Expansion Of Function Research Articles

The profile of soliton molecules for integrable complex coupled Kuralay equations

Abstract This study focuses on mathematically exploring the Kuralay equation, which is applicable in diverse fields such as nonlinear optics, optical fibers, and ferromagnetic materials. This study aims to investigate various soliton solutions and analyze the integrable motion of the induced space curves. This study employs traveling wave transformation, converting the partial differential equation (PDE) into an ordinary differential equation (ODE). Soliton solutions are derived utilizing both the generalized Jacobi elliptic function expansion (JEFE) method and novel extended direct algebraic (EDA) methods. The outcomes encompass a diverse range of soliton solutions, including double periodic waves, shock wave solutions, kink-shaped soliton solutions, solitary waves, bell-shaped solitons, and periodic wave solutions, obtained using Mathematica. In contrast, the EDA method produces dark, bright, singular, combined dark-bright solitons, dark-singular combined solitons, solitary wave solutions, etc. Visual representation of these soliton solutions is accomplished through 3D, 2D, and contour graphics, with a meticulous selection of parametric values. The graphical presentation underscores the influence of the parameters on the soliton propagation.

Bifurcation and multi-stability analysis of microwave engineering systems: Insights from the Burger–Fisher equation

The present article depicts the research being done on the microwave effect realized by the often-used Burger-Fisher equation. A particular view is on the emergence of multi-stability and the bifurcations associated with microwave engineering systems. A novel rational, trigonometric, and hyperbolic form of the traveling waves is furnished by the resolution of the non-linear issue with the aid of the advanced exp (−Ψ(η))-expansion function parameterization. Firstly, we will solve the exact form of the Burger-Fisher equation, which clarifies the behavior of the equation in different conditions. Subsequently, bifurcation analysis techniques will be employed to study the nuanced relationship between the system parameters and the emergence of multistability phenomena. Through our results, we exposed the complicated essential features of microwave physics and established crucial parameters that determine a system’s behavior. Next, we cover control principle issues and practical applications in microwave engineering problems. This model accommodates the essential features of multi-stable dynamic systems and provides an important framework for creating microwave devices and circuits.The main aim of this research work is to analyze the phenomenon of multi-stability and bifurcation in microwave engineering systems by applying Burger-Fisher equation. The study intends to obtain new solutions to the PDEs through the application of a new method, the exp (−Ψ(η))-expansion function method that uses rational, trigonometric, and hyperbolic traveling wave solutions. Existing research of the Burger-Fisher equation is not explicit and by solving the exact form the research aims at exploring the different conditions under which the equation behaves and studying the delicate interactions between the parameters of the multistable system.

Globality of the DPW construction for Smyth potentials in the case of SU1,1

We construct harmonic maps into SU1,1/U1 starting from Smyth potentials ξ, by the DPW method. In this method, harmonic maps are obtained from the Iwasawa factorization of a solution L of L−1dL=ξ. However, the Iwasawa factorization in the case of a noncompact group is not always global. We show that L can be expressed in terms of Bessel functions and from the asymptotic expansion of Bessel functions we solve a Riemann-Hilbert problem to give a global Iwasawa factorization. In this way we give a more direct proof of the globality of our solution than in the work of Dorfmeister-Guest-Rossman [5], while avoiding the general isomonodromy theory used by Guest-Its-Lin [11], [12].

Unraveling a growth-promoting potential for plants: Genome-wide identification and expression state of the TCP gene family in Juglans mandshurica

The TCP gene family stands as a pivotal factor in regulating plant growth, development, and resilience to abiotic stress. Despite extensive research and identification of TCP genes across diverse plant species, the intricate functionality and evolutionary expansion of TCP genes within Juglans mandshurica remain relatively uncharted territories, necessitating thorough investigation. In this work, 35 JmTCP genes belonging to two distinct subfamilies were identified in the genome of J. mandshurica, which were unevenly distributed on 13 chromosomes. To gain insights into structural characteristics, a comprehensive analysis encompassing gene structure was conducted, motif composition, and conserved domain examination. Furthermore, cis-acting element and protein interaction network analyses were leveraged to elucidate potential biological functions associated with these genes. Transcriptome data unveiled that JmTCP12 and JmTCP29 are essential for the development of walnut exocarps, embryos, male and female flowers. Furthermore, the results of the genetic transformation experiments demonstrated that JmTCP31 possesses the capability to significantly promote leaf development and expedite the flowering cycle. Collectively, this study offers novel insights into the molecular mechanisms underlying the TCP gene family's contributions to growth and development in J. mandshurica, enriching understanding of this essential gene family in plants and shedding light on potential applications in agricultural biotechnology.

