Grand Canyon University

The complex and heterogeneous nature of cancer necessitates advanced modeling techniques to better understand tumor dynamics and inform treatment strategies. This paper explores the application of stochastic modeling in cancer research, focusing on five key areas: tumor growth kinetics, evolutionary dynamics of cancer, treatment response and resistance, spatial modeling of tumor progression, and clinical applications of stochastic models. We first examine how stochastic models capture the randomness in tumor growth and proliferation, providing insights into cellular behaviors that deterministic models may overlook. Next, we investigate the evolutionary dynamics that govern tumor heterogeneity and the emergence of resistance, highlighting the role of genetic mutations and environmental pressures. The paper also discusses how stochastic modeling can improve predictions of treatment responses, elucidating mechanisms behind therapy resistance in various tumor subpopulations. Furthermore, we address the significance of spatial modeling in understanding tumor interactions within their microenvironment, shedding light on processes such as metastasis. Finally, we emphasize the translational potential of these mathematical frameworks, demonstrating how they can enhance personalized medicine approaches in oncology. By integrating stochastic modeling into cancer research, this work contributes to a deeper understanding of cancer biology and paves the way for improved patient outcomes.

Purpose This study examines how innovation strategy enables the survival of entrepreneurial ventures in Ghana's challenging business environment. Drawing on the dynamic capabilities theory, we investigate whether organizational adaptability, conceptualized as a meta-capability that integrates sensing, seizing and transforming capacities, mediates the relationship between innovation and survival. We also examine whether competitive intensity, regulatory environment and market dynamism condition this pathway. Design/methodology/approach Using a two-wave time-lagged survey of formal entrepreneurial ventures in Ghana conducted between April and May 2024, the study employs hierarchical regression and bootstrapped moderated mediation analysis. Of the 377 questionnaires distributed, 328 valid responses were received (87% response rate), with 178 male respondents (54.3%) and 150 female respondents (45.7%). Multiple procedural and statistical safeguards, including temporal separation and marker variable techniques, ensure robust findings free from common method bias. Findings Innovation strategy enhances the survival of entrepreneurial ventures both directly and indirectly through organizational adaptability, which functions as an integrated meta-capability that combines sensing, seizing and transforming capabilities. While competitive intensity and supportive regulatory environments amplify the innovation-adaptability-survival pathway, market dynamism shows no significant moderating effect. This non-effect is consistent with Ghana's “consistently dynamic” conditions, where firms internalize adaptive routines as standard practice rather than reacting to each shift as exceptional. Research limitations/implications The focus on formal ventures may overlook informal enterprises, which constitute a significant portion of entrepreneurial activity in emerging economies. Practical implications Entrepreneurial ventures should not only build comprehensive innovation strategies but also translate these into adaptive routines that support survival. In markets where change is the norm, firms benefit more from developing stable internal adaptive frameworks than from reactive responses to each market shift. Policymakers should streamline regulatory processes and provide targeted support for innovation to enhance capability building. Originality/value This study advances dynamic capabilities theory by demonstrating how innovation builds survival capacity in emerging economies. It challenges conventional assumptions about environmental dynamism, showing its influence is more limited than expected when volatility becomes normalized.

Sharing research code in an open access version-controlled repository offers significant benefits for both science as a whole and for individual researchers. In this article, we focus on this practice, which is fully aligned with the NIH's Gold Standard Science (GSS) program as well as FAIR (findable, accessible, interoperable, reusable) and TRUST (transparency, responsibility, user focus, sustainability, technology) principles. Gold Standard Science supports open science by emphasizing transparency, reproducibility, and the use of best practices that enable others to verify and extend research. Pairing a research article's cited data snapshot with a versioned, environment-specific code release, deposited in a companion code repository, ensures that, upon submission to a medical journal, readers and reviewers can directly verify results. An executable and updatable companion code repository complements, rather than replaces, established research data repositories. When code underlying medical research results is made openly available, then other scientists can inspect, run, and validate analyses. These activities enhance reproducibility, which is a core aim of GSS. Shared code also facilitates collaborative innovation by allowing researchers to extend the utility of the code to new datasets and applications. For researchers, code sharing can increase visibility, credibility, and citation impact. Demonstrating transparency through shared executable and updatable code builds trust with journal readers, peer reviewers, funders, and peers. Shared code in an open access repository signals adherence to high standards of scientific integrity and attracts opportunities for collaboration. A researcher who shares code receives recognition as a leader in reproducible, trustworthy research consistent with NIH's GSS principles.

This study presents explicit evaluations of the series \begin{equation*} \sum_{k=1}^\infty \frac{H_{k/n}^{(p)}}{k^q} \quad \text{and} \quad \sum_{k=1}^\infty \frac{(-1)^k H_{k/2n}^{(p)}}{k^q}, \quad p,q,n \in \mathbb{Z}_{\ge 1},\; q \ne 1, \end{equation*} for odd values of $p+q$. These explicit evaluations are expressed in terms of the Riemann zeta function and the Hurwitz zeta function.

This reflective practice explores the disparity I encountered as an ordained Assemblies of God woman in ministry between Pentecostal theology and praxis for allowing women in lead pastoring roles. Although the Assemblies of God fully ordains women into all offices and positions, my experience led me to believe that it was uncommon and rare for women to be in those types of leadership roles in the Church. Blocked from being allowed to submit my resume for a lead pastor role in various churches, the responses I received from district leaders as to why my resume was disallowed to be considered involved my gender, high education level, and my “lack of experience.” A small sampling of statistics led me to believe this was happening on a broader scale. This reflective practice reveals my intuitive feelings about the reasons behind these disparities within the Assemblies of God, and the challenges women still continue to face. It shares my journey as a doctoral student and the process I went through while researching this challenge. The lessons learned will serve as a valuable tool with which the Assemblies of God can be equipped to fill in that gender gap.