This paper is related to the fractional view analysis of Helmholtz equations, using innovative analytical techniques. The fractional analysis of the proposed problems has been done in terms of Caputo-operator sense. In the current methodology, first, we applied the r-Laplace transform to the targeted problem. The iterative method is then implemented to obtain the series form solution. After using the inverse transform of the r-Laplace, the desire analytical solution is achieved. The suggested procedure is verified through specific examples of the fractional Helmholtz equations. The present method is found to be an effective technique having a closed resemblance with the actual solutions. The proposed technique has less computational cost and a higher rate of convergence. The suggested methods are therefore very useful to solve other systems of fractional order problems.

In this article, we are interested in a new generic class of nonlocal fractional impulsive differential inclusions with linear sectorial operator and Lipschitz multivalued function in the setting of finite dimensional Banach spaces. By modifying the definition of PC-mild solutions initiated by Shu, we succeeded to determine new conditions that sufficiently guarantee the existence of the solutions. The results are obtained by combining techniques of fractional calculus and fixed point theorem for contraction maps. We also characterize the topological structure of the set of solutions. Finally, we provide a demonstration to address the applicability of the theoretical results.

The effects of mixing orders of tannic acid (TA), starch and α-amylase on the enzyme inhibition of TA were studied, including mixing TA with α-amylase before starch addition (order 1), mixing TA with pre-gelatinized starch before α-amylase addition (order 2) and co-gelatinizing TA with starch before α-amylase addition (order 3). It was found that the enzyme inhibition was always highest for order 1 because TA could bind with the enzyme active site thoroughly before digestion occurred. Both order 2 and 3 reduced α-amylase inhibition through decreasing binding of TA with the enzyme, which resulted from the non-covalent physical adsorption of TA with gelatinized starch. Interestingly, at low TA concentration, α-amylase inhibition for order 2 was higher than order 3, while at high TA concentration, the inhibition was shown with opposite trend, which arose from the difference in the adsorption property between the pre-gelatinized and co-gelatinized starch at the corresponding TA concentrations. Besides, both the crystalline structures and apparent morphology of starch were not significantly altered by TA addition for order 2 and 3. Conclusively, although a polyphenol may have an acceptable inhibitory activity in vitro, the actual effect may not reach the expected one when taking processing procedures into account.

Plants offer a simpler and cheaper alternative to mammalian animal models for the study of Endoplasmic Reticulum glycoprotein folding Quality Control (ERQC). In particular, the Arabidopsis thaliana (At) innate immune response to bacterial peptides provides an easy means of assaying ERQC function in vivo. A number of mutants that are useful to study ERQC in planta have been described in the literature, but only for a subset of these mutants the innate immune response to bacterial elicitors has been measured beyond monitoring plant weight and some physio-pathological parameters related to the plant immune response. In order to probe deeper into the role of ERQC in the plant immune response, we monitored expression levels of the PHI-1 and RET-OX genes in the At ER α-Glu II rsw3 and the At UGGT uggt1-1 mutant plants, in response to bacterial peptides elf18 and flg22. The elf18 response was impaired in the rsw3 but not completely abrogated in the uggt1-1 mutant plants, raising the possibility that the latter enzyme is partly dispensable for ERF signalling. In the rsw3 mutant, seedling growth was impaired only by concomitant application of the At ER α-Glu II NB-DNJ inhibitor at concentrations above 500 nM, suggesting residual activity in this mutant. The study highlights the need for extending plant innate immune response studies to assays sampling EFR signalling at the molecular level.

This paper proposes a definition of fractional line integral, generalising the concept of fractional definite integral. The proposal replicates the properties of the classic definite integral, namely the fundamental theorem of integral calculus. It is based on the concept of fractional anti-derivative used to generalise the Barrow formula. To define the fractional line integrals the Gr\"unwald-Letnikov and Liouville directional derivatives are introduced and their properties described. The integral is defined first for broken line paths and afterwards to any regular curve

We do fuzzification the concept of domination in crisp graph by using membership values of nodes, α-strong and arcs. In this paper, we introduce a new variation on the domination theme which we call vertex domination. We determine the vertex domination number γ_v for several classes of fuzzy graphs, specially complete fuzzy graph and complete bipartite fuzzy graphs. The bounds is obtained for the vertex domination number of fuzzy graphs. Also the relationship between M-strong arcs and α-strong is obtained. In fuzzy graphs, monotone decreasing property and monotone increasing property is introduced. We prove the vizing’s conjecture is monotone decreasing fuzzy graph property for vertex domination. we prove also the Grarier-Khelladi’s conjecture is monotone decreasing fuzzy graph property for it. We obtain Nordhaus-Gaddum (NG) type results for these parameters. The relationship between several classes of operations on fuzzy graphs with the vertex domination number of them is studied.

The central limit theorem (CLT) and its generalization to stable distributions have been widely described in literature. However, many variations of the theorem have been defined and often their applicability in practical situations is not straightforward. In particular, the applicability of the CLT is essential for a derivation of heterogeneous ensemble of Brownian particles (HEBP). Here, we analyze the role of the CLT within the HEBP approach in more detail and derive the conditions under which the existing theorems are valid.

This paper describes a proposed fractional filter-based multi-scale underwater and hazy image enhancement algorithm. The proposed system combines a modified global contrast operator with fractional order-based multi-scale filters used to generate several images, which are fused based on entropy and standard deviation. The multi-scale-global enhancement technique enables fully adaptive and controlled colour correction and contrast enhancement without over exposure of highlights when processing hazy and underwater images. This in addition to illumination/reflectance estimation coupled with global and local contrast enhancement. The proposed algorithm is also compared with the most recent available state-of-the-art multi-scale fusion de-hazing algorithm. Experimental comparisons indicate that the proposed approach yields better edge and contrast enhancement results without halo effect, colour degradation and is faster and more adaptive than all other algorithms from the literature.

This paper deals with the analysis of trends in road accidents on major highways in Brazil. Using updated time series techniques, our results indicate that a low degree of long memory was detected in the series with shocks having transitory effects over time. We further find that the number of accidents taking place in Brazil has been reducing over time, though in the presence of negative shocks, the recovery is not going to be immediate due to the long memory nature of the data. Despite the absence of relevant investment relating to infrastructure expansion, it is worth mentioning the consolidation of a nationwide tolled road system in Brazil involving concessions to private administrators, alongside more severe traffic laws that can impose limitations on driving licences.

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

Our aim in this paper is to establish some new Hermite-Hadamard- Mercer type integral inequalities by utilizing the fractional proportional-integral operators.For this purpose, Hermite-Hadamard-Mercer inequalities for di¤er- antiable mappings whose derivatives in absolute value are convex.

Cannabinoids, mainly cannabidiol (CBD) and Δ9-tetrahydrocannabinol (THC), are the most studied group of compounds obtained from Cannabis sativa because of their several pharmaceutical properties. Current evidence suggests a crucial role of cannabinoids as potent anti-inflammatory agents for the treatment of chronic inflammatory diseases; however, the mechanisms remain largely unclear. Cytokine storm, a dysregulated severe inflammatory response by our immune system, is involved in the pathogenesis of numerous chronic inflammatory disorders, including coronavirus disease 2019 (COVID-19), which results in the accumulation of pro-inflammatory cytokines. Therefore, we hypothesized that CBD and THC reduce the levels of pro-inflammatory cytokines by inhibiting key inflammatory signalling pathways. The nucleotide-binding and oligomerization domain (NOD)-like receptor family pyrin domain-containing 3 (NLRP3) inflammasome signalling has been implicated in a variety of chronic inflammatory diseases, which results in the release of pyroptotic cytokines, interleukin-1β (IL-1β) and IL-18. Likewise, the activation of the signal transducer and activator of transcription-3 (STAT3) causes increased expression of pro-inflammatory cytokines. We studied the effects of CBD and THC on lipopolysaccharide (LPS)-induced inflammatory response in human THP-1 macrophages and primary human bronchial epithelial cells (HBECs). Our results revealed that CBD and, for the first time, THC, significantly inhibited NLRP3 inflammasome activation following LPS + ATP stimulation, leading to a reduction in the levels of IL-1β in THP-1 macrophages and HBECs. CBD attenuated the phosphorylation of nuclear factor-κB (NF-κB) and both cannabinoids inhibited the generation of oxidative stress post-LPS. Our multiplex ELISA data revealed that CBD and THC significantly diminished the levels of IL-6, IL-8, and tumor necrosis factor-α (TNF-α) after LPS treatment in THP-1 macrophages and HBECs. In addition, the phosphorylation of STAT3 was significantly downregulated by CBD and THC in THP-1 macrophages and HBECs, which was in turn, attributed to the reduced phosphorylation of tyrosine kinase-2 (TYK2) by CBD and THC after LPS stimulation in these cells. Overall, CBD and THC were found to be effective in alleviating the LPS-induced cytokine storm in human macrophages and primary HBECs, at least via modulation of NLRP3 inflammasome and STAT3 signalling pathways. The encouraging results from this study warrant further investigation of these cannabinoids in vivo.

We consider a model of predator-prey interaction at fractional-order where the predation obeys the ratio-dependent functional response and the prey is linearly harvested. For the proposed model, we show the existence, uniqueness, non-negativity as well as the boundedness of the solutions. Conditions for the existence of all possible equilibrium points and their stability criteria, both locally and globally, are also investigated. The local stability conditions are derived using the Magtinon's theorem, while the global stability is proven by formulating an appropriate Lyapunov function. The occurance of Hopf bifurcation around the interior point is also shown analytically. At the end, we implement the Predictor-Corrector scheme to perform some numerical simulations.

Exact and soliton type solutions have great importance in propagation of surface waves, fluid dynamics, optics, and many other elds of nonlinear sciences. In this study, the explicit and exact soliton type solutions for two space-time fractional Equal- Width (FEW) equations with conformable derivative are procured via the hyperbolic function approach. The wave type solutions are represented in some hyperbolic and trigonometric functions.

To determine the mode of action of the effects of phytoalexins in soybeans, we analyzed enzyme inhibition kinetics using Michaelis–Menten plots and the Lineweaver–Burk plots. The results showed that glyceollin showed competitive inhibition, genistein showed noncompetitive, daidzein was uncompetitive, and luteolin showed a mixed mode of action. The Ki values were determined using a Dixon plot as: glyceollin, 18.99; genistein, 15.42; luteolin, 16.81; and daidzein, 9.99 μM, respectively. Furthermore, potential synergistic effects between glyceollin and the three designated polyphenols were investigated. A combination of glyceollin and luteolin (the ratio of 3:7 of glyceollin and luteolin) had synergistic effects on α-glucosidase inhibition according to combination index (CI)-isobologram equation. Collectively, these results showed that a combination of glyceollin and luteolin has the potential to inhibit α-glucosidase activity via a synergistic mode of action.

The seeds of cultivated peanut, Arachis hypogaea, are an agronomically important crop produced for human nutrition, oilseed and feed stock. Peanut seed is the single most expensive variable input cost and thus producers require seed with excellence performance in terms of germination efficiency. During the maturation process, triglycerides are stored in oil bodies as an energy resource during germination and seedling development. The stability of oil body membranes is essential for nutrient mobilization during germination. This study focused on evaluating the phytosterol composition in seed components including the kernel, embryo (heart), and seed coat or skin. Samples of different maturity classes were analyzed for macronutrient and phytosterol content. The three most abundant phytosterols, β-sitosterol, campesterol, and stigmasterol, comprised 82.29%, 86.39%, and 94.25% of seed hearts, kernels, and seed coats, respectively. Stigmasterol concentration was highest in the seed kernel providing an excellent source of this sterol known to have beneficial effects on human health. Peanut hearts contained the highest concentration of sterols by mass potentially providing protection and resources for the developing seedling. The amount of α-tocopherol increases in peanut hearts during the maturation process providing protection from temperature stress and stability required for seedling vigor. These results suggest that phytosterols may play a significant role in the performance of seeds and provides a possible explanation for the poor germination efficiency of immature seeds.