Efficient and Accurate Force Replay in Cosmological-baryonic Simulations

We construct time-evolving gravitational potential models for a Milky Way–mass galaxy from the FIRE-2 suite of cosmological-baryonic simulations using basis function expansions. These models capture the angular variation with spherical harmonics for the halo and azimuthal harmonics for the disk, and the radial or meridional plane variation with splines. We fit low-order expansions (four angular/harmonic terms) to the galaxy’s potential for each snapshot, spaced roughly 25 Myr apart, over the last 4 Gyr of its evolution, then extract the forces at discrete times and interpolate them between adjacent snapshots for forward orbit integration. Our method reconstructs the forces felt by simulation particles with high fidelity, with 95% of both stars and dark matter, outside of self-gravitating subhalos, exhibiting errors ≤4% in both the disk and the halo. Imposing symmetry on the model systematically increases these errors, particularly for disk particles, which show greater sensitivity to imposed symmetries. The majority of orbits recovered using the models exhibit positional errors ≤10% for 2–3 orbital periods, with higher errors for orbits that spend more time near the galactic center. Approximate integrals of motion are retrieved with high accuracy even with a larger potential sampling interval of 200 Myr. After 4 Gyr of integration, 43% and 70% of orbits have total energy and angular momentum errors within 10%, respectively. Consequently, there is higher reliability in orbital shape parameters such as pericenters and apocenters, with errors ∼10% even after multiple orbital periods. These techniques have diverse applications, including studying satellite disruption in cosmological contexts.

Angular fractals in thermal QFT

We show that thermal effective field theory controls the long-distance expansion of the partition function of a d-dimensional QFT, with an insertion of any finite-order spatial isometry. Consequently, the thermal partition function on a sphere displays a fractal-like structure as a function of angular twist, reminiscent of the behavior of a modular form near the real line. As an example application, we find that for CFTs, the effective free energy of even-spin minus odd-spin operators at high temperature is smaller than the usual free energy by a factor of 1/2d. Near certain rational angles, the partition function receives subleading contributions from “Kaluza-Klein vortex defects” in the thermal EFT, which we classify. We illustrate our results with examples in free and holographic theories, and also discuss nonperturbative corrections from worldline instantons.

On the third coefficient in the TYCZ–expansion of the epsilon function of Kähler–Einstein manifolds

In this paper we compute the third coefficient arising from the TYCZ-expansion of the ε-function associated to a Kähler-Einstein metric and discuss the consequences of its vanishing.

Enhanced reversible data hiding using difference expansion and modulus function with selective bit blocks in images

The rapid growth of Information and communication technology not only has positive impacts but also unveils opportunities for data and information security threats. In recent years, many researchers have worked on developing methods to enhance data security, particularly through data hiding techniques aimed at safeguarding communications by concealing their existence. With the same objective in mind, this study introduces a novel method for Reversible Data Hiding (RDH) based on a combination of difference expansion (DE) and a modulus function. Our method enables the embedding of 3-bit data into 2-bit Least Significant Bit (LSB) difference values of pixel pairs formed in rectangular blocks. Based on the experimental results, the payload capacity of our method can reach 0.3953 bpp with a PSNR of 53.5900 dB on common images and 0.5764 bpp with a PSNR of 52.9234 dB on medical images. Our method consistently achieves high payload capacity with good visual quality, and our method surpasses previous approaches in terms of performance, payload capacity, and visual quality.

Stellar Bars Form Dark Matter Counterparts in TNG50

Dark matter (DM) bars that shadow stellar bars have been previously shown to form in idealized simulations of isolated disk galaxies, but have yet to be studied in a fully cosmological context. In this work, we analyze a population of disk galaxies within the TNG50 simulation to determine the characteristics of their dark bars. We estimate bar strength and orientation using both the in-plane Fourier A 2 density moments and the quadrupolar coefficients of the spherical harmonic basis function expansions of the density. We additionally present two novel methods for measuring the bar pattern speed Ω p and rotation axis orientation using these coefficients, and apply them to one sample galaxy located in a TNG50 subbox. Consistent with isolated simulations, DM bars are shorter than their stellar counterparts and are 75% weaker in A 2. DM bars dominate the shape of the inner halo potential and are apparent in the time series of quadrupolar coefficients. In our selected subbox galaxy, the stellar and dark bars remain co-aligned throughout the last 8 Gyr and have identical Ω p . Pattern speed Ω p evolves considerably over the last 8 Gyr, consistent with torques on the bars due to dynamical friction and gas accretion, and is seen to increase following a merger at t lb = 1.5 Gyr. Rather than remaining static in time, the bar rotation axis displays both precession and nutation possibly caused by torques outside the plane of rotation. We find that the shape of the stellar and DM mass distributions are tightly correlated with Ω p .

