Alabama State University

In this paper, an economic competition–cooperation model is examined, which has one core enterprise and four satellite enterprises. This extends previous smaller models in the literature mathematically. The unique positive solution to the original solution after a change of variables corresponds to a trivial equilibrium of a linearized system. The instability of this linearized solution implies the instability of the positive solution to the original system. The instability of the positive solution and boundedness will force this system to have a periodic solution. Some sufficient conditions to guarantee the periodic oscillation of the solutions for this model are provided, and computer simulations are given to support the present criteria.

In this paper, a modified gene expression model with discrete delays is studied. The oscillatory behavior of the solutions is investigated. Make the change of variables, and the model will be linearized to a time-delayed system. The instability of the trivial solution of the linearized system implies the instability of the equilibrium point of the original model. It will generate a periodic oscillatory solution in which the original system has only one equilibrium point. We extend the result in the literature from stability to oscillation of the model. Some sufficient conditions to guarantee the oscillation of the solutions are provided, and computer simulations are given to support the present result.

A refined form of the Jensen–Mercer inequality has recently been introduced in the literature. Utilizing this improved inequality, we derive several new variants of the Hermite–Hadamard–Mercer type inequality, along with related estimates involving the beta function. These results serve to extend and generalize various existing inequalities. To demonstrate the validity of our findings, we provide numerical examples supported by both graphical and computational analyses. In addition, we explore applications of our results to specific means, including the arithmetic, harmonic, geometric, logarithmic, and p-logarithmic means. We hope that this work will stimulate further investigations in this area.

Abstract Description Background Racial disparities in colorectal cancer (CRC) are driven by unique tumor biology. African American (AA) and European American (EA) CRC patients exhibit distinct gene expression and tumor microenvironment (TME) profiles. This study leverages gene expression, TME profiling, and machine learning to identify race-specific biomarkers for precision oncology. Methods Differentially expressed genes and TME composition were analyzed in AA and EA CRC patients. Immune cell distributions in the TME were visualized using t-SNE, and machine learning models (XGBoost, Random Forest, SPLSDA) were applied to prioritize biomarkers based on gene expression and TME features. Results AA tumors upregulated IL33, BRAF, and PIK3CA, indicating a pro-inflammatory, proliferative phenotype linked to aggressive CRC, while EA tumors upregulated KRAS, VEGFA, and BCL2, suggesting angiogenic and anti-apoptotic pathways. TME analysis revealed an inflammatory profile in AA tumors, with higher epithelial, B, and myeloid cells, whereas EA tumors had increased plasma and B cells, indicating adaptive immunity. Unique immune patterns by race identified through AI/ML. Race-specific biomarkers included BRAF V600E for both groups, with strategies suggesting immune modulation for AA and angiogenesis inhibition for EA patients. Conclusion The study underscores distinct inflammatory and angiogenic mechanisms in AA and EA CRC, supporting precision oncology approaches to improve outcomes across racial groups. Funding Sources This work was partially supported by the National Institutes of Health (Award Numbers SC1CA193758 and U54CA118638), the National Cancer Institute (Award Number R01CA256724), the American Cancer Society (Award Number CHERC-MSI-21-166-01-CHERC-MSI), Department of Defense (Award Number W81XWH1810429). Topic Categories Computational and Systems Immunology (COMP)

The online version contains supplementary material available at 10.1007/s12298-025-01669-0.

Abstract This chapter explores the subtle yet insidious nature of vampire leaders within academic institutions. Using allegorical references from vampire mythology, it examines how these figures manipulate power dynamics, exploit subordinates, and create toxic work environments. Drawing from case studies, the chapter outlines the various disguises vampire leaders adopt to maintain control, from charismatic manipulators to authoritarian figures. The chapter provides tools to recognize these harmful leaders, empowering faculty and staff to challenge their influence. It argues that awareness and collective action are necessary to dismantle their stronghold over academic institutions.

Abstract This chapter delves into the far-reaching consequences of vampire leadership on academic institutions. From declining faculty morale to reputational damage, the discussion highlights how these leaders create environments of fear, stagnation, and intellectual suppression. Case studies illustrate the psychological toll on faculty and students, demonstrating the erosion of academic freedom and innovation. The chapter also examines institutional decline, showing how toxic leadership undermines an institution’s ability to attract and retain top talent. It calls for structural reforms and leadership accountability to combat these detrimental effects and restore institutional integrity.