Expansion Of Function Research Articles

Renal Tubular Epithelial Cell-Derived IL-7 Drives Expansion and Protective Effects of Double-Negative T Cells in Acute Kidney Injury

ABSTRACT Background Previous studies have demonstrated that double-negative (DN) αβ T cells play an important role in immune responses during ischemic acute kidney injury (AKI). Here, we investigate the role of γ-chain cytokines in driving DN T cell proliferation in steady state and AKI, focusing on IL-2, IL-7, and IL-15. Methods We assessed DN T cell proliferation in vitro in response to IL-2, IL-7, and IL-15, with co-culture experiments using renal tubular epithelial cells (RTECs) and IL-7 blockade. In vivo, wild-type and IL-7r knockout mice were studied to evaluate the impact of IL-7 on DN T cell expansion and kidney function during AKI. Human RTECs confirmed the relevance of these findings. Results All three cytokines promoted DN T cell proliferation in vitro, with IL-7 inducing the most robust expansion. Co-culture experiments showed RTECs as a key IL-7 source, and blockade reduced DN T cell expansion. In vivo, IL-7 complexes administered to wild-type mice increased DN T cells and selectively expanded the PD-1+ subset. IL-7 deficiency worsened renal outcomes during AKI. Human RTECs activated peripheral human DN T cells in vitro. Conclusion These results establish IL-7 as pivotal for DN T cell expansion and highlight RTECs’ role in DN T cell homeostasis.

A mechanistic, functional, and clinical perspective on targeting CD70 in cancer.

The oncoimmunology research has witnessed notable advancements in recent years. Reshaping the tumor microenvironment (TME) approach is an effective method to improve antitumor immune response. The T cell-mediated antitumor response is crucial for favorable therapeutic outcomes in several cancers. The United States Food and Drug Administration (FDA) has approved immune checkpoint inhibitors (ICIs) for targeting the immune checkpoint proteins (ICPs) expressed in various hematological and solid malignancies. The ICPs are T cell co-inhibitory molecules that block T cell activation and, thus, antitumor response. Currently, most of the FDA-approved ICIs are antagonistic antibodies of programmed death-ligand 1 (PD-L1), programmed cell death protein 1 (PD-1), and cytotoxic T-lymphocyte-associated protein 4 (CTLA-4). In contrast to ICPs, the T cell costimulatory molecules are required for T cell activation, expansion, and effector function. However, the abrupt expression of these costimulatory molecules in tumors presents a concern for T cell-mediated antitumor response. One of the T cell costimulatory molecules, the cluster of differentiation 70 (CD70), has emerged as a druggable target in various hematological and solid malignancies due to its role in T cell effector function and immune evasion. The present review describes the expression of CD70, factors affecting the CD70 expression, the physiological and clinical relevance of CD70, and the current approaches to target CD70 in hematological and solid malignancies.

Higher Harmonic Generation Arising from the Bessel Function Expansions of the Carrier-Envelope-Phase Driven by the Femtosecond Optical Kerr Effect

Higher Harmonic Generation Arising from the Bessel Function Expansions of the Carrier-Envelope-Phase Driven by the Femtosecond Optical Kerr Effect

On a continued fraction expansion of the special function $$e^{x}E_{1}(x)$$ and an explicit expression of the continued fraction convergents

On a continued fraction expansion of the special function $$e^{x}E_{1}(x)$$ and an explicit expression of the continued fraction convergents

Niche-derived Semaphorin 4A safeguards functional identity of myeloid-biased hematopoietic stem cells.

Somatic stem cell pools comprise diverse, highly specialized subsets whose individual contribution is critical for the overall regenerative function. In the bone marrow, myeloid-biased hematopoietic stem cells (myHSCs) are indispensable for replenishment of myeloid cells and platelets during inflammatory response but, at the same time, become irreversibly damaged during inflammation and aging. Here we identify an extrinsic factor, semaphorin 4A (Sema4A), which non-cell-autonomously confers myHSC resilience to inflammatory stress. We show that, in the absence of Sema4A, myHSC inflammatory hyper-responsiveness in young mice drives excessive myHSC expansion, myeloid bias and profound loss of regenerative function with age. Mechanistically, Sema4A is mainly produced by neutrophils, signals via a cell surface receptor, plexin D1, and safeguards the myHSC epigenetic state. Our study shows that, by selectively protecting a distinct stem cell subset, an extrinsic factor preserves functional diversity of somatic stem cell pool throughout organismal lifespan.