Neurotrophic factor Neuritin modulates T cell electrical and metabolic state for the balance of tolerance and immunity.

The adaptive T cell response is accompanied by continuous rewiring of the T cell's electric and metabolic state. Ion channels and nutrient transporters integrate bioelectric and biochemical signals from the environment, setting cellular electric and metabolic states. Divergent electric and metabolic states contribute to T cell immunity or tolerance. Here, we report in mice that neuritin (Nrn1) contributes to tolerance development by modulating regulatory and effector T cell function. Nrn1 expression in regulatory T cells promotes its expansion and suppression function, while expression in the T effector cell dampens its inflammatory response. Nrn1 deficiency in mice causes dysregulation of ion channel and nutrient transporter expression in Treg and effector T cells, resulting in divergent metabolic outcomes and impacting autoimmune disease progression and recovery. These findings identify a novel immune function of the neurotrophic factor Nrn1 in regulating the T cell metabolic state in a cell context-dependent manner and modulating the outcome of an immune response.

Neurotrophic factor Neuritin modulates T cell electrical and metabolic state for the balance of tolerance and immunity

The adaptive T cell response is accompanied by continuous rewiring of the T cell’s electric and metabolic state. Ion channels and nutrient transporters integrate bioelectric and biochemical signals from the environment, setting cellular electric and metabolic states. Divergent electric and metabolic states contribute to T cell immunity or tolerance. Here, we report in mice that neuritin (Nrn1) contributes to tolerance development by modulating regulatory and effector T cell function. Nrn1 expression in regulatory T cells promotes its expansion and suppression function, while expression in the T effector cell dampens its inflammatory response. Nrn1 deficiency in mice causes dysregulation of ion channel and nutrient transporter expression in Treg and effector T cells, resulting in divergent metabolic outcomes and impacting autoimmune disease progression and recovery. These findings identify a novel immune function of the neurotrophic factor Nrn1 in regulating the T cell metabolic state in a cell context-dependent manner and modulating the outcome of an immune response.

An analytical method for effective dynamic properties of SH wave in piezoelectric nanocomposites with coated nano-fibers

In this paper, a generalized self-consistent model of nanocoated fiber composite material considering interface effect is established by using the Gurtin-Murdoch surface/interface elasticity theory, elastic wave theory and micromechanics methods, and the propagation of anti-plane shear electroelastic wave in infinite nano-piezoelectric material is analyzed. Based on the wave function expansion method, the displacement potential and electric potential functions of each phase medium in composite materials are described, and the function expressions of displacement, electric potential, stress and electric displacement are obtained. The dynamic effective shear modulus of piezoelectric reinforced composites is obtained by satisfying the boundary conditions of the electroelastic coupling surface/interface theory and the multiple scattering formulas. The effects of coating thickness, coating material parameters, interfacial shear modulus and piezoelectric properties on dynamic effective shear modulus at different incident frequencies are discussed. The results show that the effective shear modulus fluctuates obviously with the increase of frequency. The effective shear modulus increases with the increase of interfacial shear modulus and piezoelectric constant, and is more sensitive to the change of interfacial shear modulus. The effective shear modulus is more affected by the interface effect on the outer surface of the coating than the inner interface, and the effect of interface mechanical properties decreases with the increase of coating stiffness. The larger the parameter of the coating material, the larger the dynamic effective shear modulus and the smaller the influence of the interface effect.

Weak integration allows novel fin shapes and spurs locomotor diversity in reef fishes.

In complex functional systems composed of many traits, selection for specialized function can induce trait evolution by acting directly on individual components within the system, or indirectly through networks of trait integration. However, strong integration can also hinder diversification into regions of trait space that are not aligned with axes of covariation among traits. As a result, non-independence among traits may limit capacity for functional expansion. We explore this dynamic in the evolution of fin shapes in 106 species from 38 families of coral reef fishes, a polyphyletic assemblage that shows exceptional diversity in locomotor function. Despite strong shared developmental pathways and expectations of a strong match between form and function, we find that species that share swimming mode show substantial disparity in fin shape, and preferred swimming mode is a poor predictor of fin shape. The evolution of fin shape is weakly integrated across the four functionally dominant fins in swimming (the pectoral, caudal, dorsal, and anal fins) and integration is weakened as derived swimming modes evolve. The weak integration among fins in the ancestral locomotor condition provides a primary axis of diversification while allowing for substantial off-axis diversification via independent trait responses to selection. However, the evolution of novel locomotor modes coincides with a loss of integrated axes of covariation among fins. Our study highlights the need for additional work on the functional consequences of fin shape in fishes and impact of evolutionary integration on functions other than locomotion.

