Automated lung sound detection via Bi-GRU-modified SqueezeNet architecture with new stock well feature set.

This paper presents a family of Fourier eigenfunctions indexed by the space dimension d. These eigenfunctions are radial and built upon some generalized exponential integral function. For d = 1, 2, 3, they are integrable or square integrable and give new explicit examples of Fourier eigenfunctions in the usual or Fourier-Plancherel sense. For d ≥ 4 , the functions are examples of non standard eigenfunctions, i.e. eigenfunctions in the sense of distribution. The discovery of these eigenfunctions stems from research in thermal lens spectroscopy, at the intersection of thermodynamics and optics. Their use could simplify the analysis of thermo-optical systems, paving the way for applications in optical computing, material studies and thermodynamics.

This study emphasizes the construction of various types of solitary wave solutions of the M-truncated fractional (2 + 1)-dimensional Kadomtsev–Petviashvili-modified equal-width (KPmEW) equation, which models various long-wavelength phenomena, such as water waves, ferromagnetic waves, and matter-wave pulses. A modified form of the trial equation method is employed to investigate the wave structures of the proposed fractional nonlinear model. Through this approach, a wide spectrum of rational, exponential, hyperbolic, and Jacobi elliptic function solutions is derived. The corresponding wave profiles are visualized in two and three dimensions to elucidate their physical characteristics. The analytical findings are verified using the symbolic software Mathematica. The obtained results extend previous studies and provide new insights into the dynamic behaviour of fractional nonlinear evolution equations.

A massive vector field is a highly promising candidate for dark matter in the Universe. A salient property of dark matter is its negligible or null coupling to ordinary matter, with the exception of gravitational interaction. This poses a significant challenge in producing the requisite amount of dark particles through processes within the Standard Model. In this study, we examine the production of a vector field during inflation due to its direct interaction with the inflaton field through kinetic and axionlike couplings as well as the field-dependent mass. The gradient-expansion formalism, previously proposed for massless Abelian gauge fields, is extended to include the longitudinal polarization of a massive vector field. We derive a coupled system of equations of motion for a set of bilinear functions of the vector field. This enables us to address the nonlinear dynamics of inflationary vector field production, including backreaction on background evolution. To illustrate this point, we apply our general formalism to a low-mass vector field whose kinetic and mass terms are coupled to the inflaton via the Ratra-type exponential function. The present study investigates the production of its transverse and longitudinal polarization components in a benchmark inflationary model with a quadratic inflaton potential. It has been demonstrated that pure mass coupling is able to enhance only the longitudinal components. By turning on also the kinetic coupling, one can get different scenarios. As the coupling function decreases, the primary contribution to the energy density is derived from the transverse polarizations of the vector field. Conversely, for an increasing coupling function, the longitudinal component becomes increasingly significant and rapidly propels the system into the strong backreaction regime.

We establish the generalized parametric logarithmic Sobolev inequalities in the Gagliardo-Nirenberg form for variable exponential space with log Holder exponential function. Employing the generalized parametric logarithmic Sobolev inequalities, we establish the existence of weak solutions to the boundary problem for the hyperbolic equation with logarithmic nonlinearity and involving variable exponents.

This study applies the generalized exponential rational function technique to construct new optical soliton solutions of the nonlinear conformable Schrödinger equation with Kudryashov’s nonlinear refractive index governed by the quadrupled-power law and dual nonlocal nonlinearity. Various analytical solutions, including bright, dark, and wave solitons, are derived within the conformable fractional framework. The effects of the fractional-order parameter and temporal parameter on the obtained solutions are illustrated through contour, two-dimensional, and three-dimensional plots. The results reveal how fractional dynamics influence soliton structure, amplitude, and propagation behaviour. These findings contribute to a deeper understanding of pulse evolution and stability in nonlinear optical fibres and related photonic systems.

The paper presents the development of a correlation model for initial tensile elastic modulus for flexible polymers as a function of Shore hardness in OO and A scale based on measurement. Measured polymers are in groups of silicone rubber, nitrile butadiene rubber (NBR), thermoplastic polyurethane (TPU) and silicone. The model is composed of piecewise exponential functions with fixed coefficients chosen to minimize the S2 error norm and absolute value of relative error at the measured data points. Every chosen section of the hardness scale has one exponential function correlating the hardness to tensile elastic modulus with the argument in the form of a polynomial up to the fourth degree. The coefficients for the polynomial arguments were determined by enforcing interpolation conditions in a chosen set of points in the logarithmic scale for the elastic modulus. The correlation model possesses C0 continuity. For each material, five specimens were used for hardness measurements and five for the elastic modulus testing. The correlation model gives a positive value for elastic modulus of 0 for hardness, and a "finite", "reasonable" value of 100 for hardness and is monotonic. Tensile properties were evaluated using true stress and logarithmic (Hencky) strain, with iterative correction of the changing cross-sectional area to account for large strain. The maximum relative error achieved in the correlation model for the OO scale is 13.4%, while for the A scale it is 7%. The developed model provides a practical and rapid method for estimating the initial tensile elastic modulus from non-destructive hardness measurements and is particularly useful in industrial applications and in the development of material models for dental surgery simulations.