Numerical differentiation of fractional order derivatives based on inverse source problems of hyperbolic equations

In this paper, we mainly study the numerical differentiation problem of computing the fractional order derivatives from noise data of a single variable function. Firstly, the numerical differentiation problem is reformulated into an inverse source problem of first order hyperbolic equation, and the corresponding solvability and the conditional stability are provided under suitable conditions. Then, four regularization methods are proposed to reconstruct the unknown source of hyperbolic equation which is the numerical derivative, and they are implemented by utilizing the finite dimensional expansion of source function and the superposition principle of hyperbolic equation. Finally, Numerical experiments are presented to show effectiveness of the proposed methods. It can be conclude that the proposed methods are very effective for small noise levels, and they are simpler and easier to be implemented than the previous PDEs-based numerical differentiation method based on direct and inverse problems of parabolic equations.

The effects of skewness and kurtosis on production and hedging decisions: a Gram-Charlier expansion approach

In this study, we propose a Gram-Charlier expansion approach to investigate the impact of skewness and kurtosis on production and hedging decisions. Consistent with the existing literature, we find that skewness and kurtosis do not affect decisions regarding optimal production; however, they significantly influence optimal hedging decisions. We observe that positive skewness with platykurtic spot prices or negative skewness with leptokurtic spot prices often leads to over-hedging when the initial forward contract price exceeds its expected value. Conversely, under-hedging is expected when the initial forward contract price falls below its expected value. In other conditions, skewness can either promote or impede speculative future trading. Using the Gram-Charlier expansion of the spot price density function, we find that optimal future positions depend on forward prices, the hedgers’ risk preference, and the spot price distribution. Simulations validate our findings on the impact of skewness and kurtosis on future hedging. Finally, we analyze of a cotton storage and forward contracting dataset to illustrate the application of our methodology and support our theoretical results.

On the Martínez–Kaabar Fractal–Fractional Reduced Pukhov Differential Transformation and Its Applications

This paper addresses the extension of the Martinez–Kaabar fractal–fractional calculus (simply expressed as MK calculus) to the context of reduced differential transformation, with applications to the solution of some partial differential equations. Since this differential transformation is derived from the Taylor series expansion of real-valued functions of several variables, it is necessary to develop this theory in the context of such functions. Firstly, classical elements of the analysis of functions of several real variables are introduced, such as the concept of partial derivative and Clairaut’s theorem, in terms of the MK partial α,γ-derivative. Next, we establish the fractal–fractional (FrFr) Taylor formula with Lagrange residue and discuss a sufficient condition for a function of class Cα,γ∞ on an open and bounded set D⊂R2 to be expanded into a convergent infinite series, the so-called FrFr Taylor series. The theoretical study is completed by defining the FrFr reduced differential transformation and establishing its fundamental properties, which will allow the construction of the FrFr reduced Pukhov differential transformation method (FrFrRPDTM). Based on the previous results, this new technique is applied to solve interesting non-integer order linear and non-linear partial differential equations that incorporate the fractal effect. Finally, the results show that the FrFrRPDTM represents a simple instrument that provides a direct, efficient, and effective solution to problems involving this class of partial differential equations.

