Expansion Of Function Research Articles

Batch Normalization Is Blind to the First and Second Derivatives of the Loss

We prove that when we do the Taylor series expansion of the loss function, the BN operation will block the influence of the first-order term and most influence of the second-order term of the loss. We also find that such a problem is caused by the standardization phase of the BN operation. We believe that proving the blocking of certain loss terms provides an analytic perspective for potential detects of a deep model with BN operations, although the blocking problem is not fully equivalent to significant damages in all tasks on benchmark datasets. Experiments show that the BN operation significantly affects feature representations in specific tasks.

A detailed analysis of the improved modified Korteweg-de Vries equation via the Jacobi elliptic function expansion method and the application of truncated M-fractional derivatives

Using the Jacobi elliptic function expansion method, which is improved by the novel use of truncated M-fractional derivatives, we thoroughly analyze the improved modified Korteweg-de Vries problem in this paper. Not only does this method provide new insight into the improved modified Korteweg-de Vries Equation, but it also represents a giant leap forward for nonlinear differential equations. Periodic, solitary, and trigonometric waves are among the answers found by us; all of them have important consequences for mathematical physics and engineering.The MATLAB-generated visual representations of our results are crucial because they provide aconcrete shape to the once intangible mathematical ideas. In addition to showing the solutions, these images highlight the waves' dynamic behaviors and stability under various conditions, providing a better understanding of the physical processes that the improved modified Korteweg-de Vries equation attempts to explain. The graphic representations in this study demonstrate how the equation can be used to simulate complicated systems in many scientific disciplines. The relevance of our findings goes beyond only theoretical studies. Our study lays the groundwork for more accurate predictive models in fields including quantum physics, optical fibers, and fluid dynamics by giving exact and concrete solutions to the improved modified Korteweg-de Vries equation. The combination of the Jacobi Elliptic Function Expansion Method with truncated M-fractional derivatives provides a robust framework for solving comparable complicated differential equations, which in turn opens up new research and development opportunities. Overall, this research both deepens our understanding of the Improved Modified Korteweg-de Vries equation and provides more evidence that theoretical mathematics can be useful in solving practical problems. Mathematical modeling and computational visualization have the potential to make substantial contributions to engineering and the sciences, and our results support a multidisciplinary approach to study.

Abstract 3849: Frontline ibrutinib-based therapy enhances CART cell functions in patients with CLL: Analysis of the phase 3 randomized clinical trial ECOG-ACRIN E1912

