In this paper we address some variants for the products of Hadamard and Patterson. We prove that all zeros of the Riemann $\Xi$--function are real. We also prove that the Riemann hypothesis is true. The equivalence theorems associated with the Riemann zeta--function are obtained in detail.

This paper attempts to extend the Riemann Zeta function of a complex number to a function of a matrix and/or a tensor $A$, namely $$\zeta (A)=\sum _{n=1}^{\infty} \frac{1}{n^{A}}= \sum _{n=1}^{\infty} \sum_{k=1}^n\lambda_k A^k$$ and inverse $$A=\sum _{n=1}^{\infty} \sum_{k=1}^n \mu(n)\lambda_k \zeta(A^k)$$ where $\mu(n)$ is the M\"obius function, $A$ is a complex matrix or tensor with any order, and $\lambda_k$ is eigenvalue of the matri/tensor $A$. This kind of calculations on the Riemann Zeta function has never been seen in the literature. Some examples are provided.

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.

In this article we propose the integral, series and product representations for the Ramanujan zeta-function. We suggest a variant for the Conrey-Ghosh product for the entire Ramanujan zeta-function. We present some variants for the product for the Ramanujan $\Xi$-function. We prove that all of its zeros are real. Along the way we obtain the truth of the Riemann-Hardy conjecture.

The primary purpose of this article is to deduce specific order estimates for the \textit{Mertens Function} $M(n)$, which facilitates us to analyze the location of zeros of the \textit{Riemann Zeta function} $\zeta(s)$. The paper also provides a brief overview about the notion of the \textit{Mertens Function} $M(n)$ and \textit{Redheffer Matrices} $\mathbb{A}_{n}$. In addition to learning about various \textit{spectral properties} of $ \mathbb{A}_{n}$, we shall also deduce the relation between these two, which, eventually would lead us to establish a necessary and sufficient condition for the \textit{Riemann Hypothesis} to hold true, as justified by \textit{Redheffer} himself. We shall also observe several numerical evidence as well as theoretical justification behind the falsity of the famous \textit{Mertens Hypothesis}, along with how researchers over the years have approached towards deriving an estimate of the smallest possible natural number $n$ for which the first such violation of the theorem occurs, utilizing numerous conjectures annotating about the order of $M(n)$. Readers who are highly motivated in pursuing research in any of the topics relevent to the contents of this paper will surely find the \texttt{References} section to be extremely resourceful.

It is due to Littlewood that the truth of the Riemann theorem implies that of the Lindel\"{o}f conjecture. This paper aims to use the idea of Littlewood to prove the Lindel\"{o}f conjecture for the Riemann zeta function. The Lindel\"{o}f $\mu $ function at the critical line is zero, with use of the Riemann theorem for the entire Riemann zeta function, proved based on the work of Heath-Brown. Our result is given to show that the Lindel\"{o}f conjecture, connected with the proof of the moment conjecture, is true.

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.

Plant cells' ability to withstand abiotic stress is strongly linked to modifications in their mechanical characteristics. Nevertheless, the lack of a workable method for consistently tracking plant cell mechanical properties severely restricts our comprehension of the mechanical alterations in plant cells under stress. With Polyethylene Glycol (PEG6000), we created a drought-like environment, and we used the Double Resonator Piezoelectric Cytometry (DRPC) method to dynamically and non-invasively track changes in the stress (ΔS) created and viscoelasticity (storage modulus G' and loss modulus G") of protoplasts and suspension cells of rice during drought stress. The findings demonstrate that, rice suspension cells and protoplasts react mechanically differently to 5%–15% PEG6000 stress, implying distinct resistance mechanisms. However, neither of them can withstand 25% PEG6000 stress, they respond mechanically similarly to 25% PEG6000 stress. The results of DRPC are further corroborated by the morphological alterations of rice cells and protoplasts observed under an optical microscope. To sum up, the DRPC technique functions as a precise cellular mechanical sensor and offers novel research tools for the evaluation of plant cell adversity and differentiating between the mechanical reactions of cells and protoplasts under abiotic stress.

Riemann’s method is one of the definitive ways of solving Cauchy’s problem for a second order linear hyperbolic partial differential equation in two variables. The first review of Riemann’s method was published by E. T. Copson in 1958. This study extends that work. Firstly, three solution methods were overlooked in Copson’s original paper. Secondly, several new approaches for finding Riemann functions have been developed since 1958. Those techniques are included here and placed in the context of Copson’s original study. There are also numerous equivalences between Riemann functions that have not previously been identified in the literature. Those links are clarified here by showing that many known Riemann functions are often equivalent due to the governing equation admitting a symmetry algebra isomorphic to $SL(2,R)$. Alternatively, the equation admits a Lie-Bäcklund symmetry algebra. Combining the results from several methods, a new class of Riemann functions is then derived which admits no symmetries whatsoever.

Proposed fundamental laws of biology and a model of health and disease underscore the importance of the lymphatic system. The lymphatics are responsible for two of the laws of biology and the fulcrum of health and disease balancing proliferation with regeneration through the immune system. It is responsible for protection from the environment and repair of senile and damaged tissue. Life is constantly bombarded by forces that increase entropy. Lymphatics provide negative entropy to maintain health. Lymphatics help maintain cellular homeostasis removing products of metabolism. Using these principles, the role of lymphatics is investigated in salt sensitivity hypertension, cardiorenal system, the new pillar of heart failure and kidney disease - Sodium-Glucose Transport Protein 2 (SGLT2) Inhibitors, and brain diseases. The realization of organ lymphatics in maintenance of health and disease opens the avenue to new therapeutics. This is the unrealized potential of lymphatic study.

I had previously developed an approach called Gocgen approach, which claimed to prove twin prime conjecture. In this paper, I processed the previously developed Gocgen approach with the zeta function and explained the relationship between the zeta function with some formulas to offer another perspective on the zeta function, and also created a new function that explains the Gocgen approach using the zeta function. Understanding the new function created will provide insight into the frequency of prime numbers.

Prime numbers are the atoms of mathematics and mathematics is needed to make sense of the real world. Finding the Prime number structure and eventually being able to crack their code is the ultimate goal in what is called Number Theory. From the evolution of species to cryptography, Nature finds help in Prime numbers. One of the most important advances in the study of Prime numbers was the paper by Bernhard Riemann in November 1859 called “Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse” (On the number of primes less than a given quantity). In that paper, Riemann gave a formula for the number of primes less than x in terms the integral of 1/log(x) and the roots (zeros) of the zeta function defined by: Where ζ(z) is a function of a complex variable z that analytically continues the Dirichlet series. Riemann also formulated a conjecture about the location of the zeros of RZF, which fall into two classes: the "trivial zeros" -2, -4, -6, etc., and those whose real part lies between 0 and 1. Riemann's conjecture Riemann hypothesis [RH] was formulated as this: [RH] The real part of every nontrivial zero z* of the RZF is 1/2. Proving the RH is, as of today, one of the most important problems in mathematics. In this paper we will provide a proof of the RH. The proof of the RH will be built following these five parts: PART 1: Description of the RZF PART 2: The C-transformation PART 3: Application of the C-transformation to in Re(z) 0 to obtain ζ(z)=X(z)-Y(z) PART 4: Analysis of the values of z such that X(z)=Y(z), and |X(z)|=|Y(z)|, that equates to ζ(z)=0 Proof that |X(z)|=|Y(z)| only if Re(z)=1/2 Conclude that ζ(z)=0 only if Re(z)=1/2 for Re(z) 0 PART 5: We will also prove that all non-trivial zeros of ζ(z) in the critical line of the form are not distributed randomly. There is a relationship between the values of those zeros and the Harmonic function that leads to an algebraic relationship between any two zeros.

In this paper, we define a (p,v)-extension of Hurwitz-Lerch Zeta function by considering an extension of beta function defined by Parmar et al. [J. Classical Anal. 11 (2017) 81–106]. We obtain its basic properties which include integral representations, Mellin transformation, derivative formulas and certain generating relations. Also, we establish the special cases of the main results.

We monitored the water quality and hydrological conditions of a horizontal subsurface constructed wetland (HSSF-CW) in Beijing, China, for 2 years. We simulated the area rate constant and the temperature coefficient with the first-order kinetic model. We examined the relationships between the nitrogen (N) removal rate, N load, seasonal variations in the N removal rate, and environmental factors, such as the area rate constant, temperature, and dissolved oxygen (DO). The effluent ammonia (NH₄⁺-N) and nitrate (NO₃⁻-N) concentrations were significantly lower than the influent concentrations (p<0.01, n=38). The NO₃⁻-N load was significantly correlated with the removal rate (R²=0.9566, p<0.01), but the NH^₄+-N load was not correlated with the removal rate (R²=0.0187, p>0.01). The area rate constants of NO₃⁻-N and NH₄⁺-N at 20 °C were 27.01±26.49 and 16.63±10.58 m∙yr⁻¹, respectively. The temperature coefficients for NO₃⁻-N and NH₄⁺-N were estimated at 1.0042 and 0.9604, respectively. The area rate constants for NO₃⁻-N and NH₄⁺-N were not correlated with temperature (p>0.01). The NO₃⁻-N area rate constant was correlated with the corresponding load (R²=0.9625, p<0.01). The NH₄⁺-N area rate was correlated with DO (R²=0.6922, p<0.01), suggesting that the factors that influenced the N removal rate in this wetland met Liebig's law of the minimum.

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.

