Recently, Shehata et al. [37] introduced the r+1Rs(B;C; z) matrix function and established some properties. The aim of this study established to devote and derive certain basic properties including analytic properties, recurrence matrix relations, dierential properties, new integral representations, k- Beta transform, Laplace transform, fractional k-Fourier transform, fractional integral properties, the k-Riemann{Liouville and k-Weyl fractional integral and derivative operators an extended version of r+1Rs;k matrix function. We establish its relationships with other well known special matrix functions which have some particular cases in the context of three parametric Mittag-Leer matrix function, k- Konhauser and k-Laguerre matrix polynomials. Finally, some special cases of the established formulas are also discussed.

In this work, several random Boolean networks (RBN) are generated and analyzed from two characteristics: their time evolution diagram and their transition diagram. To do this, its randomness is estimated using three metrics, of which algorithmic complexity is the only one capable of revealing both transitions towards the chaotic regime and the algorithmic contribution of certain states to the transition diagram and their relationship with the order they occupy in the temporal evolution of the respective RBN.

The regulatory approvals of tumor agnostic therapies have led to reevaluation of the drug development process. Conventional models of drug development are histology-based. On the other hand, tumor agnostic drug development of a new drug (or combination) focuses on targeting a common genomic biomarker in multiple cancers, regardless of histology. Basket-like clinical trials with multiple cohorts allow clinicians to evaluate pan-cancer efficacy and toxicity. There are currently 8 tumor agnostic approvals granted by the Food and Drug Administration (FDA). This includes two immune checkpoint inhibitors, and 5 targeted therapy agents. Pembrolizumab is an anti-PD-1 antibody that was the first FDA approved tumor agnostic treatment for unresectable or metastatic microsatellite instability-high (MSI-H) or deficient mismatch repair (dMMR) solid tumors in 2017. It was later approved for tumor mutational burden-high (TMB-H) solid tumors, although the TMB cut-off used is still debated. Subsequently, in 2021, another anti-PD-1 antibody, Dostarlimab was also approved for dMMR solid tumors in the refractory setting. Patients with fusion-positive cancers are typically difficult to treat due to their rare prevalence and distribution. Gene rearrangements or fusions are present in a variety of tumors. neurotrophic tyrosine kinase (NTRK) fusions are present in a range of pediatric and adult solid tumors in varying frequency. Larotrectinib and entrectinib were approved for neurotrophic tyrosine kinase (NTRK) fusion-positive cancers. Similarly, selpercatinib was approved for Rearranged During Transfection (RET) fusion-positive solid tumors. FDA approved the first combination therapy of dabrafenib, a B-Raf Proto-Oncogene Serine/Threonine Kinase (BRAF) inhibitor, plus trametinib, a mitogen-activated protein kinase (MEK) inhibitor for patients 6 months or older with unresectable or metastatic tumors (except colorectal cancer) carrying BRAFV600E mutation. The most recent FDA tumor agnostic approval is of fam-trastuzumab deruxtecan-nxki (T-Dxd) for HER2-positive solid tumors. It is important to identify and expeditiously develop drugs that have the potential to provide clinical benefit across tumor types.

The glucocorticoid receptor alpha (GRα), a pivotal component of the ancient glucocorticoid (GC) signaling system that emerged nearly 450 million years ago, has been instrumental in directing vertebrate evolution and is essential for survival, regulating fertility and fetal development, the function of every organ and circulating cells, metabolism, immune responses, and adaptation to stress. While its anti-inflammatory properties have been recognized since the mid-20th century, GRα’s broader role as the master regulator of homeostatic corrections, particularly in health and critical illness, has only recently been fully appreciated.GRα orchestrates three key phases of homeostatic correction: the Priming Phase, where it rapidly activates early immune responses, mobilizes energy reserves, and prepares the body to mount an immediate defense against various physiological stressors, including infection and injury. During this phase, GRα enhances glucose metabolism, supports mitochondrial function, and facilitates the release of key immune cells to the site of damage, ensuring the body is equipped to handle the initial assault. The Modulatory Phase follows, in which GRα fine-tunes the inflammatory response to prevent excessive tissue damage. By balancing pro- and anti-inflammatory signals, GRα helps contain the immune response, preventing the harmful effects of prolonged inflammation while maintaining immune surveillance. This phase also involves the regulation of oxidative stress, vascular tone, and the preservation of cellular integrity to protect vital organs from injury. Finally, in the Restorative Phase, GRα plays a critical role in resolving inflammation and initiating tissue repair. During this phase, GRα supports cellular regeneration, promotes the clearance of apoptotic cells and debris, and restores anatomical and physiological balance. It aids in rebuilding tissue architecture and returning the neuroendocrine-immune system to its baseline state, ensuring long-term recovery and stability.Throughout these phases, GRα manages complex interactions, including recently discovered co-regulation with pro-inflammatory transcription factors, while also regulating mitochondrial function to ensure bioenergetic and metabolic stability during stress. In critically ill patients, depletion of bioenergetic and micronutrient reserves severely impairs GRα’s capacity to regulate immune responses, heightening the risk of morbidity and mortality.This review, in light of this new understanding, underscores the need to re-evaluate current glucocorticoid (GC) treatment strategies, emphasizing the incorporation of micronutrient support to optimize GRα function across all phases of homeostatic correction. This integrated therapeutic approach has the potential to enhance both immediate immune responses and long-term recovery in critically ill patients, offering a more comprehensive strategy for managing the complex pathobiology of critical illness. Furthermore, this integrative approach could decrease glucocorticoid dose and duration requirements and potential side effects.

The article titled "Immunoglobulins and Its Applications" provides a comprehensive overview of the structure, function, and therapeutic significance of immunoglobulins, also known as antibodies. These vital proteins, produced by plasma cells in response to immunogens, are essential components of the immune system, playing a critical role in recognizing and neutralizing pathogens such as bacteria and viruses. The article elaborates on the five primary classes of immunoglobulins (IgA, IgD, IgE, IgG, and IgM), each distinguished by its unique structural and functional properties. It discusses the molecular composition of immunoglobulins, highlighting the significance of their variable and constant regions in antigen binding. The paper also explores the diverse immune functions mediated by these proteins, including precipitation, agglutination, and neutralization of antigens. Additionally, the article emphasizes the therapeutic applications of immunoglobulins, particularly in treating immune deficiencies and other diseases. Advances in monoclonal antibody technology have significantly expanded the utility of immunoglobulins in both research and medicine, leading to the development of innovative therapeutic approaches such as humanized monoclonal antibodies and bifunctional antibodies. This comprehensive analysis underscores the critical role of immunoglobulins in both natural immunity and therapeutic interventions.