Nature-inspired metaheuristics are widely used in optimization, but their systematic adaptation to structured statistical optimization problems remains limited. We develop three domain-adaptive variants of Cuckoo Search (CS) for statistical and bioinformatics problems with different constraint structures. First, Cuckoo-PC uses a dispersion-penalized objective to jointly optimize projection indices and curve parameters in principal curve estimation. Second, a mixed-domain CS introduces integer-jump abandonment for constrained maximum likelihood estimation in single-cell gene trajectory models with continuous and discrete parameters. Third, an exact-design CS uses integrality projection to construct locally D-optimal exact designs for the Emax pharmacokinetic model with autoregressive errors, where small-sample approximate-design rounding can be unreliable. Across these applications, simulation studies and comparative experiments against PSO, DE, and GA over 30 independent trials show improved objective values or reconstruction metrics in the reported multimodal, non-convex, and mixed-integer settings. The results support the practical value of embedding problem-specific structure directly into the search dynamics, while also highlighting the trade-off between accuracy and the additional computational cost of population-based search. Computer codes are publicly available at https://github.com/ElvisCuiHan/CuckooPC.

This paper presents a quasi-sequential optimal design framework for toxicology experiments, specifically applied to sea urchin embryos. The authors propose a novel approach combining robust optimal design with adaptive, stage-based testing to improve efficiency in toxicological studies, particularly where traditional uniform designs fall short. The methodology uses statistical models to refine dose levels across experimental phases, aiming for increased precision while reducing costs and complexity. Key components include selecting an initial design, iterative dose optimization based on preliminary results, and assessing various model fits to ensure robust, data-driven adjustments. Through case studies, we demonstrate improved statistical efficiency and adaptability in toxicology, with potential applications in other experimental domains.

Transition probability estimation plays a critical role in multi-state modeling, especially in clinical research. This paper investigates the application of semi-Markov and Markov renewal frameworks to the EBMT dataset, focusing on six clinical states encountered during hematopoietic stem cell transplantation. By comparing Aalen-Johansen (AJ) and Dabrowska-Sun-Horowitz (DSH) estimators, we demonstrate that semi-Markov models, which incorporate sojourn times, provide a more nuanced and temporally sensitive depiction of patient trajectories compared to memoryless Markov models. The DSH estimator consistently yields smoother probability curves, particularly for transitions involving prolonged states. We use empirical process theory and Burkholder-Davis-Gundy inequality to show weak convergence of the estimator. Future work includes extending the framework to accommodate advanced covariate structures and non-Markovian dynamics.

The Kolmogorov-Smirnov statistic is usually introduced as a supremum, but its finite-sample behavior is governed by a more local question: where does the empirical process first cross a boundary? This letter gives a partial answer through a finite-sample crossing ledger. The ledger rewrites the Smirnov- Birnbaum-Tingey one-sample formula as an explicit hitting-time law and yields a stable log-scale tail evaluator. For two samples, it gives one-wall and two-wall exact lattice recursions for arbitrary sample sizes, with the balanced reflection formula appearing as a special closed form. The same viewpoint explains the Dvoretzky-Kiefer-Wolfowitz-Massart inequality as an exponential compression of exact crossing sums and shows where exact distribution-free counting stops: under a composite null, fitted parameters change the path itself. Simulations and two small data diagnostics illustrate the resulting calibration warning.

Learning from large-scale pre-trained models with strong generalization ability has shown remarkable success in a wide range of downstream tasks recently, but it is still underexplored in the challenging few-shot class-incremental learning (FSCIL) task. It aims to continually learn new concepts from limited training samples without forgetting the old ones at the same time. In this paper, we introduce DSS-Prompt, a simple yet effective approach that transforms the pre-trained Vision Transformer with minimal modifications in the way of prompts into a strong FSCIL classifier. Concretely, we synergistically utilize two complementary types of prompts in each Transformer block: static prompts to bridge the domain gap between the pre-training and downstream datasets, thus enabling better adaption; and dynamic prompts to capture instance-aware semantics, thus enabling easy transfer from base to novel classes. Specially, to generate dynamic prompts, we leverage a pre-trained multi-modal model to extract input-related diverse semantics, thereby generating complementary input-aware prompts, and then adaptively adjust their importance across different layers. In this way, on top of the prompted visual embeddings, a simple prototype classifier can beat state-of-the-arts without further training on the incremental tasks. We conduct extensive experiments on four benchmarks to validate the effectiveness of our DSS-Prompt and show that it consistently achieves better performance than existing approaches on all datasets and can alleviate the catastrophic forgetting issue as well.