Recently, we have applied the generalized Littlewood theorem concerning contour integrals of the logarithm of analytical function to find the sums over inverse powers of zeroes for the incomplete Gamma- and Riemann zeta- functions, polygamma functions, and elliptical functions. Here, the same theorem is applied to study such sums for the zeroes of the Hurwitz zeta-function , including the sum over the inverse first power of its appropriately defined non-trivial zeroes. We also study some related properties of the Hurwitz zeta-function zeroes. In particular, we show that for any natural N and small real epsilon, when z tends to n=0, -1, -2… we can find at least N zeroes of zeta in the - vicinity of 0 for sufficiently small epsilon, as well as one simple zero tending to 1, etc.

In this review, we outline our current understanding of the mechanisms involved in the absorption, storage, and transport of dietary vitamin A to the eye, the trafficking of rod opsin protein to the photoreceptor outer segments, which encompasses the logistical backbone required for visual function. Two key mechanisms of this process are emphasized in this manuscript: Ocular and systemic vitamin A membrane transporters, and rhodopsin transporters. Understanding the complementary mechanisms responsible for the generation and proper transport of the retinylidene opsin to the photoreceptor outer segment will eventually shed light on the importance of genes encoded by these proteins, and their relationship on normal visual function and in the pathophysiology of retinal degenerative diseases.

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 $x \geq 13.1$.

This paper attempts to propose a Riemann spring model via an analogy between the Riemann Zeta function of a complex number and the elastic spring in series.

Sepsis is a serious disease that can lead to mortality. The etiology of the disease is connected to how the body as a host reacts toward microbes such as bacteria, viruses, and fungi invasion. Current research shows that during sepsis, the reaction toward microbe attacks takes two main phases. The first is known as a cytokine storm, while the second is a vicious cycle of pro-inflammatory responses followed by a strict anti-inflammatory response led by CD4+ Tregs. Various immunomodulatory therapies have been proposed to break the cycle of pro- and anti-inflammatory reactions to sepsis. However, clinical trials did not show promising results, indicating further research into the mechanism that Treg uses to inhibit proinflammatory reactions. We used next-generation sequencing (NGS) analysis of bulk RNA-seq and single-cell RNA-seq data to examine the exact molecular pathways used by Treg to inhibit the immune response in sepsis. Our approach identified ACOD1 (Aconitate Decarboxylase 1) as a primary mediator of Treg suppression of immune cells. We identified and validated CD36 as a downstream target of ACOD1. CD36 is a known metabolite regulator in Tregs. Taken together, our results indicate that targeting ACOD1 could prove valuable in regulating Treg function during sepsis.

Proteomics research has become one of the most important topics in the fields of life science and natural science. At present, research on protein–protein interaction networks (PPINs) mainly focuses on detecting protein complexes or function modules. However, existing approaches are either ineffective or incomplete. In this paper, we investigate function module detection mechanisms in PPIN, including open databases, existing detection algorithms and recent solutions. After that, we describe the proposed solution based on simplified swarm optimization (SSO) algorithm and gene ontology knowledge. The proposed solution implements SSO algorithm for clustering proteins with similar function, and imports biological gene ontology knowledge for further identifying function complexes and improving detection accuracy. Furthermore, we use four different categories of species dataset for experiment: Fruitfly, Mouse, Scere, and Human. The testing and analysis result show that the proposed solution is feasible, efficient and could achieve a higher accuracy of prediction than existing approaches.

Relationships between the Farey sequence and the Riemann hypothesis other than the Franel-Landau theorem are discussed. Whether a function similar to Chebyshev’s second function is square-root close to a line having a slope different from 1 is discussed. The nontrivial zeros of the Riemann zeta function can be used to approximate many functions in analytic number theory. For example, it could be said that the nontrival zeta function zeros and the Möbius function generate in essence the same function - the Mertens function. A different approach is to start with a sequence that is analogous to the nontrivial zeros of the zeta function and follow the same procedure with both this sequence and the nontrivial zeros of the zeta function to generate in essence the same function. A procedure for generating such a function is given.

The aim of this study was to investigate the physicochemical characterization and biological activities of chitosan (CH) based composite films with the incorporation of chestnut flower essential oil (CFEO). The composite films were prepared by casting method and characterized in terms of structural, morphological and mechanical properties via FT-IR, XRD, UV, SEM and TGA. The results proved the significantly increased water vapor permeability (WVP), heat resistance, antibacterial and antioxidant capabilities of CH-CFEO films. The incorporation of CH and CFEO enhanced the UV blocking, which made the film shield almost all UV light. Films with the tensile strength of 6.37 ± 0.41 MPa and elongation at break of 22.57 ± 0.35% were got with 6 mg mL-1 CFEO. Subsequently, the fruit preservation experiments also confirmed that the composite films could effectively extend the shelf life of bananas through their excellent water vapor and oxygen barrier. These desirable performances enable our newly developed composite films to be a remarkable packaging material to solve the fresh fruit preservation dilemma.

Background: In most cases, intra-labyrinthine schwannoma (ILS) occurs in patients with unilateral hearing deterioration or neurofibromatosis type II (NF II). The pattern of localization of these tumors is various but affects mostly the cochlea. Extirpation of the ILS, if hidden by the cochlea modiolus, is difficult under the aspect of complete removal. Therefore, a tissue removal device (TRD) was designed and tested in temporal bones. The principle of handling the new device is a pushing and pipe cleaner handling inside the cochlea. This present study aimed to describe the first in vivo experience with the newly developed TRD for removing cochlear intra-labyrinthine schwannoma. Methods: In three patients, the TRD was used for the tumor removal of ILS. In two patients with a cochlear schwannoma in combination with a cochlea implantation and one patient suffering from NF II, a cochlear schwannoma was removed with the TRD. The access was performed with a posterior tympanotomy, an enlarged round window approach, and an additional second-turn access. The device was inserted and extracted gradually from the second turn access until the rings were visible in the second turn access. By pushing and pipe cleaner handling, the tumors were removed. An MRI control was performed on the day postoperatively with a T1 GAD sequence. Results: Tumor removal with the TRD was performed in a 15-minute procedure. MRI control confirmed a complete removal on the postoperative day in both cases. Conclusion: In vivo handling of the device confirmed a straightforward handling for tumor removal. MRI scanning showed a complete removal of the tumor by the TRD.

In the paper, we prove a joint limit theorem in terms of weak convergence of probability measures on $\mathbb{C}^2$ defined by means of the Epstein ζ(s;Q) and Hurwitz ζ(s,α) zeta-functions. The limit measure in the theorem is explicitly given. For this, some restrictions on the matrix Q and parameter α are required. The theorem obtained extends and generalizes Bohr-Jessen’s results characterising asymptotic behaviour of the Riemann zeta-function.

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 $m$.

Arctic feedbacks will accelerate climate change and could jeopardise mitigation efforts. The permafrost carbon feedback releases carbon to the atmosphere from thawing permafrost and the sea ice albedo feedback increases solar absorption in the Arctic Ocean. A constant positive albedo feedback and zero permafrost feedback have been used in nearly all climate policy studies to date, while observations and models show that the permafrost feedback is significant and that both feedbacks are nonlinear. Using novel dynamic emulators in the integrated assessment model PAGE-ICE, we investigate nonlinear interactions of the two feedbacks with the climate and economy under a range of climate scenarios consistent with the Paris Agreement. The permafrost feedback interacts with the land and ocean carbon uptake processes, and the albedo feedback evolves through a sequence of nonlinear transitions associated with the loss of Arctic sea ice in different months of the year. The US’s withdrawal from the current national pledges could increase the total discounted economic impact of the two Arctic feedbacks until 2300 by $25 trillion, reaching nearly $120 trillion, while meeting the 1.5 °C and 2 °C targets will reduce the impact by an order of magnitude.

Diarrhoea is a serious cause of mortality worldwide that can lead to dehydration, gut barrier function impairment, nutrient malabsorption, and alterations of the gut microbiota (dysbiosis). Current solutions for its management, such as oral rehydration salts (ORS), inhibitors of the gut motility, antibiotics, and living probiotics only partially counteract the mechanisms of the disease and do not provide a full coverage of the problem. Potential risks of the use of living probiotic strains, particularly in immunocompromised patients, can be eliminated with the use of tyndallized (heat-killed) postbiotic bacteria and yeast. ABB C22® is a postbiotic combination of three tyndallized yeasts, namely Saccharomyces boulardii, Saccharomyces cerevisiae, and Kluyveromyces marxianus. To assess the action of the postbiotic combination on diarrhoea, immune and gut epithelial cell signaling assays, gut barrier formation assay and rotavirus gene expression assay were performed. ABB C22® showed a strong anti-inflammatory effect, an induction of the build-up of the gut epithelium, and a degree of protection against rotavirus infection. These experimental studies support the use of the postbiotic ABB C22® as a solution for the management of diarrhoea and gastrointestinal conditions, alone or in combination with existing but incomplete treatments.

In recent experimental studies, we reported the aggravating effects of Asian sand dust (ASD) on male reproductive function in mice. However, the effects of fetal ASD exposure on male reproductive function have not been investigated. The present study investigated the effects of fetal ASD exposure on reproductive function in male offspring. Using pregnant CD-1 mice, ASD was administered intratracheally on days 7 and 14 of gestation, and the reproductive function of male offspring was determined at 5, 10, and 15 weeks after birth. The secondary sex ratio was significantly lower in the fetal ASD-exposed mice than in the controls. Histologic examination showed partial vacuolation of seminiferous tubules in immature mice. Moreover, daily sperm production (DSP) was significantly less in the fetal ASD-exposed mice than in the controls. DSP in the fetal ASD-exposed mice was approximately 10% less than the controls at both 5 and 10 weeks. However, both the histologic changes and the DSP decrease were reversed as the mice matured. These findings suggest that ASD exposure affects both the fetal development and the reproductive function of male offspring. In the future, it will be necessary to clarify the onset mechanisms of ASD-induced male fetus death and male reproductive disorders.