The spectral ζ-function for quasi-regular Sturm–Liouville operators

In this work, we analyze the spectral ζ-function associated with the self-adjoint extensions, TA,B, of quasi-regular Sturm–Liouville operators that are bounded from below. By utilizing the Green’s function formalism, we find the characteristic function, which implicitly provides the eigenvalues associated with a given self-adjoint extension TA,B. The characteristic function is then employed to construct a contour integral representation for the spectral ζ-function of TA,B. By assuming a general form for the asymptotic expansion of the characteristic function, we describe the analytic continuation of the ζ-function to a larger region of the complex plane. We also present a method for computing the value of the spectral ζ-function of TA,B at all positive integers. We provide two examples to illustrate the methods developed in the paper: the generalized Bessel and Legendre operators. We show that in the case of the generalized Bessel operator, the spectral ζ-function develops a branch point at the origin, while in the case of the Legendre operator it presents, more remarkably, branch points at every nonpositive integer value of s.

Dynamic Stress Analysis of a Strip Plate with Elliptical Holes Subjected to Incident Shear Horizontal Waves

The dynamic stress analysis of a strip plate with elliptical holes under the action of an incident SH wave was performed using a complex function method and a successive mirror method. Firstly, a complex plane coordinate system of elliptic holes was established by using the complex variable function method and integral transformation method. The elliptic hole wave field and stress were established using the wave function expansion method. Then, the relation between the argument angle of any point on the edge of the ellipse hole and the angle between the vertical line and the coordinate axis was established. Using boundary conditions to solve the unknown coefficients in the equation, finally, the integral equation was simplified to a linear equation by means of the effective truncation method, and the steady-state response of dynamic stress under different parameters was analyzed. In addition, by comparing the finite element solution with the numerical solution, the accuracy of the results was effectively verified. The results show that the studied geometric model can provide solid theoretical support for the inspection of plate and shell structures, which is of great significance in practical engineering.

Exploration of Soliton Solutions for the Kaup–Newell Model Using Two Integration Schemes in Mathematical Physics

ABSTRACTThis research deals with the Kaup–Newell model, a class of nonlinear Schrödinger equations with important applications in plasma physics and nonlinear optics. Soliton solutions are essential for analyzing nonlinear wave behaviors in different physical systems, and the Kaup–Newell model is also significant in this context. The model's ability to represent subpicosecond pulses makes it a significant tool for the research of nonlinear optics and plasma physics. Overall, the Kaup–Newell model is an important research domain in these areas, with ongoing efforts focused on understanding its various solutions and potential applications. A new version of the generalized exponential rational function method and ‐expansion function method are utilized to discover diverse soliton solutions. The generalized exponential rational function method facilitates the generation of multiple solution types, including singular, shock, singular periodic, exponential, combo trigonometric, and hyperbolic solutions in mixed forms. Thanks to ‐expansion function method, we obtain trigonometric, hyperbolic, and rational solutions. The modulation instability of the proposed model is examined, with numerical simulations complementing the analytical results to provide a better understanding of the solutions' dynamic behavior. These results offer a foundation for future research, making the solutions effective, manageable, and reliable for tackling complex nonlinear problems. The methodologies used in this study are robust, influential, and practicable for diverse nonlinear partial differential equations; to our knowledge, for this equation, these methods of investigation have not been explored before. The accuracy of each solution has been verified using the Maple software program.

Static/quasi-static thermomechanical analysis of 3D thin-walled beam structures based on CUF considering radiation dissipation condition

Thin-walled structures are widely applied in spacecraft as structural components due to their lightweight property. Extreme thermal environment in space may cause highly unfavorable thermal responses in thin-walled structures. Therefore, accurately predicting the thermal-coupling responses of thin-walled structures is of great engineering significance. In order to avoid the disadvantages of 3D finite element model caused by an abundance of computational degrees of freedom, the present paper proposes a thermo-mechanical coupling model based on Carrera Unified Formulation (CUF) for the static and quasi-static thermal response of space thin-walled structures. The longitudinal direction of the structures is discretized by one-dimensional linear and cubic finite elements (B2 and B4), whereas Lagrange expansion functions are used for the description of temperature fields and displacement fields within the cross-section. The governing differential equations of thermal-coupling problems are derived in a unified form according to the principle of virtual displacement and the weighted residual method. In order to demonstrate the accuracy of the numerical results, a convergence analysis is conducted on both beam elements and expansion forms. The results reveal that piece-wise quadratic beam theories approximated with B4 elements are accurate enough for the prediction of thermally-induced displacements, while the high-order cubic cross-sectional expansion is required for the description of stresses. Finally, influences of factors like angle of solar radiation, local shadows, emissivity and thermal conductivity on static and quasi-static displacement distributions are discussed. This research may pave a high-efficiency computational method for solving static/quasi-static thermally induced response of space thin-walled structures.

