Fox and Lu introduced a Langevin framework for discrete-time stochastic models of randomly gated ion channels such as the Hodgkin-Huxley (HH) system. They derived a Fokker-Planck equation with state-dependent diffusion tensor [ ] and suggested a Langevin formulation with noise coefficient matrix [ ] such that SS[ ]. Subsequently, several authors introduced a variety of Langevin equations for the HH system. In this article, we present a natural 14-dimensional dynamics for the HH system in which each directed edge in the ion channel state transition graph acts as an independent noise source, leading to a 14 [ ] 28 noise coefficient matrix [ ]. We show that (1) the corresponding 14D system of ordinary differential equations is consistent with the classical 4D representation of the HH system; (2) the 14D representation leads to a noise coefficient matrix [ ] that can be obtained cheaply on each time step, without requiring a matrix decomposition; (3) sample trajectories of the 14D representation are pathwise equivalent to trajectories of Fox and Lu's system, as well as trajectories of several existing Langevin models; (4) our 14D representation (and those equivalent to it) gives the most accurate interspike interval distribution, not only with respect to moments but under both the [ ] and [ ] metric-space norms; and (5) the 14D representation gives an approximation to exact Markov chain simulations that are as fast and as efficient as all equivalent models. Our approach goes beyond existing models, in that it supports a stochastic shielding decomposition that dramatically simplifies [ ] with minimal loss of accuracy under both voltage- and current-clamp conditions.

In this paper, we introduce the newly generated Ristić–Balakrishnan–Topp–Leone–Gompertz-G family of distributions. Statistical and mathematical properties of this new family including moments, moment generating function, incomplete moments, conditional moments, probability weighted moments, distribution of the order statistics, stochastic ordering, and Rényi entropy are derived. The unknown parameters of the family are inferred using the maximum likelihood estimation technique. A Monte Carlo simulation study is performed to investigate the convergence of the maximum likelihood estimation. Three real-life data sets are used to demonstrate the flexibility and capacity of the new family of distributions.

Prefrontal cortical activity represents stimuli in working memory tasks in a low-dimensional manifold that transforms over the course of a trial. Such transformations reflect specific cognitive operations, so that, for example, the rotation of stimulus representations is thought to reduce interference by distractor stimuli. Here we show that rotations occur in the low-dimensional activity space of prefrontal neurons in naïve male monkeys (Macaca mulatta), while passively viewing familiar stimuli. Moreover, some aspects of these rotations remain remarkably unchanged after training to perform working memory tasks. Significant training effects are still present in population dynamics, which further distinguish correct and error trials during task execution. Our results reveal automatic functions of prefrontal neural circuits allow transformations that may aid cognitive flexibility.

This paper introduces the Lomax-exponentiated odds ratio–G (L-EOR–G) distribution, a novel framework designed to adeptly navigate the complexities of modern datasets. It blends theoretical rigor with practical application to surpass the limitations of traditional models in capturing complex data attributes such as heavy tails, shaped curves, and multimodality. Through a comprehensive examination of its theoretical foundations and empirical data analysis, this study lays down a systematic theoretical framework by detailing its statistical properties and validates the distribution’s efficacy and robustness in parameter estimation via Monte Carlo simulations. Empirical evidence from real-world datasets further demonstrates the distribution’s superior modeling capabilities, supported by compelling various goodness-of-fit tests. The convergence of theoretical precision and practical utility heralds the L-EOR–G distribution as a groundbreaking advancement in statistical modeling, significantly enhancing precision and adaptability. The new model not only addresses a critical need within statistical modeling but also opens avenues for future research, including the development of more sophisticated estimation methods and the adaptation of the model for various data types, thereby promising to refine statistical analysis and interpretation across a wide array of disciplines.

In this study, we introduce the modified Burr III Odds Ratio–G distribution, a novel statistical model that integrates the odds ratio concept with the foundational Burr III distribution. The spotlight of our investigation is cast on a key subclass within this innovative framework, designated as the Burr III Scaled Inverse Odds Ratio–G (B-SIOR-G) distribution. By effectively integrating the odds ratio with the Burr III distribution, this model enhances both flexibility and predictive accuracy. We delve into a thorough exploration of this distribution family’s mathematical and statistical properties, spanning hazard rate functions, quantile functions, moments, and additional features. Through rigorous simulation, we affirm the robustness of the B-SIOR-G model. The flexibility and practicality of the B-SIOR-G model are demonstrated through its application to four datasets, highlighting its enhanced efficacy over several well-established distributions.