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.

Chronic kidney disease patients treated by hemodialysis present a high cardio-vascular morbidity and mortality. There is an imperative need for novel biomarkers in identifying and to offer possible therapeutically intervention in these patients. We performed a prospective observational cohort study on 77 patients in the period October 2021 – October 2023. We measured serum plasma levels of Interleukin 1-Beta, Galectin 3, human suppression of tumorigenicity factor 2, bone morphogenetic protein 2 and fibroblastic growth factor 23 at the inclusion. We evaluated the correlations of these biomarkers with cardiac function and structure evaluated by echocardiography. Mean age was 61.02 (±11.81) years, 45 (56.2%) males and with a dialysis vintage of 4.95 (2.4-7.8) years. Median ejection fraction was 51 (43-54 %) and more than two thirds of the patients presented valvular calcifications. Overall mortality was 22%. Interleukin 1-Beta correlated positively with ejection fraction and global longitudinal strain and negatively with left atrium diameter and left ventricle tele systolic diameter. Galectin 3 values negatively correlated with aortic valve fibrosis and mitral valve calcifications and human suppression tumorigenity factor 2 negatively correlated with mitral valve calcifications. Some of these novel biomarkers could be used to better asses the cardio-vascular disease in patients on maintenance hemodialysis.

Diarrhoea is a serious cause of mortality worldwide that can lead to dehydration, gut barrier function impairment, nutrient malabsorption, and alterations of the gut microbiota (dysbiosis). Current solutions for its management, such as oral rehydration salts (ORS), inhibitors of the gut motility, antibiotics, and living probiotics only partially counteract the mechanisms of the disease and do not provide a full coverage of the problem. Potential risks of the use of living probiotic strains, particularly in immunocompromised patients, can be eliminated with the use of tyndallized (heat-killed) postbiotic bacteria and yeast. ABB C22® is a postbiotic combination of three tyndallized yeasts, namely Saccharomyces boulardii, Saccharomyces cerevisiae, and Kluyveromyces marxianus. To assess the action of the postbiotic combination on diarrhoea, immune and gut epithelial cell signaling assays, gut barrier formation assay and rotavirus gene expression assay were performed. ABB C22® showed a strong anti-inflammatory effect, an induction of the build-up of the gut epithelium, and a degree of protection against rotavirus infection. These experimental studies support the use of the postbiotic ABB C22® as a solution for the management of diarrhoea and gastrointestinal conditions, alone or in combination with existing but incomplete treatments.

This paper is devoted to the study of multi-dimensional integral transform with Fox H-function in the kernel in weighted spaces integrable functions in the domain R+n with positive coordinates. Mapping properties such as the boundedness, the range, the representations of the considered transformation are established.

In this article, it is demonstrated that if the zeta function does not have a sequence of zeros whose real part converges to 1, then it cannot have any zeros in the critical strip, showing that the Riemann Hypothesis is false.

In this study, a simple approach to solving the Riemann Hypothesis, one of the most prominent unsolved problems in the field of Number Theory in mathematics and one of the “Millenium Prize Problems”, is presented. The Riemann Hypothesis, a conjecture about distribution of prime numbers, has remained unsolved since it was first proposed by German mathematician, Bernhard Riemann in 1859. This paper introduces an analytic continuation of the Zeta Function as well as symmetric approach through integration by parts to address this hypothesis. The proposed solution is obtained through analytical continuation in the critical strip 0<Re(s)<1 to establish that Re(s)=1/2.

Proof of the Riemann hypothesis is obtained using the properties of the Gamma function, the Bernoulli function, and limitations imposed by the rational relations of the complex roots of the Riemann zeta function, and the rational relations of the complex Gamma functions.

In this article the reduction of a $n$-dimensional space to a $k$-dimensional space is considered as a reduction of $N^n$ states to $N^k$ states, where $N$ stands for the number of single-particle states per unit of spatial length. It turns out, this space reduction could be understood as another definition of inflation. It is shown that the introduction of the non-associativity of the algebra of physical fields in a homogeneous space leads to a nonlinear equation, the solutions of which can be considered as two-stage inflation. Using the example of reduction $T\times R^7$ to $T\times R^3$, it is shown that there is a continuous cross-linking of the Friedmann and inflationary stages of algebraic inflation at times $10^{-15}$ with the number of baryons $10^{80}$ in the Universe. In this paper, we construct a new gravitational constant based on a nonassociative octonion algebra.

In this article the reduction of a $n$-dimensional space to a $k$-dimensional space is considered as a reduction of $N^n$ states to $N^k$ states, where $N$ stands for the number of single-particle states per unit of spatial length. It turns out, this space reduction could be understood as another definition of inflation. It is shown that the introduction of the non-associativity of the algebra of physical fields in a homogeneous space leads to a nonlinear equation, the solutions of which can be considered as two-stage inflation. Using the example of reduction $T\times R^7$ to $T\times R^3$, it is shown that there is a continuous cross-linking of the Friedmann and inflationary stages of algebraic inflation at times $10^{-15}$ with the number of baryons $10^{80}$ in the Universe. In this paper, we construct a new gravitational constant based on a nonassociative octonion algebra.

We derive new infinite series involving Fibonacci numbers and Riemann zeta numbers. The calculations are facilitated by evaluating linear combinations of polygamma functions of the same order at certain arguments.

In order to solve the problem of feature extraction of underwater acoustic signals in complex ocean environment, a new method for feature extraction from ship radiated noise is presented based on empirical mode decomposition theory and permutation entropy. It analyzes the separability for permutation entropies of the intrinsic mode functions of three types of ship radiated noise signals, and discusses the permutation entropy of the intrinsic mode function with the highest energy. In this study, ship radiated noise signals measured from three types of ships are decomposed into a set of intrinsic mode functions with empirical mode decomposition method. Then, the permutation entropies of all intrinsic mode functions are calculated with appropriate parameters. The permutation entropies are obviously different in the intrinsic mode functions with the highest energy, thus, the permutation entropy of the intrinsic mode function with the highest energy is regarded as a new characteristic parameter to extract the feature of ship radiated noise. After that, the characteristic parameters, namely, the energy difference between high and low frequency, permutation entropy, and multi-scale permutation entropy, are compared with the permutation entropy of the intrinsic mode function with the highest energy. It is discovered that the four characteristic parameters are at the same level for similar ships, however, there are differences in the parameters for different types of ships. The results demonstrate that the permutation entropy of the intrinsic mode function with the highest energy is better in separability as the characteristic parameter than the other three parameters by comparing their fluctuation ranges and the average values of the four characteristic parameters. Hence, the feature of ship radiated noise can be extracted efficiently with the method.

To advance probiotic research, a comprehensive understanding of bacterial interactions with human physiology at the molecular and cellular levels is fundamental. Lacticaseibacillus rhamnosus LGG® is a bacterial strain that has long been recognized for its beneficial effects on human health. Probiotic effector molecules derived from LGG®, including secreted proteins, surface-anchored proteins, polysaccharides, and lipoteichoic acids, that interact with host physiological processes have been identified. In vitro and animal studies have revealed that specific LGG® effector molecules stimulate epithelial cell survival, preserve intestinal barrier integrity, reduce oxidative stress, mitigate excessive mucosal inflammation, enhance IgA secretion, and provide long-term protection through epigenetic imprinting. Pili on the cell surface of LGG® promote adhesion to the intestinal mucosa and ensure close contact to host cells. Extracellular vesicles produced by LGG® recapitulate many of these effects through their cargo of effector molecules. Collectively, the effector molecules of LGG® exert a significant influence on both the gut mucosa and immune system, that promotes intestinal homeostasis and immune tolerance.

The uncertainty in the secondary path of an Active Noise Control (ANC) headphone affects the waterbed effect and stability of the feedback system. This study focuses on the uncertainty of the secondary path when real users wear headphones, and proposes a new uncertainty constraint based on the measured results of the secondary path transfer function under different wearing conditions of dummy head and limited subjects. This constraint and a cascaded second-order infinite impulse response filter with fixed coefficients are used to formulate a control strategic function, which is optimized by the Improved Grey Wolf Optimizer (IGWO) algorithm to obtain the optimal controller with better noise reduction performance. The proposed method and simulation model are validated based on the experimental test results. The results demonstrate that the safety factor and waterbed suppressing factor contained in the proposed uncertainty constraint ensures more stable noise reduction and effective suppression of the waterbed effect for new subjects without a priori data.

Although a growing number of evidence emphasizes superior of VATS over conventional thoracotomy, still is little known about early postoperative diaphragm muscle function after lobectomy via these two approahces. To fill the gap in existing literature, we conducted comparative study between VATS and conventional thoracotomy in terms of postoperative diaphragm muscle function, assessing its contractility, strength, magnitude of effort and potential risk of dysfunction such as: atrophy and paralysis. A total of 59 patients (30 after VATS), who underwent anatomical pulmonary resection at our institution, were enrolled into this study. The control group was consisted of 28 health subjects without medical condition could contribute to diaphragm dysfunction. Diaphragm muscle was assessed before and after surgery using ultrasonography. We found that both surgical approaches were associated with postoperative impairment of diaphragm muscle function - compared to baseline data. Postoperative reduction of diaphragm contraction was demonstrated in all of 59 patients. In case of control group, the differences between measurements were no observed. We noted that lobectomy via thoracotomy was linked with greater percentage of patients with diaphragm paralysis or/and atrophy that VATS. Similar findings were observed in refer to diaphragm magnitude effort, as well as, diaphragm contraction strength, where minimal invasive surgery was associated with better diaphragm function parameters - in comparison to thoracotomy. Disturbance of diaphragm work was reported both at operated and non-operated side. Upper right and left lobectomy was connected with greater diaphragm function impairment than other segments. In conclusion, VATS technique seems to be less invasive than conventional thoracotomy providing a better postoperative function of a main respiratory muscle.