The abnormal assembly of α-synuclein (α-Syn) is an initial step in the formation of Lewy bodies in the brain, which finally causes the neuronal death, being considered as a pathological hallmark in Parkinson’s disease (PD). Certain food bioactives or their metabolites at very low concentrations can trespass the blood brain barrier (BBB) that might, thereafter, act simultaneously. The aim of this work was to evaluate the inhibitory and destabilising capacities on α-Syn kinetics and the neuroprotective effects of three well-known bioactive compounds able to cross the BBB and present in foods; melatonin (MEL), protocatechuic acid (PCA) and hydroxytyrosol (HT), and their combinations. For this purpose, different in vitro techniques (Thioflavin T (ThT), Transmission Electronic Microscopy (TEM), electrophoresis and MTT assay) were used. All tested compounds and their combinations were able to abolish the toxicity induced by α-Syn. In addition, the combination of PCA (100 µM) +HT (100 µM) showed the highest inhibitory effect against α-Syn fibril formation and destabilises α-Syn fibrils (88 and 62%, respectively). This is the first time that MEL, PCA and HT prove a joint effect against α-Syn aggregation and toxicity when they are tested together.

The aim of this expository article is to present recent developments in the centuries-old discussion on the interrelations between several types of domination in graphs. However, the novelty even more prominent in the newly discovered simplified presentations of several older results. Domination can be seen as arising from real-world application and extracting classical results as first described by this article.The main part of this article, concerning a new domination and older one, is presented in a narrative that answers two classical questions: (i) To what extend must closing set be dominating? (ii) How strong is the assumption of domination of a closing set? In a addition, we give an overview of the results concerning domination. The problem asks how small can a subset of vertices be and contain no edges or, more generally how can small a subset of vertices be and contain other ones. Our work was as elegant as it was unexpected being a departure from the tried and true methods of this theory that had dominated the field for one fifth a century. This expository article covers all previous definitions. The inability of previous definitions in solving even one case of real-world problems due to the lack of simultaneous attentions to the worthy both of vertices and edges causing us to make the new one. The concept of domination in a variety of graphs models such as crisp, weighted and fuzzy, has been in a spotlight. We turn our attention to sets of vertices in a fuzzy graph that are so close to all vertices, in a variety of ways, and study minimum such sets and their cardinality. A natural way to introduce and motivate our subject is to view it as a real-world problem. In its most elementary form, we consider the problem of reducing waste of time in transport planning. Our goal here is to first describe the previous definitions and the results, and then to provide an overview of the flows ideas in their articles. The final outcome of this article is twofold: (i) Solving the problem of reducing waste of time in transport planning at static state; (ii) Solving and having a gentle discussions on problem of reducing waste of time in transport planning at dynamic state. Finally, we discuss the results concerning holding domination that are independent of fuzzy graphs. We close with a list of currently open problems related to this subject. Most of our exposition assumes only familiarity with basic linear algebra, polynomials, fuzzy graph theory and graph theory.

The bilateral tempered fractional derivatives are introduced generalising previous works on the one-sided tempered fractional derivatives and the two-sided fractional derivatives. An analysis of the tempered Riesz potential is done and showed that it cannot be considered as a derivative.

Sentinel-2 provides the opportunity to map the snow cover at unprecedented spatial and temporal resolution at global scale. Here we calibrate and evaluate a simple empirical function to estimate the fractional snow cover (FSC) in open terrain using the normalized difference snow index (NDSI) from 20 m resolution Sentinel-2 images. The NDSI is computed from flat surface reflectances after masking cloud and snow-free areas. The NDSI-FSC function is calibrated using Pléiades very high resolution images and evaluated using independent datasets including SPOT 6/7 satellite images, time lapse camera photographs, terrestrial lidar scans and crowd-sourced in situ measurements. The calibration results show that the FSC can be represented with a sigmoid-shaped function 0.5×tanh(a×NDSI+b)+0.5 where a = 2.65 and b = -1.42 yielding a root mean square error of 25%. Similar RMSE are obtained with different evaluation datasets with a high topographic variability. With this function, we estimate that the confidence interval on the FSC retrievals is 38% at the 95% confidence level.

To enhance the mechanical properties (i.e. strength and elongation) of the face-centered cubic (fcc) α-phase in the Au-Cu-Al system, this study focused on the introduction of the martensite phase (doubled B19 (DB19) crystal structure of Au2CuAl) via the manipulation of alloy compositions. Fundamental evaluations, such as microstructure observations, phase identifications, thermal analysis, tensile behavior examinations, and reflectance analysis have been conducted. The presence of fcc annealing twins was both observed in the optical microscope (OM) and the scanning electron microscope (SEM) images. Both the strength and elongation of the alloys were greatly promoted while the DB19 martensite phase was introduced into the alloys. Amongst all the prepared specimens, the 47Au41Cu12Al and the 44Au44Cu12Al alloys performed the optimized mechanical properties. The enhancement of strength and ductility in these 2 alloys was achieved while the stress plateau was observed during the tensile deformation. A plot of the ultimate tensile strength (UTS) against fracture strain was constructed to illustrate the effects of the introduction of the DB19 martensite phase on the mechanical properties of the alloys. Regardless of the manipulation of the alloy compositions and the introduction of the DB19 martensite phase, the reflectance stayed almost identical to pure Au.

This study develops a predictor-corrector algorithm for the numerical simulation of IVPs involving singular generalized fractional derivatives with Mittag-Leffler kernels. The proposed algorithm converts the considered IVP into a Volterra-type integral equation and then uses Trapezoidal rule to obtain approximate solutions. Numerical approximate solutions of some singular generalized fractional derivative with Mittag-Leffler kernels models have been presented to demonstrate the efficiency and accuracy of the proposed algorithm. The algorithm describes the influence of the fractional derivative parameters on the dynamics of the studied models. The suggested method is expected to be effectively employed in the field of simulating generalized fractional derivative models

In this work epitaxial Au islands have been grown on epitaxial α-Fe2O3 thin film by pulsed laser deposition on SrTiO3(111) substrate. Both Au and α-Fe2O3 layer show an island-type growth with an average particle size of 40 and 62 nm, respectively. The crystallographic coupling of lattices is confirmed with a rotation of 30º between the in-plane crystallographic axes of α-Fe2O3(0001) structure and those of SrTiO3(111) substrate and between the in-plane crystallographic axes of Au(111) and those of α-Fe2O3(0001) structure. α-Fe2O3 is the only phase of iron oxide identified before and after its functionalization with Au nanoparticles. In addition, its structural character-istics are also preserved after Au deposition, with minor changes at short-range order. The func-tional character of the complex systems as gas sensor has been proven at room temperature. Con-ductance measurements of Au(111)/α-Fe2O3(0001)/ SrTiO3(111) system show that the incorpora-tion of Au islands on top of the α-Fe2O3(0001) layer induces an enhancement of the gas-sensing ac-tivity for CO and CH4 gas in comparison to a bare α-Fe2O3(0001) layer grown on SrTiO3(111).

In this study, by using Least Square Method, the dataset for the Gross Domestic Product per capita is modeled as a function satisfying the fractional differential equation. The function itself is assumed to be the finite summation of its previous values and the derivatives with unknown coefficients. Then, the prediction for the upcoming years is done by having an approach dividing the dataset into 4 regions corresponding to four different tasks. The mathematical model of the Gross Domestic Product (GDP) per capita of the countries (and union) which are Brazil, China, European Union (EU), India, Italy, Japan, UK, the USA, Spain, and Turkey is constructed with a new methodology called as the deep assessment method which comes from the expressing an arbitrary function modeling the dataset as the finite summation of its previous values and the derivatives with unknown coefficient. The method uses the fractional calculus properties combining with Least Square Method and is compared to Long short-term memory (LSTM) algorithm which is a special type of neural network used for time sequences in general.

In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long–range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long–range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations and agent–based models. Reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first–passage time distributions. Research has lead us to question whether the observed long–range memory is a result of actual long–range memory process or just a consequence of non–linearity of Markov processes. As our most recent result we discuss the long–range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the ARFIMA sample series. Our newly obtained results seem indicate that new estimators of self–similarity and long–range memory for analyzing systems with non–Gaussian distributions have to be developed.

Here we present Hilfer-Polya, psi-Hilfer Ostrowski and psi-Hilfer-Hilbert- Pachpatte types fractional inequalities. They are univariate inequalities involving left and right Hilfer and -Hilfer fractional derivatives. All estimates are with respect to norms ||.||p, 1 <_ p <_infinite. At the end we provide applications.

For the first time, We do fuzzification the concept of domination in crisp graph on a generalization of fuzzy graph by using membership values of vertices, α-strong edges and edges. In this paper, we introduce the first variation on the domination theme which we call vertex domination. We determine the vertex domination number γ_v for several classes of t-norm fuzzy graphs which include complete t-norm fuzzy graph, complete bipartite t-norm fuzzy graph, star t-norm fuzzy graph and empty t-norm fuzzy graph. The relationship between effective edges and α-strong edges is obtained. Finally, we discuss about vertex dominating set of a fuzzy tree with respect to a t-norm ⨂ by using the bridges and α-strong edges equivalence.

In this paper, the deformation and phase transformation of disorder α phase at (α + γ) two phase region in as-forged Ti-44Al-8Nb-(W, B, Y) alloy are investigated by hot compression and hot packed rolling. Detailed microstructural evolution demonstrates that the as-deformed microstructure is significantly affected by deformation conditions. The mircrostructure differences are mainly due to temperature drop and strain rate. The evolution of α lamelae into α grains is detailed descripted. Moreover, the disorder α lamellae can also be decomposed into some new α grains by the assisted decomposition mechanism of γ grains. Microstructure evolution model of current TiAl alloy at 1250 °C during hot rolling is built.

In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations as approximations of some type of fractional nonlinear birth--death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While FDEs appear more flexible in fitting empirical data, our ODEs offered better fits to two out of three data sets. Important differences in transient dynamics between these modeling approaches are discussed.

Background. The treatment of coronary stenosis relies on invasive high risk surgical assessment to generate the fractional flow reserve diagnostics index, a ratio of distal to proximal pressures in respect of coronary atherosclerotic plaque causing stenosis. Non-invasive methods are therefore a need of the times. This study proposes an extensible mathematical description of the coronary vasculature that permits rapid estimation of the coronary fractional flow reserve. Methods. By adapting an existing closed loop model of human coronary blood flow, the effects of large vessel stenosis and microvascular disease on fractional flow reserve were quantified. Several simula-tions generated flow and pressure information which was used to compute fractional flow re-serve under a spectrum of conditions including focal stenosis, diffuse stenosis, and microvascular disease. Sensitivity analysis stratified the influence of model parameters on the index. The model was simulated as coupled non-linear ordinary differential equations and numerically solved us-ing an implicit higher order method. Results. Large vessel stenosis affected fractional flow re-serve. The model predicts that the presence, rather than severity, of microvascular disease affect coronary flow deleteriously. Sensitivity analysis revealed that heart rate may not affect the index. Conclusions. The model provides a computationally inexpensive instrument for future in silico coronary blood flow investigations as well as clinical-imaging decision making. A combination of focal and diffuse stenosis appears to be essential in reducing the index. In addition to pressure measurements in the large epicardial vessels, diagnosis of microvascular disease is essential. The independence of the index with respect to heart rate suggests that computationally inexpensive steady state simulations may provide sufficient information to reliably compute the index.