AdaSwitch: Adapting switch from Adam to SGDM by exponential function

Scribble-based weakly supervised segmentation methods have shown promising results in medical image segmentation, significantly reducing annotation costs. However, existing approaches often rely on auxiliary tasks to enforce semantic consistency and use hard pseudo labels for supervision, overlooking the unique challenges faced by models trained with sparse annotations. These models must predict pixel-wise segmentation maps from limited data, making it crucial to handle varying levels of annotation richness effectively. In this paper, we propose MaCo, a weakly supervised model designed for medical image segmentation, based on the principle of "from few to more." MaCo leverages Masked Context Modeling (MCM) and Continuous Pseudo Labels (CPL). MCM employs an attention-based masking strategy to perturb the input image, ensuring that the model's predictions align with those of the original image. CPL converts scribble annotations into continuous pixel-wise labels by applying an exponential decay function to distance maps, producing confidence maps that represent the likelihood of each pixel belonging to a specific category, rather than relying on hard pseudo labels. We evaluate MaCo on three public datasets, comparing it with other weakly supervised methods. Our results show that MaCo outperforms competing methods across all datasets, establishing a new record in weakly supervised medical image segmentation.

Subthalamic deep brain stimulation alleviates the gait sequence effect and freezing of gait in Parkinson's disease.

Extracellular vesicles (EVs) are emerging as promising nanocarriers for delivering molecules, including proteins. Various exogenous methods are proposed for loading EVs with specific cargo proteins. While the loading yield and the heterogeneity of cargo distribution are crucial quality attributes, a comprehensive quantification of these properties is still lacking. Here, we characterize the heterogeneity of EVs loaded with a model cargo protein, GFP, using various exogenous methods. A combination of biophysical methods is applied to quantify the overall yield and cargo distribution at both the ensemble and single-particle levels. Among the loading methods evaluated, electroporation is most effective for associating GFP with EVs. However, the GFP molecules per vesicle is fewer than 100, representing approximately 4% of the maximum protein capacity that EVs can potentially accommodate. Across all loading methods, the distribution of protein content per vesicle displays significant heterogeneity and follows an exponential decay function, with a higher prevalence of vesicles featuring lower protein content and fewer with higher content. Moreover, loading efficiency increases with EV size. This study shows that overall yields of exogenous loading methods to associate proteins with EVs remain modest and the resulting distribution of cargo proteins associated with EVs is highlyheterogeneous.

ABSTRACT In this paper, we introduce diverse new central special polynomials and numbers utilizing two types of ‐exponential functions. We first consider ‐central factorial numbers and polynomials of the second kind and investigate some of their properties and formulas, such as addition formulas, summation formulas, ‐derivative properties, and Jackson integral representations. As part of our main content, we define trivariate central ‐Bell polynomials and acquire several identities and relations, such as some summation and addition formulas, three ‐derivative properties, two Jackson integral representations, two implicit summation formulas, and a symmetric identity. We investigate an important correlation between these two new ‐polynomials and provide some of its consequences. Then, we provide many correlations between new and old ‐polynomials and ‐numbers, such as the ‐Stirling numbers and polynomials of the second kind, the ‐combinatorial Simsek polynomials and numbers of the first kind, the newly defined ‐polynomials and ‐numbers, ‐Euler polynomials, and ‐Bernoulli polynomials. Also, we consider a new ‐extension of Stirling numbers of the second kind and type 2 ‐Bernoulli polynomials and derive some mixed correlations related to the other new and old ‐polynomials and ‐numbers. Furthermore, we compute two ‐operator formulas for trivariate central ‐Bell polynomials and two ‐operator formulas for bivariate and one‐variable ‐central factorial polynomials of the second kind. In the end, we present graphical illustrations and zero distribution patterns of these newly introduced ‐polynomials, which exhibit a striking and structured scattering in the real and complex planes, offering both aesthetic appeal and deep analytical significance.