In this article, author performs computational analysis for the generalized zeta functions by using computational software Mathematica. To achieve the purpose recently obtained difference equations are used. These difference equations have a computational power to compute these functions accurately while they can not be computed by using their known integral represenations. Several authors investigated such functions and their analytic properties, but no work has been reported to study the graphical representations and zeors of these functions. Author performs numerical computations to evaluate these functions for different values of the involved parameters. Taylor series expansions are also presented in this research.

The Mobius function is commonly used to define Euler's totient function and the Mangoldt function. Similarly, the summatory Mobius function (the Mertens function) can be used to define the summatory totient function and the summatory Mangoldt function (the second Chebyshev function).

The quiet-time solar wind electrons feature non-thermal characteristics when viewed from the perspective of their velocity distribution functions. They typically have an appearance of being composed of a denser thermal “core” population plus a tenuous energetic “halo” population. At first, such a feature was empirically fitted with the Kappa velocity space distribution function, but ever since the ground-breaking work by Tsallis, the space physics community has embraced the potential implication of the Kappa distribution as reflecting the non-extensive nature of the space plasma. From the viewpoint of microscopic plasma theory, the formation of non-thermal electron velocity distribution function can be interpreted in terms of the plasma being in a state of turbulent quasi equilibrium. Such a finding brings forth the possible existence of a profound inter-relationship between the non-extensive statistical state and the turbulent quasi-equilibrium state. The present paper further develops the idea of solar wind electrons being in the turbulent equilibrium, but unlike the previous model, which involves the electrostatic turbulence near the plasma oscillation frequency (i.e., Langmuir turbulence), the present paper considers the impact of transverse electromagnetic turbulence, particularly, the turbulence in the whistler-mode frequency range. It is found that the coupling of spontaneously-emitted thermal fluctuations and the background turbulence leads to the formation of non-thermal electron velocity distribution function of the type observed in the solar wind during quiet times. This demonstrates that the whistler-range turbulence represents an alternative mechanism for producing the Kappa-like non-thermal distribution, especially close to the Sun and in the near-Earth space environment.

The Hamiltonian of a quantum mechanical system has an affiliated spectrum. If this spectrum is the sequence of prime numbers, a connection between quantum mechanics and the nontrivial zeros of the Riemann zeta function can be made. In this case, the Riemann zeta function is analogous to chaotic quantum systems, as the harmonic oscillator is for integrable quantum systems. Such quantum Riemann zeta function analogies have led to the Bender-Brody-Müller (BBM) conjecture, which involves a non-Hermitian Hamiltonian that maps to the zeros of the Riemann zeta function. If the BBM Hamiltonian can be shown to be Hermitian, then the Riemann Hypothesis follows. As such, herein we perform a symmetrization procedure of the BBM Hamiltonian to obtain a unique Hermitian Hamiltonian that maps to the zeros of the analytic continuation of the Riemann zeta function, and provide an analytical expression for the eigenvalues of the results. The holomorphicity of the resulting eigenvalues is examined. Moreover, a second quantization of the resulting Schrödinger equation is performed, and a convergent solution for the nontrivial zeros of the analytic continuation of the Riemann zeta function is obtained. Finally, from the holomorphicity of the eigenvalues it is shown that the real part of every nontrivial zero of the Riemann zeta function converges at σ = 1/2.

This longitudinal study examined the development of executive function and calibration accuracy in pre-adolescents. Two hundred sixty two students(127 females) from grades 4 (n = 91), 5 (n = 89) and 6 (n = 82) took measures of executive function and performance calibration in a sport task, three times within a period of 20 months. A latent growth curve modeling analysis showed a significant relation between the rates of change of executive function and calibration. Further, the results showed a dynamic interplay in the development of executive function and calibration. There were significant inter-individual differences in the estimated population means both in executive function and calibration and in the rate of change of executive function, but not in the rate of change for calibration. The age of the participants had a positive effect only on the estimated population mean of executive function.

Stimulation of the alpha 7 nicotinic acetylcholine receptor (α7nAChR) has shown beneficial effects in several acute inflammatory disease models. This study aims to examine whether treatment with the selective α7nAChR agonist PHA 568487 can dampen inflammation and thereby improve cardiac function after myocardial infarction in mice. The possible anti-inflammatory properties of α7nAChR agonist PHA 568487 were tested in vivo using the air pouch model and in a permanent occlusion model of acute myocardial infarction in mice. Hematology parameters and cytokine levels were determined. Infarct size and cardiac function were assessed via echocardiography 24 h and one week after the infarction. Treatment with α7nAChR agonist PHA 568487 decreased 12 (CCL27, CXCL5, IL6, CXCL10, CXCL11, CXCL1, CCL2, MIP1a, MIP2, CXCL16, CXCL12 and CCL25) out of 33 cytokines in the air pouch model of acute inflammation. However, α7nAChR agonist PHA 568487 did not alter infarct size, ejection fraction, cardiac output or stroke volume at 24 h nor at 7 days after the myocardial infarction compared with control mice. In conclusion, despite promising immunomodulatory effects in the acute inflammatory air pouch model, α7nAChR agonist PHA 568487 did not affect infarct size or cardiac function after a permanent occlusion model of acute myocardial infarction in mice. Consequently, this study does not strengthen the hypothesis that stimulation of the α7nAChR is a future treatment strategy for acute myocardial infarction when reperfusion is lacking. However, whether other agonists of the α7nAChR can have different effects remains to be investigated.

The standard approach to integrable nonlinear evolution equations (NLEE) usually uses the following steps: 1) Lax representation $[L,M]=0$; 2)~construction of fundamental analytic solutions (FAS); 3) reducing the inverse scattering problem (ISP) to a Riemann-Hilbert problem (RHP) $\xi^+(x,t,\lambda) =\xi^-(x,t,\lambda) G(x,t\lambda)$ on a contour $\Gamma$ with sewing function $G(x,t,\lambda)$; 4) soliton solutions and possible applications.Step 1) involves several assumptions: the choice of the Lie algebra $\mathfrak{g}$ underlying $L$, as well as its dependence on the spectral parameter, typically linear or quadratic in $\lambda$. In the present paper we propose another approach which substantially extends the classes of integrable NLEE.Its first advantage is that one can effectively use any polynomial dependence in both $L$ and $M$. We use the following steps: A) Start with canonically normalized RHP with predefined contour $\Gamma$; B) Specify the $x$ and $t$ dependence of the sewing function defined on $\Gamma$; C) Introduce convenient parametrization for the solutions $ \xi^\pm(x,t,\lambda)$ of the RHP and formulate the Lax pair and the nonlinear evolution equations (NLEE); D) use Zakharov-Shabat dressing method to derive their soliton solutions. This needs correctly taking into account the symmetries of the RHP. E) Define the resolvent of the Lax operator and use it analyze its spectral properties.

Acidic ostreolysin A/pleurotolysin B (OlyA/PlyB, formerly known as ostreolysin (Oly), and basic 20 kDa equinatoxins (EqTs) are cytolytic proteins isolated from the edible mushroom Pleurotus ostreatus and the sea anemone Actinia equina, respectively. Both toxins, although from different sources, share many similar biological activities: (i) colloid-osmotic shock by forming pores in cellular and artificial membranes enriched in cholesterol and sphingomyelin; (ii) increased vascular endothelial wall permeability in vivo and perivascular oedema; (iii) dose-dependent contraction of coronary vessels; (iv) haemolysis with pronounced hyperkalaemia in vivo; (v) bradycardia, myocardial ischemia and ventricular extrasystoles accompanied by progressive fall of arterial blood pressure and respiratory arrest in rodents. Both types of toxins are haemolytic within nanomolar range concentrations, and it seems that hyperkalaemia plays an important role in toxin cardiotoxicity. However, it was observed that the haemolytically more active EqT III is less toxic than EqT I, the most toxic and least haemolytic EqT. In mice, EqT II is more than 30 times more toxic than OlyA/PlyB when applied intravenously. These observations imply that haemolysis with hyperkalaemia is not the sole cause of the lethal activity of both toxins. Additional mechanisms responsible for lethal action of the two toxins are direct effects on heart, coronary vasoconstriction and related myocardial hypoxia. In this review, we appraise the pathophysiological mechanisms related to the chemical structure of OlyA/PlyB and EqTs, as well as their toxicity.

During fertilization, the fusion of the spermatozoa with the oocytes causes the release of calcium from the oocyte endoplasmatic reticulum. This, in turn, triggers a series of calcium ion (Ca2+) oscillations, a process known as oocyte activation. The sperm-specific factor responsible for oocyte activation is phospholipase C zeta (PLCζ). Men undergoing intracytoplasmic sperm injection (ICSI) with their spermatozoa lacking PLCζ are incapable of generating Ca2+oscillation, leading to fertilization failure. The immunofluorescence assay is the most used technique to assess the expression and localization of PLCζ and to diagnose patients with reduced/absent ability to activate the oocytes. In these patients, the use of assisted oocyte activation (AOA) technique can help to yield successful ICSI results and shorten the time of pregnancy. However, the production of a stable PLCζ recombinant protein represents a new powerful therapeutic approach to treating individuals with this condition. We aim to conduct a systematic review focusing on the expression, level, and localization of PLCζ, discussing the novel genetic mutation associated with its impairment. In addition, we highlight the benefits of AOA, looking at new and less invasive methods to diagnose and treat cases with PLCζ dysfunction ability.