The methods for constructing solutions to integro-differential equations of the Volterra type are considered. The equations are related to fractional conformable derivatives. Explicit solutions of homogeneous and inhomogeneous equations are constructed and a Cauchy-type problem is studied. It should be noted that the considered method is based on the construction of normalized systems of functions with respect to a differential operator of fractional order.

The manuscript surveys the special functions of the Fox-Wright type. These functions are generalizations of the hypergeometric functions. Notable representatives of the type are the Mittag-Leffler functions and the Wright function. The integral representations of such functions are given and the conditions under which these function can be represented by simpler functions are demonstrated. The connection with generalized fractional differential and integral operators is demonstrated and discussed.

Hematite (-Fe2O3) with uniform hexagonal flakes morphology has been successfully synthesized using a combination of gelatin as natural template with F127 via hydrothermal method. The resulting hematite was investigated as adsorbent and photocatalyst for removal of ibuprofen as pharmaceutical waste. Hexagonal flake-like hematite was obtained following calcination at 500 oC with the average size was measured at 1-3 µm. Increasing the calcination temperature to 700 oC transformed the uniform hexagonal structure into cubic shape morphology. Hematite also showed high thermal stability with increasing the calcination temperatures, however, the surface area was reduced from 47 m2/g to 9 m2/g. FTIR analysis further confirmed the formation Fe-O-Fe bonds, and the main constituent elements of Fe and O were observed in EDX analysis for all samples. Fe2O3-G samples have an average adsorption capacity of 55-25.5 mg/g at 12-22% of removal efficiency when used as adsorbent for ibuprofen. The adsorption capacity was reduced with increasing the calcination temperatures due to the reduction of available surface area of the hexagonal flakes when transformed into cube. Photocatalytic degradation of ibuprofen using hematite flakes achieved 50% of removal efficiency meanwhile combination of adsorption and photocatalytic degradation further removed 80% of ibuprofen in water/hexane mixtures.

Anyon is collective excitation of two dimensional electron gas subjected to strong magnetic field, carrying fractional charges and exotic statistical character beyond fermion and boson. So far, anyons with serial fractional charges only exist in fractional quantum Hall effect. It is still a challenge to find new serial of fractional charges in other physical system and develop an unified mathematical physics theory based on the same root. Here a topological path fusion theory of propagating electrons in magnetic flux lattice is proposed to explore the physical origin of fractional charges based on a generalization of Feynman's path integral theory and Thurston's train track theory. This mathematical physics theory generated the existed serial of fractional charges in fractional quantum Hall effect and predicted new serial of fractional charges. A serial of irrational charges are predicted in one dimensional lattice of magnetic fluxes. Fractionally charged anyons are also generated in two dimensional and three dimensional lattice of train tracks of electric currents, revealing an exact correspondence between knot lattice model and train track model. A new explanation for the modular symmetry of complex Hall conductance and composite fermion in fractional quantum Hall effect is also derived from this topological path fusion theory. Experimental observation of anyon in three dimensions can be realized by constructing three dimensional interlocking magnetic fluxes or mapping magnetic fluxes into forbidden zones in multi-connected space filled by solid state material. A photonic crystal with porous nano-structures is a promising system for detecting fractional charges and paves a new way for topological quantum computation.

We report the results of our study of approved drugs as potential treatments for COVID 19, based on the application of various bioinformatics predictive methods. The drugs studied include chloroquine, ivermectin, remdesivir, sofosbuvir, boceprevir, and α-difluoromethylornithine (DMFO). Our results indicate that these small molecules selectively bind to stable, kinetically active residues and residues adjoining them on the surface of proteins and inside protein pockets, and that some prefer hydrophobic over other active sites. Our approach is not restricted to viruses and can facilitate rational drug design, as well as improve our understanding of molecular interactions, in general.

In this research article we solve the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional order differential equations. To guarantee the synchronization and anti-synchronization of these systems, we use the well-known PID control theory and the Lyapunov-Krasovskii stability theory for discrete systems of variable fractional order.We illustrate the results obtained through simulation with examples, in which it can be seen that our results are satisfactory, thus achieving synchronization and anti-synchronization of chaotic systems of variable fractional order with discrete time delay.

Background: Night-migratory birds sense the Earth´s magnetic field by an unknown molecular mechanism. Theoretical and experimental evidence support the hypothesis that light-induced formation of a radical-pair in European robin cryptochrome 4a, ErCry4a, is the primary signalling step in the retina of the bird. In the present work, we investigated a possible route of cryptochrome signalling involving the α-subunit of the cone specific heterotrimeric G protein from European robin. Methods: Protein-protein interaction studies include surface plasmon resonance, pulldown affinity binding and Förster resonance energy transfer. Results: Surface plasmon resonance studies showed direct interaction revealing high to moderate affinity for binding of non-myristoylated and myristoylated G protein to ErCry4a, respectively. Pulldown affinity experiments confirmed this complex formation in solution. We validated these in vitro data by monitoring the interaction between ErCry4a and G protein in a transiently transfected neuroretinal cell line using Förster resonance energy transfer. Conclusions: Our results suggest that ErCry4a and the G protein also interact in vivo and might constitute the first biochemical signalling step in radical-pair-based magnetoreception.

Antimicrobial resistance (AMR) has been a serious threat to human health, and combination therapy is proved to be an economic and effective strategy to fight the resistance. However, the abuse of drug combinations would conversely accelerate the spread of AMR. In our previous work, it had been concluded that the mutant selection indexes (SIs) of one agent against a specific bacterial strain are closely related to the proportions of two agents in a drug combination. To discover probable correlations, predictors and laws for further proposing feasible principles and schemes guiding the AMR-preventing practice, here three aspects were further explored. First, the power function (y=ax^b, a > 0) correlation between the SI (y) of one agent and the ratio value (x) of two agents in a drug combination was further established based on the mathematical and statistical analyses for those experimental data, and two rules a₁ × MIC₁ = a₂ × MIC₂ and b₁ + b₂ = -1 were discovered from both equations of y=a₁x^b1 and y=a₂x^b2 respectively for two agents in drug combinations. Simultaneously, it was found that one agent with larger MPC alone for drug combinations show greater potency for narrowing itself MSW and preventing the resistance. Second, a new concept as mutation-preventing selection index (MPSI) was proposed and used for evaluating the mutation-preventing potency difference of two agents in drug combinations, and the positive correlation between the MPSI and the mutant prevention concentration (MPC) or minimal inhibitory concentration (MIC) was subsequently established. Inspired by this, the significantly positive correlation, contrary to previous reports, between the MIC and the corresponding MPC of antimicrobial agents against pathogenic bacteria was established using one hundred and eighty-one of data pairs reported. These results together of above three aspects indicate that the MPCs in alone and combination are very important indexes for drug combinations to predict the mutation-preventing effects and the trajectories of collateral sensitivity, and while the MPC of an agent can be roughly calculated from its corresponding MIC. Subsequently, the former conclusion was further verified and improved by the antibiotic exposure to forty-three groups designed as different drug concentrations and various proportions. The results further proposed that the C/MPC for the agent with larger proportion in drug combinations can be considered as a predictor and is the key to judge whether the resistance and the collateral sensitivity occur to two agents. Based on these above correlations, laws, and their verification experiments, some principles were proposed, and a diagram of the mutation-preventing effects and the resistant trajectories for drug combinations with different concentrations and ratios of two agents was presented. Simultaneously, the reciprocal of MPC alone (1/MPC), proposed as the stress factors of two agents in drug combinations, together with their SI in combination, is the key to predict the mutation-preventing potency and control the trajectories of collateral sensitivity. Finally, a preliminary scheme for antimicrobial combinations preventing the AMR was further proposed for subsequent improvement research and clinic popularization, based on the above analyses and discussion. Moreover, some similar conclusions were speculated for triple or multiple drug combinations.

Nanofluids are a novel class of heat transfer fluid that plays a vital role in industries. In mathematical investigations, these fluids are modeled in terms of traditional integer-order partial differential equations (PDEs). It is recognized that traditional PDEs cannot decode the complex behavior of physical flow parameters and memory effects. Therefore, this article intends to study the mixed convection heat transfer in nanofluid over an inclined vertical plate via fractional derivatives approach. The problem in hand is modeled in connection with Atangana-Baleanu fractional derivatives without singular and local kernel having strong memory. The human blood is considered as base fluid dispersing carbon nanotube (CNTs) (single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes(MWCNTs )) into it to form blood-CNTs nanofluid. The nanofluids are considered to flow in a saturated porous medium under the influence of an applied magnetic field. The exact analytical expressions for velocity and temperature profiles are acquired using the Laplace transform technique and plotted in various graphs. The empirical results indicate that the memory effect decreases with increasing fractional parameters in the case of both temperature and velocity profiles. Moreover, the temperature profile is higher for blood-SWCNTs by reason of higher thermal conductivity whereas, this trend is opposite in case of velocity profile due densities difference.

Degradation of intracellular components through autophagy is a fundamental process to maintain cellular integrity and homeostasis. Recently a glycogen-selective autophagy pathway has been described, termed ‘glycophagy’. Glycogen is a primary storage depot and regulator of glucose availability, and glycophagy is emerging as a critical physiological process involved in energy metabolism. Glycophagy-mediated degradation of glycogen appears to operate in parallel with the well-described canonical pathway of glycogenolysis involving glycogen phosphorylase. Evidence suggests that starch-binding domain protein-1 (Stbd1) is a key glycogen-binding protein involved in tagging glycogen for glycophagy, and that Gabarapl1 is primarily involved as the Atg8 family protein recruiting the Stbd1-glycogen complex into the forming glycophagosome. The nuances of glycophagy protein machinery, regulation and lysosomal glucose release are yet to be fully elucidated. In this mini-review, we critically analyze the current evidence base for glycophagy as a selective-autophagy process of physiological importance and highlight areas where further investigation is warranted.

In magneto-photoluminescence (magneto-PL) spectra of quasi-two dimensional islands (quantum dots) having seven electrons and Wigner-Seitz radius rs~1.5, we revealed a suppression of magnetic field (B) dispersion, paramagnetic shifts and jumps of the energy of the emission components for filling factors &gt;1 (B&lt;10 T). Additionally, we observed B-hysteresis of the jumps and a dependence of all these anomalous features on rs. Using a theoretical description of the magneto-PL spectra and an analysis of the electronic structure of these dots based on the single-particle Fock-Darwin spectrum and many-particle configuration-interaction calculations, we show that these observations can be described by the rs-dependent formation of the anyon (magneto-electron) composites (ACs) involving single-particle states having non-zero angular momentum and that the anyon states observed involve Majorana modes (MMs), including zero-B modes having equal number of vortexes and anti-vortexes, which can be considered as Majorana anyons. We show that the paramagnetic shift corresponds to a destruction of the equilibrium self-formed ~5/2 AC by the external magnetic field and that the jumps and their hysteresis can be described in terms of Majorana qubit states controlled by B and rs. Our results show a critical role of quantum confinement in the formation of magneto-electrons and implies the liquid-crystal nature of fractional quantum Hall effect states, Majorana anyon origin of the states having even , i.e., composite fermions, which provide new opportunities for topological quantum computing.

