Dr. Shusen Pu

The article introduces a distributional model called the Modified Linear Failure Rate Odd Ratio-G model. This model combines the exponentiated odd ratio with the Linear Failure Rate distribution. The mathematical and statistical properties of the proposed model are investigated, and several special cases and parameter estimation methods are discussed. The model is validated using three real-world bathtub shaped data sets.

The recent interest in learning-augmented algorithms has motivated us to explore their applicability in quantum computing, specifically during the noisy intermediate-scale quantum (NISQ) era. This paper introduces a learning-augmented algorithm-like approach to enhance the Quantum Approximate Optimization Algorithm (QAOA) for max-cut problems, by improving initial parameter estimation. We trained a random forest regression model on the optimal solution parameters from various max-cut graphs, and then used this model to guess better initial parameters for previously unseen graphs. Experimental results demonstrate that our approach reduces the number of iterations of quantum computation required, thereby reducing noise and error. These findings indicate that integrating learning-augmented algorithm techniques can enhance the computational feasibility of solving QAOA problems in the NISQ era.

This comprehensive study delves into the examination and application of novel statistical distributions, namely the Ristić-Balakrishnan-Topp-Leone-Exponentiated half Logistic-G (RB-TL-EHL-G) family of distributions, emphasizing their paramount importance in reliability and medical data modeling. We meticulously explore a multitude of this family of novel distributions, accentuating their respective features, properties, and real-world applicability. The probability density, the cumulative distribution, the hazard rate, and the quantile functions are provided. The density functions of the RB-TL-EHL-G family are expanded, enabling a deeper understanding of their statistical properties, including various moments, generating functions, order statistics, stochastic orderings, probability weighted moments, and the Rényi entropy. A significant portion of the investigation is dedicated to the intensive analysis of various data sets, to which these distributions are fitted, unveiling noteworthy insights into their behavior and performance. Furthermore, the discussions extend to a comparative study, delineating the advantages and limitations of each distribution, fostering a deeper understanding and selection criteria for practitioners.

This paper presents a new methodology for generating continuous statistical distributions, integrating the exponentiated odds ratio within the framework of survival analysis. This new method enhances the flexibility and adaptability of distribution models to effectively address the complexities inherent in contemporary datasets. The core of this advancement is illustrated by introducing a particular subfamily, the “Type 2 Gumbel Weibull-G family of distributions”. We provide a comprehensive analysis of the mathematical properties of these distributions, including statistical properties such as density functions, moments, hazard rate and quantile functions, Rényi entropy, order statistics, and the concept of stochastic ordering. To test the robustness of our new model, we apply five distinct methods for parameter estimation. The practical applicability of the Type 2 Gumbel Weibull-G distributions is further supported through the analysis of three real-world datasets. These real-life applications illustrate the exceptional statistical precision of our distributions compared to existing models, thereby reinforcing their significant value in both theoretical and practical statistical applications.

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.

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 paper, we introduce the newly generated Ristic-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 Renyi 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.

Stochastic oscillations can be characterized by a corresponding point process; this is a common practice in computational neuroscience, where oscillations of the membrane voltage under the influence of noise are often analyzed in terms of the interspike interval statistics, specifically the distribution and correlation of intervals between subsequent threshold-crossing times. More generally, crossing times and the corresponding interval sequences can be introduced for different kinds of stochastic oscillators that have been used to model variability of rhythmic activity in biological systems. In this paper we show that if we use the so-called mean-return-time (MRT) phase isochrons (introduced by Schwabedal and Pikovsky) to count the cycles of a stochastic oscillator with Markovian dynamics, the interphase interval sequence does not show any linear correlations, i.e., the corresponding sequence of passage times forms approximately a renewal point process. We first outline the general mathematical argument for this finding and illustrate it numerically for three models of increasing complexity: (i) the isotropic Guckenheimer-Schwabedal-Pikovsky oscillator that displays positive interspike interval (ISI) correlations if rotations are counted by passing the spoke of a wheel; (ii) the adaptive leaky integrate-and-fire model with white Gaussian noise that shows negative interspike interval correlations when spikes are counted in the usual way by the passage of a voltage threshold; (iii) a Hodgkin-Huxley model with channel noise (in the diffusion approximation represented by Gaussian noise) that exhibits weak but statistically significant interspike interval correlations, again for spikes counted when passing a voltage threshold. For all these models, linear correlations between intervals vanish when we count rotations by the passage of an MRT isochron. We finally discuss that the removal of interval correlations does not change the long-term variability and its effect on information transmission, especially in the neural context.

Neurons in the dorsolateral prefrontal cortex (dlPFC) and posterior parietal cortex (PPC) are activated by different cognitive tasks and respond differently to the same stimuli depending on task. The conjunctive representations of multiple tasks in nonlinear fashion in single neuron activity, is known as nonlinear mixed selectivity (NMS). Here, we compared NMS in a working memory task in areas 8a and 46 of the dlPFC and 7a and lateral intraparietal cortex (LIP) of the PPC in macaque monkeys. NMS neurons were more frequent in dlPFC than in PPC and this was attributed to more cells gaining selectivity in the course of a trial. Additionally, in our task, the subjects' behavioral performance improved within a behavioral session as they learned the session-specific statistics of the task. The magnitude of NMS in the dlPFC also increased as a function of time within a single session. On the other hand, we observed minimal rotation of population responses and no appreciable differences in NMS between correct and error trials in either area. Our results provide direct evidence demonstrating a specialization in NMS between dlPFC and PPC and reveal mechanisms of neural selectivity in areas recruited in working memory tasks.

Molecular fluctuations can lead to macroscopically observable effects. The random gating of ion channels in themembrane of a nerve cell provides an important example. The contributions of independent noise sources to the variability of action potential timing have not previously been studied at the level of molecular transitions within a conductance-based model ion-state graph. Here we study a stochastic Langevin model for the Hodgkin-Huxley (HH) system based on a detailed representation of the underlying channel stateMarkov process, the "14x28D model" introduced in (Pu and Thomas in Neural Computation 32(10):1775-1835, 2020). We show how to resolve the individual contributions that each transition in the ion channel graph makes to the variance of the interspike interval (ISI). We extend the mean return time (MRT) phase reduction developed in (Cao et al. in SIAM J Appl Math 80(1):422-447, 2020) to the second moment of the return time from an MRT isochron to itself. Because fixed-voltage spike detection triggers do not correspond to MRT isochrons, the inter-phase interval (IPI) variance only approximates the ISI variance. We find the IPI variance and ISI variance agree to within a few percent when both can be computed. Moreover, we prove rigorously, and show numerically, that our expression for the IPI variance is accurate in the small noise (large system size) regime; our theory is exact in the limit of small noise. By selectively including the noise associated with only those few transitions responsible for most of the ISI variance, our analysis extends the stochastic shielding (SS) paradigm (Schmandt and Galan in Phys Rev Lett 109(11):118101, 2012) from the stationary voltage clamp case to the current clamp case. We show numerically that the SS approximation has a high degree of accuracy even for larger, physiologically relevant noise levels. Finally, we demonstrate that the ISI variance is not an unambiguously defined quantity, but depends on the choice of voltage level set as the spike detection threshold. We find a small but significant increase in ISI variance, the higher the spike detection voltage, both for simulated stochastic HH data and for voltage traces recorded in in vitro experiments. In contrast, the IPI variance is invariant with respect to the choice of isochron used as a trigger for counting "spikes."