive behavioral therapy (CBT) and third-wave CBT (e.g., mindfulness) are considered first-line treatments for obesity, but it is unknown to what extent they can improve or sustain executive functioning. This pilot randomized controlled trial examined if a CBT-based generalized weight management intervention would affect executive functioning and executive function-related brain activity in individuals with obesity or overweight. Participants were randomized to an intervention condition (N=24) that received the Noom Weight program or to a control group (N=26) receiving weekly educational newsletters. EEG measurements were taken during Flanker, Stroop, and N-back tasks at baseline and months 1 through 4. After 4 months, the intervention condition evidenced greater accuracy over time and, to some extent, neural markers of executive function (error-related negativity and beta and gamma band powers) compared to the control group on the Flanker and Stroop tasks. The intervention condition also lost more weight than controls (-7.1 pounds vs. +1.0 pounds). Given mixed evidence on whether CBT-based interventions can change markers of executive function, this study contributes preliminary evidence that a multicomponent CBT-based weight management intervention (i.e., that provide both support for weight management and is based on CBT) can help individuals sustain executive function compared to controls.

Studies show that executive functions and motor development are associated among each other and with learning ability. A more technological lifestyle, related with digital culture, should be considered an important component to stimulate children. In addition, digital games constitute an element of the digital culture in which children are inserted. The aim of this study is to present a systematic mapping of the literature involving executive functions, motor development and the use of digital games in intervention programs for elementary school children, from 6 to 11 years old. Four databases were searched: PubMed, Scielo, Science Direct and SCOPUS, including publications between 2012 and March 2021. The initial results indicated 4881 works. After the selection process, 15 investigations that presented the central theme of the study were selected. The main results indicate that intervention strategies are quite heterogeneous. Most of the studies demonstrated significant positive effects after intervention protocols and were conducted in Europe and 46% of the studies were conducted in a school environment. No researches were identified that involved technological solutions involving executive functions, motor development and digital games in an integrated manner, constituting a field of future scientific research.

The visual system is regulated by the nervous through neurotransmitters, which play an important role in visual and ocular functions. One of those neurotransmitters is acetylcholine, a key molecule that plays a diversity of biological functions. On the other hand, acetylcholinesterase, the enzyme responsible for the hydrolysis of acetylcholine, is implicated in cholinergic function. However, several studies showed that in addition to their enzymatic functions, Acetylcholinesterase exerts non-catalytic functions. In recent years, the importance of evaluating all possible functions of acetylcholine-acetylcholinesterase has been evidenced. Nevertheless, there is evidence that suggests cholinesterase activity in the eye can regulate some biological events both in structures of the anterior and posterior segment of the eye and therefore in the visual information that is processed in the visual cortex. Hence, the evaluation of cholinesterase activity could be a possible marker of alterations in cholinergic activity not only in ocular disease but also in systemic diseases.

In this paper, the author derives an explicit form of Heaviside Step Function, which evidently constitutes a fundamental concept of Operational Calculus and is also involved in many other fields of applied and engineering mathematics.In particular, this special function is exhibited in a very simple manner as a summation of four inverse tangent functions. The novelty of this work is that the proposed exact formulae are not performed in terms of miscellaneous special functions, e.g. Bessel functions, Error function, Beta function etc and also are neither the limit of a function, nor the limit of a sequence of functions with point – wise or uniform convergence.Hence, this formula may be much more appropriate and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

Saif et al. (J. Math. Comput. Sci. 21 (2020) 127-135) considered modified Laplace transform and developed some of their certain properties and relations. Motivated by this work, in this paper, we define modified Sumudu transform and investigate many properties and relations including modified Sumudu transforms of the power function, sine, cosine, hyperbolic sine, hyperbolic cosine, exponential function, and function derivatives. Moreover, we attain two shifting properties and a scale preserving theorem for the modified Sumudu transform. We give modified inverse Sumudu transform and investigate some relations and examples. Furthermore, we show that the modified Sumudu transform is the theoretical dual transform to the modified Laplace transform.

Most large fibers in central nervous system of vertebrates are decussated. The cause or the evolutionary force of this phenomenon is not convincingly described. Here we show a pattern for this nervous system property that simultaneously is found to a more basic rule in evolution.The idea here is the "function to anatomy" theorem. We claim that functions of physical, biochemical, enzymatic, etc., in lower scale of living organisms "emerge" to anatomy in larger scales. And reversely, the anatomy we see in multicelular organisms are/were functions in microscopic scales.We propose descriptions, predictions, and a probable road map to what this can implicate in biological and medical issues.

Three Dimensional Variational data assimilation or analysis (3DVAR) is one of most classical methods for providing the initial values for numerical models. In this method, the dimensions of the background error covariance and the observational error covariance matrices are large. Therefore, it is difficult to get the inverse of the covariance matrices and to reduce the orders of these matrices without information loss. With the use of the Sylvester Equation, on the basis of a new linear regression, a new cost function for 3DVAR was given. For the first-guess m×n field, there is an approximate 1−(m²+n²)/(mn×mn) reduction with m>1 & n>1 by using the cost function. The results of the numerical experiments show that the effect of this algorithm is no worse than that of the old cost function for 3DVAR.