New inequalities for permanents and hafnians and some generalizations

We show new upper bounds for permanents and hafnians, which are particularly useful for complex matrices. Multidimensional permanents and hyperhafnians are considered as well. The permanental bounds improve on a Hadamard type inequality of Carlen et al. [An inequality of Hadamard type for permanents. Methods Appl Anal. 2006;13(1):1–17. doi: 10.4310/MAA.2006.v13.n1.a1] and Cobos et al. [Multilinear forms of Hilbert type and some other distinguished forms. Integral Equ Oper Theory. 2006;56(1):57–70. doi: 10.1007/s00020-005-1412-2]. Our proofs are based on a more general inequality, which can be applied to generalized Laplace type expansions of the matrix functions under consideration. As application, we show new bounds on the characteristic function of a random diagonal sum. A numerical comparison shows the performance of some of our permanental bounds.

The theory of Barlow packings: Basic properties and cohesive energies from exact lattice summations within the sticky hard-sphere model.

The theory of periodic Barlow multi-lattices (X1X2…XN)∞ with Xi ∈ {A, B, C} and Xi ≠ Xi+1 of stacked two-dimensional hexagonal close-packed layers is presented and used to derive exact lattice sum expressions in terms of fast converging Bessel function expansions for inverse power potentials. We describe in detail the mathematical properties of Barlow sphere packings and demonstrate that only two basic lattice sums are required to describe all periodic packings. For the sticky hard-sphere model with an attractive inverse power law potential, we find a linear correlation between the cohesive energies of different Barlow packings and the face-centered cubic packing fraction. We introduce an efficient algorithm for enumerating the unique periodic Barlow sequences for any given period N. The theory and lattice sums introduced here pave the way for the future treatment of Barlow multi-lattices.

Enhancing the stability and performance of Ni-rich cathode materials through Ta doping: a combined theoretical and experimental study.

As the demand for high-energy batteries to power electric vehicles continues to grow, Ni-rich cathode materials have emerged as promising candidates due to their high capacity. However, these materials are prone to rapid degradation under increased voltages, posing significant challenges for their long-term stability and safety. In this study, we investigate the effects of tantalum (Ta) doping on the performance and stability of LiNi0.80Mn0.1Co0.1O2 (NMC811) cathode materials. Using a combined theoretical and experimental approach, we employ density functional theory (DFT) and cluster expansion models to analyze the electronic structure and oxygen vacancy formation enthalpy in Ta-doped NMC811. Experimental validation is conducted using cycling and gas measurements via on-line electrochemical mass spectrometry (OEMS) on in-house synthesized cathode active materials. Both theoretical and experimental approaches show an improvement in oxygen binding due to tantalum doping, with the DFT results highlighting the impact of Ni4+ concentration on the proximity of the vacancy. Our results suggest that Ta doping inhibits the formation of oxygen vacancy-induced side phases, reducing cracking and enhancing the longevity and safety of Ni-rich cathodes.

Active invisible metamaterial of elastic waves with double targets in a thick plate

Wave invisibility has received increasing attention due to its great theoretical value and application to aerospace, military and other fields. In this work, the invisible flexural cloak for double hole targets in an elastic thick plate is proposed and proportional integral derivative (PID) active control is applied. Based on Mindlin thick plate theory and wave function expansion method, the wave equation for the thick plate is derived and scattering mode coefficients are obtained. The influences of structural and material parameters on dynamic stress concentration, scattering amplitude and scattering cross section (SCS) for double targets are investigated. With the consideration of specific hole targets, the cloaking configuration includes cloaks 1 and 2 and consists of periodically arranged piezoelectric (PZT) patches. Every PZT patch is attached to the active circuit with PID control function. The theoretical and experimental results illustrate that the cloak can achieve an invisible function for double targets within multiple frequency regions. On the other hand, the cloak can reduce the dynamic stress concentration, scattering amplitude and SCS of the thick plate. Different from the original structure without control, the effective frequency range of the PID active cloak can be widely extended.