Complex diseases such as cancer are caused by changes in the Gene Regulatory Networks. Systems that model the complex dynamics of these networks along with adapting to real gene expression data are closer to reality and can help understand the creation and treatment of cancer. In this paper, for the first time, modelling of gene regulatory networks is performed using delayed nonlinear variable order fractional systems in the state space by a new tool called GENAVOS. This tool uses gene expression time series data to identify and optimize system parameters. This software has several tools for analyzing system dynamics. The results show that the nonlinear variable order fractional systems have very good flexibility in adapting to real data. We found that regulatory networks in cancer cells actually have a larger delay parameter than in normal cells. It is also possible to create chaos, periodic and quasi-periodic oscillations by changing the delay, degradation and synthesis rates. Our findings indicate a profound effect of time-varying order on these networks, which may be related to a type of cellular memory due to epigenetic and environmental factors. We showed that by changing the delay parameter and the variable order function for a normal cell system, its behavior changes and becomes quite similar to the behavior of a cancer cell. This work also confirms the effective role of the miR-17-92 cluster in the cancer cell cycle. GENAVOS is available at https://github.com/hanif-y/GENAVOS with its user guide and MATLAB codes.

The purpose of the research is to investigate the unique solvability of a nonlocal boundary value problem for a loaded equation of parabolic-hyperbolic type in a special domain. Methods: Using representations of a general regular solution, the existence and uniqueness of the problem posed is proved. Results: A new method for proving the unique solvability of nonlocal boundary value problems for one loaded equation of mixed type in a special domain has been formed and developed. Conclusions: The obtained results make it possible to solve some problems of genetics, immunology, transonic gas dynamics and thermal physics, which are associated with displacement.

α-amylase inhibitors (aAIs) have been proved efficient for the management of type 2 diabetes. This study aimed to search the potential aAIs produced by microbial fermentation. Among various bacterial strains, Pseudomonas aeruginosa TUN03 was found as a potential aAI - producing strain, and shrimp heads powder (SHP) was screened as the most suitable C/N source for fermentation. P. aeruginosa TUN03 exhibited the highest aAIs productivity (3100 U/mL) in the medium containing 1.5% SHP with the initial pH of 7-7.5, and fermentation was performed at 27.5 °C in 2 days. Further, aAIs compounds were investigated for scale-up production in a 14 L – bioreactor system, and the results highlighted high yield (4200 U/mL) in much shorter fermentation time (12 h) compared to fermentation in flasks. The bioactivity-guided purification resulted in the isolation of one major target compound. This active compound was confirmed as hemi-pyocyanin (HPC), with good purity, via using high-performance liquid chromatography and gas chromatography-mass spectrometry. Notably, HPC demonstrated potent activity comparable to acarbose, a commercial antidiabetic drug; this is the first-ever report of aAI activity of HPC. The docking study indicated that HPC inhibits α-amylase via binding to amino acid Arg421 at the biding site on enzyme α-amylase with good binding energy (-9.3 kcal/mol) and creating two linkages of H-acceptor.

In this article, we consider the three dimensional $\alpha$-fractional nonlinear delay differential system of the form \begin{align*} D^{\alpha}\left(u(t)\right)&=p(t)g\left(v(\sigma(t))\right),\\D^{\alpha}\left(v(t)\right)&=-q(t)h\left(w(t))\right),\\D^{\alpha}\left(w(t)\right)&=r(t)f\left(u(\tau(t))\right),~ t \geq t_0, \end{align*} where $0 < \alpha \leq 1$, $D^{\alpha}$ denotes the Katugampola fractional derivative of order $\alpha$. We have established some new oscillation criteria of solutions of differential system by using generalized Riccati transformation and inequality technique. The obtained results are illustrated with suitable examples.

Nonalcoholic fatty liver disease (NAFLD) is becoming the leading cause of hepatocellular carcinoma (HCC), liver-related mortality, and liver transplantation. There is reasonable epidemiological cohort data to recommend surveillance of patients with NAFLD based upon the incidence of HCC. The American Gastroenterology Association (AGA) expert review published in 2020 recommend that NAFLD patients with cirrhosis or advanced fibrosis estimated by non-invasive tests (NITs) should consider HCC surveillance. NITs include fibrosis-4 (FIB-4) index, the enhanced liver fibrosis (ELF) test, FibroScan, and MR elastography. The recommended surveillance modality is abdominal ultrasound (US) given that it is cost effective and noninvasive with good sensitivity. However, US is limited in obese patients and those with NAFLD. In NAFLD patients with a high likelihood of having an inadequate US or if US is attempted but inadequate, CT or MRI may be utilized. The GALAD score, consisting of age, gender, AFP, lens culinaris-agglutinin-reactive fraction of AFP (AFP-L3), and protein induced by vitamin K absence or antagonist-II (PIVKA-II), can help to identify high risk of incident HCC in NAFLD patients. Innovative parameters including Mac-2 binding protein glycated isomer , type IV collagen 7S, free apoptosis inhibitor of macrophage, combination of single nucleoside polymorphisms are expected to be established. Considering a large number of NAFLD population, optimal screening tests must meet several criteria including high sensitivity, cost effectiveness and availability.

In the present work we study the existence of solutions for hybrid nonlinear fractional integrodifferential equations. We developed an algorithm by using the operator theoretical techniques in order to obtain the approximate solutions. The main results depend on the Dhage iteration method that were incorporated with the modern hybrid fixed point theorems. The approximate solutions were obtained by using Lipschitz conditions and weaker form of mixed partial continuity. Further, we provide some examples to explain the hypotheses and the related results.

Patients with transfusion-dependent thalassemia (TDT) show disorders in calcium metabolism. The α-klotho protein is predominantly expressed in tissues that are involved in calcium homeostasis, and lowered levels are associated with bone disease. Aim of the study. To study the associations between low α-klotho status and calcium metabolism in relation to iron status in children with TDT. Methods. α-klotho, calcium, parathyroid hormone (PTH), calcyphosin, vitamin D3, phosphorous, fibroblast growth factor receptor 2 (FGFR2), as well as iron and erythron biomarkers were measured in 60 children with TDT and 30 healthy control children. Results. A meaningful part of TDT patients showed lowered α-klotho levels, and those children also showed low serum total and ionized calcium concentrations. TDT patients showed increased PTH, FGFR2, and calcyphosin and lowered vitamin D3 as compared with healthy children. The α-klotho levels were significantly correlated with total and ionized calcium (positively) and with iron overload biomarkers and the number of blood transfusions (inversely). Partial Least Squares path analysis showed that 40.1% of the variance in serum total calcium could be explained by the regression on α-klotho, vitamin D3 (both positively), and calcyphosin (inversely) and that the effects of the latter are mediated by iron overload and the number of blood transfusions. Conclusion. In TDT, iron overload and its consequences may induce lowered levels of α-klotho which in turn may lead to lower calcium thereby explaining at least in part the effects of TDT on bone metabolism including spontaneous pathological fractures, osteoporosis, osteopenia, and skeletal deformities.

The Landau damping effect was observed in collisionless plasma, as a microscopic resonant mechanism between electromagnetic radiation and the collective modes. In this paper we demonstrate the occurrence of the Landau damping at macroscopic scale in the interaction between water waves and anharmonic lattice of magnetic buoys. By coupling the Navier-Stokes equations for incompressible fluid with the nonlinear dynamics of an anharmonic magnetic lattice we obtain a resonant transfer of momentum and energy between the two systems. The velocity of the flow is obtained in the Stokes approximation with Basset type of drag force. The dynamics of the buoys is calculated in the surfactant approximation for a specific frequency, then we use Fourier analysis to obtain the general time variable interaction. After involving an integral Dirichlet transform we obtain the time dependent expression of the drag force, the interaction waves-lattice with a new term in the form of a Caputo fractional derivative. We compare the results of the model with experiments performed in a wave tank with free floating magnetic buoys under the action of small amplitude gravitational waves. This configuration can be applied in studies for the attenuation with resonant damping of rogue waves, storms or tsunamis.

Meprin α is a zinc metalloproteinase (metzincin) that has been implicated in multiple diseases, including fibrosis and cancers. It has proven difficult to find small molecules that are capable of selectively inhibiting meprin α, or its close relative meprin β, over numerous other metzincins which, if inhibited, would elicit unwanted effects. We recently identified possible molecular starting points for meprin α-specific inhibition through an HTS effort (see part I, preceding paper). In part II we report the optimization of a potent and selective hydroxamic acid meprin α inhibitor probe which may help define the therapeutic potential for small molecule meprin α inhibition and spur further drug discovery efforts in the area of zinc metalloproteinase inhibition.

The main idea of this paper is to investigate the exact solutions and dynamic properties in optical nanofibers, which is modeled by space-time fractional perturbed nonlinear schr\"odinger equation involving Kerr law nonlinearity with conformal fractional derivative. Firstly, by the complex fractional traveling wave transformation, the traveling wave system of the original equation is obtained, then a conserved quantity, namely the Hamiltonian is constructed, and the qualitative analysis of this system is conducted via this quantity by classifying the equilibrium points. Moreover, the prior estimate of the existence of the soliton and periodic solution is established via the bifurcation method. Furthermore, all exact traveling wave solutions are constructed to illustrate our results explicitly by the complete discrimination system for polynomial method.

Differences in fish assemblages’ structure and their relation with environmental variables (due to the variations in sampled seasons, habitats, and zones), were analyzed in two adjacent estuaries on the north Pacific coast of Mexico. Environmental variables and fish catches were registered monthly between August 2018 and October 2020. Multivariate analyses were conducted to define habitats and zones based on their environmental characteristics, and the effect of this variability on fish assemblages’ composition, biomass, and diversity (α and β) was evaluated. A total of 12,008 fish individuals of 143 species were collected using different fishing nets. Multivariate analyses indicated that fish assemblages’ structure was different between zones due to the presence, height, and coverage of distinct mangrove species. Additionally, factors such as depth and salinity showed effects on fish assemblages’ diversity (α and β-nestedness), which presented higher values in the ocean and remained similar in the rest of the analyzed zones and habitats. These results and the differences in species replacement (β-turnover) indicate the singularity of fish assemblages at estuaries (even in areas very close to the ocean), and the necessity to establish local management strategies for these ecosystems.

Some α-Pyrone derivatives isolated from Alternaria phragmospora fungus showed promising anti leukemic activities, while others were inactive. CRM1/XPO1 (chromosome region maintenance 1 protein, also called exportin1 or PO1 in humans) has been chosen as a target for antileukemic molecular docking study for those compounds to understand their modes of interaction and structure activity relationships. The results showed that two (2 and 4), out of six, natural α-Pyrone derivatives exhibited well-established interactions with the amino acids of the receptor, which was in agreement with the experimental anti-leukemic results of these compounds. Moreover, twenty hypothetical chemically modified α-Pyrone derivatives (7-27) have been designed. Compounds 7, 8, 22 and 24 showed more efficient docking properties than the previously considered natural compounds.

In this paper it is shown that mathematical description of strain, constitutive law and dynamics obtained by direct replacement of integer order derivatives with Caputo or Riemann-Liouville fractional order partial derivatives, having integral representation on finite interval, in case of a guitar string, is nonobjective. The basic idea is that different observers, using this type of descriptions, obtain different results which cannot be reconciled, i.e. transformed into each other using only formulas that link the coordinates of the same point in two fixed orthogonal reference frames and formulas that link the numbers representing the same moment of time in two different choices of the origin of time measuring. This is not an academic curiosity! It is rather a problem: which one of the obtained results is correct?

We investigated preschool-aged children’s understanding of early fractional tasks and how that performance correlates with fine motor skills and use of gestures while counting. Participants were 33 preschoolers aged 4 to 5 in two Southeastern public elementary schools. Children were tested individually in an interview-like setting. Mathematics tasks were presented in a paper and pencil format and the Grooved Pegboard test assessed fine motor skills. Finally, utilization of gestures was evaluated by taking a behavioral rating of the child’s hand morphology, accuracy of gestures, and synchrony of gestures and spoken word while performing a counting task. Results indicate performance on fractional reasoning tasks significantly predicts both fine motor ability and accuracy of gestures.