(1) Background: Ulcerative colitis (UC) is characterized by immune system dysregulation with frequent extraintestinal manifestations, including airways involvement. Reduction in CO diffusing capacity and functional alterations in small airways have been described. The extended analysis of Fractional Exhaled Nitric Oxide (FeNO), may distinguish the sites of production and the presence of small airways inflammation being a useful, non-invasive marker for these patient’s follow up. The aim of our study was to compare PFTs, FeNO and CANO values of UC patients with different clinical disease activity and healthy subjects to reveal lung function abnormalities and the presence of subclinical airway inflammation. (2) Methods: We enrolled 42 adult outpatients with different clinical activity stages of UC (mean age 39±13 years) and a healthy control group of 41 subjects (mean age 29±3 years). C-reactive protein (CRP) and FeNO values at different flows (50,100 and 200 ml/sec) were collected. All patients performed pulmonary function tests (PFT’s) with static volumes and diffusing capacity (DLCO). (3) Results: FENO, CANO and CRP values were significantly increased in UC patients when compared with controls (p=0.02 and p&lt;0.0001, respectively) and proportionally to the disease activity (FeNO class 3: 27.1 ppb vs class 1-2: 6.2 ppb; CANO values class 3: 8.1 ppb vs class 1-2: 2.0 ppb (p &lt; 0.0001). TLC and DLCO were significantly reduced in UC patients compared to controls (p=0.011 and p&lt;0.0001, respectively). (4) The results of this study show significant lung functional abnormalities in UC patients and suggest the presence of airway inflammation directly correlated with the disease activity suggesting an integrated approach in routine assessment.

In this paper, we derive Von Koch's inequality without using the Riemann Hypothesis. As well known, Von Koch's inequality is equivalent to the Riemann Hypothesis. Namely, we show that the Riemann Hypothesis is true. Furthermore, we show that the upper limit of its can be lowered.

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

In this study, a commercial sodium butyrate protected by a new buffer salt solution (NSB) was tested to determine whether it can be used as an antibiotic alternative in broiler production. 192 1-day-old broilers were randomly allocated to three dietary treatments: soybean meal diet (CON), antibiotic diet (ANT, basal diet + 100 mg/kg aureomycin), and NSB (basal diet + 800 mg/kg NSB). The growth performance, serum anti-inflammatory cytokines, intestinal morphology, gut barrier function, antioxidative parameters, SCFAs content, and cecal microbiota were analyzed. The result showed that NSB significantly improved ADFI, ADG (p < 0.01), and decreased FCR (p < 0.01). Serum anti-inflammatory cytokine IL-10 was up-regulated (p < 0.01), and pro-inflammatory TNF-α was down-regulated (p < 0.05) by NSB supplementation. H&E results showed that VH and VH: CD ratio significantly increased (p < 0.05) in the jejunum and ileum in the NSB group. Furthermore, ZO-1 (p < 0.01), claudin-1 (p < 0.01), and occludin (p < 0.05) in the jejunum and claudin-1 (p < 0.01) and mucin-2 (p < 0.05) in the ileum significantly up-regulated in the NSB group, respectively. Additionally, SOD (p < 0.05) and T-AOC/MDA ratio (p < 0.01) in the jejunum and SOD in the ileum were significantly increased (p < 0.05) in the NSB group. The MDA level also significantly increased (p < 0.01) in the ANT group in the jejunum. Propionic acid (p < 0.05) and butyric acid (p < 0.01) content significantly increased in the NSB group in the jejunum and ileum segments. The 16S rRNA sequencing results showed no significant difference (p > 0.05) in alpha and beta diversity among the groups. LEFSe analysis also indicated that Peptostreptococcaceae, Colidextribacter, Firmicutes, Oscillospira, and Erysipelatoclostridiaceae, which promote SCFA production (p < 0.05), were identified as dominant taxon-enriched bacterial genera in the NSB group. The Spearman correlation analysis revealed that Colidextribacter with ADFI, ADG, VH, claudin-1 (p < 0.05), and unclassified_f__Peptostreptococcaceae with ADFI, IL-10, and ZO-1 were positively correlated (p < 0.05). Furthermore, ADFI and ADG with IL-10, claudin-1, SOD, T-AOC, and butyric acid (p < 0.05), and similarly, ADG with VH (p < 0.05) showed a positive correlation. In conclusion, NSB enhanced the growth performance by improving jejunum and ileum morphology, serum anti-inflammatory cytokines, regulating intestinal barrier function and antioxidant capacity, SCFAs content, and cecum microbiota, showing its potential use as an alternative to antibiotics in poultry nutrition.

The present study aims to develop an efficient numerical method for computing the diffraction and radiation of water waves with horizontal long cylindrical structures, such as floating breakwaters. A higher-order scheme is used to discretize geometry of the structure as well as the relevant physical quantities. As the kernel of this method, Wehausen’s free-surface Green function is calculated by a newly-developed Gauss-Kronrod adaptive quadrature algorithm after elimination of its Cauchy-type singularities. To improve computational efficiency, a Chebyshev approximation approach is applied to a fast calculation of the Green function that needs evaluation thousands of times. In addition, OpenMP parallel technique is used to the formation of influence coefficient matrix, which significantly reduces CPU time. Finally, computations are performed on wave exciting forces and hydrodynamic coefficients for the long cylindrical structures, either floating or submerged. Comparison with other numerical and analytical methods demonstrates good performance of the present method.

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.

Two distinct measures of information, connected respectively to the amplitude and phase of the wave function of a particle, are proposed. There are relations between the time derivatives of these two measures and their gradients on the configuration space, which are equivalent to the wave equation. The information related to the amplitude measures the strength of the potential coupling of the particle (which is itself aspatial) with each volume of its configuration space, i.e. its tendency to participate in an interaction localized in a region of ordinary physical space corresponding to that volume. The information connected to the phase is that required to obtain the time evolution of the particle as a persistent entity starting from a random succession of bits. It can be considered as the information provided by conservation principles. The meaning of the so-called "quantum potential" in this context is briefly discussed.

A previous report showed that the urine output of HPLBII-P in patients with diabetes mellitus and SARS-Cov-2 infection was increased as a sign of glomerular dysfunction. . The aim of this report was to investigate the relation of urine output of HPLBII-P to diabetes mellitus in two large community-based elderly populations i.e. the ULSAM and PIVUS cohorts. Methods HPLBII-P was measured by ELISA in the urine of a community-based cohort of 839 men (ULSAM) collected at 77 years of age and in urine of a community-based cohort of 75-year-old men, n=387, and women, n=401 (PIVUS). KIM-1, NGAL and Albumin were measured in urine and Cathepsin S and Cystatin C in serum. Results HPLBII-P was significantly raised among males with diabetes in the ULSAM (p

A concise proof of the Riemann Hypothesis is presented by clarifying the Hadamard product expansion over the zeta zeros, demonstrating that the Riemann Hypothesis is true.

In this paper we establish some generalizations of Opial’s inequal- ities for Riemann-Stieltjes integral and for two functions. Applications related to trapezoid and Grüss’ ’type inequalities are also given.

The main objective of this present paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. Also, we give some results related to the newly defined fractional operator such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

Leishmanial skin lesions are characterized by inflammatory hypoxia alongside the activation of hypoxia inducible factors, HIF-1a and HIF-2a, and subsequent expression of the HIF-a target VEGF-A during Leishmania major infection. However, the factors responsible for HIF-a activation are not known. We hypothesize hypoxia and pro-inflammatory stimuli contribute to HIF-a activation during infection. RNASeq on leishmanial lesions found transcripts associated with HIF-1a signaling are induced. To determine whether hypoxia contributes to HIF-a activation, we followed the fate of myeloid cells infiltrating from the blood and into hypoxic lesions. Recruited myeloid cells experience hypoxia when they enter inflamed lesions, and the length of time in lesions increases their hypoxic signature. To determine whether pro-inflammatory stimuli in the inflamed tissue can also influence HIF-a activation, we subjected macrophages to various pro-inflammatory stimuli and measured VEGF-A. While parasites alone did not induce VEGF-A, and pro-inflammatory stimuli only modestly induce VEGF-A, HIF- stabilization increases VEGF-A during infection. HIF-a stabilization does not impact parasite entry, growth or killing. Alternatively, the absence of ARNT/HIF- signaling enhances parasite internalization. Altogether, these findings suggest HIF-a is active during infection, and while macrophage HIF-a activation promotes lymphatic remodeling through VEGF-A production, HIF-a activation does not impact parasite internalization or control.

Zeta potential refers to the electrokinetic potential present in colloidal systems, exerting significant influence on the diverse properties of nano-drug delivery systems. The impact of dielectric constant on the zeta potential and charge inversion of highly charged colloidal particles, immersed in a variety of solvents spanning from polar, such as water, to nonpolar solvents, and in the presence of multivalent salts, was investigated through primitive model Monte Carlo (MC) simulations. Zeta potential ξ is decreased as decreasing the dielectric constant of the solvent, and upon further increase in the salinity and the valency of the salt. At elevated levels of salt, the colloidal particles become overcharged, in all solvents. As a result, their apparent charge becomes opposite in sign to the stoichiometric charge. This reversal of charge intensifies until reaching a saturation point with further increase in salinity, as a result, their apparent charge becomes opposite in sign to the stoichiometric charge. This reversal of charge intensifies until reaching a saturation point with further increase in salinity.