Nature-inspired meta-heuristic algorithms are increasingly used in many disciplines to tackle challenging optimization problems. Our focus is to apply a newly proposed nature-inspired meta-heuristics algorithm called CSO-MA to solve challenging design problems in biosciences and demonstrate its flexibility to find various types of optimal approximate or exact designs for nonlinear mixed models with one or several interacting factors and with or without random effects. We show that CSO-MA is efficient and can frequently outperform other algorithms either in terms of speed or accuracy. The algorithm, like other meta-heuristic algorithms, is free of technical assumptions and flexible in that it can incorporate cost structure or multiple user-specified constraints, such as, a fixed number of measurements per subject in a longitudinal study. When possible, we confirm some of the CSO-MA generated designs are optimal with theory by developing theory-based innovative plots. Our applications include searching optimal designs to estimate (i) parameters in mixed nonlinear models with correlated random effects, (ii) a function of parameters for a count model in a dose combination study, and (iii) parameters in a HIV dynamic model. In each case, we show the advantages of using a meta-heuristic approach to solve the optimization problem, and the added benefits of the generated designs.

Nature-inspired metaheuristic algorithms are important components of artificial intelligence, and are increasingly used across disciplines to tackle various types of challenging optimization problems. This paper demonstrates the usefulness of such algorithms for solving a variety of challenging optimization problems in statistics using a nature-inspired metaheuristic algorithm called competitive swarm optimizer with mutated agents (CSO-MA). This algorithm was proposed by one of the authors and its superior performance relative to many of its competitors had been demonstrated in earlier work and again in this paper. The main goal of this paper is to show a typical nature-inspired metaheuristic algorithmi, like CSO-MA, is efficient for tackling many different types of optimization problems in statistics. Our applications are new and include finding maximum likelihood estimates of parameters in a single cell generalized trend model to study pseudotime in bioinformatics, estimating parameters in the commonly used Rasch model in education research, finding M-estimates for a Cox regression in a Markov renewal model, performing matrix completion tasks to impute missing data for a two compartment model, and selecting variables optimally in an ecology problem in China. To further demonstrate the flexibility of metaheuristics, we also find an optimal design for a car refueling experiment in the auto industry using a logistic model with multiple interacting factors. In addition, we show that metaheuristics can sometimes outperform optimization algorithms commonly used in statistics.

Principal curve is a well-known statistical method oriented in manifold learning using concepts from differential geometry. In this paper, we propose a novel metric-based principal curve (MPC) method that learns one-dimensional manifold of spatial data. Synthetic datasets Real applications using MNIST dataset show that our method can learn the one-dimensional manifold well in terms of the shape.

IntroductionContinuous glucose monitoring (CGM) devices capture longitudinal data on interstitial glucose levels and are increasingly used to show the dynamics of diabetes metabolism. Given the complexity of CGM data, it is crucial to extract important patterns hidden in these data through efficient visualization and statistical analysis techniques.MethodsIn this paper, we adopted the concept of glucodensity, and using a subset of data from an ongoing clinical trial in pediatric individuals and young adults with new-onset type 1 diabetes, we performed a cluster analysis of glucodensities. We assessed the differences among the identified clusters using analysis of variance (ANOVA) with respect to residual pancreatic beta-cell function and some standard CGM-derived parameters such as time in range, time above range, and time below range.ResultsDistinct CGM data patterns were identified using cluster analysis based on glucodensities. Statistically significant differences were shown among the clusters with respect to baseline levels of pancreatic beta-cell function surrogate (C-peptide) and with respect to time in range and time above range.DiscussionOur findings provide supportive evidence for the value of glucodensity in the analysis of CGM data. Some challenges in the modeling of CGM data include unbalanced data structure, missing observations, and many known and unknown confounders, which speaks to the importance of--and provides opportunities for--taking an approach integrating clinical, statistical, and data science expertise in the analysis of these data.