There is no simple method to measure glomerular filtration rate (GFR) in swine, an established model to study renal disease. We developed a protocol to measure GFR in conscious swine with the plasma clearance of iohexol. We used two groups: testing and validation, of 8 animals each. Ten milliliters of iohexol (6.47 g) were injected by the marginal auricular vein and blood samples (3 ml) were collected from the orbital sinus at different points after injection. GFR was determined considering two models: two-compartments (CL2: all samples) and one-compartment (CL1: the last six samples). In the testing group, CL1 overestimated CL2 by ~30%: CL2=245±93 and CL1=308±123 ml/mn. This error was corrected by a first order polynomial quadratic equation to CL1, which was considered the simplified method: SM=-47.909+(1.176xCL1)–(0.00063968xCL1²). SM showed narrow limits of agreement with CL2, and a concordance correlation of 0.97 and a total deviation index of 14.73%. Similar results were obtained for the validation group. This protocol is reliable, reproducible, can be performed in conscious animals, uses a single dose of the marker, and requires a reduced number of samples avoiding urine collection. Finally, it portends a significant improvement in animal-welfare conditions and handling necessities in experimental trials.

Hash tables are widely used. They rely on good quality hash functions. Popular data structure libraries either provide no hash functions or weak hash functions for sets or maps, making it impossible or impractical to use them as keys in other tables. This article presents three algorithms for hashing a set, two of which are simple to implement, practically fast, and can be combined. The quality evaluations follow the method of [1, chapter 2]. The insight that we are looking for commutative semigroups suggests that even better methods than symmetric polynomials may be found.

We have now identified two thermodynamically distinct types (A and B) of energetic processes naturally occurring on Earth. Type A energy processes such as the classical heat engines, apparently well follow the second law of thermodynamics; Type B energy processes, such as the newly discovered thermotrophic function that isothermally utilizes environmental heat energy to do useful work in driving ATP synthesis, which follows the first law of thermodynamics (conservation of mass and energy) but does not have to be constrained by the second law, owing to their special asymmetric functions. Several Type-B energy processes such as asymmetric-function-gated isothermal electricity and epicatalysis have been created through human efforts. The innovative efforts on Type-B processes to enable isothermally utilizing endless environmental heat energy could help to liberate all peoples from their dependence on fossil fuel energy, thus helping to reduce greenhouse gas CO2 emissions and control climate change towards a sustainable future for the humanity on Earth.

This paper presents a novel adaptive fault-tolerant neural-based control design for wind turbines with unknown dynamic and unknown wind speed. By utilizing the barrier Lyapunov function in the analysis of the Lyapunov direct method, the constrained behavior of the system is provided in which the rotor speed, its variation and generated power remain in the desired bounds. In addition, input saturation is also considered in terms of smooth pitch actuator bounding. Furthermore, by utilizing a Nussbaum-type function in designing the control algorithm, the unpredictable wind speed variation is captured without requiring accurate wind speed measurement, observation or estimation. Moreover, with the proposed adaptive analytic algorithms, together with the use of radial basis function neural networks, a robust adaptive and fault-tolerant control scheme is developed without the need for precise information about the wind turbine model nor the pitch actuator faults. Additionally, the computational cost of the resultant control law is reduced by utilizing a dynamic surface control technique. The effectiveness of the developed design is verified using theoretical analysis tools and illustrated by numerical simulations on a high-fidelity wind turbine benchmark model with different fault scenarios. Comparison of the achieved results to the ones that can be obtained via an available industrial controller shows the advantages of the proposed scheme.

The Colebrook equation is a popular model for estimating friction loss coefficients in water and gas pipes. The model is implicit in the unknown flow friction factor . To date, the captured flow friction factor can be extracted from the logarithmic form analytically only in the term of the Lambert -function. The purpose of this study is to find an accurate and computationally efficient solution based on the shifted Lambert -function also known as the Wright -function. The Wright -function is more suitable because it overcomes the problem with the overflow error by switching the fast growing term of the Lambert -function to the series expansions that further can be easily evaluated in computers without causing overflow run-time errors. Although the Colebrook equation transformed through the Lambert -function is identical to the original expression in term of accuracy, a further evaluation of the Lambert -function can be only approximate. Very accurate explicit approximations of the Colebrook equation that contains only one or two logarithms are shown. The final result is an accurate explicit approximation of the Colebrook equation with the relative error of no more than 0.0096%. The presented approximations are in the form suitable for everyday engineering use, they are both accurate and computationally efficient.

This paper introduces an approach that chooses the fault detection by calculating probabilities using probability mass function (pmf) and cumulative distribution function (CDF). This work used a method for multiple stuck-at faults by producing a new test pattern in combinational circuits. We assumed that existence of all multiple faults is only because of one single component that is faulty. A complete test set can be created by all possible single stuck-at faults in a combinational circuit using some combination of gates. The test set generation fault detection method is applied on two different 3-bit input variable and 4-bit input variable circuits. The probability of error occurrence is calculated at both 3-bit and 4-bit input variable circuits. The resulting feature is used to obtain maximum error occurrence probability to detect faults by the logic used that the complexity of the circuit is inversely proportional to the fault occurrence probability. Then again, undetectability is directly proportional to the complexity of the circuit. Therefore, finest feasible circuit should have large input variable components with less complexity to reduce the fault occurrence probability.

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

In this study, we consider a Lambert series whose coefficients are the sum of divisors function. Utilizing the Lambert series in the sequel we introduce a normalized linear operator JR_(α,β) (z) by applying the convolution with Rabotnov function. We then, acquire sufficient conditions for JR_(α,β) (z) to be Univalent, Starlike and Convex respectively. In each component of this study, we expand the derived results by applying two Robin's inequalities, one of which is equivalent to the Riemann hypothesis.