Abstract Introduction: Despite the remarkable activity of CD19-directed chimeric antigen receptor T cell therapy (CART19), durable remissions remain low, especially in chronic lymphocytic leukemia (CLL). Ibrutinib is an oral irreversible inhibitor of Bruton’s tyrosine kinase and is a first line therapy for CLL. Preclinical and early clinical data indicate that ibrutinib plus CART19 may be synergistic through inhibition of IL2-inducible T cell kinase. To systematically study the effects of prior ibrutinib treatment on subsequent CART functions, we utilized blood samples from the pivotal clinical trial E1912 (NCT02048813). E1912 was a phase 3 randomized trial comparing treatment with ibrutinib/rituximab (IR) to fludarabine/cyclophosphamide/rituximab (FCR) in previously untreated patients with CLL, which led to the FDA approval of ibrutinib as a first-line therapy in CLL. Methods: We evaluated the ex vivo expansion and effector functions of T cells and CART19 generated from patients (n=12) with CLL progression following treatment with IR or FCR. We generated CART19 from longitudinal samples obtained at baseline (pretreatment), 6 months post-treatment, 12 months post-treatment, and disease progression. Isolated T cells were lentivirally transduced to express CD28- or 41BB-costimulated CAR19. To assess antigen specific killing and proliferation, untransduced T cells or CART19 were co-cultured at a 1:1 ratio with the CD19+ cell line, JeKo-1, as a surrogate for CLL cells. Results: Ex vivo T cell expansion increased from an average of 1.5-fold at baseline to 6.7-fold at 6 months, 11.6-fold at 12 months, and 16.9-fold at progression, following ibrutinib-based therapy (p = 0.02, 0.04, and 0.04, respectively). Improved T cell expansion was independent of disease burden (p = 0.89, 0.73, and 0.54 for expansion vs B cell count at 6 months, 12 months, and progression). T cell expansion significantly worsened following treatment with FCR-based therapy compared to ibrutinib-based therapy (0.6- vs 11.6-fold at 12 months and 0.9- vs 16.9-fold at progression; p = 0.031 and 0.039, respectively). Starting at 6 months post-IR, CART19 demonstrated improved antitumor activity and antigen-specific proliferation against JeKo-1. There was no significant difference in the expansion of 41BB- vs CD28-costimulated CART19 following ibrutinib treatment. However, 41BB-CART19 showed enhanced antigen-specific proliferation upon stimulation with JeKo-1 (p = 0.008, 0.02, and 0.02 at 6 months, 12 months, and progression). Conclusion: Our results indicate significant improvement in T cell expansion and CART19 cell functions in patients with CLL following frontline ibrutinib-based therapy, and worsening T cell functions after FCR treatment. Improvement in T cell functions is independent of malignant B cell eradication and is more significant in 41BB-costimulated CART19. Citation Format: Truc Ngoc Huynh, Victoria Wang, Tait Shanafelt, Elizabeth L. Siegler, Carli M. Stewart, Kun Yun, Long K. Mai, Olivia Sirpilla, James H. Girsch, Claudia Manriquez-Roman, Jennifer M. Feigin, Makena Rodriguez, Brooke L. Kimball, Hong Xia, Reona L. Sakemura, Ismail Can, Omar L. Gutierrez-Ruiz, Ekene J. Ogbodo, Erin E. Tapper, Lionel A. Fonkoua, Mehrdad T. Hefazi, Michael W. Ruff, Sameer Parikh, Neil E. Kay, Saad J. Kenderian. Frontline ibrutinib-based therapy enhances CART cell functions in patients with CLL: Analysis of the phase 3 randomized clinical trial ECOG-ACRIN E1912 [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 3849.

Revisiting the bound states of a confined delta potential

The stationary states of a particle under the influence of a delta potential confined by impenetrable walls are investigated using the method of expansion in orthogonal functions. The eigenfunctions of the time-independent Schrödinger equation are expressed in closed form by using a pair of closed-form expressions for series available in the literature. The analysis encompasses both attractive and repulsive potentials with arbitrary couplings. Confinement significantly impacts the quantum states and introduces a scenario of double degeneracy including the ground state. Analysis extends to discuss the transition to unconfinement. This research holds particular significance for educators and students engaged in mathematical methods applied to physics and quantum mechanics within undergraduate courses, offering valuable insights into the complex relationships among profiles of potentials, boundary conditions, and the resulting quantum phenomena.

Numerical stability of the branched continued fraction expansion of Horn's hypergeometric function $H_4$

In this paper, we consider some numerical aspects of branched continued fractions as special families of functions to represent and expand analytical functions of several complex variables, including generalizations of hypergeometric functions. The backward recurrence algorithm is one of the basic tools of computation approximants of branched continued fractions. Like most recursive processes, it is susceptible to error growth. Each cycle of the recursive process not only generates its own rounding errors but also inherits the rounding errors committed in all the previous cycles. On the other hand, in general, branched continued fractions are a non-linear object of study (the sum of two fractional-linear mappings is not always a fractional-linear mapping). In this work, we are dealing with a confluent branched continued fraction, which is a continued fraction in its form. The essential difference here is that the approximants of the continued fraction are the so-called figure approximants of the branched continued fraction. An estimate of the relative rounding error, produced by the backward recurrence algorithm in calculating an nth approximant of the branched continued fraction expansion of Horn’s hypergeometric function H4, is established. The derivation uses the methods of the theory of branched continued fractions, which are essential in developing convergence criteria. The numerical examples illustrate the numerical stability of the backward recurrence algorithm.