Heat Kernel estimations for the simple random walk

In this paper, we investigate the convergence rate of the heat kernel defined on locally finite graphs in the one-dimensional simple random walk case. The heat kernel represents the transition density and can be estimated by approximating the factorial. Through asymptotic expansions of certain functions and Taylor expansions of some terms, upper and lower bounds of the heat kernel can be derived.

Taylor Formula and Its Application Problem

Taylor formula and Taylor series are particularly important in mathematical analysis teaching and are tools for numerical calculation. Their applications are very extensive, including calculating limits, indefinite integrals, definite integrals, high - order derivative values, determining the series are convergent or divergent, proving inequalities, approximate treatment, solving differential equations, and proving identities. This paper mainly introduces the definition of Taylor’s formula, the formula along with related proof, and the application of approximate calculation, indefinite integral, inequality proof. It was developed in the study of function expansions to provide a fine description of how a function behaves near a certain point. The significance of Taylor’s formula is that it provides a way to expand a function into an infinite series, so that the properties of a function near a certain point can be studied. It can increase the quality of teaching as well as broaden the scholastic problem - solving ideas and improving their ability to solve problems.

LMC Calls, Milky Way Halo Answers: Disentangling the Effects of the MW–LMC Interaction on Stellar Stream Populations

The infall of the LMC into the Milky Way (MW) has dynamical implications throughout the MW’s dark matter halo. We study the impact of this merger on the statistical properties of populations of simulated stellar streams. Specifically, we investigate the radial and on-sky angular dependence of stream perturbations caused by the direct effect of stream–LMC interactions and/or the response of the MW dark matter halo. We use a time-evolving MW–LMC simulation described by basis function expansions to simulate streams. We quantify the degree of perturbation using a set of stream property statistics including the misalignment of proper motions with the stream track. In the outer halo, direct stream–LMC interactions produce a statistically significant effect, boosting the fraction of misaligned proper motions by ∼25% relative to the model with no LMC. Moreover, there is on-sky angular dependence of stream perturbations: the highest fractions of perturbed streams coincide with the same on-sky quadrant as the present-day LMC location. In the inner halo, the MW halo dipole response primarily drives stream perturbations, but it remains uncertain whether this is a detectable signature distinct from the LMC’s influence. For the fiducial MW–LMC model, we find agreement between the predicted fraction of streams with significantly misaligned proper motions, ϑ¯>10° , and Dark Energy Survey data. Finally, we predict this fraction for the Rubin Observatory Legacy Survey of Space and Time (LSST) footprint. Using LSST data will improve our constraints on dark matter models and LMC properties, as it is sensitive to both.

Resonant and Non-Resonant Impurity States Related to GaAs/AlGaAs Quantum Well Sub-Bands.

The energy positions and wave function shapes of the ground and excited states of impurities, including resonance states, are studied using the expansion of the impurity wave function in basis functions. The structures under study are rectangular GaAs/AlGaAs quantum wells with four different widths. In all cases, the impurity binding energy (relative to the corresponding sub-band) has a maximum at or near the center of the quantum well, decreases as the heterointerface is approached, and apparently has a limit of 0 if the impurity moves deeper into the barrier. If the impurity moves away from the center of the quantum well, then the "center of mass" of the electron charge of non-resonant impurity states follows the impurity atom, and the "center of mass" of the electron charge of the resonant impurity states moves away from it. The effect is more pronounced for the ground and first resonance states for wider quantum wells, and the shifts reach a maximum when the impurity atom is positioned near the midpoint of the path between the quantum well center and the heterointerface.