In this research paper an algorithm for the derivation of methods based on theorems and axioms of fuzzy logic is presented, analyzed and applied. This new proposed procedure generates fuzzy methods and evaluates the value of fuzzy propositions through fuzzy implication. The new implications of the family should satisfy a number of axioms. Also, we denote the conditions in order to satisfy the maximum number of axioms. Moreover, authors state and prove theorems focusing on fuzzy implication, observing the rule: the fuzzy function of fuzzy implication is strong and that lead to fuzzy negation. In addition, the optimal number of repetitions is calculated according to the expected truth value. The formulas produced are verified through the use of temperature and humidity values over a certain period of time and in a certain geographical area in Greece. The basic steps of the methodology are the fuzzification of the data given ​​using four membership degree functions and the application of the membership degrees of temperature and humidity values on a new type of fuzzy implication. Finally, we observed that the isosceles trapezium gave the best results and the type of fuzzy implication can be effectively applied.

Vitamin K occupies a unique and often obscured place among its fellow fat-soluble vitamins. Evidence is mounting however, that vitamin K (VK) may play an important role in the visual system apart from the hepatic carboxylation of hemostatic related proteins. However, to our knowledge, no review covering the topic has appeared in the medical literature. Recent studies have confirmed that matrix Gla protein (MGP), a vitamin K-dependent protein (VKDP), is essential for the regulation of intraocular pressure in the mouse. The PREDIMED (Prevención con Dieta Mediterránea) study, a randomized trial involving 5860 adults at risk for cardiovascular disease, demonstrated a 29% reduction in the risk of cataract surgery in participants with the highest tertile of dietary vitamin K1 (PK) intake compared with the lowest tertile. However, the specific requirements of the eye and visual system (EVS) for VK, and what might constitute an optimized VK status, is currently unknown and largely unexplored. It is the intention therefore of this narrative review to provide an introduction concerning VK and the visual system, review ocular VK biology, and to provide some historical context to recent discoveries. Potential opportunities and gaps in current research efforts will be touched upon, in the hope of raising awareness, and encouraging continued VK related investigations in this important and highly specialized sensory system.

In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several power series whose coefficients involve the Catalan numbers.

Aluminum, a contentious trace element found in the environment, has been demonstrated to have harmful effects on both humans and animals. In contrast, Sempervivum tectorum, an evergreen plant, has been found to offer numerous beneficial effects for both humans and animals. Therefore, this study aims to assess the protective effect of S. tectorum on certain reproductive biomarkers in male rats exposed to aluminum. Thirty-five Wistar rats were randomly divided into five groups: NTC (no-treatment control) received distilled water; NC (negative control) received drinking water containing 1 mg/L aluminum sulfate (AS); E1 received 1 mg/L AS along with an 8% S. tectorum extract; PC (positive control) received only 8% S. tectorum extract; E2 received 1 mg/L AS for three months followed by 8% extract for one month. The study analyzed testosterone, LH, FSH, body weight, and the histological structure of the testis, epididymis, and prostate, as well as the levels of zinc, manganese, copper, and iron in these organs. Significant decreases in body weight, testis, and epididymis size were observed in the aluminum-exposed groups compared to the control, whereas these decreases were not significant in the S. tectorum-treated groups compared to the control. Aluminum exposure led to significant decreases in testosterone and LH levels, with FSH levels showing a non-significant decrease in males, which were mitigated significantly by the administration of the plant extract. Histological analysis revealed alterations in the testis, epididymis, and prostate of the AS-exposed groups, including necrosis of seminiferous tubule epithelium and Leydig cells in the testis, and basal epithelial necrosis in the epididymis and prostate. Aluminum levels increased in all organs studied, while levels of zinc, copper, iron, and manganese decreased, showing a negative and significant correlation with aluminum levels. The aqueous extract of S. tectorum demonstrated a protective effect on certain studied biomarkers in male rats affected by aluminum exposure.

We propose a neural-network-based watermarking method that introduces the quantized activation function that approximates the quantization of JPEG compression. Many neural-network-based watermarking methods have been proposed. Conventional methods have acquired robustness against various attacks by introducing an attack simulation layer between the embedding network and the extraction network. The quantization process of JPEG compression was replaced by the noise addition process in the attack layer of the conventional methods. In this paper, we propose a quantized activation function that can simulate the JPEG quantization standard as it is in order to improve the robustness against the JPEG compression. Our quantized activation function consists of several hyperbolic tangent functions and is applied as an activation function for neural networks. Our network was introduced in the attack layer of ReDMark proposed by Ahmadi et al. to compare it with their method. That is, the embedding and extraction networks had the same structure. We compared the usual JPEG compressed images and the images applying the quantized activation function. The results showed that a network with quantized activation functions can approximate JPEG compression with high accuracy. We also compared the bit error rate (BER) of estimated watermarks generated by our network with those generated by ReDMark. We found that our network was able to produce estimated watermarks with lower BERs than those of ReDMark. Therefore, our network outperformed the conventional method with respect to image quality and BER.