Waxy rice is one of the most popular traditional crops served as a staple food in China. In this study, the effect of different factors including α-amylase activity, protein, and amylopectin structure on the pasting properties of four waxy rice varieties were investigated. Rice flours treated with AgNO3 solution, DL-dithiothreitol (DTT) or protease, suggested that both α-amylase activity and protein significantly decrease the pasting viscosity of waxy rice flours. Chain length distribution of amylopectin as measured by high performance ion exchange chromatography (HPAEC-PAD) showed that starch with higher ratio of short chain leading to a higher pasting viscosity. X-Ray diffractograms showed that the crystal type of all the four varieties of rice starches were characteristic A-type. Relative crystallinity of each rice starch was further calculated, and a higher crystallization resulted in a higher viscosity. Our study would provide a fundamental knowledge of the relationship between different factors and waxy starch pasting properties, as well as be a reference for controlling the quality of waxy rice starch-based food.

Meprin α and β are zinc-dependent proteinases implicated in multiple diseases including cancers, fibrosis, and Alzheimer’s. However, until recently, only a few inhibitors of either meprin were reported and no inhibitors are in pre-clinical development. Moreover, inhibitors of other metzincins developed in previous years are not effective in inhibiting meprins suggesting the need for de novo discovery effort. To address the paucity of tractable meprin inhibitors we developed ultra-high throughput assays and conducted parallel screening of >650,000 compounds against each meprin. As a result of this effort, we identified 5 selective meprin α hits belonging to three different chemotypes (triazole-hydroxyacetamides, sulfonamide-hydroxypropanamides, and phenoxy-hydroxyacetamides). These hits demonstrated a nanomolar to micromolar inhibitory activity against meprin α with low cytotoxicity and >30-fold selectivity against meprin β and other related metzincincs. These are the most selective inhibitors of meprin α to date.

Type 2 diabetes mellitus (T2D) is a metabolic disorder characterized by inappropriate insulin function. Despite wide progress in genome studies, defects in gene expression for diabetes prognosis still incompletely identified. Prolonged hyperglycemia activates NF-κB, which is a main player in vascular dysfunctions of diabetes. Activated NF-κB, triggers expression of various genes that promote inflammation and cell adhesion process. Alteration of pro-inflammatory and profibrotic gene expression contribute to the irreversible functional and structural changes in the kidney resulting in diabetic nephropathy (DN). To identify the effect of some important NF-κB related genes on mediation of DN progression, we divided our candidate genes on the basis of their function exerted in bloodstream into three categories (Proinflammatory; NF-κB, IL-1B, IL-6, TNF-α and VEGF); (Profibrotic; FN, ICAM-1, VCAM-1) and (Proliferative; MAPK-1 and EGF). We analyzed their expression profile in leukocytes of patients and explored their correlation to diabetic kidney injury features. Our data revealed the overexpression of both proinflammatory and profibrotic genes in DN group when compared to T2D group and were associated positively with each other in DN group indicating their possible role in DN progression. In DN patients, increased expression of proinflammatory genes correlated positively with glycemic control and inflammatory markers indicating their role in DN progression. Our data revealed that the persistent activation NF-κB and its related genes observed in hyperglycemia might contribute to DN progression and might be a good diagnostic and therapeutic target for DN progression. Large-scale studies are needed to evaluate the potential of these molecules to serve as disease biomarkers.

The Sanshui Basin (SSB) is located at the northern continental margin of the South China Sea and characterized by a continental rift basin. The bimodal volcanic rocks in SSB record the early Cenozoic magmatic activity in the South China Block, on the magmatic evolution process of bimodal volcanic rocks are poorly understood. Clinopyroxenes in bimodal volcanic rocks in the SSB provide an opportunity to investigate the magma process during magma ascent. We classified nine types of clinopyroxene phenocrysts according to the different compositions and textures types in cogenetic basalt-trachyandesite-comenditic trachyte, the composition of unzoned clinopyroxene have an evolution sequence of diopside- hedenbergite- aegirine with the decrease of Mg#, and the trace element contents of unzoned clinopyroxenes also increase systematically during magma evolution, indicating that the genesis of clinopyroxene dominated by fractional crystallization in a closed magma system; however, the clinopyroxenes with reverse zoning and multiple zoning record the process of magma mixing and recharge indicating an open magma system. Whilst fractional crystallization is the dominated process, magma mixing, recharge, and crystal settling complicate magma evolution. Thermobarometric calculations show that clinopyroxene phenocrysts in bimodal volcanic rocks of SSB are distributed in the whole crust during magma ascent. We have established a magma plumbing system, which provides a new constrain for the complex magmatic evolution history in the SSB by detailed mineral-scale analysis.

In this paper, using the two integers that describe the stationary 2-dimensional wave and the charge quantization along with the balance between the Lorentz force and electrical force, we succeed in deriving the fractional quantum Hall effect and the integer quantum Hall effect; we find that the latter exists as a special case of the former. Moreover, using the derived expression describing the fractional quantum Hall effect, a relationship between the plateau in the resistivity of the sample and the applied magnetic field is obtained. The findings of this model agree well with experimental measurements. Because the two integers that describe the stationary 2-dimensional wave and the charge quantization along with the force balance have concrete physical meanings in this work, we could provide a clear picture of the origin of both the integer quantum Hall effect and the fractional quantum Hall effect.

Immersive experiences in green areas and particularly in forests have long been known to produce beneficial effects for human health. However, the exact determinants and mechanisms leading to healthy outcomes remain to be elucidated. The purpose of this study was to investigate whether inhaling plant-emitted biogenic volatile compounds, namely monoterpenes (MTs), can produce specific effects on anxiety. Data from 505 subjects participating in 39 structured forest therapy sessions in different Italian sites, were collected. Monoterpenes air concentration was measured at each site. STAI State questionnaires were administered before and after the sessions as a measure of anxiety. A propensity score matching analysis was then performed, considering an above-average exposure to inhalable air MTs as the treatment: the estimated effect was -1.28 STAI-S points (95% C.I. -2.51 to -0.06, p = 0.04), indicating that the average effect of exposure to high MT air concentrations during forest therapy sessions is to decrease anxiety.

For solving the fractional differential equations in computational fluid dynamics (CFD), it’s complicated and difficult by the Laplace and Fourier transforms. Based on the Caputo fractional derivative, the analytical solutions for unsteady unidirectional flows of a generalized Oldroyd-B fluid are deduced by the separation of variables method. Results show that the analytical solutions are given easily, and have good university. For some specific parameter values, the well-known analytical solutions for the generalized second grade fluid, the generalized Upper-Convected Maxwell (UCM) fluid as well as the ordinary Oldroyd-B fluid can be obtained.

Autonomous differential equations of fractional order and non-singular kernel are solved. While solutions can be obtained through numerical, graphical, or analytical solutions, we seek an implicit analytical solution.

In this study, we first present a time-fractional L$\hat{e}$vy diffusion equation of the exponential option pricing models of European option pricing and the risk-neutral parameter. Then, we modify a particular L$\hat{e}$vy-time fractional diffusion equation of European-style options. Introduce a more general model from the models based on the L$\hat{e}$vy-time fractional diffusion equation and review some recent findings regarding of the Europe option pricing of risk-neutral free.

A new type of ordinary differential equation is introduced and discussed, namely, the time-dependent order ordinary differential equations. These equations can be solved via fractional calculus and are mapped into Volterra integral equations of second kind with singular integrable kernel. The solutions of the time-dependent order differential equations smoothly deforms solutions of the classical integer order ordinary differential equations into one-another, and can generate or remove singularities. An interesting symmetry of the solution in relation to the Riemann zeta function and Harmonic numbers was also proved.

Andrographis paniculata leaves have been widely used in traditional medicine due to their rich content of phenolic compounds. In this study, we evaluated the total phenolic and flavonoid content of Andrographis paniculata leaf extracts (ALE), as well as its antioxidant activities against DPPH, ABTS, and hydrogen peroxide radicals. Additionally, we conducted cell viability assays, RT-PCR, and western blot analysis to investigate the biochemical effects of ALE on UVB-induced HaCaT cells. Our results revealed that ALE exhibited a high concentration of polyphenols and flavonoids, which were associated with potent abiotic antioxidant properties. Furthermore, ALE treatment effectively abrogated the damage caused by UVB radiation on key molecules such as hyaluronan synthase 1, Aquaporin 3, and loricrin in HaCaT cells. ALE also demonstrated the ability to reduce the overactivation of mitogen-activated protein kinases (MAPKs) and the expression of pro-inflammatory cytokines, including interleukin-6 and interleukin-1β in UVB-induced HaCaT cells. Additionally, ALE positively influenced the peroxisome proliferator-activated receptor alpha in these cells. Overall, our findings highlight the antioxidant and anti-inflammatory effects of ALE, as well as its significant role in modulating skin barrier functions. These results contribute to the growing body of evidence supporting the therapeutic potential of ALE in skincare and dermatological applications.

COVID-19 outbreak started in the Chinese city of Wuhan and spread around the globe in months due to its high contagious level. Hence, this disease posed a great challenge to researchers and mathematicians. Numerous mathematical models have been suggested to visualize the spreading speed and trends of this pandemic. In this paper, a comparison of a widely established and accepted method, the Susceptible-Exposed-Infected-Quarantined-Recovered-Death-Insusceptible (SEIQRDP) model with a newly-proposed fractional-order SEIQRDP is studied. Densely populated Countries of Asia (Pakistan, India, and Bangladesh) have been chosen as data sets and both algorithms have been applied to their data. The same comparison technique has also been used on the data of two polar countries, New Zealand and Russia, that validated our findings. Error comparison of both algorithms has been recorded in a tabulated form which shows multi-fold erroneous trends over WHO data of selected countries.

Four discrete models using the exact spectral derivative discretization finite difference (ESDDFD) method are proposed for a chaotic five-dimensional, conformable fractional derivative financial system incorporating ethics and market confidence. Since the system considered was recently studied using the conformable Euler finite difference (CEFD) method and found to be hyperchaotic, and the CEFD method was recently shown to be valid only at fractional index , the source of the hyperchaos is in question. Through numerical experiments, illustration is presented that the hyperchaos previously detected is in part an artifact of the CEFD method as it is absent from the ESDDFD models.

Power series expansions are useful in approximation theory and mathematical physics. The manuscript presents several types of fractional Taylor expansions of sufficiently smooth functions. This is achieved by employing an incremental regularization procedure to the computation of the derivative. The series are constructed in an algorithmic way, which allows for its implementation in computer algebra systems.

Leucine-rich α-2 glycoprotein1 (LRG1) is a member of the leucine-rich repeat (LRR) family that was implicated in multiple diseases including cancer, aging and heart failure as well as diabetes and obesity. LRG1 plays a key role in diet-induced hepatosteatosis and insulin resistance by mediating the crosstalk between adipocytes and hepatocytes. LRG1 also promotes hepatosteatosis by upregulating de novo lipogenesis in the liver and suppressing fatty acid β oxidation. In this study, we investigated the association of LRG1 with obesity markers including leptin and other adipokines in adolescents (11-14 years; n=425). BMI-for-age classification based on WHO growth charts was used to define obesity. Plasma LRG1 was measured by ELISA while other markers were measured by multiplexing assay. Median (IQR) of LRG1 levels was higher in obese [30 (25, 38) µg/mL] and overweight [30 (24, 39) µg/mL] adolescents, compared to normal-weight participants [27 (22, 35) µg/mL]. The highest tertile of LRG1 had an OR [95%CI] of 2.55 [1.44, 4.53] for obesity. LRG1 was positively correlated to plasma levels of HsCRP (R=0.2), Leptin (R=0.2) and Chemerin (R=0.24) with p<0.001. Additionally, it was positively associated with plasma level of IL6 (R=0.17) and IL10 (R=0.14) but not TNF-α. In conclusion, LRG1 levels are increased in obese kids and associate with increased levels of adipogenic markers. These results suggest the usefulness of LRG1 as an early biomarker for obesity and its related pathologies in adolescents.