Advances in Wearable Multifunctional Devices Based on Human‐Body Energy Harvesting

AbstractWearable electronics with multi‐functionalities are widely utilized in various domains, including everyday living, healthcare, military training, and sports. Advances in flexible electronic technology, new materials, artificial intelligence technology, and sensor technology have accelerated the rapid development of smart wearable devices toward multifunctional and highly integrated trends. The energy supply technology based on the human‐body energy harvesting method endows wearable, multifunctional electronic devices with sustainable, renewable, and self‐powered characteristics, which proposes a solution strategy for the function expansion and energy supply of wearable devices. Herein, this paper discusses recent research on various methods of harvesting human body energy and wearing parts respectively, focusing on the new materials, structures, and processes involved in the representative studies, as well as the impact on energy harvesting and output, and functional applications. Furthermore, the challenges and obstacles faced in the creation of wearable multifunctional devices based on human self‐sufficiency and propose solution strategies to propel them in order to advance the creation of the next wave of intelligent wearable technology are also discussed.

Phase distribution and circular dichroism switchable terahertz chiral metasurface.

Chiral metasurfaces have many applications in the terahertz (THz) band, but they still lack modulation flexibility and functionality expansion. This paper presents a terahertz chiral metasurface with switchable phase distribution and switchable circular dichroism (CD). The metasurface unit consists of a metallic inner ring embedded in vanadium oxide and a vanadium oxide outer ring, state switching by thermal control of vanadium oxide and a change in the frequency of the incident wave. Based on the switchable phase distribution, we designed a focusing vortex beam generator with adjustable focal lengths through simulation. Based on the switching CD capability, we simulate its mode switching in near-field imaging using numerical simulation, and innovatively propose an optical encryption method. Utilizing the chiral property, we also designed dual-channel switchable holographic imaging in the same frequency band, which combined with the state change of VO2 can realize a total of 4 holograms switching. Our proposed metasurface is expected to provide new ideas for the study of optical encryption and wavefront modulation of dynamics.

On the convergence of series of fractional Hasse derivative bases in Fréchet spaces

This paper introduces a generalization of the Hasse derivative in the sense of the complex conformable derivative. The definition coincides with the classical version of the Hasse derivative of order . Accordingly, a new base, named complex conformable Hasse derivative bases (CCHDBs), is defined. We investigate the existence of expansions of analytic functions in a series of CCHDBs in Fréchet space on closed and open disks, open regions surrounding closed disks, for all entire functions and at the origin. Moreover, an upper bound for the order and type of the CCHDBs is obtained and proved to be attainable. The ‐property of CCHDBs is also discussed. Our results improve and extend the analog results in the complex analysis related to the classical complex derivative of a base of polynomials (BPs). The obtained results clarify several implications for the CCHDBs of special functions such as Euler, Bernoulli, Chebyshev, Bessel, and Gontcharaff polynomials.

Ab Initio Driven Exploration on the Thermal Properties of Al-Li Alloy.

Al-Li alloys are feasible and promising additives in advanced energy and propellant systems due to the significantly enhanced heat release and increased specific impulse. The thermal properties of Al-Li alloys directly determine the manufacturing, storage safety, and ignition delay of propellants. In this study, a neural network potential (NNP) is developed to investigate the thermal behaviors of Al-Li alloys from an atomistic perspective. The novel NNP demonstrates an excellent predictive ability for energy, atomic force, mechanical behaviors, phonon vibrations, and dynamic evolutions. A series of NNP-based molecular dynamics simulations are performed to investigate the effect of Li doping on the thermal properties of Al-Li alloys. All calculated results for Al-Li alloys are consistent with experimental values for Al, ensuring their validity in predicting Al-Li interactions. The simulation results suggest that a minor increment in the Li content results in a slight change in the melting point, thermal expansion, and radical distribution functions. These three properties are associated with the lattice characteristics; nonetheless, it causes a substantial reduction in thermal conductivity, which is related to the physical properties of the elements. The lower thermal conductivity allows heat accumulation on the particle surface, thereby speeding up the surface premelt and ignition. This provides an alternative atomic explanation for the improved combustion performance of Al-Li alloys. These findings integrate insights from the field of alloy material science into crucial combustion applications, serving as an atomistic guide for developing manufacturing techniques.