Badminton is one of the most popular racket sports played by children up to the elderly worldwide. Everyone can practice and play badminton as a leisure or competitive sport, regardless of age, experience, or skill level. It does not require physical contact among players and expensive equipment. Compared with closed-skill exercise (e.g., running, swimming), open-skill exercise (e.g., badminton, table tennis) has been reported to intervene more with cognitive function and prevent cognitive decline. In this review, we outline the characteristics of badminton’s beneficial effects on physical and cognitive aspects. The characteristics presented here indicate that intervention with regular badminton exercise could effectively improve cognitive function and prevent cognitive decline in the elderly.

Due to its time effective, joint friendly and highly customizable character whole-body-electromyostimulation (WB-EMS) is regarded as a feasible solution for a large variety of training issues particularly in the area of non-athletic application. To identify gaps in research and summarize prevalent evidence we conducted an evidence map on outcomes addressed by WB-EMS trials in middle-aged to older, non-athletic adults. Based on a comprehensive systematic search in five databases and two study registers according to PRISMA, 54 projects published in 80 articles were included. More than 90% of the studies reported outcomes related to the physical fitness or function domain. Body composition parameters were addressed by two thirds of the projects. Health-related outcomes addressed by WB-EMS included cancer/neoplasm (n=7), endocrine regulation (n=8), glucose metabolism (15), nervous system diseases (n=2), cardiovascular system diseases (n=22), non-specific chronic low back pain (n=4), osteopenia (n=5) and diseases of the renal system (n=12). Outcomes related to inflammation were addressed 18 times. Of importance, no studies reported clinically relevant adverse effects related to the WB-EMS intervention. In summary, while considerable evidence on outcomes related to fitness/function and body composition is prevalent, evidence gaps of WB-EMS research were particular evident for diseases of the nervous and cerebrovascular system.

In patients with schizophrenia, metabolic syndrome is associated with cognitive impairments. We carried out a second analysis of data from a longitudinal trial to examine the relationship between weight gain and cognitive function in patients with first-episode schizophrenia (FES) over the first 6-month antipsychotic treatment. Baseline and 6-month endpoint measurements were taken for both cognitive function and body weight. Linear and logistic regression analyses were applied to investigate the bidirectional relationship between weight gain and cognitive function. Clinically relevant weight gain (CRW) was defined as an increase in body weight ex-ceeding 7%. The final analysis included 337 participants. Lower baseline scores in processing speed (OR=0.837, p=0.007), working memory and attention (OR=0.889, p=0.043), and executive function (OR=0.863, p=0.006) domains were significantly associated with CRW at the 6-month endpoint. After adjusting for confounders, CRW was found to be associated with improvement in the Brief Visuospatial Memory Test (p=0.036). The findings suggest that patients with lower baseline cognitive performance experienced more substantial weight gain. Conversely, weight gain was correlated with cognitive improvements, particularly in the domain of visual learning and memory. This suggested a potential bidirectional relationship between weight gain and cog-nitive function in patients with first-episode schizophrenia.

Radial basis function (RBF) networks are often viewed as instable when used in multi-layered architectures and therefore are mostly used in a single-layered manner. Universal approximation theorems for single-layered RBF networks further render deeper architectures useless. However, deep neural networks have proven their effectiveness on many different tasks. We show that deeper RBF architectures with multiple radial basis function layers are achievable and able to learn. We introduce an initialization scheme for deep RBF networks based on k-means clustering and covariance estimation. We further show how to make use of convolutions to speed up the calculation of a Mahalanobis distance in a partially-connected fashion, similar to convolutional neural networks (CNNs). Finally, we evaluate our approach on image classification as well as speech emotion recognition tasks. Our results show that deep RBF networks perform similar to simple CNNs.

Evidence suggests that COVID-19 infection can cause lasting health consequences. Multidiscipli-nary rehabilitation services have been recommended to reduce the sequalae. However, the effec-tiveness of physical exercise interventions remains insufficiently documented. The aim of this study was to develop and implement a specific and well tolerated protocol-based, intervention to reduce muscle weakness in older adults impacted by COVID-19. Forty six older adults random-ized into Intervention and Control Groups. Isometric and isokinetic strength assessments were conducted for selected muscle groups using JBA Staniak® torquemeter and Biodex System 3 dy-namometer. Functional abilities were evaluated with the Time Up and Go test and Chair Stand Tests. Men in intervention group demonstrated a significant improvement in static conditions for knee flexors (KF), trunk extensors (TE) and trunk flexors (TF) and in dynamic conditions for knee extensors (KE). Women in intervention group showed significant improvement in static condition for EF, KF, TE and TF and in dynamic for a KE and for a KF. The interaction GROUP x TESTING SESSION was significant for Chair test (s) and Chair test (n). Our results demonstrate the effec-tiveness of a well-tolerated, protocol-based approach that can be used to diminish long lasting functional deficits in post-covid survivors.

ozone-based chemiluminescence detection (CLD) has been widely applied for determining nitric oxide (NO) and its derived species in many different fields, such as environmental monitoring and biomedical research. In humans CLD was applied to determine exhaled NO and NO metabolites in biological samples. The main advantages of CLD are high sensitivity and selectivity for quantitative analysis in a wide dynamic range. Combining CLD with analytical separation techniques like gas or liquid chromatography allows the analytes to be quantified with less disturbance from matrix components or impurities. Sampling techniques like microdialysis and flow injection analysis may be coupled to CLD with the possibility of real-time monitoring of NO. However, details and precautions in experimental practice need to be addressed and clarified to avoid wrongly estimating. Therefore, using CLD as a detection tool requires a deep understanding of sample preparation procedure and chemical reactions used for liberating NO from its derived species. In this review, we discuss the advantages and pitfalls of CLD for determining NO species, the different applications and combinations with other analytical techniques, and provide general practical notes for sample preparation. These guidelines should help other researchers understand CLD data and select the best procedure for detecting NO species.