The interaction of solution of poly (diallyldimethylammonium) chloride, PDADMAc and sodium dodecylsulfate, SDS has been studied using conductometric, densimeter and zeta potential methods. the critical micellization concentration (cmc) was determinated with conductance results and increased with the addition of PDADMAc comparing with solutions containing pure SDS. Further the degree of dissociation,  and thermodynamic parameters viz. free energy of micellization, and entropy of micellization, has been evaluated. there results demonstrated that surfactant/polymer complex is governed by both electrostatic and hydrophobic interactions. The apparent molar volume, Vϕ and adiabatic compressibility, Kϕ;s have been determined for the SDS solution from density and speed sound data. the negative charge of the SDS solutions with polymer shows that these complexes probably do not contain surfactant in the form of micelles.

In the paper, the authors generalize the notion "k-Mittag-Leffler function'', establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function.

Introduction: This study aimed to validate the psychometric properties of the German eHealth Impact Questionnaire (eHIQ-G), which is divided into two independently administered and scored parts. Methods: 162 people with MS browsed one of two possible websites containing information on MS and completed an online survey. Internal consistency was assessed by Cronbach’s alpha and structural validity by Confirmatory Factor Analysis. Construct validity was examined by assessing correlations with the eHealth Literacy Questionnaire and the General Self-Efficacy Scale. Moreover, the mean difference of the eHIQ-G score between the two websites was investigated. Results: Cronbach’s alpha for the eHIQ-G subscales ranged from .833 to .885. The eHIQ-G part 1 achieved acceptable levels of goodness-of-fit indices, whereas the fit for the eHIQ-G part 2 was poor and likewise for the alternative modified models. The correlations with the reference instruments were 0.08 – 0.62 and as expected. Older age was related with lower eHIQ-G part 1 score, whereas no significant effect was found for education. Although not significant, the website ‘AMSEL’ reached higher mean scores on eHIQ part 2. Conclusion: The eHIQ-G has good internal consistency, and sufficient structural and construct validity. It will facilitate the measurement of the impact of websites providing health information.

This work uses a new approach to investigate the Riemann hypothesis, drawing conclusions about its trueness. It is based on the more general method presented in a very recent publication, by the same author, showing in detail how to approach that very well-known and interesting problem. This is achieved by means of the theory of dynamical systems (Poincaré index associated to equilibria of 2-dimensional systems) and the study of the zeros of the Dirichlet eta function, defined by a Dirichlet series. By using the well-known fact that the zeros of the eta function include all zeros of the Riemann zeta function in the (open) critical strip, excluded the critical line, ((0,1/2) ∪ (1/2,1)) × (−∞,∞), the development proceeds using only the eta function. In addition, the open and simply connected region (1/2,1) × (0,∞) is used along the text, taking into account the symmetries of zeros of the functions under analysis in the critical strip. The basic line of proof is to find the mathematical expression for the Poincaré index of the vector field associated to the eta function, assuming the existence of a zero of the eta function outside the critical line (in (1/2,1) × (0,∞)), and investigating the resulting unfoldings. Eventually, an inconsistency occurs and the proof ends by contradiction.

Real and complex analytic functions are largely studied in the field of complex analysis and are seen as very useful tools in solving problems in mathematics, physics and engineering. Real and complex numbers are a subset of semi-structured complex numbers (a new number set created to algebraically solve division by zero). Nevertheless, the properties of analytic functions made up of semi-structured complex variables (called semi-structured complex analytic functions) is yet to be explored. This limits the range of possible problems that can be resolved using analytic functions). In this regard, the aim of this paper was to expound upon the properties of semi-structured complex analytic functions and show their application in solving engineering problems. The results of this paper included (1) developing a full set of Cauchy–Riemann Equations for the semi-structured complex -space; (2) define sufficient and necessary conditions for a semi-structured complex function to be analytic; (3) determine the relationship between semi-structured complex analytic functions, Laplace’s Equations and Poisson’s Equations; and (5) provide an example of the use of these functions.

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.

This paper presents Chebyshev Type inequalities for the Riemann-Liouville variable-order fractional integral operator using two synchronous functions on the set of real numbers. It is the first result of its kind in the current literature using variable-order Riemann-Liouville fractional integral operator. Some special cases for the result obtained in the paper are discussed.

In this paper we provide some bounds for the error in approximating the Riemann-Stieltjes integral $\int_{a}^{b}f (t) du (t)$ by the generalized trapezoidal rule \begin{equation*} \left[ u\left( b\right) -u\left( x\right) \right] f\left( b\right) +\left[ u\left( x\right) -u\left( a\right) \right] f\left( a\right) \end{equation*} under various assumptions for the integrand $f$ and the integrator $u$ for which the above integral exists. Applications for continuous functions of selfadjoint operators and unitary operators in Hilbert spaces are provided as well.

Primary ciliary dyskinesia (PCD) is caused by pathologic variants in over 50 different genes that affect the structure and function of motile cilia. Low nasal NO (nNO) is a biomarker for diagnosis in patients with features of PCD; but the reason why it is low is unclear. At the cellular level, a characteristic feature shared by most PCD patients is that antigens and other particles are not cleared from the epithelial surface. Poor antigen clearance results in pro-oxidant pathway activation and airway epithelial damage and may predispose PCD patients to DUOX1- and IL33- mediated asthma. Secondary ciliary dysfunction, such as that caused by viruses or by smoking, can also contribute to asthma development. Variants in genes underlying the function of cilia, can be associated with poor lung function, even in the absence of PCD. Single nucleotide polymorphisms in PCD – related genes can be associated with increased asthma severity. The role of cilia and antigen stasis is the pathophysiology of asthma is an important area for research, because specific airway clearance techniques and other therapeutic interventions, such as antioxidants, could be of value in preventing the development of asthma and asthma-like symptoms.

In mammals, the oviduct (or the Fallopian tube in humans) can be divided into the infundibulum (responsible for oocyte pick-up), ampulla (site of fertilization), isthmus (where preimplantation embryos develop), and uterotubal junction (where embryos transit to the uterus). The oviductal fluid, as well as extracellular vesicles produced from the oviductal epithelial cells, referred to as oEVs, have been shown to improve the fertilization process, prevent polyspermy, and aid in embryo development. oEVs contain molecular cargos (such as miRNAs, mRNAs, proteins, and lipids) that can be delivered and fuse to recipient cells. oEVs produced from the ampulla appear to be functionally distinct from those produced from the isthmus. In multiple species including mice, cats, dogs, pigs, and cows, oEVs can be incorporated into the oocytes, sperm, and embryos. In this review, we show the positive impact of oEVs on gamete function as well as blastocyst development and how they may improve embryo quality in in vitro conditions in an assisted reproductive technology setting for rodents, domestic animals, farm animals, and humans.

In this article, we present solutions for one of the oldest mathematical problems, the Collatz Conjecture, and provide a proof for the Riemann Hypothesis, utilizing a new number theory based on newly discovered number properties, which will also be presented in this paper. This is made possible through the Sophy-Peter mathematical framework, built upon this new number theory. The Collatz Conjecture will be disproven, but as an alternative, the Oscillating Theorem will be introduced, with its correctness proven within this article. Furthermore, we present the general version of the Riemann zeta function, developed based on the new number theory. The correctness of this function is verified by comparing it with existing results of the zeta function. Using this approach and the Sophy-Peter framework, we have successfully proven the Riemann Hypothesis, long considered a millennium problem. Moreover, since the general zeta function is proven, this implies the correctness of the new number theory and the Sophy-Peter framework.

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

One of the most important unresolved mysteries in mathematics is the Riemann Hypothesis, which suggests a fundamental connection between the non-trivial zeros of the Riemann zeta function and the distribution of prime numbers. Here, we explore the fascinating union of trigonometric functions, prime numbers, and the Riemann zeta function through an examination of the zeros in the statement ln(sec(π·n log(n))). We demonstrate a strong mathematical connection between these components, providing information on the mysterious properties of prime numbers and their complex relationships to basic mathematical operations. Our thorough investigation adds to the current discussion of the Riemann Hypothesis by offering possible solutions and deepening our comprehension of the intricate relationship between number theory and analytic functions.

This article is a study on the (k,s)-Riemann-Liouville fractional integral, a generalization of the Riemann-Liouville fractional integral. Firstly, we introduce several properties of the extended integral of continuous functions. Furthermore, we make the estimation of the Box dimension of the graph of continuous functions after the extended integral. It presents that the upper Box dimension of the (k,s)-Riemann-Liouville fractional integral for any continuous functions is no more than the upper Box dimension of the functions on the unit interval I=[0,1], which indicates that the upper Box dimension of the integrand f(x) will not be increased by the σ-order (k,s)-Riemann-Liouville fractional integral ksD−σf(x) where σ&gt;0 on I. Additionally, we prove that the fractal dimension of ksD−σf(x) of one-dimensional continuous functions f(x) is still one.

