Special Functions Research Articles

12419 Single-nuclei Sequencing Of Normal Donor Cadaveric Parathyroid Glands Reveals Distinct Cellular Subpopulations With Key Differences In Gland Anatomical Location And Suppressed Vs Non-suppressed Physiological Status

Abstract Disclosure: T. Glinin: None. E. Khanafshar: None. J.A. Sosa: Advisory Board Member; Self; Novo Nordisk, AstraZeneca, Eli Lilly & Company. Grant Recipient; Self; Exelixis, Inc., Eli Lilly & Company. J. Koh: None. Despite the significant clinical burden of parathyroid disorders, little is known at the molecular level about the cellular composition of normal parathyroid glands (PTGs). We performed a single-nuclei RNAseq study of six cadaveric PTGs (three from the superior anatomical location, three inferior) from four donors (two female). A board-certified pathologist confirmed that the sequenced PTGs were histologically normal. Using the split-pool method, we sequenced 83,693 nuclei, generating 1.7B reads. Data integration was performed with the Harmony algorithm in Seurat 5.0.1. Cluster analysis revealed 14 discrete populations of PTG origin. Gene set enrichment identified clusters corresponding to endothelial cells, neurons, microglia, mast cells, dendritic cells, stromal fibroblasts, macrophages, and smooth muscle. The remaining six clusters were closely related but distinct populations sharing markers including PTH, CaSR, SPOCK3, PRKCE, and PLCB1 (p<2e-300 for group specificity) but with differentially expressed gene (DEG) patterns between clusters suggestive of specialized functions in VEGF signaling (KIAA1549L), GPCR downstream signaling (GRM7, ADGRL3), and subcellular spatial organization (SYNE1) (p<2e-24 for cluster specificity). Superior and inferior PTGs were distinguished by 8 superior-specific DEGs (p<2e-245) including HOXB3, expressed in 71% of superior PTG cells vs 6% of inferior PTG cells. Enhanced expression of HOXB3, a homeobox transcription factor found to inhibit tumorigenesis in multiple tissues, could explain in part why adenomas are three times less likely to arise in superior PTGs. During procurement, one of the presumptive normal donors was found to have a single grossly enlarged, hypercellular PTG, elevated PTH (140 pg/ml), and hypercalcemia (11.2 mg/dL), consistent with primary hyperparathyroidism (PHPT). In PHPT patients with a single tumor, contralateral PTGs are functionally suppressed by the dominant adenoma. We compared the histologically normal suppressed and unsuppressed PTGs. Fifteen genes were more highly expressed in suppressed PTGs, including LRP2, a multi-ligand receptor known to bind PTH (p = 2e-300). Fourteen genes were more highly expressed in unsuppressed PTGs (p<2.14e-296), including PDE11A, NRG2, NRXN3, and PRLR, which are all associated with GABA receptor signaling (q = 2.8e-5). These data independently support our group’s prior work proposing a role for the GABA receptor in PHPT. Differential expression in endothelial cells, neurons, and fibroblasts from suppressed PTGs suggests that non-endocrine cells may also be responsive to changes in PTG activity. Finally, the different proportions of cells with suppressed or unsuppressed gene expression signatures observed between clusters suggests that PTGs incorporate distinct populations of cells reflective of physiological activity or functional suppression. Presentation: 6/2/2024

Extension of Pochhammer symbol, generalized hypergeometric function and τ-Gauss hypergeometric function

Abstract We introduce new extension of the extended Pochhammer symbol and gamma function by using the extended Mittag-Leffler function. We also present extension of the generalized hypergeometric function as well as some of their special cases by using this extended Pochhammer symbol. Further, we define the extension of the τ-Gauss hypergeometric function. Integral and derivative formulas involving the Mellin transform and fractional calculus techniques associated with this extended τ-Gauss hypergeometric function are also given. Also, new extended τ-Gauss hypergeometric function also provides a few more interesting and well-known results. This enriches the theory of special functions. The obtained results are believed to be newly presented.

Analysis of scalar fields with series convolution

Wave equations for some curved spacetimes may involve functions that prevent a solution in a closed form. In some cases, these functions can be eliminated by transformations and the solutions can be found analytically. In the cases where such transformations are not available, the infinite series expansions of these functions can be convoluted with the power series solution ansatz. We study such an example where the solution is based on a special function.

Azimuthal geodesics in closed FLRW cosmological models

We study geodesics in Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological models and give the full set of solutions. For azimuthal geodesics, in a closed universe, we give the angular distance traveled by a test particle moving along such a geodesic during one cycle of expansion and recollapse of the universe. We extend previous results regarding the path followed by light rays to the two-fluid case, also including a cosmological constant, as well as to massive test particles. Our work contains various new results and explicit formulas, often using special functions which naturally appear in this setting. Published by the American Physical Society 2024

Resilience of dermis resident macrophages to inflammatory challenges.