The C-type lectin-like receptor 2 (CLEC-2) is expressed on platelets and mediates binding to podoplanin (PDPN) on various cell types. The binding to circulating tumor cells (CTCs) leads to platelet activation and promote metastatic spread. The increased level of soluble CLEC-2 (sCLEC-2), presumably, released from activated platelets was shown in patients with thromboinflammatory and malignant disease. However, the functional role of sCLEC-2 and the mechanism of sCLEC-2 release is not known. In this study, we focused on the effect of platelet activation on CLEC-2 expression and the sCLEC-2 plasma level in cancer patients. First, citrated blood from healthy volunteer donors (n=20) was used to measure the effect of platelet stimulation by classical agonists and PDPN on aggregation, CLEC-2 expression on platelets by flow cytometry, sCLEC-2 release to the plasma by ELISA and total CLEC-2 expression by Western blot analysis. Second, sCLEC-2 was determined in plasma samples from healthy donors (285) and patients with colorectal carcinoma (CRC; 194), melanoma (160), breast cancer (BC; 99) or glioblastoma (49). PDPN caused a significant increase of the aggregation response induced by classical agonists. ADP or PDPN stimulation of platelets caused a significant decrease of CLEC-2 on platelets and sCLEC-2 in the plasma, whereas, total CLEC-2 in platelet lysates remained the same. Thus, the increased plasma level of sCLEC-2 is not a suitable biomarker of platelet activation. In patients with CRC (median 0.9 ng/mL), melanoma (0.9 ng/mL) or BC (0.7 ng/mL) we found significantly lower sCLEC-2 levels (p&lt;0.0001), whereas, glioblastoma patients displayed higher levels (2.6 ng/mL; p=0.0233) compared to healthy controls (2.1 ng/mL). The low sCLEC-2 plasma level observed in most of the tumor entities of our study, presumably, results from the internalization of sCLEC-2 by activated platelets or binding of sCLEC-2 to CTC.

Changes in the atomic and electronic structure of silicon carbide 3C-SiC (β-SiC), resulting from lead adsorption, have been studied within the density functional theory. The tests were conducted for three representative surfaces with varying degrees of lead coverage. Results indicate that chemisorption occurs, with the strongest binding, found on the hexagonal surface (111) in interaction with three dangling bonds. The adsorption energy rises with increasing coverage, especially as the surface approaches saturation. Analysis of the data was focused on parameters important for corrosion processes such as bond distances, binding energies, Bader charges and charge density difference.

Diminished ovarian reserve can be regarded as a sentinel indicator to foreshadow severe follicular loss and, ultimately, systemic aging. The negative slope of human ovulatory fidelity begins with a robust follicular endowment which gradually declines over time. In contrast, the youthful ovarian phenotype requires the coordinated work of endothelial, granulosa, immune, perivascular, stromal and possibly germline stem cells. Such a diverse tissue matrix can, in general, be influenced by platelet (PLT)-derived factors but this has not yet been specifically confirmed in the ovary after platelet-rich plasma (PRP). How could a comparable response be validated? Here a prospective, experimental study is proposed whereby eligible patients already undergoing scheduled laparoscopy provide ovarian tissue via biopsy submitted for co-culture with autologous Ca⁺² activated PRP. Recognizing the interlocking, central roles of nuclear factor κB (NF-κB) and tumor necrosis factor-α (TNF-α), incubated samples would be assessed for these in vitro before vs. after PRP exposure, in addition to stereomicroscopy. A mathematical model is available to track NF-κB oscillations and estimate gene expression, cell development, growth, apoptosis, and key immune and inflammatory actions. Since NF-κB and TNF-α are discharged in activated PLT releasate (or react to its cargo proteins) this audit permits extraction of response markers observed post-stimulus, thus linking discrete signals to transcriptional output, cellular fitness, and ovarian cytoarchitecture. From this, a hypothesis could emerge where intraovarian PRP is found to make no direct impact on follicles, although modified ovarian field function and curtailed local entropy incidentally favor optimized oocyte competence as a secondary effect.

Outdoor air pollution is a leading cause of death and premature death globally. Motorcycle-taxi drivers were most at risk associated with occupational exposure to ambient air pollution in urban areas. Therefore, a cross-sectional study was conducted to determine the influencing factors and prediction of lung function impairment in 308 motorcycle-taxi drivers living in Bangkok and adjacent provinces between February and June 2022. The study design included: data collection using questionnaires applied from the Thai version of ATS-DLD-78A: American Thoracic Society Division of Lung Diseases and Department of Disease Control, Ministry of Public Health, Thailand; a collection of respirable dust, and ambient air pollution parameters measured by per-sonal air sampling pump and real-time air quality index (AQI) station, and lung function determined by the spirometer. The results showed that 14 factors were significantly associated with lung function impairment (p<0.05). Apparently, seven influencing factors showing the most association were included: gender, the height of the subjects, history of allergies, exposure to respirable dust, mask types, helmet types, and family history of lung disease. The lung function impairment of motorcycle-taxi drivers was significantly predicted in 28.1% by regression analysis of these seven variables (R2=0.281). Therefore, this is the first report on influencing factors and prediction of lung function impairment among motorcycle-taxi drivers. These findings would be very useful for preventing and controlling measure ambient air pollution, setting policies and strategies to mitigate the risks for motorcycle-taxi drivers and the other ex-posed population.