Bergamot flavonoids have been shown to prevent metabolic syndrome, non-alcoholic fatty liver disease (NAFLD) and stimulate autophagy in animal models and patients. To investigate further the mechanism of polyphenol-dependent effects, we performed RT2-PCR array analysis on 168 metabolism, transport and autophagy-related genes expressed in rat livers exposed for 14 weeks to different diets: standard, cafeteria (CAF) and CAF diet supplemented with 50 mg/kg of Bergamot Polyphenol Fraction (BPF). CAF diet caused a strong upregulation of the gluconeogenesis pathway (Gck, Pck2) and a moderate (>1.7 fold) induction of genes regulating lipogenesis (Srebf1, Pparg, Xbp1), lipid and cholesterol transport or lipolysis (Fabp3, Apoa1, Lpl) and inflammation (Il6). However, only one -oxidation gene (Cpt1a) and a few autophagy genes were modulated in the CAF group compared to controls. While most of these transcripts were significantly modulated by BPF, we observed a particularly potent effect on lipogenesis genes, like Acly, Acaca, Fasn and Scd1, which were suppressed far below the mRNA levels of control livers as confirmed by alternative primers-based RT2-PCR analysis and western blotting. These effects were accompanied by downregulation of pro-inflammatory cytokines (Il6, Tnfa, and Il10) and diabetes-related genes. Few autophagy (Map1Lc3a, Dapk) and no -oxidation gene expression changes were observed, suggesting minor transcriptional effects on autophagy. In conclusion, chronic BPF supplementation efficiently prevents NAFLD by modulating hepatic energy metabolism and inflammation gene expression programs, with no effect on -oxidation, but profound suppression of de-novo lipogenesis.

Nitric oxide (NO) is synthesized and is involved in various physiological and developmental process regulation in all kingdoms of life. Fungi have been less explored in terms of endogenous NO biology than mammals, plants, and bacteria. In this review, we summarize and discuss the studies to date on intracellular NO biosynthesis and function in fungi. Two mechanisms for NO biosynthesis, NO synthase (NOS)-mediated arginine oxidation, and nitrate and nitrite reductase-mediated nitrite reduction, are most frequently reported. Furthermore, we summarize the multifaceted functions of NO in fungi, as well as its role as a signaling molecule in fungal growth regulation, development, abiotic stress, virulence regulation, and metabolism. Finally, we present potential directions for future research on fungal NO biology.

The placenta is a vital organ of pregnancy, regulating adaptation to pregnancy, gestational-parent/fetal exchange and ultimately fetal development and growth. Not surprisingly, in cases of placental dysfunction - where aspects of placental development or function become compromised - adverse pregnancy outcomes can result. One common placenta-mediated disorder of pregnancy is preeclampsia (PE), a hypertensive disorder of pregnancy with a highly heterogeneous clinical presentation. The wide array of clinical characteristics observed in pregnant individuals and neonates of a PE pregnancy are likely the result of distinct forms of placental pathology underlying the PE diagnosis, explaining why no one common intervention has proven effective in the prevention or treatment of PE. The historical paradigm of placental pathology in PE highlights an important role for utero-placental malperfusion, placental hypoxia and oxidative stress, and a critical role for placental mitochondrial dysfunction in the pathogenesis and progression of the disease. In the current review, the evidence of placental mitochondrial dysfunction in the context of PE will be summarized, highlighting how altered mitochondrial function may be a common feature across distinct PE subtypes. Further, advances in this field of study and therapeutic targeting of mitochondria as a promising intervention for PE will be discussed.

Voltage-gated Ca²⁺ (Ca_v) channels play pivotal roles in regulating gene transcription, neuronal excitability, and neurotransmitter release. In order to meet the spatial and temporal demands of visual signaling, Ca_v channels exhibit unusual properties in the retina compared to their counterparts in other areas of the nervous system. Here, we review current concepts regarding the specific subtypes of Ca_v channels expressed in the retina, their intrinsic properties and forms of modulation, and how their dysregulation could lead to retinal disease.

In this study, the analysis of the changes of SARS-CoV-2 Orf3a protein during pandemic is reported. Orf3a, a conserved protein in the Coronaviruses, is involved in virus replication and release. A software workflow able to carry out a quick, systematic and repeatable screening of the SARS-CoV-2 genome isolates to detect protein mutations, was utilized to scan 70,752 high-quality SARS-CoV-2 genomes available in GISAID databank at the end of August 2020. All ORF3a mutations in the virus genomes were grouped according to the collection date interval and over the entire data set. The considered intervals were start of collection-February, March, April, May, June, July and August 2020. The top five most frequent variants were examined within each collection interval. Overall, seventeen variants have been isolated. Ten of the seventeen mutant sites occur within the transmembrane (TM) domain of ORF3a and are in contact with the central pore or side tunnels. The other variant sites are in different places of the Orf3a structure. Within the entire sample, the five most frequent mutations are V13L, Q57H, Q57H+A99V, G196V and G252V. The same analysis identified 28 sites identically conserved in all the genome isolates. These sites are possibly involved in stabilization of monomer, dimer, tetramerization and interaction with other cellular components. The results here reported can be helpful to understand virus biology and to design new therapeutic strategies.

G-quadruplexes are noncanonical nucleic acid structures formed from stacked guanine tetrads. They are frequently used as building blocks and functional elements in fields such as synthetic biology and also thought to play widespread biological roles. G-quadruplexes are often studied as monomers but can also form a variety of higher-order structures. This increases the structural and functional diversity of G-quadruplexes, and recent evidence suggests that it could also be biologically important. In this review we describe the types of multimeric topologies adopted by G-quadruplexes and highlight what is known about their sequence requirements. We also summarize the limited information available about potential biological roles of multimeric G-quadruplexes and suggest new approaches that could facilitate future studies of these structures.

6G is already being planned and will employ much higher frequencies, leading to a revolutionary era in communication between people as well as things. It is well known that weather, especially rain, can cause increased attenuation of signal transmission for higher frequencies. The standard methods for evaluating the effect of rain on symbol error rate are based on long-term averaging. These methods are an inaccurate, which results with an inefficient system design. This is critical regarding bandwidth scarcity and energy consumption and requires a more significant margin of effort to cope with the imprecision. Recently we have developed a new and more precise method for calculating communication system performance in case of rain, using the probability density function of rain rate. For high rain rate (above 10mm/hr), for a typical set of parameters, our method shows the symbol error rate in this range to be higher by orders of magnitude than that found by ITU standard methods. Our model also indicates that sensing and measuring the rain rate probability is important in order to provide the required bit error rate to the users. To the best knowledge of the authors, this novel analysis is unique. It can constitute a more effi-cient performance metric for the new era of 6G communication and prevent disruption due to incorrect system design. Keywords: atmospheric propagation, communication system performance, attenuation, com-munication

Glutamine is the most abundant and versatile amino acid in the body. In health and disease, the rate of glutamine consumption by immune cells is similar or greater than glucose. For instance, in vitro and in vivo studies have determined that glutamine is an essential nutrient for lymphocyte proliferation and cytokine production, macrophage phagocytic plus secretory activities and neutrophil bacterial killing. Glutamine release to the circulation and availability is mainly controlled by key metabolic organs, such as the gut, liver and skeletal muscles. During catabolic/hypercatabolic situations glutamine can become essential for metabolic function, but its availability may be compromised due to impairment of homeostasis in the inter-tissue metabolism of amino acids. For this reason, glutamine is currently part of clinical nutrition supplementation protocols and/or recommended for immune suppressed individuals. However, in a wide range of catabolic/hypercatabolic situations (e.g. ill/critically ill, post-trauma, sepsis, exhausted athletes) it is currently difficult to determine whether glutamine parenteral or enteral supplementation should be recommended based on the amino acid plasma concentration (glutaminemia). Although the beneficial immune based effects of glutamine supplementation is already established, many questions and evidence for positive in vivo outcomes still remain to be presented. Therefore, this paper provides an integrated review on how glutamine metabolism in key organs is important to cells of the immune system. We also discuss glutamine metabolism, action and important issues related to the effects of glutamine supplementation in catabolic situations.

The scattering eigenstates of any Hamiltonian of electrons, coupled through a two-body force and moving on a one-dimensional lattice, are shown to be Bethe's wave-functions. The energy of the groundstate is compared with values, obtained previously for the Hubbard Hamiltonian by means of Bethe's wave-function and within the framework of the correlated Fermi gas. The same analysis is applied to electrons, interacting on neighbouring sites. The significance of those various groundstates is assessed with help of thermodynamics.

Because it can make exact double-strand breaks in DNA, CRISPR-Cas9 can help almost every species and type of cell. It is a powerful way to change the DNA code. CRISPR-Cas9 can be used for a lot more than just changing genes. We are close to being able to do high-throughput gene screening, epigenome editing, in-vivo cell tagging, and RNA change. With the help of CRISPR-Cas9, the function of genes can be studied better, and more realistic disease models can be made. The revolutionary new discipline of gene editing has the potential to profoundly impact healthcare and the life sciences. By simplifying the process of creating double-strand breaks in the DNA of almost any species or kind of cell, CRISPR-Cas9 has revolutionized gene editing. Numerous applications have been found for the CRISPR-Cas9 system. High-throughput gene screening, RNA modification, live-cell chromosome marking, and epigenome editing are all examples. CRISPR-Cas9 facilitates gene research, leading to the development of CRISPR-based disease models. CRISPR-Cas9-based methods of altering the genome will aid researchers in learning more about sickness and discovering better ways to cure it, despite the fact that there are still many questions and large difficulties to answer.