To enhance gas pre-extraction efficiency in low-permeability, high-gas coal seams and eliminate the danger of coal and gas outbursts at the Wulihou Coal Mine, this study analyzed the influence of the three stress zones surrounding cavitation holes (employed in alternating cavitation gas extraction technology) on gas extraction, based on the stress distribution characteristics around these holes. Two indices—the pressure relief zone area ratio and the plastic zone area ratio—were proposed to evaluate the pressure relief effect induced by the cavitation process. The effectiveness of cavitation holes for pressure relief and permeability enhancement was investigated using FLAC3D numerical simulation. Results indicate that as the cavitation hole size increases, the area of the associated stress relief zone expands, with its spatial extent best characterized by an exponential function. Similarly, the area of the plastic zone surrounding the cavitation hole also expands and is well-described by a cubic function. Both the pressure relief zone area ratio and the plastic zone area ratio exhibit an initial increase followed by a decrease with increasing cavitation hole radius, reaching their peak values within the radius range of [0.4, 0.5] m. Therefore, the optimal radius for cavitation holes is recommended to be between 0.4 m and 0.5 m. This research provides valuable reference for evaluating the pressure relief and permeability improvement effects, as well as for optimizing the aperture of hydraulic cavitation boreholes in high-gas coal seams.

This work investigates the dynamics of a generalized [Formula: see text]-dimensional Painlevé integrable model with conformable derivative from various viewpoints, illustrating the evolution of nonlinear phenomena across one temporal dimension and three spatial dimensions. The Kudryashov auxiliary equation approach and Bernoulli’s equation method are utilized to construct various traveling wave solutions in the form of hyperbolic and exponential functions. The new solutions are illustrated through contour, two-dimensional, and three-dimensional graphs, illustrating various dynamical structures with diverse parameter sets for a more thorough understanding of the physical principles. The findings reveal various soliton types such as bell-shaped, bright, and dark solitons. The present solutions indicate that the current algorithm are highly effective and robust tools, making them suitable for solving a wide range of applied differential equations, including those with fractional and integer orders. Additionally, the study investigates the current conformable model of equations by investigating the influence of the conformable parameter and the time parameter on the present solutions.

This study explores the fractional (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation, a higher-order nonlinear model known for capturing complex wave behaviors influenced by spatial and dispersive effects. To obtain a variety of solitary wave solutions including dark, bright, and mixed solitons — three advanced analytical approaches are employed: the Riccati modified extended simple equation method, the modified [Formula: see text]-expansion method, and the newly improved generalized exponential rational function method. The model is first simplified into an ordinary differential equation using a fractional wave transformation. Mathematical simulations illustrate how key parameters affect wave propagation, highlighting the strength and flexibility of the proposed techniques in handling complex nonlinear systems. By demonstrating the effectiveness of these modern analytical methods and revealing distinctive features of nonlinear dynamics, this research offers valuable insights into higher-dimensional nonlinear equations and wave phenomena.

This work investigates the dynamical behavior of the fractional Fisher–Kolmogorov–Petrovsky–Piskunov equation. The model under consideration has significant implications for reaction–diffusion processes and mathematical physics. By use of the wave transform with the [Formula: see text]-fractional derivative, the nonlinear ordinary differential equation of the governing model is extracted. The advanced approaches such as the modified F-expansion method, the modified generalized Riccati equation technique, and the modified generalized exponential rational function technique are utilized to study the model. It comprises numerous types of different solutions such as mixed, dark, bright–dark, singular, bright, complex, combined solitons, hyperbolic, periodic, and exponential solutions. We examine a comprehensive chaotic analysis to examine in depth at how the system behaves in a nonlinear way. This shows how sensitive it is to initial conditions and how strange attractors arise in phase space. Using different parameter selections, the behavior of the solutions is shown in three-dimensional, two-dimensional, and their related contour representations. By validating the effectiveness of current methodologies and elucidating the nonlinear dynamic characteristics of the proposed model, this work substantially advances the disciplines of higher-dimensional nonlinear wave fields and nonlinear science. The results of this study will help identify and elucidate numerous innovative soliton solutions. These solutions are expected to be of great significance in the fields of mathematical physics and other areas of nonlinear science.