Rockfall simulation via spherical harmonic based discrete element method

The trajectory of falling rock is significantly affected by its shape. In order to capture the falling rock shape, spherical harmonic function expansion method is used. The reasonable order of spherical harmonic function expansion items is determined according to the error analysis. Spherical harmonic based discrete element method is utilized to simulate the rockfall process of cylindrical and irregular shape rocks. The influences of the rock and terrain shapes on the rockfall trajectory are analyzed. The results show that the shape of falling rock can be described precisely by spherical harmonic function expansion method, and only a little data should be stored. The predicted trajectory of cylindrical rockfall is close to the experimental result. Spherical and block falling rocks usually show more regular horizontal displacement, lateral offset and jump height during the motion process. Those motion quantities for long strip and flaky falling rocks are more sensitive to their initial rotations. Terrain has a strong influence on rockfall trajectory, falling rocks are prone to move along or rest at mountain valleys.

Multimodal stimulation screens reveal unique and shared genes limiting T cell fitness

Genes limiting Tcell antitumor activity may serve as therapeutic targets. It has not been systematically studied whether there are regulators that uniquely or broadly contribute to Tcell fitness. We perform genome-scale CRISPR-Cas9 knockout screens in primary CD8 Tcells to uncover genes negatively impacting fitness upon three modes of stimulation: (1) intense, triggering activation-induced cell death (AICD); (2) acute, triggering expansion; (3) chronic, causing dysfunction. Besides established regulators, we uncover genes controlling Tcell fitness either specifically or commonly upon differential stimulation. Dap5 ablation, ranking highly in all three screens, increases translation while enhancing tumor killing. Loss of Icam1-mediated homotypic Tcell clustering amplifies cell expansion and effector functions after both acute and intense stimulation. Lastly, Ctbp1 inactivation induces functional Tcell persistence exclusively upon chronic stimulation. Our results functionally annotate fitness regulators based on their unique or shared contribution to traits limiting Tcell antitumor activity.

Dynamic response of semi-cylindrical depression, cylindrical cavity and type-III crack to SH wave in half-space anisotropic media

In this study, the anti-plane dynamic response of an elastic half-space anisotropic medium containing surface semi-cylindrical depressions and internal cylindrical cavity and type-III crack is solved analytically. The wave function expansion method, the complex function method and the Green's function method can be used to effectively construct the free wave field equation and the scattered wave field equation in the case of SH wave incidence, in which the scattered wave field generated by the crack is constructed by the Green's function method and the "crack cut" method. For the scattered wave field generated by a circular cavity is constructed using the mirror method, where the positional offset coefficient in the mirror method of a half-space anisotropic medium is introduced, which well solves the problem of the asymmetry of the scattered wave field. Finally, the effects of anisotropic strength of the medium, SH wave incidence angle and dimensionless incident wave number on the surface displacement amplitude (|W|), dynamic stress concentration factor (DSCF) at the boundary of the circular cavity and dynamic stress intensity factor (DSIF) at the crack tip are investigated in both frequency and time domains under different working conditions, and conclusions different from those of isotropic medium are obtained, which provide some theoretical references for the earthquake-resistant design of the underground structure with canyon topography and the surface building.

Dynamic anti-planar characteristics of circular holes in laminated structures under the action of line source

Based on the complex variable function method and the wave function expansion method, the dynamic anti-plane characteristics of the circular hole in the laminated structure under line source excitation were studied. To deal with the interface problem within the laminated structure, the idea of “fit” is adopted to construct continuity conditions that satisfy displacement and stress. The circular hole boundary stress-free condition is used, the wave field is constructed using the mirror method, and the unknown coefficients of the scattered wave field are solved through Fourier series expansion, and finally the total wave field in the laminated structure is obtained. Taking the dynamic stress distribution of a circular hole in a laminated structure as a specific calculation example, the effects of changes in line source position, layer thickness, and medium hard-soft ratio on the dynamic stress concentration coefficient around the circular hole are discussed. The results show that when the line source load is applied directly above the circular hole and the lower layer is narrow, the dynamic stress concentration coefficient will have a sudden change compared with other situations. When other conditions are the same, under low, medium, and high-frequency wave fields, the dynamic stress concentration caused by different soft-to-hard ratios shows completely different rules. These rules can be used to better detect defects in laminated structures.