Polyphenols, long-used components of medicinal plants, have drawn great interest in recent years as potential therapeutic agents because of their safety, efficacy, and wide range of biological effects. Approximately 74% of the world's population still uses plant-based medicines, indicating the ongoing significance of phytochemicals for human health. The study emphasizes the growing body of research examining the role of polyphenols in uncovering their anti-adipogenic and anti-obesity properties. Functions of polyphenols including phenylpropanoids, flavonoids, terpenoids, alkaloids, glycosides, and phenolic acids are distinct due to changes in chemical diversity, and structural characteristics. This review methodically investigates the mechanism of how naturally occurring polyphenols mediate obesity and metabolic function. To this end, hormonal control of hunger has the potential to inhibit pro-obesity enzymes such as pancreatic lipase, the promotion of energy expenditure, and the modulation of adipocytokine production. Specifically, polyphenols affect insulin, a hormone that is essential for regulating blood sugar, and they also play a role in part in a complex web of factors that affect the progression of obesity. This review also explores the immunomodulatory properties of polyphenols, providing insight into their ability to improve immune function. The effects of polyphenols on gut health, improving the number of commensal bacteria, cytokine production suppression, and immune cell mediation, including natural killer cells and macrophages. Taken together, continuous studies are required for prudent and precise mechanisms underlying polyphenols' therapeutic potential in obesity and immunomodulation. In the interim, this review emphasizes the holistic approach to health and promotes the consumption of a wide range of foods and drinks high in polyphenols. This review lays the groundwork for future developments, indicating that the components of polyphenols and their derivatives may provide the answer to urgent worldwide health issues. This compilation of the body of knowledge paves the way for future discoveries in the global treatment of pressing health concerns in obesity and metabolic diseases.

This work presents a new type of chaotic dynamical system originated from Dirichlet Eta function. Although the exposition describes only a bidimensional instance, it is certainly possible to construct higher dimensional such models. The novelty resides in the multitude of interesting characteristics concentrated in only one kind of dynamical system, mainly because of its simple abstract definition - it provokes dissipative, chaotic and itinerant behavior, and its paths typically display nonrecurring quasi-attractors and associate regions of ruin. In addition, it is discrete and nonautonomous, being additively driven by a simple real vector sequence. Also, the defining formulas have parameters which permit to activate bifurcatory effects, mainly related to setting the number of quasi-attractors and overall geometric complexity and diversity. In this fashion, it holds a certain similarity with classical itinerant chaotic systems, but it is a completely different object. One of its parameters is very influential and may be intuitively compared to a type of "potential energy", capable of changing the duration of sojourns etc. In this fashion, there is a potential opportunity to employ artificial inference techniques for designing specific structures on paths. Of course, the other parameters are also relevant, but not necessarily in the control of the number of quasi-attractors and the permanence periods near them. It is important to state that the described system was found during a previous investigation about certain features of the Riemann hypothesis, using the Dirichlet Eta function instead of the Riemann Zeta function - the components of the system under study here were part of certain series whose convergence had to be established, and that scenario produced this very positive side effect. The text also suggests an atypical, but important, potential application in philosophy: the representation of the Hindu concepts of Samsara and Moksha.

The concerning worldwide increase of obesity and chronic metabolic diseases such as T2D, dyslipidemia, and cardiovascular disease motivates further investigations into preventive and alternative therapeutic approaches. Over the past decade, there is growing evidence that the formation and activation of thermogenic adipocytes (brown and beige) may serve as therapy to treat obesity and its associated diseases owing to its capacity to increase energy expenditure and to modulate circulating lipids and glucose levels. Thus, understanding the molecular mechanism of brown and beige adipocytes formation and activation will facilitate the development of strategies to combat metabolic disorders. Here, we provide a comprehensive overview of pathways and players involved in the development of brown and beige fat as well as the role of thermogenic adipocytes in energy homeostasis and metabolism. Also, we discuss the alterations in brown and beige adipose tissue function during obesity and, explore the therapeutic potential of thermogenic activation to treat metabolic syndrome.

Key features of glycogen metabolism in excitable tissues are not well-explained by current concepts. Glycogen stores in brain and skeletal muscle are generally considered to function as local glucose reserves, to be utilized during transient mismatches between glucose supply and demand; however, quantitative measures show that blood glucose supply is likely never rate-limiting for energy metabolism in either brain or muscle under physiological conditions. These tissues nevertheless do normally utilize glycogen during intervals of increased energy demand, despite the availability of free glucose, and despite the ATP cost of cycling glucose through glycogen polymer. This seemingly wasteful shunt can be explained by considering the effect of glycogenolysis on the amount of energy derived from ATP (ΔG’ATP). ΔG’ATP is diminished by elevations in Pi, such as occur at sites of rapid ATP hydrolysis and net phosphocreatine consumption. Glycogen utilization counters this effect by sequestering Pi in glycolytic metabolites (glycogen_n + Pi → glycogen_n-1 + glucose-1-phosphate → phosphorylated glycolytic intermediates), and thereby maintains the amount of energy obtained from ATP at sites of rapid ATP consumption. This thermodynamic effect may be particularly important in the narrow, spatially constricted astrocyte processes that ensheath neuronal synapses. This effect can also explain the co-localization of glycogen and cytosolic phosphocreatine in brain astrocytes, glycolytic super-compensation in brain when glycogen is not available, and aspects of exercise physiology in muscle glycogen phosphorylase deficiency (McArdle’s disease).

The association between the choice of general anesthetic agents and the risk of acute kidney injury (AKI) and long-term renal function after nephrectomy has not yet been evaluated. We reviewed 1087 cases of partial or radical nephrectomy. The incidence of postoperative AKI, new-onset chronic kidney disease (CKD) stage 3a and CKD upstaging were compared between different general anesthetic agent groups: propofol, sevoflurane, and desflurane. Four different propensity score analyses were performed to minimize confounding for each pair of comparison (propofol vs sevoflurane; propofol vs desflurane; sevoflurane vs desflurane; propofol vs volatile agents). Study outcomes were compared before and after matching. Kaplan-Meier survival curve analysis was performed to compare renal survival determined by the development of CKD stage 3a between groups up to 36 months after nephrectomy before and after matching. Propofol was associated with a lower incidence of AKI, CKD upstaging and a higher three-year renal survival after nephrectomy compared to sevoflurane or desflurane group after matching (AKI: propofol 23.2% vs. sevoflurane 39.5%, P=0.004, vs. desflurane 34.3%, P=0.031; CKD upstaging: propofol 27.2% vs. sevoflurane 58.4%, P<0.001, vs. desflurane 48.6%, P=0.017; Log-rank test propofol vs. sevoflurane P<0.001, vs. desflurane P=0.015). Propofol was also associated with a lower incidence of new-onset CKD after nephrectomy compared to sevoflurane after matching (P<0.001). However, there were no significant differences between sevoflurane and desflurane. In conclusion, propofol, compared to volatile agents, may be the reasonable choice of general anesthetic agent for nephrectomy to attenuate postoperative renal dysfunction. Randomized prospective trials are warranted to test this hypothesis.

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.

The problem of reliable function computation is extended by imposing privacy, secrecy, and storage constraints on a remote source whose noisy measurements are observed by multiple parties. The main additions to the classic function computation problem include 1) privacy leakage to an eavesdropper is measured with respect to the remote source rather than the transmitting terminals’ observed sequences; 2) the information leakage to a fusion center with respect to the remote source is considered as a new privacy leakage metric; 3) the function computed is allowed to be a distorted version of the target function, which allows to reduce the storage rate as compared to a reliable function computation scenario in addition to reducing secrecy and privacy leakages; 4) two transmitting node observations are used to compute a function. Inner and outer bounds on the rate regions are derived for lossless and lossy single-function computation with two transmitting nodes, which recover previous results in the literature. For special cases that include invertible and partially-invertible functions, and degraded measurement channels, exact lossless and lossy rate regions are characterized, and one exact region is evaluated for an example scenario.

SETMAR is a protein lysine methyltransferase that is involved in several DNA processes, including DNA repair via the non-homologous end joining (NHEJ) pathway, regulation of gene expression, illegitimate DNA integration, and DNA decatenation. However, SETMAR is an atypical protein lysine methyltransferase since in anthropoid primates, the SET domain is fused to an inactive DNA transposase. The presence of the DNA transposase domain confers to SETMAR a DNA binding activity towards the remnants of its transposable element, which has resulted in the emergence of a gene regulatory function. Both the SET and the DNA transposase domains are involved in the different cellular roles of SETMAR, indicating the presence of novel and specific functions in anthropoid primates. In addition, SETMAR is dysregulated in different types of cancer, indicating a potential pathological role. While some light has been shed on SETMAR functions, more research and new tools are needed to better understand the cellular activities of SETMAR and to investigate the therapeutic potential of SETMAR.

Phospholipases are a family of lipid altering enzymes that can either reduce or increase bioactive lipid levels. Bioactive lipids elicit signaling responses, activate transcription factors, promote g-coupled protein activity, and modulate membrane fluidity that mediate cellular function. Phospholipases and the bioactive lipids they produce are important regulators on immune cell activity, dictating both pro-inflammatory and pro-resolving activity. During atherosclerosis, pro-inflammatory and pro-resolving activities govern atherosclerosis progression and regression respectively. This review will look at the interface of phospholipase activity, immune cell function, and atherosclerosis.

Cardiac dynamics are traditionally linked to a left ventricle, right ventricle and septum morphology, a topography that differs from the heart’s 5-century-old anatomic description of containing a helix and circumferential wrap architectural configuration. Torrent Guasp’s helical ventricular myocardial band (HVMB) defines this anatomy and its structure, explains why the heart’s 6 dynamic actions of narrowing, shortening, lengthening, widening, twisting and uncoiling happen. This database raises questions about deductions behind “accepted cardiac mechanics”, and its functional aspects will challenge and overturn them. These suppositions include the LV, RV, and septum description, timing of mitral valve opening, isovolumic relaxation period, reasons for torsion/twisting, untwisting, reasons for longitudinal and circumferential strain, echocardiographic sub segmentation, resynchronization, RV function dynamics, and diastolic dysfunction’s cause and unrecognized septum impairment. Torrent Guasp’s revolutionary contributions may alter future understanding of the diagnosis and treatment of cardiac disease.

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.