Prostate cancer is the most common cancer among men in Poland. A significant proportion of prostate cancers can be cured, providing longer survival. Patients have the opportunity to undergo minimally invasive treatment methods like brachytherapy, while maintaining their previous quality of life. The disease itself, as well as treatment complications, primarily affect the functioning of the urinary and digestive systems and impact the sexual sphere. Aim: This study aims to assess the quality of life of patients after prostate brachytherapy. Methods: The research was conducted at the Lower Silesian Oncology Centre in Wroclaw. The study included fifty men aged between 51 and 85 years. The following questionnaires were used: EORTC QLQ-C30, QLQ-PR25. Scales: Katz, Mini-MAC, PSS-10. Moreover, the study used a self-designed survey covering socio-demographical factors. Results: Prostate brachytherapy has a significant impact on the degree of sexual dysfunction. Compared to sexually inactive individuals, sexually active individuals exhibit fewer negative psychological symptoms. Choosing a destructive coping strategy intensifies the occurrence of symptoms, lowers patients' level of independence, and negatively affects their quality of life. Conclusions: Brachytherapy contributes to worsening sexual function and temporarily affects urinary system function, which may lower the overall quality of life in patients.

Background: This study aimed to assess the relationship between age-related changes in Neuro-filament Light Chain (NFL), a marker of neuronal function, and various factors including muscle function, body composition, and metabolomic markers. Methods: The study included 40 partici-pants, aged 20 to 85 years. NFL levels were measured, and muscle function, body composition, and metabolomic markers were assessed. Results: NFL levels increased significantly with age, particularly in men. Negative correlations were found between NFL levels and measures of mus-cle function, such as grip strength, walking speed, and chair test performance, indicating a decline in muscle performance with increasing NFL. These associations were more pronounced in men. NFL levels also negatively correlated with muscle quality in men, as measured by 50 kHz phase angle. In terms of body composition, NFL was positively correlated with markers of fat mass and negatively correlated with markers of muscle mass, predominantly in men. Metabolomic analy-sis revealed significant associations between NFL levels and specific metabolites, with gen-der-dependent relationships observed. Conclusions: This study provides insights into the rela-tionship between circulating serum NFL, muscle function, and aging. The findings highlight gen-der differences and contribute to our understanding of age-related changes in neuronal function and their impact on muscle health.

The occurrence of the COVID-19 pandemic has affected all aspects of our routine life. Here, we briefly reveal the less paid attention aspect, vocabulary. We extracted words from online news outlets during the first three months of the pandemic. The extracted words included many aspects, which we categorised into eight classes according to their functions and implications. We found out the top three dominant classes of vocabularies with the highest frequency compared to others, namely medical, economic and governance. The temporality in the pandemic timeline was vital in making sense of the predominant vocabulary. This paper is a rare preliminary report which provides a valuable insight into future articles with much more comprehensive data and analysis.

We establish certain modular equations of degree three based on some results of Ramanujan's theta functions.

Background Some patients with mild cognitive impairment (MCI) experience gait disturbances. However, there are few reports on the relationship between gait disturbance and cognitive function in patients with MCI. Therefore, we investigated the neural correlates of gait characteristics related to cognitive dysfunction. Methods Eighty patients diagnosed with MCI from three dementia centres in Gangwon-do, Korea were recruited for this study. We defined MCI as a Clinical Dementia Rating global score of 0.5 or higher, with a memory domain score of 0.5 or greater. The patients were classified as having either early or late MCI based on their Mini Mental Status Examination z-scores. Multiple logistic regression analysis was performed to examine the association between the gait characteristics and cognitive impairment. Analyses included variables such as age, sex, years of education, number of comorbidities, body mass index and height. Results Gait velocity, step count, step length, heel-to-heel base support, swing and stance phase duration, and support time were associated with cognitive function. A decrease in gray matter volume in the right pericalcarine area was associated with gait characteristics related to cognitive dysfunction. An increase in the curvature of gray matter in the right entorhinal, right lateral orbitofrontal, right cuneus, and right and left pars opercularis areas was also associated with gait characteristics related to cognitive dysfunction. Conclusion Since gait impairment is an important factor in determining activities of daily living in patients with mild cognitive impairment, the evaluation of gait and cognitive functions in patients with mild cognitive impairment is important.

The impact of a non-anticholinergic spasmolytic drug (drotaverine hydrochloride) on 23 heart rate (HR), HR variability (HRV) and gastrointestinal tract (GIT) motility in the normal, resting 24 horses was determined. Ten adult riding horses had ECG recordings for 180 minutes after treat-25 ment with drotaverine (180 mg) or saline. Horses from the drotaverine group presented a de-26 creased of GIT contraction for two hours after treatment, but also showed drowsiness. Drotaverine 27 caused a reduction in cardiac vagal modulation of HR at T30 (P=0.050) and T60 (P=0.008) compared 28 to those receiving saline. RMSSD and high frequency (HF) recorded significantly low values after 29 drotaverine treatment by the end of the study, suggesting a decrease in parasympathetic activity. 30 HRV analysis indicated that drotaverine decreased both the low frequency (LF) and Lf/HF ratio 31 reflecting a decrease in sympathetic system. Non linear parameters registered low values after 32 drotaverine administration pointing a diminished in parasympathetic (for SD1) and sympathetic 33 (for SD2) activity. Decreased HRV was suggestive for a pervasive state of sympathetic hypervigi-34 lance of horses. The marked effect of drotaverine on HRV and GIT function in horses should be 35 taken into consideration when evaluating a clinical response to this drug in diseases associated 36 with smooth muscle spasm.