Ordering Effect of Charge-Charge Repulsion in Doped Antiferromagnetic Lattices: A Coupled Cluster Study.

In quantum chemistry, single-reference Coupled Cluster theory, and its refinements introduced by Bartlett, has become a "gold-standard" predictive method for taking into account electronic correlations in molecules. In this article, we introduce a new formalism based on a Coupled Cluster expansion of the wave function that is suited to describe model periodic systems and apply this methodology to the case of hole-doped antiferromagnetic two-dimensional (2D)-square spin-lattices as a proof of concept. More precisely, we focus our study on 1/5 and 1/7 doping ratios and discuss the possible ordering effect due to large hole-hole repulsion. Starting from one of the equivalent single determinants exhibiting a full spin alternation and the most remote location of the holes as a single reference, the method incorporates some corrections to the traditional Coupled Cluster formalism to take into account the nonadditivity of excitation energies to multiply excited determinants. The amplitudes of the excitations, which are possible on the excited determinants but impossible on the reference, are evaluated perturbatively, while their effect is treated as a dressing in the basic equations. The expansion does not show any sign of divergence of the wave operator. Finally, the probabilities of holes moving toward the first- and second-neighboring sites are reported, which confirms the importance of the hole-hole repulsion and offers a picture of how stripes expand around its central line in the "stripe phases" observed in cuprates.

Ramanujan-Berndt-type integrals of order four and series associated with Jacobi elliptic functions

In this paper, we evaluate in closed forms two families of infinite integrals containing hyperbolic and trigonometric cosine functions in their integrands. We call them Ramanujan-Berndt-type integrals of order four since they initiated the study of similar integrals. We establish explicit evaluations of twelve classes of hyperbolic sums by special values of the Gamma function by two completely different approaches, which extend those sums considered by Xu, Yang, Zhao and the second author previously. We discover the first by refining two results of Ramanujan concerning some q-series. For the second we compare both the Fourier series expansions and the Maclaurin series expansions of a few Jacobi elliptic functions. Furthermore, by contour integrations we convert two families of Ramanujan-Berndt-type integrals of order four to the above hyperbolic sums, all of which can be evaluated in closed forms. We then discover explicit formulas for one of the two families. Moreover, we provide many examples which enable us to formulate a conjectural explicit formula for the other family of the Ramanujan-Berndt-type integrals at the end, and obtain some results on Barnes' multiple zeta function.

Analytical solutions and instability analysis of truncated M-fractional coupled dispersionless equations

Abstract This paper comprehensively investigates the truncated M-fractional coupled dispersionless equations, a nonlinear system of partial differential equations characterized by its M-fractional derivative. The Jacobi elliptic function expansion method is employed to derive analytical solutions for the coupled system. In addition, the modulation instability of the solutions is thoroughly explored, providing a detailed exposition of the mathematical framework governing the system. The analytical solutions are graphically illustrated and analyzed to highlight their physical significance. These findings have significant applications in nonlinear optics, offering new insights into wave propagation and stability within such systems.

ANALYSIS OF OPTIMAL PORTFOLIO ON FINITE AND SMALL-TIME HORIZONS FOR A STOCHASTIC VOLATILITY MODEL WITH MULTIPLE CORRELATED ASSETS

In this paper, we consider the portfolio optimization problem in a financial market where the underlying stochastic volatility model is driven by [Formula: see text]-dimensional Brownian motions. At first, we derive a Hamilton–Jacobi–Bellman equation including the correlations among the standard Brownian motions. We use an approximation method for the optimization of portfolios. With such approximation, the value function is analyzed using the first-order terms of expansion of the utility function in the powers of time to the horizon. The error of this approximation is controlled using the second-order terms of expansion of the utility function. It is also shown that the one-dimensional version of this analysis corresponds to a known result in the literature. We also generate a close-to-optimal portfolio near the time to horizon using the first-order approximation of the utility function. It is shown that the error is controlled by the square of the time to the horizon. Finally, we provide an approximation scheme to the value function for all times and generate a close-to-optimal portfolio.