The skin serves as a complex barrier organ populated by tissue-resident macrophages (TRMs), which play critical roles in defense, homeostasis, and tissue repair. This review examines the functions of dermis resident TRMs in different inflammatory settings, their embryonic origins, and their long-term self-renewal capabilities. We highlight the M2-like phenotype of dermal TRMs and their specialized functions in perivascular and perineuronal niches. Their interactions with type 2 immune cells, autocrine cytokines such as IL-10, and their phagocytic clearance of apoptotic cells have been explored as mechanisms for M2-like dermal TRM self-maintenance and function. In conclusion, we address the need to bridge murine models with human studies, with the possibility of targeting TRMs to promote skin immunity or restrain cutaneous pathology.

Assessing physics-informed neural network performance with sparse noisy velocity data

The utilization of data in physics-informed neural network (PINN) may be considered as a necessity as it allows the simulation of more complex cases with a significantly lower computational cost. However, doing so would also make it prone to any issue with the data quality, including its noise. This study would primarily focus on developing a special loss function in the PINN to allow an effective utilization of noisy data. However, a study regarding the data location and amount was also conducted in order to allow a better data utilization in PINN. This study was conducted on a lid-driven cavity flow at Re = 200, 1000, and 5000 with a dataset of less than 100 velocity data and a maximum noise of 10% of the maximum velocity. The results show that by ensuring the data are distributed in a certain configuration, it has zero noise, and by using as much data as possible, the computational cost of PINN can be significantly reduced compared to without using any data at all. For Re = 200, it is 7.4 faster by using data, and this speedup is potentially higher for higher Re cases. For the noise in particular, it does not only make the PINN more inaccurate but also necessitate the usage of more data as this is the only way to make it more accurate. This issue though is capable to be solved with our new method, which only uses the data as an approximate solution, and the governing equation would figure out the details. This method was also shown to be capable to improve the PINN accuracy with the potential to almost completely eliminating the noise effect.

Casimir energy of hyperbolic orbifolds with conical singularities

In this article, we obtain the explicit expression of the Casimir energy for compact hyperbolic orbifold surfaces in terms of the geometrical data of the surfaces with the help of zeta-regularization techniques. The orbifolds may have finitely many conical singularities. In computing the contribution to the energy from a conical singularity, we derive an expression of an elliptic orbital integral as an infinite sum of special functions. We prove that this sum converges exponentially fast. Additionally, we show that under a natural assumption known to hold asymptotically on the growth of the lengths of primitive closed geodesics of the (2, 3, 7)-triangle group orbifold, its Casimir energy is positive (repulsive).

Bi-univalent characteristics for a particular class of Bazilevič functions generated by convolution using Bernoulli polynomials

Special functions and special polynomials have been used and studied widely in the context of Geometric function theory of Complex Analysis by the many authors. Here, in our present investigations, making use of the convolution, we first introduce a new subclass of Bazilevivč bi-univalent functions involving the Bernoulli Polynomials. We then find the first two Taylor-Maclaurin coefficient | a 2 | and | a 3 | for our defined functions class. We then calculate the bounds for the Fekete Szegö inequality for the defined function class. Also some known consequences of our main results are highlighted in the form of Corollaries.

CALCULATION OF FLAT SHELLS BY THE BOUNDARY ELEMENT METHOD

This article describes the iterative process of solving the problem of the stress-strain state of a long flexible cylindrical panel. Stress-strain state and the study of the stability of flat shells taking into account the physical, mechanical properties of the material, the process of deformation change. It is based on sequential approximation methods and the boundary element method (MGE). The results of algorithmic weighting are presented in the form of a table showing what value each band represents. The equations are determined by solving twelve unknown values of functions at the ends of the segment. Linear problems of elasticity theory and plate theory fundamental solutions have a simple form, so the method is widely used here. For flat shells, the matrix of fundamental solutions is determined by complex volumetric expressions, and for flat shells - by special functions. Therefore, there is little research on solving problems in the theory of flat shells by the boundary element method. In this regard, an urgent topic of research is the development of methods of boundary integral equations for solving linear and nonlinear problems in the theory of flat shells based on the application of fundamental solutions defined by simple analytical expressions. The scientific novelty of the work consists in the development of a methodology for assessing the reliability of thin-walled spatial structures using the boundary element method.

Borel transform and integral identities involving λ$$ \lambda $$‐Bessel and λ$$ \lambda $$‐Tricomi matrix functions

This paper focuses on integrals and Borel transforms concerning ‐Bessel and ‐Tricomi functions, employing an umbral perspective as a central approach. Differintegral techniques, presently utilized in calculus, offer a rich reserve of tools that can be utilized across a broad spectrum of problems encompassing the realm of special functions and beyond. Employing integral transforms akin to the Borel type and the related formalism proves to be a potent approach, facilitating a connection between umbral and operational methodologies. By integrating these perspectives, we establish a novel and effective method for deriving integrals of hybrid special functions and achieving the summation of their corresponding generating functions.