Selecting the optimal activation function for training deep neural networks has always been challenging because it significantly impacts the neural network’s performance and training speed. At this point, researchers are more likely to employ RELU than other well-known activation functions. After RELU, researchers have proposed many activation functions to improve RELU. None of them was capable of surpassing RELU as their most significant rival. SWISH outperformed RELU in several challenging experiments like classification, object detection, and tracking. Replacing RELU units with SWISH, which improves performance in many tasks. This paper proposed a new activation function surpassing Google’s brain’s SWISH function, Which we named AIF. Experiments indicate that our proposed activation function outperforms SWISH in various tasks.

In this work we derive a generalized series expansion of the acrtangent function by using the enhanced midpoint integration (EMI). Algorithmic implementation of the generalized series expansion utilizes a simple two-step iteration. This approach significantly improves the convergence and requires no surd numbers in computation of the arctangent function.

Cognitive function, arthrogryposis, obstetrics palsy, children, motor disorder

By solving a Marchenko equation, Green's functions at an arbitrary (inner) depth level inside an unknown elastic layered medium can be retrieved from single-sided reflection data, which are to be collected at the top of the medium. So far, an exact solution could only be obtained if the medium obeys stringent monotonicity conditions and if all forward-scattered (non-converted and converted) transmissions between the acquisition level and the inner depth level are known a-priori. We introduce an alternative Marchenko equation by revising the window operators that are applied in its derivation. We also introduce an auxiliary equation for transmission data, which are to be collected at the bottom of the medium, and a coupled equation, which is based on both reflection and transmission data. We show that the joint system of the Marchenko equation, the auxiliary equation and the coupled equation can be succesfully inverted when broadband reflection and transmission data are available. This results in a novel methodology for elastodynamic Green's function retrieval from two-sided data. Apart from these data, our approach requires P- and S-wave transmission times between the inner depth level and the top of the medium, as well as two angle-dependent amplitude scaling factors, which can be estimated from the data by enforcing energy conservation.

Antibodies constitute a major component of serum on protein mass basis. We also know that the structural diversity of these antibodies exceeds that of all other proteins in the body and they react with an immense number of molecular targets. What we still cannot quantitatively describe is, how antibody abundance is related to affinity, specificity and cross reactivity. This ignorance has important practical consequences: we also do not have proper biochemical units for characterizing polyclonal serum antibody binding. The solution requires both a theoretical foundation, a physical model of the system, and technology for the experimental confirmation of theory. Here we argue that the quantitative characterization of interactions between serum antibodies and their targets requires systems-level physical chemistry approach and generates results that should help create maps of antibody binding landscape.

An approach to estimating the objective function value of minimization maximum lateness problem is proposed. It is shown how to use transformed instances to define a new continuous objective function. After that, using this new objective function, the approach itself is formulated. We calculate the objective function value for some polynomially solvable transformed instances and use them as interpolation nodes to estimate the objective function of the initial instance. What is more, two new polynomial cases, that are easy to use in the approach, are proposed. In the end of the paper numeric experiments are described and their results are provided.

Let's define $\delta(x) = (\sum_{{q\leq x}}{\frac{1}{q}}-\log \log x-B)$, where $B \approx 0.2614972128$ is the Meissel-Mertens constant. The Robin theorem states that $\delta(x)$ changes sign infinitely often. Let's also define $S(x) = \theta(x) - x$, where $\theta(x)$ is the Chebyshev function. It is known that $S(x)$ changes sign infinitely often. We define the another function $\varpi(x) = \left(\sum_{{q\leq x}}{\frac{1}{q}}-\log \log \theta(x)-B \right)$. We prove that when the inequality $\varpi(x) \leq 0$ is satisfied for some number $x \geq 3$, then the Riemann hypothesis should be false. The Riemann hypothesis is also false when the inequalities $\delta(x) \leq 0$ and $S(x)\geq 0$ are satisfied for some number $x \geq 3$ or when $\frac{3 \times \log x + 5}{8 \times \pi \times \sqrt{x} + 1.2 \times \log x + 2} + \frac{\log x}{\log \theta(x)} \leq 1$ is satisfied for some number $x \geq 13.1$.

Robin criterion states that the Riemann Hypothesis is true if and only if the inequality $\sigma(n) < e^{\gamma } \times n \times \log \log n$ holds for all natural numbers $n > 5040$, where $\sigma(n)$ is the sum-of-divisors function and $\gamma \approx 0.57721$ is the Euler-Mascheroni constant. Let $q_{1} = 2, q_{2} = 3, \ldots, q_{m}$ denote the first $m$ consecutive primes, then an integer of the form $\prod_{i=1}^{m} q_{i}^{a_{i}}$ with $a_{1} \geq a_{2} \geq \cdots \geq a_{m} \geq 0$ is called an Hardy-Ramanujan integer. If the Riemann Hypothesis is false, then there are infinitely many Hardy-Ramanujan integers $n > 5040$ such that Robin inequality does not hold and $n < (4.48311)^{m} \times N_{m}$, where $N_{m} = \prod_{i = 1}^{m} q_{i}$ is the primorial number of order $m$.