In this article, the new Hermite–Hadamard type inequalities are studied via generalized s-convexity on fractal sets. These inequalities derived on fractal sets are shown to be the generalized s-convexity on fractal sets. We proved that the absolute values of the first and second derivatives for the new inequalities are the generalization of s-convexity on fractal sets.

Creating self-learning algorithms, developing deep neural networks and improving other methods that "learn" for various areas of human activity is the main goal of the theory of machine learning. It helps to replace the human with a machine, aiming to increase the quality of production. The theory of artificial neural networks, which already have replaced the humans in problems of detection of moving objects, recognition of images or sounds, time series prediction, big data analysis and numerical methods remains the most dispersed branch of the theory of machine learning. Certainly, for each area of human activity it is necessary to select appropriate neural network architectures, methods of data processing and some novel tools from applied mathematics. But the universal problem for all these neural networks with specific data is the achieving the highest accuracy in short time. Such problem can be resolved by increasing sizes of architectures and improving data preprocessing, where the accuracy rises with the training time. But there is a possibility to increase the accuracy without time growing, applying optimization methods. In this survey we demonstrate existing optimization algorithms of all types, which can be used in neural networks. There are presented modifications of basic optimization algorithms, such as stochastic gradient descent, adaptive moment estimation, Newton and quasi-Newton optimization methods. But the most recent optimization algorithms are related to information geometry, for Fisher-Rao and Bregman metrics. This approach in optimization extended the theory of classic neural networks to quantum and complex-valued neural networks, due to geometric and probabilistic tools. There are provided applications of all introduced optimization algorithms, what delighted many kinds of neural networks, which can be improved by including any advanced approaches in minimization of the loss function. Afterwards, we demonstrated ways of developing optimization algorithms in further researches, engaging neural networks with progressive architectures. Classical gradient based optimizers can be replaced by fractional order, bilevel and, even, gradient free optimization methods. There is a possibility to add such analogues in graph, spiking, complex-valued, quantum and wavelet neural networks. Besides the usual problems of image recognition, time series prediction, object detection, there are many are other tasks for modern theory of machine learning, such as solving problem of quantum computations, partial differential and integro-differential equations, stochastic processes and Brownian motion, making decisions and computer algebra.

High dietary phosphate intake and poor adherence to phosphate-binding-therapy elevate the risk of hyperphosphatemia in maintenance hemodialysis (HD; MHD) patients. Therefore, chronic kidney disease-related mineral and bone disorder (CKD-MBD) indicators increase; consequently, risks of CKD-MBDs and inflammation are elevated. This double-blind, randomized control trial intervention study was designed to investigate the possibility of reducing blood CKD-MBD indicators and modulating inflammatory indicators by consuming low-phosphate (LP) meals accompanied by a minimum dose of a calcium-based phosphate binder (CaCO3). MHD patients were recruited and randomly assigned to an LP meal group (LP group) or a control group. After initial data collection, blood collection, and dietary counseling, subjects were asked to consume a washout diet for 1 week. During the washout diet period, subjects consumed their usual diet but took 1 tablet of calcium carbonate (1CaCO3) as a phosphate binder with each meal. After the washout diet period, subjects in the LP group and control group respectively consumed LP meals and regular meals twice a day for 1 week. Meat in the LP meals was boiled before the regular cooking process, but meat in control meals was not. All meals were supplied by a central kitchen so that the contents of phosphate and other nutrients could be identified. In total, 40 MHD patients completed the study program. After 1 week of the dietary intervention, the blood Ca x P product and dietary phosphate had significantly decreased in the LP group compared to the control group (p&lt;0.05). The LP group had significantly lower variations in dietary phosphate intake, blood calcium, Ca x P product, and tumor necrosis factor (TNF)-α than the control group by comparing differences between after the dietary intervention and the baseline (△after intervention - baseline, p&lt;0.05). The increase in dietary phosphate intake (△3rd - 2nd dietary phosphate intake) augmented the increase in the TNF-α level by 6.24-fold (odds ratio [95% confidence interval]: 6.24 [1.12~34.92], p&lt;0.05). These results highlighted the conclusion that LP meals accompanied by a minimum dose of CaCO3 downregulated pro-inflammation by reducing CKD-MBD indicators which was triggered by decreasing dietary phosphate intake.

Background: Vascular inflammation plays a crucial role in peripheral arterial disease (PAD), although the role of the mediators involved has not yet been properly defined. The aim of this work is to investigate gene expression and plasma biomarkers in chronic limb-threating ischemia (CLTI). Methods: Using patients from the GHAS trial, both blood and ischemic muscle samples were obtained to analyze plasma markers and mRNA expression, respectively. Statistical analy-sis was performed by using univariate (Spearman, t-Student, X2) and multivariate (multiple lo-gistic regression) tests. Results: 35 patients were available at baseline (29 for mRNA expression). Baseline characteristics (mean): Age:71.4±12.4 (79.4% male); TNF-α:10.7±4.9; hs-CRP:1.6±2.2; Neutrophil-to-lymphocyte ratio (NLR):3.5±2.8. Plasma TNF-α was found elevated (≥8.1) in 68.6% of patients, while high hs-CRP (≥0.5) in 60.5%. Diabetic patients with high level of inflammation showed significantly higher levels of NOX4 expression at baseline (p=0.0346). Plasma TNF-α had a negative correlation with eNOS expression (-0.5, p=0.015) and hs-CRP with VEGF-A (-0.63, p=0.005). The expression of NOX4 was parallel to that of plasma TNF-α (0.305, p=0.037), especial-ly in DM. Cumulative mortality at 12-month was related to NLR ≥3 (p=0.019) and TNF-α ≥8.1 (p=0.048). The best cut-off point for NLR to predict mortality was 3.4. Conclusions: NOX4 and TNF-α are crucial for the development and complications of lower limb ischemia, especially in DM. hs-CRP could have a negative influence on angiogenesis too. NLR and TNF-α represent suita-ble markers of mortality in CLTI. These results are novel because they connect muscle gene expres-sion and plasma information in patients with advanced PAD, deepening the search of new and ac-curate targets for this condition.

This paper reports a new global Mittag-Leffler synchronization criterion with regard to fractional-order hyper-chaotic financial systems by designing the suitable impulsive control and the state feedback controller. The significance of this impulsive synchronization lies in the fact that the backward economic system can synchronize asymptotically with the advanced economic system under the effective impulse macroeconomic management means. Matlab LMI-toolbox is utilized to deduce the feasible solution in numerical example, which shows the effectiveness of the proposed methods. It is worth mentioning that the LMI-based criterion usually requires the activation function of the system to be Lipschitz, but the activation function in this paper is fixed and truly nonlinear, which cannot be assumed to be Lipschitz continuous. This is another mathematical difficulty overcome in this paper.

In this paper we study solutions and drift homogenization for a class of viscous lake equations by using the method of semigroups of bounded operators. Suppose that the initial value i.e.,for some Hölder continuous function onwith smooth function value satisfying and Then the initial value problem (2) for viscous lake equations has a unique smooth local strong solution. Using this result we study the drift homogenization for three-dimensional stationary Stokes equation in the usual sense

Zinc, being a part of many proteins and enzymes, plays an important role in the vital processes of the body. Racemic α-lipoic acid (LA) has a wide range of biological activities: antioxidant, antidiabetic, anticancer, and it is also used in diseases such as Parkinson's and Alzheimer's. Nowadays, the synthesis and structural studies of new zinc complexes with biologically active compounds are of great importance for drug discovery. This work shows the studies carried out on the synthesis, structure, identification, also biological activity using in silico methods of a complex compound based on LA and zinc. A complex compound of zinc with LA (ZnLA) was synthesized in the presence of LA and zinc acetate in ethanol. The identification of ZnLA by (FT-IR, XRD and TGA-DTA), also DFT calculations at the B3LYP/def2-TZVPP level of theory was performed. The molecular docking investigation involved docking ZnLA with two different protein receptors such us Glycogen phosphorylase (2GPA) and Kv potassium channel beta subunit (1ZSX) using CB-Dock 2 server and Auto-Dock Vina program to determine the mechanism of action and biological activity. This study reveals potential ligand-protein interactions at the atomic level and suggests that the treatment of diabetes (non-insulin dependent) with ZnLA.

We present here seven new zircon (U-Th)/He (ZHe) ages and three new zircon fission track ages (ZFT) analyzed from an age-elevation profile (Machu Picchu, Peru). ZFT data present older ages in comparison with the other thermochronological data, whereas the ZHe data interestingly present similar ages than the ones obtained with apatite (U-Th)/He (AHe). It has been proposed that He retention in zircon is linked to the damage dose, with an evolution of the closure-temperature from low values associated to low α-dose (<1016 α/g), subsequently increasing before decreasing again at very high α-dose (>1018 α /g). Studies have been focused on the He diffusion behavior at high α-dose, but little is known at low dose. We propose that the ZHe closure temperature at α-dose ranging from 0.6×1015 to 4×1016 α/g is in the range of ~60-80°C. This value is lower than the one proposed in the current damage model ZRDAAM and demonstrates that the ZHe and AHe methods could have similar closure temperatures at low α-dose (i.e. similar ages). These new data strengthen our previous geological conclusions and even highlight an about twice more important cooling rate than the one deduced from AHe and apatite fission-track data alone registered at Machu Picchu.

Curcuma longa is only a rich source of curcumin (1) and its major analogues demethoxycurcumin (2) and bisdemethoxycurcumin (3) among the Curcuma species. The content ratio of these three curcumins in turmeric is depended on the varieties and growing environment. Recently, curcumin (1) has been reported as potential inhibitor of hepatic and enzymatic protein tyrosine phosphatase 1B (PTP1B) and its related disorders such as hypertriglyceridemia, hyperlipidemia and liver steatosis. Thus, we further purified curcumins (1–3) from C. longa and investigated their inhibitory effects against PTP1B and α-glucosidase enzymes. As the result, curcumins (1–3) exhibited potential PTP1B inhibition with IC50 values of 37.8 ± 1.4, 45.3 ± 0.7, and 72.6 ± 1.1 μM, respectively, and α-glucosidase inhibition with similar manner (IC50 values of 78.2 ± 0.2, 82.4 ± 0.6, and 90.6 ± 1.0 μM, respectively). These results reveal a key role of methoxylation in the variation of PTP1B and α-glucosidase inhibitory activity for these curcumins. In addition, density functional theory (DFT) was used accompanying with molecular docking (MD) to analyze the ligand stability and the interaction of curcumins (1–3) with PTP1B and glucoside hydrolase proteins. Assay-based results and the MD data obtained are highly correlation suggesting that the deterioration of the enzyme activity caused by the distortion of structural conformation of PTP1B and glucoside hydrolase may be related to the arrangement of amino acids in protein structure. This reported for the first time that inhibitory effects of curcumins (1–3) against PTP1B and glucoside hydrolase have been examined in vitro and in silico as well.