Fitting Log-Gaussian Cox Processes Using Generalized Additive Model Software

While log-Gaussian Cox process regression models are useful tools for modeling point patterns, they can be technically difficult to fit and require users to learn/adopt bespoke software. We show that, for suitably formatted data, we can actually fit these models using generalized additive model software, via a simple line of code, demonstrated on R by the popular mgcv package. We are able to do this because a common and computationally efficient way to fit a log-Gaussian Cox process model is to use a basis function expansion to approximate the Gaussian random field, as is provided by a generic bivariate smoother over geographic space. We further show that if basis functions are parameterized appropriately then we can estimate parameters in the spatial covariance function for the latent random field using a generalized additive model. We use simulation to show that this approach leads to model fits of comparable quality to state-of-the-art software, often more quickly. But we see the main advance from this work as lowering the technology barrier to spatial statistics for applied researchers, many of whom are already familiar with generalized additive model software.

Multi-objective design optimization of a transonic axial fan stage using sparse active subspaces

In this paper, a multi-objective optimization strategy for efficient design of turbomachinery blades using sparse active subspaces is implemented for a turbofan stage design. The proposed strategy utilized sparse polynomial chaos expansion on a limited dataset to generate a function from which the differential and the covariance matrix can be obtained. Active subspace was used to compute the active variables via singular value decomposition and a hybrid polynomial correlated function expansion was used to construct a surrogate model on the active subspace. Coupled with freeform method and multi-objective genetic algorithm, an automated optimization loop was run at a single operating condition. An improvement in stage efficiency and total pressure ratio of 2.97% and 1.15% was achieved for the optimum design compared with the baseline. Additionally, total pressure loss coefficient decreased by 5.88%, exit flow angle by 34.65% and shock strength by 5.32%. The coupled effect of change in stagger angle, forward sweep, forward lean, and chord length reduced the recirculation at the hub, and blockage at the shroud due the tip leakage flow by decreasing the blade loading. The threshold value hyperparameter was found to be the most influential and must be accurately determined.

An in-depth analysis and derivation of extremum conditions based on gradient information

This paper explores the necessary conditions for extremum in both constrained and unconstrained problems by extracting fundamental principles of constraint conditions. We provide a precise geometric understanding of the Lagrange Multiplier, prioritizing analytical insight. Beginning with a geometric interpretation of the gradient, we leverage the expansion of functions and their images to comprehend extremum and detail the Lagrangian derivation process.We expand the base vectors of the constraint surface into those of the full space and use a transition matrix to assess the function's extremum. This demonstrates how the second derivative matrix is transformed into its full-space representation to discern extrema in optimization problems. Additionally, we introduce incremental variables to optimize the second-order derivative matrix in full space, providing a novel perspective to solve extremal necessary conditions.

Child support grant expansion and cognitive function among women in rural South Africa: Findings from a natural experiment in the HAALSI cohort.

Cash transfers are a promising but understudied intervention that may protect cognitive function in adults. Although South Africa has a rapidly ageing population, little is known about the nature of association between cash transfers and cognitive function in this setting. We leveraged age-eligibility expansions to South Africa's Child Support Grant (CSG) to investigate the association between duration of CSG eligibility and cognitive function of biological mothers of child beneficiaries in South Africa. We analysed 2014/2015 baseline data from 944 women, aged 40-59 years with at least one CSG-eligible child, enrolled in the population-representative HAALSI cohort in Agincourt, South Africa. Duration of CSG eligibility for each mother was calculated based on the birth dates of all their children and the CSG age-eligibility expansion years (2003-2012). Cognitive function was measured using a cognitive battery administered at the HAALSI baseline interview. Linear regression was used to estimate the association between duration of CSG eligibility, dichotomized as low (≤10 years) and high (>10 years) eligibility, and cognitive function z-scores of the mothers. High vs. low duration of CSG eligibility, was associated with higher cognitive function z-scores in the full sample [β: 0.15 SD units; 95% CI: 0.04, 0.26; p-value = 0.01]. In mothers with one to four lifetime children, but not five or more, high vs. low duration of CSG eligibility, was associated with higher cognitive function z-scores [β: 0.19 SD units; 95% CI: 0.05, 0.34, p-value = 0.02]. Government cash transfers given to support raising children may confer substantial protective effects on the subsequent cognitive function of mothers. Further studies are needed to understand how parity may influence this relationship. Our findings bring evidence to policymakers for designing income supplementation programmes to promote healthy cognitive ageing in low-income settings.