The aim of this article is to introduce the new notion on a given graph. The notions of valued set, valued function, valued graph and valued quotient are introduced. The attributes of these new notions are studied. Valued set is about the set of vertices which have the maximum number of neighbors. The kind of partition of the vertex set to the vertices of the valued set is introduced and its attributes are studied. The behaviors of classes of graphs under these new notions are studied and the algebraic operations on these sets in the different situations get new result to understand the classes of graphs, these notions and the general graphs better and more.

The largest part of the image encryption algorithms operates on the pixel as a central element by implementing diffusion confusion and eventually a permutation. On the other side, a permutation applied at the bit level changes not only the pixel value, but also its location within the image. In this work, we will propose a new technology of medical and color image encryption, based on chaotic permutations acting at the bit level, and a diffusion confusion ensured by an application of the method of Vigenere largely improved and adapted to the subject. Simulations performed on a large number of images of different sizes and formats ensure that our method is not subject to any known attacks.

Muscle is one of the most critical organs for mammals, which governs multiple movement and physiological functions. Circular RNA (circRNA) is a kind of novel endogenous RNA without 5'-Caps and 3'-poly(A) structures formed by pre-mRNA's back-splicing. RNA binding proteins (RBPs) control the production and degradation of circRNA, help nucleus-cytoplasm transport and locate circRNA, and regulate circRNA translation. Therefore, circRNAs and the chaperoned RBPs play critical roles in muscle growth, development, and disease progression. In this review, we systematically characterize the possible molecular mechanism of circRNA-protein interactions. Also, we summarize the latest researches on circRNA-protein interactions in muscle development and diseases. Besides, we provide several valid prediction methods and experimental verification approaches. Our review reveals the importance of circRNAs and their protein chaperones and provides a reference for further study in this field.

We recently found that in human osteoblasts Homer1 complexes to CaSR and mediates AKT initiation via mTORC2 leading to beneficial effects in osteoblasts including -catenin stabilization and mTORC1 activation (doi: 10.1074/jbc.RA118.006587). Herein we further investigated the relationship between Homer1 and CaSR and demonstrate a link between the protein levels of CaSR and Homer1 in human osteoblasts in primary culture. Thus, when siRNA was used to suppress the CaSR, we observed upregulated Homer1 levels and when siRNA was used to suppress Homer1 we observed downregulated CaSR protein levels using immunofluorescence staining of cultured osteoblasts as well as western blot analyses of cell protein extracts. This finding was confirmed in vivo as the bone cells from osteoblast specific CaSR(-/-) mice showed increased Homer1 expression compared to wild-type. Furthermore, when the commonly used osteosarcoma cell lines MG63 and SAOS-2 were compared to primary osteoblasts, higher levels of Homer1 protein were associated with increased protein levels of the CaSR as well as mTOR and Rictor. CaSR and Homer1 protein were both expressed in osteocytes embedded in the long bones of wild-type mice, and immunofluorescent studies of these cells revealed that Homer1 protein sub-cellular localization was markedly altered in the osteocytes of CaSR(-/-) mice compared to wt. The study identifies additional roles for Homer1 in the control of the protein level and subcellular localization of CaSR in cells of the osteoblast lineage, in addition to its established role of mTORC2 activation downstream of the receptor.

We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer multicomponent mass is broken into fixed number of fragments and calculate the combinatorial multiplicity of all distributions in the set. We define random fragmentation by the condition that the probability of distribution be proportional to its multiplicity and obtain the partition function and the mean distribution in closed form. We then introduce a functional that biases the probability of distribution to produce in a systematic manner fragment distributions that deviate to any arbitrary degree from the random case. We corroborate the results of the theory by Monte Carlo simulation and demonstrate examples in which components in sieve cuts of the fragment distribution undergo preferential mixing or segregation relative to the parent particle.

The performance of choice-reaction tasks during athletic movement has been demonstrated to evoke unfavorable lower limb biomechanics. However, the mechanism of this observation is unknown. We conducted a systematic review examining the association between 1) the biomechanical and functional safety of unplanned sports-related movements (e.g. jumps/runs with spontaneously indicated landing leg/cutting direction) and 2) markers of perceptual-cognitive function (PGF). A literature search in three databases (Pubmed, ScienceDirect, Google Scholar) identified five relevant articles. Study quality, rated by means of a modified Downs & Black checklist, was moderate to high (average: 13.5/16 points). Four of five papers, in at least one parameter, found either an association of lower PGF and reduced task safety or significantly reduced task safety in low vs. high PGF performers. Yet, as a) the outcomes, populations and statistical methods of the included trials were highly heterogeneous and b) only two out of five studies had an adequate control condition (pre-planned movement task), evidence was classified as conflicting. In sum, PGF may represent a factor increasing injury risk during unplanned sports-related movements but future research strengthening the evidence of this association is warranted.

If a clear and valid no-go for Einsteinian hidden parameters is real, it must in no way be possible to violate the CHSH with a local hidden variables based computer simulation. In the paper we show that with the use of a modied Glauber-Sudarshan method it is possible to violate the CHSH.The criterion value comes close to the quantum value and is approximately 2.4. The proof (POC) is presented with the use of an R computer program. The important snippets of the code are discussed and the complete code is presented in an appendix.

In this article, we establish sharp trigonometric-polynomial bounds for unnormalized sinc function.