We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has connections with biased walks on digraphs. Within this framework, we introduce a space-time generalization of the Poisson process as a strictly increasing walk with discrete Mittag-Leffler jumps subordinated to a (continuous-time) fractional Poisson process. We call this process ‘space-time Mittag-Leffler process’. We derive explicit formulae for the state probabilities which solve a Cauchy problem with a Kolmogorov-Feller (forward) difference-differential equation of general fractional type. We analyze a “well-scaled” diffusion limit and obtain a Cauchy problem with a space-time convolution equation involving Mittag-Leffler densities. We deduce in this limit the ‘state density kernel’ solving this Cauchy problem. It turns out that the diffusion limit exhibits connections to Prabhakar general fractional calculus. We also analyze in this way a generalization of the space-time fractional Mittag-Leffler process. The approach of construction of good Laplacian generator functions has a large potential in applications of space-time generalizations of the Poisson process and in the field of continuous-time random walks on digraphs.

Recent studies have confirmed that lung microvascular endothelial injury plays a critical role in the pathophysiology of COVID-19. Our group and others have demonstrated the beneficial effects of H2S in several pathological processes and provided a rationale for considering the therapeutic implications of H2S in COVID-19 therapy. Here, we evaluated the effect of the slow-releasing H2S donor, GYY4137, on the barrier function of a lung endothelial cell monolayer in vitro, after challenging the cells with plasma samples from COVID-19 patients or inactivated SARS-CoV-2 virus. We also assessed how the cytokine/chemokine profile of patients’ plasma, endothelial barrier permeability, and disease severity correlated with each other. Alterations of barrier permeability after treatments with patient plasma, inactivated virus, and GYY4137 were monitored and assessed by electrical impedance measurements in real-time. We present evidence that GYY4137 treatment reduced endothelial barrier permeability after plasma challenge and completely reversed the endothelial barrier disruption caused by inactivated SARS-CoV-2 virus. We also showed that disease severity correlated with the cytokine/chemokine profile of the plasma but not with barrier permeability changes in our assay. Overall, these data demonstrate that treatment with H2S-releasing compounds has the potential to ameliorate SARS-CoV-2–associated lung endothelial barrier disruption.

White noise is fundamentally linked to many processes, it has a flat power spectral density and a delta-correlated autocorrelation. Operators acting on white noise can result in coloured noise, whether they operate in the time domain, like fractional calculus, or in the frequency domain, like spectral processing. We investigate whether any of the white noise properties remain in the coloured noises produced by the action of an operator. For a coloured noise, which drives a physical system, we provide evidence to pinpoint the mother process from which it came. We demonstrate the existence of two indices, that is, kurtosis and codifference, whose values can categorise coloured noises according to their mother process. Four different mother processes are used in this study: Gaussian, Laplace, Cauchy, and Uniform white noise distributions. The mother process determines the kurtosis value of the coloured noises that are produced. It maintains its value for Gaussian, never converges for Cauchy, and takes values for Laplace and Uniform that are within a range of its white noise value. In addition, the codifference function maintains its value for zero lag-time essentially constant around the value of the corresponding white noise.

Shigella and Salmonella have been implicated in neonatal sepsis, food poisoning, and bacteremia. Their increasing resistance to antibiotics has undermined treatment options, constituting a public health crisis. Also, the scarcity of new antibiotics in the development pipeline compounds multidrug-resistance (MDR). Hence, there is a need to potentiate antibiotics to mitigate resistance. This study leveraged riboflavin to re-sensitize fluoroquinolones and carbapenems against MDR Shigella and Salmonella spp. Disk diffusion, microbroth-dilution, chequerboard, and time-kill assays were used to determine resistance profiles and riboflavin-antibiotic activity. Biofilm-formation and bacterial viability (after riboflavin-antibiotic challenge) was determined with crystal-violet and Macrophage infection assays, respectively. Strains exhibited &gt;80% resistance to fluoroquinolones and carbapenems, with 160–320 µg MIC ranges and 0.5–2 FIC, indicating no synergy. At 40–80 µg riboflavin, there was two-fold reduction in bacterial survival, with meropenem-riboflavin exhibiting significant reduction and FIC of 0.075 indicating high synergistic activity. Biofilm-formation was altered (from strong to weak phenotype) with 40 µg riboflavin-antibiotic treatment. There was a 40–70% reduction in bacterial survival in THP-1 cells treated with meropenem-riboflavin after 3 hours, and complete clearance between 24-48 hpi. Riboflavin potentiated fluoroquinolones and meropenem, leading to modulation of the host immune response for the clearance of the strains.

Astrocytes have been implicated in a wide range of neurodegenerative diseases, with the literature indicating harmful or beneficial roles on a case-by-case basis. On such conditions, these cells are capable of secreting several inflammatory factors and also promote synapse elimination and remodeling. These responses are possible because they sense their surroundings via several receptors, including metabotropic glutamate receptor (mGluR5). However, mGluR5 activation in astrocytes under neuroinflammatory conditions can be neuroprotective or have the opposite effect. In this work, we investigated the role of mGluR5 in hiPSC-derived astrocytes subjected to pro-inflammatory stimulation by recombinant TNF-α (rTNF-α). Our results show that mGluR5 blockade by CTEP is capable of reducing pro-inflammatory cytokines (IL-6, IL-8 and TNF-α) release in rTNF-α-stimulated astrocytes, but, in contrast, leads to an augmented expression of the pan-reactive marker SERPINA3. Additionally, CTEP enhances synaptoneurosomes phagocytosis by astrocytes in both non-stimulated and TNF-α-stimulated conditions, indicating that mGluR5 blockade alone is enough to drive synaptic material engulfment. Finally, mGluR5 antagonism as well as rTNF-α stimulation leads to a reduction in the expression of synaptogenic molecules. Altogether, these data suggest a complex role for mGluR5 in human astrocytes, since its blockage may have beneficial and detrimental effects under inflammatory conditions.

Fabry disease is a lysosomal storage disorder caused by the deficiency of the α-galactosidase-A enzyme. Cardiac, renal, and neurological involvement significantly reduces life expectancy. Until a few years ago, treatment options for Fabry disease were limited to enzyme replacement therapy with agalsidase alfa or beta administered by intravenous infusion every 2 weeks. Migalastat (Galafold®) is an oral pharmacological chaperone that increases enzyme activity of “amenable” mutations. The safety and efficacy of migalastat were supported in the phase III FACETS and ATTRACT studies, compared to available enzyme replacement therapies; showing a reduction in left ventricular mass, and stabilization of kidney function and plasma Lyso-Gb3. Similar results were confirmed in subsequent extension publications, both in patients who started migalastat as their first treatment and in patients who were previously on enzyme replacement therapy and switched to migalastat. In this review we describe the safety and efficacy of switching from enzyme replacement therapy to migalastat in patients with Fabry disease and “amenable” mutations, referring to publications available to date.

The operation status of manufacturing equipment is directly related to the reliability of the operation of manufacturing equipment and the continuity of operation of the production system. Based on the analysis of the operation status of manufacturing equipment and its characteristics, it is proposed that the concept of assessing the operation status of manufacturing equipment can be realized by applying real-time acquisition of accurate inspection data of important parts of weak motion units and comparing them with their motion status evaluation criteria. Through the study of the application characteristics of fractional-order calculus theory, a differential data fusion model based on the fractional-order differential operator is established. The advantages of Internet of Things (IoT）technology and fractional order differential fusion algorithm are integrated to obtain real-time high-precision data of the operating parameters of manufacturing equipment, and the research objective of operating condition assessment of manufacturing equipment is realized. The feasibility and effectiveness of the method are verified by the application of the method in machining center operation status assessment.

This study investigated whether export performance is correlated with innovation. We explicitly considered five types of innovation: a) process innovation; b) product innovation; c) process and product innovation; d) product innovation new to the firm; and e) product innovation new to the market. We en-larged the findings of R&D-export and R&D-investment relations using a vast sample of cross-European firms. We considered innovation as endogenous and determined by R&D through a process characterized by the role of the regional technological environment. Our analysis enabled us to propose an integrated model incorporating R&D, innovation and export, in a framework of simultaneous equations which consider their mutual correlations. To the best of our knowledge, this work is the first in recent years to empirically compute the relation between R&D and tangible investment at the micro level. Econometric results showed that product and process innovation are positively linked to the export intensity of European manufacturing firms. The results also showed complementarity effects between the two kinds of innovation. The av-erage effect on export intensity from carrying out process innovation is larger than that found for product innovation, except in cases where the product is new to the market. When both types of innovation have been carried out, a larger effect results than that found for product or process innovation alone. Furthermore, the average marginal effect on export intensity from innovations of any kind among those studied here is highly positive and significant.

Eurycomanone and eurycomalactone are known quassinoids present in the roots and stems of Eurycoma longifolia. These compounds had been reported to have cytotoxic effects, however, their mechanism of action in a few cancer cell lines have yet to be elucidated. This study was aimed to investigate the anti-cancer effects and mechanisms of action of eurycomanone and eurycomalactone in cervical (HeLa), colorectal (HT29) and ovarian (A2780) cancer cell lines via Sulforhodamine B assay. Their mechanism of cell death was evaluated based on Hoechst 33342 assay and in silico molecular docking toward DHFR and TNF-α as putative protein targets. Eurycomanone and eurycomalactone exhibited in vitro anti-cancer effects manifesting IC50 values of 4.58 ± 0.090 µM and 1.60 ± 0.12 µM (HeLa), 1.22 ± 0.11 µM and 2.21 ± 0.049 µM (HT-29), and 1.37 ± 0.13 µM and 2.46 ± 0.081 µM (A2780) respectively. They induced apoptotic cancer cell death in dose- and time-dependent manners. Both eurycomanone and eurycomalactone were also predicted to have good inhibitory potential as demonstrated by the docking into TNF-α with binding affinity of -8.83 and -7.51 kcal/mol, respectively, as well as into DHFR with binding affinity results of -8.05 and -8.87 kcal/mol, respectively. These results support the evidence of eurycomanone and eurycomalactone as anti-cancer agents via apoptotic cell death mechanism that could be associated with TNF-α and DHFR inhibition as among possible protein targets.

Fibroblast activation protein (FAP) is a membrane-tethered serine protease overexpressed in the reactive stromal fibroblasts of &gt; 90% human carcinomas, which makes it a promising target for developing radiopharmaceuticals for imaging and therapy of carcinomas. Here, we synthesized two novel (R)-pyrrolidin-2-yl-boronic acid-based FAP-targeted ligands; SB02055 (DOTA-conjugated (R)-(1-((6-(3-(piperazin-1-yl)propoxy)quinoline-4-carbonyl)glycyl)pyrrolidin-2-yl)boronic acid) and SB04028 (DOTA-conjugated ((R)-1-((6-(3-(piperazin-1-yl)propoxy)quinoline-4-carbonyl)-D-alanyl)pyrrolidin-2-yl)boronic acid). natGa- and 68Ga-complexes of both ligands were evaluated in preclinical studies and compared to previously reported natGa/68Ga-complexed PNT6555. Enzymatic assays showed that FAP binding affinities (IC50) of natGa-SB02055, natGa-SB04028 and natGa-PNT6555 were 0.41±0.06, 13.9±1.29 and 78.1±4.59 nM, respectively. PET imaging and biodistribution studies in HEK293T:hFAP tumor-bearing mice showed that while [68Ga]Ga-SB02055 presented with a nominal tumor uptake (1.08±0.37 %ID/g), [68Ga]Ga-SB04028 demonstrated clear tumor visualization with ~1.5-fold higher tumor uptake (10.1±0.42 %ID/g) compared to [68Ga]Ga-PNT6555 (6.38±0.45 %ID/g). High accumulation in the bladder indicated renal excretion of all three tracers. [68Ga]Ga-SB04028 displayed low background level uptake in most normal organs, and comparable to [68Ga]Ga-PNT6555. However, since its tumor uptake was considerably higher than [68Ga]Ga-PNT6555, the corresponding tumor-to-organ uptake ratios for [68Ga]Ga-SB04028 were also significantly greater than [68Ga]Ga-PNT6555. Our data demonstrate that (R)-(((quinoline-4-carbonyl)-D-alanyl)pyrrolidin-2-yl)boronic acid is a promising pharmacophore for the design of FAP-targeted radiopharmaceuticals for cancer imaging and radioligand therapy.

