Search Results (22)

This study analyzed the non-canonical NF-κB pathway, which controls functions distinct from those of the canonical pathway. Although oscillations of NF-κB have been observed in the non-canonical pathway, a detailed mechanism explaining the observed behavior remains elusive, owing to the different behaviors observed across cell types. This study demonstrated that oscillations cannot be produced by the experimentally observed pathway alone, thereby suggesting the existence of an unknown reaction pathway. Assuming this pathway, it became evident that the oscillatory structure of the non-canonical pathway was caused by stable periodic orbits. In addition, we demonstrated that altering the expression levels of specific proteins reproduced various behaviors. By fitting 14 parameters, excluding those measured in previous studies, this study successfully reproduce nuclear retention (saturation), oscillation, and singular events that had been experimentally confirmed. The analysis also provided a comprehensive understanding of the dynamics of the RelB protein and suggested a potential inhibitory role for the unknown factor. These findings indicate that the unknown factor may be an isoform of IκB, contributing to the regulation of NF-κB signaling. Based on these models, we gained invaluable understanding of biological systems, paving the way for the development of new strategies to manipulate specific biological processes. Full article

Very recently, a straightforward method was proposed to understand galaxies and galactic clusters without using the very elusive dark matter concept. This method is called the $\kappa$-model. The main idea is to maintain the form of the usual physical laws, especially Newton’s laws of motion when gravity is weak, but only by applying a local scaling procedure for the related lengths, distances, and velocities. This local scaling appears as a correspondence principle in the $\kappa$-model. In this model, the fundamental physical constants remain universal, i.e., they are independent of a point in space and of time. The $\kappa$-model is Newtonian in its essence, but there is a relativistic extension that can easily be built. The aim of the present paper is to detail the mathematical formalism supporting it. Full article

The axiomatic structure of the $\kappa$-statistcal theory is proven. In addition to the first three standard Khinchin–Shannon axioms of continuity, maximality, and expansibility, two further axioms are identified, namely the self-duality axiom and the scaling axiom. It is shown that both the $\kappa$-entropy and its special limiting case, the classical Boltzmann–Gibbs–Shannon entropy, follow unambiguously from the above new set of five axioms. It has been emphasized that the statistical theory that can be built from $\kappa$-entropy has a validity that goes beyond physics and can be used to treat physical, natural, or artificial complex systems. The physical origin of the self-duality and scaling axioms has been investigated and traced back to the first principles of relativistic physics, i.e., the Galileo relativity principle and the Einstein principle of the constancy of the speed of light. It has been shown that the $\kappa$-formalism, which emerges from the $\kappa$-entropy, can treat both simple (few-body) and complex (statistical) systems in a unified way. Relativistic statistical mechanics based on $\kappa$-entropy is shown that preserves the main features of classical statistical mechanics (kinetic theory, molecular chaos hypothesis, maximum entropy principle, thermodynamic stability, H-theorem, and Lesche stability). The answers that the $\kappa$-statistical theory gives to the more-than-a-century-old open problems of relativistic physics, such as how thermodynamic quantities like temperature and entropy vary with the speed of the reference frame, have been emphasized. Full article

When machining high-speed steels (HSS) with micro-wire electrical discharge machining (micro-WEDM), high surface quality is achieved as standard. The value of the roughness parameter Ra is less than 0.2 μm. However, the problem is the performance of the electroerosion process (MRR), which is low. This problem is related to the mechanical and physical properties of the HSS in combination with the setting of the main technological parameters (MTP). The proposed solution to eliminate this problem relies on the selection of proper procedures for the determination of optimization criteria in relation to Ra and MTP, with the inclusion of properties of the machined material. The solution consisted in the identification of four significant physical (ρ, κ) and mechanical (Rm, HRC) indicators of HSS properties, on the basis of which a suitable combination of the process output parameters Ra and MRR can be determined through established mathematical regression models using simulation and optimization. In the next step, the proper values of the MTP output process parameter settings, which correspond to the optimized output parameters Ra and MRR during machining of HSS by micro-WEDM technology, were then obtained by the same approach. Full article