This study investigates the Modified Complex Ginzburg-Landau Equation, a fundamental nonlinear partial differential equation that plays a central role in modeling complex wave dynamics, pattern formation, and dissipative phenomena in systems such as nonlinear optics, Bose-Einstein condensates, superfluids, and plasmas. Despite its importance, obtaining exact analytical solutions and understanding their stability properties remain challenging problems with significant theoretical and practical implications. To address this challenge, the Modified Extended Direct Algebraic Method is employed to construct exact analytical solutions in a systematic and efficient manner. By transforming the governing nonlinear equation into an algebraically solvable system, a broad and unified family of exact solutions is derived. These solutions include bright and dark solitons, singular solutions, periodic and singular periodic waves, as well as solutions expressed in exponential, Weierstrass elliptic, and Jacobi elliptic function forms. In addition, a comprehensive stability analysis is carried out to examine the response of these wave structures to small perturbations and to assess their long-term dynamical behavior. The physical characteristics and dynamical features of the obtained solutions are illustrated through detailed two-dimensional and three-dimensional graphical representations for selected parameter values. The results demonstrate the effectiveness of the Modified Extended Direct Algebraic Method in analyzing complex nonlinear models and provide deeper insight into wave propagation and stability mechanisms in dissipative systems governed by the Modified Complex Ginzburg-Landau Equation.

The effect of moisture on paper is of great relevance for numerous applications ranging from printing to packaging. The uptake of water in the polymer network of the paper fibers via the liquid or vapor phase of water results in hydro- or hygro-expansion of the paper, respectively. Here, we present a detailed atomic force microscopy study of the out-of-plane hygro-expansion of paper by conducting a series of experiments for varying relative humidity. The high spatial resolution of the atomic force microscope enables measuring the out-of-plane hygro-expansion of paper fibers with subnanometer resolution. We find a linear relation between the relative humidity and the out-of-plane expansion of the paper fibers. A sorption isotherm measurement reveals a good fit with the Guggenheim-Anderson-de Boer model. The combination of the two measurements suggests that the vast increase in weight seen in the isotherm is due to water filling the pores between the fibers, where it does not result in additional out-of-plane expansion. In addition, by locking the atomic force microscopy tip at a predefined location on a paper fiber, we monitor the expansion and shrinkage of paper with a temporal resolution in the millisecond range. We find that the kinetics of the out-of-plane hygro-expansion is described using a double exponential function comprised of two exponents with different time scales, which we attribute to two separate adsorption sites.

Image reconstruction algorithms developed for structured illumination microscopy were integrated with spatial Fourier transform fluorescence recovery after photobleaching (FT-FRAP) to recover pixel-wise diffusion maps of molecular mobility across the dissolution front of model pharmaceutical compacts. The optics and acquisitions are unchanged; the novelty lies entirely in a SIM-based reconstruction that enables segmentation-free, pixel-wise diffusion mapping. The ability to quantify molecular diffusivity in amorphous solid dispersions (ASDs) is critical for rationally designing formulations containing biologically active molecules. Notably, drug loadings exceeding critical threshold values in ASDs can result in dramatic reductions in dissolution rates, which are hypothesized to arise from phase-separated drug-rich barrier layers. Molecular mobility is the defining property dictating these dissolution trends, varying spatially across the glassy core of the ASD compact, the hydrated compact, the gel-phase, and phase-separated domains. In this work, SIM-FRAP directly accesses the spatial diffusivity across this entire dissolution front in a single experiment. SIM-FRAP operates by using periodically structured illumination for photobleaching followed by spatial Fourier transformation, recentering peaks from 2D diffraction patterns, and inverse Fourier transformation to produce modulation-dependent amplitude maps. Pixel-wise fits to exponential decay functions recovered a unique diffusion coefficient at each pixel across the entire field of view (up to ∼1 million diffusion coefficients per experiment). Application of SIM-FRAP revealed both smoothly varying diffusivity across the compact and the gel phases and a discontinuous change to domains exhibiting uniform diffusivity, consistent with phase separation. Furthermore, the experimental simplicity of the SIM-FRAP approach supports its adoption in a broader scope of measurements.

The paper propounds the dominating sequential hyper geometric elementary functions, which extends the elementary functions from their sequential and dominating sequential functions to the newly introduced functions using their hyper geometric function representation. Thus six types of new functions namely dominating sequential hyper geometric trigonometric functions, dominating sequential hyper geometric inverse trigonometric functions, dominating sequential hyper geometric hyperbolic functions, dominating sequential hyper geometric inverse hyperbolic functions, dominating sequential hyper geometric exponential functions and dominating sequential hyper geometric logarithmic functions have been introduced corresponding to each standard type of elementary functions. Such functions will play an important role in expressing no elementary integral functions and will explore the domains of functions to a new height.