The Security Service of Ukraine’s counteraction to criminal offences at critical infrastructure facilities: organisational aspect

The article is devoted to the theoretical foundations of organisation and management of the process of countering criminal offences by the Security Service of Ukraine at critical infrastructure facilities. Modern technological systems and their parts related to critical infrastructure facilities are subject to unlawful encroachments. The negative dynamics of the level of threats and losses from criminal attacks on these objects requires solving existing problems, and therefore consideration of issues related to solving existing problems becomes relevant for scientists. The main purpose of the article was to study and solve the problem of organising and managing the process of countering criminal offences by the Security Service of Ukraine at critical infrastructure facilities. The methodological tools of the scientific research were based on theoretical methods of scientific knowledge; analysis and synthesis, logical and generalisation methods. Based on the results of the study, the article substantiates that an effective process of implementing organisational and managerial functions is a crucial element of organisational and tactical activities in the system of protection against criminal offences against critical infrastructure facilities and will contribute to achieving the goal of influencing the determinants of criminal offences at critical infrastructure facilities, while emphasising the importance of interaction with other governmental authorities, private enterprises and international partners. In this regard, the ways of solving the problems are proposed, in particular, the definition of the concept and content of the organisational system of the Security Service of Ukraine’s response to criminal offences at critical infrastructure facilities. In addition, the correlation between the concepts of “organisation” and “management” is determined, and their essence and significance are revealed. Taking into account the results of the study, the article identifies the directions for further scientific research, development of the problems of criminal law aspects of the Security Service of Ukraine’s counteraction to criminal offences at critical infrastructure facilities, as well as the essence and content of special management functions.

Use of Building Information Modeling (BIM) to Improve Construction Management in the USA

The construction industry in the United States faces ongoing challenges related to cost overruns, project delays, and inefficiencies in project management. Building Information Modeling (BIM) has emerged as a transformative technology with the potential to address these issues by enhancing the precision, collaboration, and decision-making processes in construction management. This paper provides a comprehensive review of the application of BIM in the U.S. construction sector, with a focus on its impact on improving construction management practices. The review explores the specific ways in which BIM contributes to project success, including its ability to streamline workflows, reduce errors, and facilitate real-time collaboration among stakeholders. Through an in-depth analysis of current literature, this paper highlights the specialized functions of BIM that are particularly beneficial for construction management in the U.S., such as clash detection, 4D scheduling, and cost estimation. The paper also examines case studies that demonstrate the successful integration of BIM in large-scale projects across the country, showcasing tangible improvements in project outcomes, including reduced project timelines and enhanced cost efficiency. Additionally, the paper delves into the challenges associated with BIM adoption in the U.S., including the need for skilled personnel, the integration of BIM with existing project management systems, and the legal and contractual implications of BIM-based collaboration. These challenges are discussed alongside strategies for overcoming them, emphasizing the importance of training, standardization, and cross-disciplinary collaboration. The findings of this review suggest that the widespread adoption of BIM in the U.S. construction industry holds significant promise for enhancing project management efficiency, improving stakeholder communication, and ultimately contributing to more successful project outcomes. The paper concludes by proposing best practices for BIM implementation in construction management, aiming to guide industry professionals in leveraging this technology to its fullest potential.

Fractional-Order Correlation between Special Functions Inspired by Bone Fractal Operators

In recent years, our research on biomechanical and biophysical problems has involved a series of symmetry issues. We found that the fundamental laws of the aforementioned problems can all be characterized by fractal operators, and each type of operator possesses rich invariant properties. Based on the invariant properties of fractal operators, we discovered that the symmetry evolution laws of functional fractal trees in the physical fractal space can reveal the intrinsic correlations between special functions. This article explores the fractional-order correlation between special functions inspired by bone fractal operators. Specifically, the following contents are included: (1) showing the intrinsic expression in the convolutional kernel function of bone fractal operators and its correlation with special functions; (2) proving the following proposition: the convolutional kernel function of bone fractal operators is still related to the special functions under different input signals (external load, external stimulus); (3) using the bone fractal operators as the background and error function as the core, deriving the fractional-order correlation between different special functions.

Inequalities for Basic Special Functions Using Hölder Inequality

Let p,q≥1 be two real numbers such that 1p+1q=1, and let a,b∈R be two parameters defined on the domain of a function, for example, f. Based on the well known Hölder inequality, we propose a generic inequality of the form |f(ap+bq)|≤|f(a)|1p|f(b)|1q, and show that many basic special functions, such as the gamma and polygamma functions, Riemann zeta function, beta function and Gauss and confluent hypergeometric functions, satisfy this type of inequality. In this sense, we also present some particular inequalities for the Gauss and confluent hypergeometric functions to confirm the main obtained inequalities.