CTIM-30. NT-I7, A LONG-ACTING INTERLEUKIN-7, PROMOTES ACTIVATION, CYTOTOXIC FUNCTION, AND SELECTIVE CLONOTYPE EXPANSION OF CD8+ T CELLS IN PATIENTS WITH HIGH GRADE GLIOMAS

Abstract Lymphopenia following chemoradiation for high grade gliomas (HGG) is common and is associated with decreased survival. NT-I7 (efineptakin alfa) is a long-acting analog of the lymphocyte pro-survival cytokine, interleukin-7. Our Phase I dose-escalation study of 19 patients with HGG demonstrated early elevations in CD4+ and CD8+ T cells in the first 4 weeks after administration of NT-I7. In this study, we explored the diversity and potential functionality of the NT-I7-expanded T cell population. A subset of 4 subjects with glioblastoma multiforme (GBM) treated at 720 µg/kg of NT-I7 during adjuvant temozolomide in our study (NCT03687957) underwent Cellular Indexing of Transcriptomes and Epitopes by Sequencing (CITE-seq) of peripheral blood. CITE-seq with TCR clonotype sequencing (10x Genomics 5’) permitted simultaneous tracking of the T cell phenotype at the protein level, individual T cell clones, and gene expression dynamics between 4 timepoints: pre-treatment, and post-treatment weeks 1, 2, and 13. Here, we report the results of differential expression analyses between timepoints and patient-specific differences in T cell clonotype expansions. Both CD4+ and CD8+ T cells in our study patients had increased expression of T cell activation markers LTB, CISH, and CD74. CD8+ T cell subsets demonstrated additional elevations in genes important in cytotoxic function (granzymes (GZMA, GZMB) and perforin (PRF1)), MHC Class II expression (HLA-DRA, HLA-DRB1), and AP-1 transcription factor subunits (JUND, JUN, JUNB, FOS, FOSB). After excluding known viral antigen clonotypes, 2 of 4 patients demonstrated TCR clonotype expansion. Notably, nearly all the expanded TCR clonotypes were found within CD8+ T cells, but not CD4+ T cells. NT-I7 promotes activation, cytotoxic function, and selective clonotype expansion of CD8+ T cells in patients with HGG. This, combined with its role in increased CD4+ T cell counts, suggests NT-I7 may be a powerful tool to restore immune function after treatment-associated lymphopenia in HGG.

A note on wavelet packet summation methods

The wavelet summation method is a method to obtain a non-linear approximation with ‘nice properties’ for a given signal. This technique has been shown to be effective in non-parametric regression and other fields, including signal denoising. By utilizing a shrinkage rule on the empirical wavelet packet coefficients, wavelet packet summation methods can be obtained. In this paper, we show that the wavelet packet expansion of any finite energy function converges pointwise almost everywhere under the wavelet packet projection, hard sampling, and soft sampling methods.

Comparative Analysis of Quasi-Linear Kalman-Type Algorithms in Estimating a Markov Sequence with Nonlinearities in the System and Measurement Equations

The so-called Kalman type algorithms (KTA) are considered, among them quasi-linear KTAs introduced as a separate class, the features of which are the Gaussian approximation of the a posteriori probability density function (p.d.f.) at each step and the procedure for processing the current measurement based on the ideology of a linear optimal algorithm. The unified structure of such algorithms and their features are discussed. Two groups are distinguished the quasi-linear KTA: the first is algorithms using Taylor series expansion of the nonlinear functions, and the second is the so-called linear regression KTA. The methods of their designing are considered, and the common features are described. Detailed attention is paid to the following KTAs: the extended Kalman filter (EKF), polynomial filters of the second and third order (PF2 and PF3), as representatives of the first group, and the Unscented and Cubature Kalman filters (UKF and CKF), as representatives the second one. Their comparative analysis is carried out using the estimation problem of a scalar Markov sequence in the presence of nonlinearities in the shaping filter and in the measurement equations. For all the studied algorithms, the formulas are given in a form convenient for comparison. Based on these formulas, possible causes of a decrease in accuracy and a violation of the consistency properties are identified. Using the previously proposed procedure based on the method of statistical tests, predictive simulation was carried out, which made it possible to confirm the conclusions obtained previously on the basis of an analysis of the formulas for the algorithms being compared. The simulation also allowed to compare the computational complexity of the compared algorithms. The results of the study may be useful to developers involved in the processing of measurement information when choosing a filtering algorithm for solving specific practical estimation problems.