In view of the problem of cracking easily and partial distortion of images after encryption or decryption, a novel image encryption and decryption algorithm based on Arnod Transform and fractional chaotic is proposed. To begin with, the Arnold transform is used to encrypt. So that the spatial confidence of the original image has been comprehensively disturbed. Secondly, the XOR involving the fractional order chaotic sequence is used to encrypt. The key sequence is dynamically generated to ensure the randomness and difference of key generation. When decryption is required, the first decryption is performed using the key and XOR. Then the second decryption is carried out by using the inverse Arnold transform, and finally the decrypted image is obtained. Experimental results show that the improved algorithm has achieved better performance in encryption and decryption.

Various factors, such as uncertainty of component parameters and uncertainty of sensor meas-urement values, contribute to the difficulty of fault detection in the landing gear retrac-tion/extension hydraulic system. In this paper, we introduce linear fractional transformation technology and uncertainty analysis theory for the construction of the diagnostic bond graph of the landing gear retraction/extension hydraulic system. In this way, interval analytical redundancy relations and fault signature matrix can be derived. Using the fault signature matrix, existing faults of the system can be preliminarily detected and isolated. Additionally, interval analytical re-dundancy relations can be used to detect system faults in detail, and cases analysis can be carried out to determine if the actuator is externally or internally leaky, and if the landing gear selector valve is reversing stuck. Compared to the traditional analytical redundancy relations, this method takes into account the negative factors of uncertainty; and compared to the traditional absolute diagnostic threshold, the interval diagnostic threshold is more accurate and sensitive.

Fractional calculus gained a lot of attention in the last couple of years. Researchers discovered that processes in various fields follow rather fractional dynamics than ordinary integer-ordered dynamics, meaning the corresponding differential equations feature non-integer valued derivatives. There are several arguments for why this is the case, one of them being that fractional derivatives’ inherit spatiotemporal memory and/or the ability to express complex naturally occurring phenomena. Another popular topic nowadays is machine learning, i.e., learning behavior and patterns from historical data. In our ever-changing world with ever-increasing amounts of data, machine learning is a powerful tool for data analysis, problem-solving, modeling, and prediction. It further provides many insights and discoveries in various scientific disciplines. As these two modern-day topics provide a lot of potential for combined approaches to describe complex dynamics, this article reviews combined approaches of fractional derivatives and machine learning from the past, puts them into context, and thus provides a list of possible combined approaches and the corresponding techniques. Note, however, that this article does not deal with neural networks, as there already is profound literature on neural networks and fractional calculus. We sorted past combined approaches from the literature into three categories, i.e., preprocessing, machine learning &amp; fractional dynamics, and optimization. The contributions of fractional derivatives to machine learning are manifold as they provide powerful preprocessing and feature augmentation techniques, can improve physically informed machine learning, and are capable of improving hyperparameter optimization. Thus, this article serves to motivate researchers dealing with data-based problems, to be specific machine learning practitioners, to adopt new tools and enhance their existing approaches.

An array of diverse processes and factors have been linked to the pathoetiology and pathophysiology of Parkinson’s disease (PD), including systemic CNS factors. This article reviews some of the many processes and factors linked to the emergence and progression of PD that culminates in the loss of substantia nigra pars compacts (SNpc) in PD patients. It is proposed that SNpc astrocytes may be a key hub, with numerous systemic and CNS factors acting to suppress the astrocyte tryptophan-melatonin pathway, leading to a loss of astrocyte melatonin and lactate for SNpc dopamine neurons. Consequently, dopamine neurons show an increase in α-synuclein, oxidative stress and suboptimal mitochondrial function, partly due to the loss of melatonin induced PTEN-associated kinase (PINK)1/parkin and mitophagy. This leads to an increase in the major histocompatibility (MHC)-1 and the chemoattraction of CD8+ T cells that destroy SNpc dopamine neurons in an ‘autoimmune’/’immune-mediated’ manner. The upstream processes driving the end-point ‘chaos’ of SNpc dopamine neuron loss are proposed to be driven by the suppression of night-time pineal melatonin, gut microbiome derived butyrate and possibly bcl2-associated athanogene (BAG)-1, which all act to suppress the glucocorticoid receptor (GR) translocation to the nucleus in all systemic and CNS cells, thereby potentiating the effects of the rising levels of cortisol over the night and accelerated rise in the course of the cortisol awakening response (CAR). The potentiation of cortisol effects at the GR has consequences for the homeostatic regulation of the diverse array of systemic and CNS microenvironments, as well as a distinct regulation of different immune and glia cells. The morning CAR is classically proposed to ‘prepare the body for the coming day’. However, the differential regulation of the GR over the circadian rhythm at night would indicate that such preparation for the coming day may be powerfully determined by night-time factors and processes. The article integrates this systemic, night-time pathoetiology with the ‘immune-mediated’ processes that ultimately drive SNpc dopamine neuron loss. This has a number of novel future research and treatment implications.

In this paper we give approximations to the Mittag-Leffler functions in terms of elementary functions using different methods. This allowed us to establish a practical method we called integerization principle. This principle states that many fractional nonlinear oscillators may be solved by means of the solution to some integer-order Duffing oscillator equation. The accuracy of the obtained results is illsutrated in concrete examples. Formulas for estimating the errors in the approximations are also provided.

Covid-19 is a lung disease caused by a Coronavirus family virus. Due to its extraordinary prevalence and death rates, it has spread quickly to every country in the world. Thus, achieving peaks and outlines and curing different types of relapses is extremely important. Given the worldwide prevalence of Coronavirus and the participation of physicians in all countries, Information has been gathered regarding the properties of the virus, its diverse types, and the means of analyzing it. Numerous approaches have been used to identify this evolving virus. It is generally considered the most accurate and acceptable method of examining the patient's lungs and chest through a CT scan. As part of the feature extraction process, a method known as fractional Fourier transform (FrFT) has been applied as one of the time-frequency domain transformations. The proposed method was applied to a database consisting of 2481 CT images. Following the transformation of all images into equal sizes and the removal of non-lung areas, multiple combination windows are used to reduce the number of features extracted from the images. In this paper, the results obtained for KNN and SVM classification have been obtained with accuracy values of 99.84% and 99.90%, respectively.

In this paper the D 3 dihedral logistic map of fractional order is introduced. The map 1 presents a dihedral symmetry D 3 . It is numerically shown that the construction and interpretation 2 of the bifurcation diagram versus the fractional order require special attention. The system stability 3 is determined and the problem of hidden attractors is analyzed. Also, analytical and numerical 4 results show that the chaotic attractor of integer order, with D 3 symmetries, looses its symmetry 5 in the fractional-order variant.

Lithium batteries are widely used due to their advantages such as high energy density, stable performance, low pollution, and long recyclable life. Accurate SOC estimation is important for the use of lithium batteries. To address the problem of low accuracy of SOC estimation by traditional methods, this paper proposes a joint method of fractional order robust unscented Kalman filter (FORUKF) and robust unscented Kalman filter (RUKF) to estimate SOC. The method is based on a fractional order model (FOM) that combines the unscented transformation (UT) technique, the H∞ observer and the joint estimator. Specifically, an adaptive genetic algorithm (AGA) was first used to identify the parameters of the FOM for lithium batteries and to verify the accuracy of the model. Estimation and updating of the ohmic resistance R0 and the capacity QN in the model in real-time by RUKF and then estimation of the SOC by FORUKF. Finally, the accuracy of FORUKF-RUKF was verified under the Federal Urban Driving Schedule (FUDS), US06 Highway Driving Schedule and Beijing Dynamic Stress Test (BJDST). According to the results, the FORUKF-RUKF estimated SOC was found to have better accuracy and robustness than the RUKF, FOUKF and EKF.

Hypertension (HT) is a very common risk factor and a frequent cause of morbidity and mortality worldwide mainly due to much increase in overweight (OW) and obesity that manifests in various forms of cardiovascular disease (CVD). There are a number of factors that may cause overweight hypertension (OHT). However, we planned to conduct the present work to study the HT and OHT men for finding the variation, interrelationship and association of important cytokines mainly serum leptin (Lep) and tumor necrosis factor-alpha (TNF-α), serum testosterone (ST), total cholesterol (TC) and inflammatory status by measuring interleukin-6 (IL-6). Three groups of subjects, the normal controls (NC; n:98; age range: 51-60 years), HT (n: 97; age range: 51-60 years) subjects, and OHT (n: 97; age range: 51-60 years) subjects were studied. Comparisons for Lep, ST, TNF-α, IL-6 and TC levels for the subject groups showed significant variations. The ST indicated significant difference only for NC vs. OHT. The IL-6 gave significant difference for NC vs. OHT and HT vs. OHT. The one-way ANOVA showed significant difference among groups for BMI, TC, IL-6, TNF-α, ST and Lep levels. Significant positive linear correlation for all groups among Lep, TNF-α, IL-6 and TC were found. The ST against TC for HT and OHT groups presented non-significant negative linear correlations. The ST showed significant negative linear correlation with other variables. Conclusively, the present study uncovers the interactive impact of serum leptin, TNF-α, testosterone, total cholesterol and IL-6 in hypertensive and overweight-related hypertensive men.

Obesity is characterized by chronic low-grade inflammation. Caveolin-1 (CAV1), a structural and functional protein found in adipose tissues (AT), is augmented in obese individuals. We aimed to define the inflammatory mediators that influence CAV1 gene regulation and associated mechanism in obesity. Using subcutaneous AT from 27 (7 lean/20 obese) normoglycemic individuals, in vitro human adipocyte models, and in vivo mice models, we found elevated CAV1 expression in obese AT and a positive correlation between the gene expression of CAV1, tumor necrosis factor alpha (TNF-α), and the nuclear factor kappa-light-chain-enhancer of activated B cells (NF-kB). CAV1 gene expression was associated with that of proinflammatory cytokines/chemokines, and their cognate receptor (r ≥ 0.447, p ≤ 0.030) but not with anti-inflammatory markers. CAV1 expression was correlated with CD163, indicating a prospective role for CAV1 in adipose inflammatory microenvironment. Unlike wild-type animals, mice lacking TNF-α exhibited reduced levels of CAV1 mRNA/proteins, which were elevated by administering exogenous TNF-α. Mechanistically, TNF-α induces CAV1 gene transcription by mediating NF-kB binding to its two regulatory elements located in the CAV1 proximal regulatory region. The interplay between CAV1 and TNF-α signaling pathway is interesting and has potential as a target for therapeutic interventions in obesity and metabolic syndromes.

This study develops a new definition of fractional derivative that mixes the definitions of fractional derivatives with singular and non-singular kernels. Such developed definition encompasses many types of fractional derivatives, such as the Riemann-Liouville and Caputo fractional derivatives for singular kernel type as well as the Caputo-Fabrizio, the Atangana-Baleanu and the generalized Hattaf fractional derivatives for non-singular kernel type. The associate fractional integral of the new mixed fractional derivative is rigorously introduced. Furthermore, newly numerical scheme is developed to approximate the solutions of a class of fractional differential equations (FDEs) involving the mixed fractional derivative. Finally, an application to computational biology is presented.