This research focuses on combating the increasing problem of antimicrobial resistance, especially in Escherichia coli (E. coli), by assessing the efficacy of aminoglycosides. The study specifically addresses the challenge of developing new therapeutic approaches by integrating experimental data with mathematical modeling to better understand the action of aminoglycosides. It involves testing various antibiotics like streptomycin (SMN), kanamycin (KMN), gentamicin (GMN), tobramycin (TMN), and amikacin (AKN) against the O157:H7 strain of E. coli. The study employs a pharmacodynamics (PD) model to analyze how different antibiotic concentrations affect bacterial growth, utilizing minimum inhibitory concentration (MIC) to gauge the effective bactericidal levels of the antibiotics. The study’s approach involved transforming bacterial growth rates, as obtained from time–kill curve data, into logarithmic values. A model was then developed to correlate these log-transformed values with their respective responses. To generate additional data points, each value was systematically increased by an increment of 0.1. To simulate real-world variability and randomness in the data, a Gaussian scatter model, characterized by parameters like κ and EC₅₀, was employed. The mathematical modeling was pivotal in uncovering the bactericidal properties of these antibiotics, indicating different PD MIC (zMIC) values for each (SMN: 1.22; KMN: 0.89; GMN: 0.21; TMN: 0.32; AKN: 0.13), which aligned with MIC values obtained through microdilution methods. This innovative blend of experimental and mathematical approaches in the study marks a significant advancement in formulating strategies to combat the growing threat of antimicrobial-resistant E. coli, offering a novel pathway to understand and tackle antimicrobial resistance more effectively. Full article

Several inequalities for convex functions are derived in this paper using the monotonicity properties of functions and a generalized weighted-type fractional integral operator, which allows the integration of a function $\kappa$ with respect to another function in fractional order. Additionally, it is clear that the results were generalizations of the previously presented findings. In addition, different types of inequalities are obtained using the basic features of mathematical analysis. Finally, we believe that the methodology used in this work will inspire additional research in this field. Full article

The potential for widespread applications of the geometric and mapping properties of functions of a complex variable has motivated this article. On the other hand, the basic or quantum (or q-) derivatives and the basic or quantum (or q-) integrals are extensively applied in many different areas of the mathematical, physical and engineering sciences. Here, in this article, we first apply the q-calculus in order to introduce the q-derivative operator ${\mathfrak{S}}_{\eta ,p,q}^{n,m}$. Secondly, by means of this q-derivative operator, we define an interesting subclass $\mathcal{T}{\aleph }_{\lambda ,p}^{n,m}(\eta ,\alpha ,\kappa )$ of the class of normalized analytic and multivalent (or p-valent) functions in the open unit disk $\mathbb{U}$. This p-valent analytic function class is associated with the class $\kappa$-$\mathcal{UCV}$ of $\kappa$-uniformly convex functions and the class $\kappa$-$\mathcal{UST}$ of $\kappa$-uniformly starlike functions in $\mathbb{U}$. For functions belonging to the normalized analytic and multivalent (or p-valent) function class $\mathcal{T}{\aleph }_{\lambda ,p}^{n,m}(\eta ,\alpha ,\kappa )$, we then investigate such properties as those involving (for example) the coefficient bounds, distortion results, convex linear combinations, and the radii of starlikeness, convexity and close-to-convexity. We also consider a number of corollaries and consequences of the main findings, which we derived herein. Full article

The following research focuses on the analytical and numerical study of an arcjet constrictor. In order to perform these analyses, a geometric design of the constrictor was proposed. The analytical study considers mathematical models proposed by Stine and Watson, related to the properties of air propellants, such as the specific enthalpy, electric conductivity, thermal conductivity, and specific heat. The numerical study considered the equations for mass, momentum, energy, and electricity that describe the interaction between the electric arc and the fluid flow. These equations were solved in ANSYS FLUENT software, in which the $\kappa$-$ϵ$ turbulence and the magnetohydrodynamic (MHD) models were used. The external routines, including user-defined functions, user-defined scalars, and user-defined memory were implemented in C++ language for source terms and linked to ANSYS FLUENT. The velocity profiles were obtained analytically for the electric arc temperatures of 9000 K, 10,000 K, and 11,000 K with peak magnitudes of 2960 m/s, 3350 m/s, and 3100 m/s, respectively, at the outlet of the constrictor. It was observed from the numerical results that the velocity magnitude of the air-based plasma inside the constrictor increases as the temperature of the electric arc rises up to 10,000 K However, above 10,000 K, the velocity magnitude decreases because at this temperature level, the air particles become completely ionized, and the specific heat of the air-based plasma decreases. The numerical simulation produced velocity profile magnitudes at two different electric arc temperatures (9000 K and 10,000 K) with peak magnitudes of 2400 m/s and 2900 m/s, respectively, at the outlet of the constrictor. The numerical and analytical results were very close with an error of 16.327%. Full article