Absorptive effects and classical black hole scattering

We describe an approach to incorporating the physical effects of the absorption of energy by the event horizon of black holes in the scattering amplitudes based post-Minkowskian, point-particle effective description. Absorptive dynamics are incorporated in a model-independent way by coupling the usual point-particle description to an invisible sector of gapless internal degrees-of-freedom. The leading order dynamics of this sector are encoded in the low-energy expansion of a spectral density function obtained by matching an absorption cross section in the ultraviolet description. This information is then recycled using the scattering amplitudes based Kosower-Maybee-O’Connell in-in formalism to calculate the leading absorptive contribution to the impulse and change in rest mass of a Schwarzschild black hole scattering with a second compact body sourcing a massless scalar, electromagnetic or gravitational field. The results obtained are in complete agreement with previous worldline Schwinger-Keldysh calculations and provide an alternative on-shell scattering amplitudes approach to incorporating horizon absorption effects in the gravitational two-body problem.

Suspension culture promoted the expansion of NK-92 cells ex vivo by enhancing the expression of IL-2 receptor.

Vigorous ex vivo expansion of NK-92 cells is a pivotal step for clinical adoptive immunotherapy. Interleukin-2 (IL-2) is identified as a key cytokine for NK-92 cells, and it can stimulate cell proliferation after binding to the IL-2 receptor (IL-2R). In this work, the differences in IL-2 consumption and IL-2R expression were investigated between the two culture modes. The results showed that suspension culture favored ex vivo expansion of NK-92 cells compared with static culture. The specific consumption rate of IL-2 in suspension culture was significantly higher than that in static culture. It was further found that the mRNA levels of the two IL-2R subunits remained unchanged in suspension culture, but the proportion of NK-92 cells expressing IL-2Rβ was increased, and the fluorescence intensity of IL-2Rβ was remarkably enhanced. Meanwhile, the proportion of cells expressing IL-2R receptor complex also increased significantly. Correspondingly, the phosphorylation of STAT5, a pivotal protein in the downstream signaling pathway of IL-2, was up-regulated. Notably, the expression level and colocalization coefficient of related endosomes during IL-2/IL-2R complex endocytosis were markedly elevated, suggesting the enhancement of IL-2 endocytosis. Taken together, these results implied that more IL-2 was needed to support cell growth in suspension culture. Therefore, the culture process was optimized from the perspective of cytokine utilization to further improve the NK-92 cell's expansion ability and function. This study provides valuable insight into the efficient ex vivo expansion of NK-92 cells.

Reliability Assessment of Power Plant Operations through Boolean Function Expansion and Mean Time to Failure Analysis

This paper presents an investigation into the reliability assessment of power plant operations using Boolean Function expansion and Mean Time to Failure (MTTF) analysis. The study focuses on a complex system comprising two power generators within a power house. The primary objective of this system i. This paper presents an investigation into the reliability assessment of power plant operations using Boolean Function expansion and Mean Time to Failure (MTTF) analysis. The study focuses on a complex system comprising two power generators within a power house. The primary objective of this system is to ensure uninterrupted power supply from the power house to critical consumers via an output main switch. Reliability calculations are conducted considering failure times of various components, including cables, generators, and main switchboards, assuming arbitrary distribution patterns. Additionally, MTTF for the system under an exponential failure time distribution is determined. Graphical representations are employed to illustrate the utility and efficacy of the proposed models to ensure uninterrupted power supply from the power house to critical consumers via an output main switch. Reliability calculations are conducted considering failure times of various components, including cables, generators, and main switchboards, assuming arbitrary distribution patterns. Additionally, MTTF for the system under an exponential failure time distribution is determined. Graphical representations are employed to illustrate the utility and efficacy of the proposed model.