Literature as a Vehicle of Mystery: On Jerzy Grotowski’s Writing

Jerzy Grotowski (1933–1999), who is considered to be one of the greatest theater artists of the 20th century, frequently expressed his ambivalent relation to words, repeating that any true knowledge has to be obtained by practice. However, all his life he created and published texts. The volume collecting them all in print runs to 1131 pages. Scholars interpreting his art (e.g. Krzysztof Rutkowski, Zbigniew Osiński) and his close collaborators, like Ludwik Flaszen, frequently times underlined the importance of Grotowski’s writings, stressing a special function literature played in this artist’s research. Following their recognitions, partly polemizing with them, one can formulate some basic assumptions concerning the character and functions of Grotowski’s writing and its relation to the main aspects of contemporary literature. This was the man of theater appears to be also an aware creator of a literature paradoxically closely related and working for mystery beyond words.

Development of an enhanced educational IDE for 8051/8052 microcontroller

This paper presents and explains the development of an IDE for microcontroller 8051/8052 with new features and functionalities. These features include a built-in editor; a keypad editor and auto enabling/disabling array of buttons for eliminating syntax errors. The implementation of the interrupts is entirely based on the 8052 datasheets by taking into consideration the “Interrupt Priorities” and “Interrupt Enables”. Multiple view windows for internal ram, external ram, program memory and special function register enhance the developed IDE. One-pass cross technique was adopted for the assembling phase. The assembler plays the role of assigning addresses, translating mnemonics, and recognizing errors by considering all the 255 instructions and directives Step-by-step, skip-line debugging, breakpoints to be inserted at any part of the source code have been included to ameliorate the students’ interaction with the system. An option is provided to users to manually create external incoming transmission for triggering purposes. The IDE passes the test and verification processes successfully.

Excel-oriented calculator for finding the values of some special functions of mathematical and theoretical physics

Excel-oriented calculator for finding the values of some special functions of mathematical and theoretical physics

Special functions with general kernel: Properties and applications to fractional partial differential equations

Abstract In this paper, we reconstruct the gamma and beta functions using a general kernel function in their integral representations. We also reconstruct the Gauss and confluent hypergeometric functions using the beta function with general kernel in their series representations. The general kernel function we use here can be chosen as any special function such as exponential function, Mittag-Leffler function, Wright function, Fox-Wright function, Kummer function or M-series. Using different choices of this general kernel function, various of the generalized gamma, beta, Gauss hypergeometric and confluent hypergeometric functions in the literature can be obtained. In this paper, we first obtain the integral representations, functional relations, summation, derivative and transformation formulas and double Laplace transforms of the special functions we construct. Furthermore, we compute the solutions of some fractional partial differential equations involving special functions with general kernel via the double Laplace transform and graph some of the solutions for specific values. Finally, we obtain the incomplete beta function with general kernel by defining the beta distribution with general kernel.

On Properties of the Hyperbolic Distribution

This paper is set to analytically describe properties of the hyperbolic distribution. This law, along with the variance-gamma distribution, is one of the most popular normal mean–variance mixtures from the point of view of various applications. We have found closed form expressions for the cumulative distribution and partial-moment-generating functions of the hyperbolic distribution. The obtained formulas use the values of the Humbert confluent hypergeometric and Whittaker special functions. The results are applied to the problem of European option pricing in the related Lévy model of financial market. The research demonstrates that the discussed normal mean–variance mixture is analytically tractable.

ARHGEF3 Regulates Hair Follicle Morphogenesis.

During embryogenesis, cells arrange into precise patterns that enable tissues and organs to develop specialized functions. Despite its critical importance, the molecular choreography behind these collective cellular behaviors remains elusive, posing a major challenge in developmental biology and limiting advances in regenerative medicine. By using the mouse hair follicle as a mini-organ system to study the formation of bud-like structures during embryonic development, our work uncovers a crucial role for the Rho GTPase regulator ARHGEF3 in hair follicle morphogenesis. We demonstrate that Arhgef3 expression is upregulated at the onset of hair follicle placode formation. In Arhgef3 knockout animals, we observed defects in placode compaction, leading to impaired hair follicle downgrowth. Through cell culture models, we show that ARHGEF3 promotes F-actin accumulation at the cell cortex and P-cadherin enrichment at cell-cell junctions. Collectively, our study identifies ARHGEF3 as a new regulator of cell shape rearrangements during hair placode morphogenesis, warranting further exploration of its role in other epithelial appendages that arise from similar developmental processes.