This study aimed to design and validate an instrument as a guideline for classroom observation and analysis of teaching–learning process in mathematics. The instrument considers 3 dimensions and 16 subdimensions with a gender perspective. A content validity process by eight expert judges is presented, built from a dialectical work between theory and empirical evidence from more than 100 classes observed and recorded on video from 19 educational centers. The degree of agreement between experts was determined with Fleiss Kappa and Kendall coefficients. Experts’ judgement scored each dimension from 1 to 3. Globally, an almost perfect strength of agreement was obtained in 6 of 16 dimensions with $\stackrel{-}{x}>2.5$, and in the other 10 dimensions, a strength of agreement was obtained between moderate and almost perfect, $\mathrm{2,14}\le \stackrel{-}{x}\le \mathrm{2,5}$. Fleiss Kappa coefficients were highest in relevance and clarity, $\kappa$ = 0.425, 95% CI [0.344, 0.506], p < 0.001 and, $\kappa$ = 0.461, 95% CI [0.375, 0.548], p < 0.001, respectively. Moreover, the degree of clarity, coherence, sufficiency, and relevance was statistically moderately agreed upon in their assessments, with an overall Kendall’s W = 0.489, p < 0.001. Full article

Prostate cancer is very frequent and is, in many countries, the third-leading cause of cancer related death in men. While early diagnosis and treatment by surgical removal is often curative, metastasizing prostate cancer has a very bad prognosis. Based on the androgen-dependence of prostate epithelial cells, the standard treatment is blockade of the androgen receptor (AR). However, nearly all patients suffer from a tumor relapse as the metastasizing cells become AR-independent. In our study we show a counter-regulatory link between AR and NF-κB both in human cells and in mouse models of prostate cancer, implying that inhibition of AR signaling results in induction of NF-κB-dependent inflammatory pathways, which may even foster the survival of metastasizing cells. This could be shown by reporter gene assays, DNA-binding measurements, and immune-fluorescence microscopy, and furthermore by a whole set of computational methods using a variety of datasets. Interestingly, loss of PTEN, a frequent genetic alteration in prostate cancer, also causes an upregulation of NF-κB and inflammatory activity. Finally, we present a mathematical model of a dynamic network between AR, NF-κB/IκB, PI3K/PTEN, and the oncogene c-Myc, which indicates that AR blockade may upregulate c-Myc together with NF-κB, and that combined anti-AR/anti-NF-κB and anti-PI3K treatment might be beneficial. Full article

Cutaneous T-cell lymphoma (CTCL) is a rare form of cancer with local as well as systemic manifestations. Concomitant bacterial infections increase morbidity and mortality rates due to impaired skin barrier and immune deficiency. In the current study, we demonstrated that the in vitro anti-lymphoma potential of erufosine is diminished by TWIST1 expression and micellar curcumin substantially increases its antineoplastic activity. Pharmacokinetic analysis showed that the micellar curcumin (MCRM) used in our study was characterized by low zeta potential, slow release of curcumin, and fast cell membrane penetration. The combination ratio 1:4 [erufosine:MCRM] achieved strong synergism by inhibiting cell proliferation and clonogenicity. The combined antiproliferative effects were calculated using the symbolic mathematical software MAPLE 15. The synergistic combination strongly decreased the expression of TWIST1 and protein kinase B/Akt as proven by western blotting. Significant reductions in NF-κB activation, induction of apoptosis, and altered glutathione levels were demonstrated by corresponding assays. In addition, the synergistic combination enhanced the anti-staphylococcal activity and prevented biofilm formation, as shown by crystal violet staining. Taken together, the above results show that the development of nanotechnological treatment modalities for CTCL, based on rational drug combinations exhibiting parallel antineoplastic and antibacterial effects, may prove efficacious. Full article

The fluid inerter described by the fractional derivative model is introduced into the traditional nonlinear energy sink (NES), which is called fractional-order NES in this paper. The slowly varying dynamic equation (SVDE) of the system coupled with fractional-order NES is obtained by the complex averaging method, in which the fractional derivative term is treated using the fractional Leibniz theorem. Then, the discriminants (Δ, Δ₁, and Δ₂) of the number of equilibrium points are derived. By using the variable substitution method, the characteristic equation for judging the stability is established. The results show: (1) the approximate SVDE is sufficient to reflect the slowly varying characteristics of the system, which shows that the mathematical treatment of the fractional derivative term is reliable; (2) the discriminant conditions (Δ₁, Δ₂) can accurately reflect the number of equilibrium points, and the corresponding range of nonlinear parameter κ can be calculated when the system has three equilibrium points. The expressions of Δ₁, Δ₂ are simpler than Δ, which is suitable for analysis and design parameters; (3) the stability discrimination methods of schemes 1 and 2 are accurate. Compared with scheme 2, scheme 1 is more prone to various responses, especially various strongly and weakly modulated responses. In scheme 2, the inertia effect of mass can be completely replaced by integer order inerter. Compared with integer order inerter, the introduction of fractional order inerter, whether in series or in parallel, means that the amplitude of the equilibrium point on the NES vibrator is smaller, but it is also for this reason that it is not easy to produce a modulated response with scheme 2, and the vibration suppression effect of the main structure is not good. Full article

Sixth-generation (6G) wireless communication scenarios are complex and diverse. Small-scale fading is a key part of wireless channels and its impact on performance in scenarios with time sensitivity and 6G ultrareliable and low latency communications (URLLC) quality-of-service requirements cannot be ignored. Therefore, it is necessary to accurately characterize small-scale fading when designing wireless communication systems. In this paper, we derive approximate closed form expressions for the probability density function, cumulative distribution function and moment-generating function of the postprocessing signal-to-noise ratio following the zero-forcing detector in a cell-free massive multiple-input multiple-output (CF mMIMO) system. CF mMIMO system is a nonorthogonal multiple access (NOMA) system that enables users to share all channel uses and can ensure the fairness of the communication quality experienced by different users. Our key contributions include the extension of the $\kappa$–$\mu$ shadowed fading model to a CF mMIMO system and the proposal of theoretical tools (the derived closed-form expression) to improve its mathematical tractability. By exploiting the statistical characterizations of the arrival and service processes, another important contribution is the exploitation of the upper bound of the queuing delay violation probability (UB-QDVP) over the Mellin transforms of the arrival and service processes in the proposed CF mMIMO system under the $\kappa$–$\mu$ shadowed fading model. Corroborated by extensive simulations, our analyses validate that the CF mMIMO system outperforms the orthogonal multiple access and power-domain NOMA systems and reveal the relationships among different small-scale fading types, energy efficiency, delay and the UB-QDVP, as well as the accuracy and effectiveness of the proposed theoretical tools based on the $\kappa$–$\mu$ shadowed fading model. Full article

Research efforts focused on developing a better understanding of the evolution of mortality over time are considered to be of significant interest—not just to the demographers. Mortality can be expressed with different parameters through multiparametric prediction models. Based on the Beta Gompertz generalized Makeham (BGGM) distribution, this study aims to evaluate and map four of such parameters for 22 countries of the European Union, over the period 1960–2045. The BGGM probabilistic distribution is a multidimensional model, which can predict using the corresponding probabilistic distribution with the following parameters: infant mortality (parameter θ), population aging (parameter ξ), and individual and population mortality due to unexpected exogenous factors/events (parameters κ and λ, respectively). This work focuses on the random risk factor (λ) that can affect the entire population, regardless of age and gender, with increasing mortality depicting developments and trends, both temporally (past–present–future) and spatially (22 countries). Moreover, this study could help policymakers in the field of health provide solutions in terms of mortality. Mathematical models like BGGM can be used to achieve and highlight probable cyclical repetitions of sudden events (such as Covid-19) in different time series for different geographical areas. GIS context is used to map the spatial patterns of this estimated parameter as well as these variations during the examined period for both men and women. Full article

The canonical nuclear factor kappa-light-chain-enhancer of activated B cells (NF-κB) signaling pathway regulates central processes in mammalian cells and plays a fundamental role in the regulation of inflammation and immunity. Aberrant regulation of the activation of the transcription factor NF-κB is associated with severe diseases such as inflammatory bowel disease and arthritis. In the canonical pathway, the inhibitor IκB suppresses NF-κB’s transcriptional activity. NF-κB becomes active upon the degradation of IκB, a process that is, in turn, regulated by the β-transducin repeat-containing protein (β-TrCP). β-TrCP has therefore been proposed as a promising pharmacological target in the development of novel therapeutic approaches to control NF-κB’s activity in diseases. This study explores the extent to which β-TrCP affects the dynamics of nuclear NF-κB using a computational model of canonical NF-κB signaling. The analysis predicts that β-TrCP influences the steady-state concentration of nuclear NF-κB, as well as changes characteristic dynamic properties of nuclear NF-κB, such as fold-change and the duration of its response to pathway stimulation. The results suggest that the modulation of β-TrCP has a high potential to regulate the transcriptional activity of NF-κB. Full article