Data augmentation for deep learning benefits model training, image transformation, medical imaging analysis and many other fields. Many existing methods generate new samples from a parametric distribution, like the Gaussian, with little attention to generate samples along the data manifold in either the input or feature space. In this paper, we verify that there are theoretical and practical advantages of using the principal manifold hidden in the feature space than the Gaussian distribution. We then propose a novel trajectory-aware principal manifold framework to restore the manifold backbone and generate samples along a specific trajectory. On top of the autoencoder architecture, we further introduce an intrinsic dimension regularization term to make the manifold more compact and enable few-shot image generation. Experimental results show that the novel framework is able to extract more compact manifold representation, improve classification accuracy and generate smooth transformation among few samples.

Nature-inspired metaheuristic algorithms are important components of artificial intelligence, and are increasingly used across disciplines to tackle various types of challenging optimization problems. We apply a newly proposed nature-inspired metaheuristic algorithm called competitive swarm optimizer with mutated agents (CSO-MA) and demonstrate its flexibility and out-performance relative to its competitors in a variety of optimization problems in the statistical sciences. In particular, we show the algorithm is efficient and can incorporate various cost structures or multiple user-specified nonlinear constraints. Our applications include (i) finding maximum likelihood estimates of parameters in a single cell generalized trend model to study pseudotime in bioinformatics, (ii) estimating parameters in a commonly used Rasch model in education research, (iii) finding M-estimates for a Cox regression in a Markov renewal model and (iv) matrix completion to impute missing values in a two compartment model. In addition we discuss applications to (v) select variables optimally in an ecology problem and (vi) design a car refueling experiment for the auto industry using a logistic model with multiple interacting factors.

Asymptotic properties of statistical estimators play a significant role both in practice and in theory. However, many asymptotic results in statistics rely heavily on the independent and identically distributed (iid) assumption, which is not realistic when we have fixed designs. In this article, we build a roadmap of general procedures for deriving asymptotic properties under fixed designs and the observations need not to be iid. We further provide their applications in many statistical applications. Finally, we apply our results to Poisson regression using a COVID-19 dataset as an illustration to demonstrate the power of these results in practice.

We provide a systematic treatment of $D$-optimal design for binary regression and quantal response models in toxicology studies. For the two-parameter case, we provide an analytical equation (WC equation) for computing the $D$-optimal design quickly and when analytical solution is not available, we apply particle swarm optimization to solve for the $D$-optimal design. Examples with various link functions are given as well as the sensitivity functions. We extend the two-parameter case to three-parameter case by providing a neat formula for the determinant of the information matrix. We also suggest practitioners to work with the neat formula to derive optimal designs for three-parameter binary regression models.

The key aim of this paper is to suggest a more quantitative approach to designing a dose–response experiment, and more specifically, a concentration–response experiment. The work proposes a departure from the traditional experimental design to determine a dose–response relationship in a developmental toxicology study. It is proposed that a model-based approach to determine a dose–response relationship can provide the most accurate statistical inference for the underlying parameters of interest, which may be estimating one or more model parameters or pre-specified functions of the model parameters, such as lethal dose, at maximal efficiency. When the design criterion or criteria can be determined at the onset, there are demonstrated efficiency gains using a more carefully selected model-based optimal design as opposed to an ad-hoc empirical design. As an illustration, a model-based approach was theoretically used to construct efficient designs for inference in a developmental toxicity study of sea urchin embryos exposed to trimethoprim. This study compares and contrasts the results obtained using model-based optimal designs versus an ad-hoc empirical design.

Motivation: Modeling single-cell gene expression trends along cell pseudotime is a crucial analysis for exploring biological processes. Most existing methods rely on nonparametric regression models for their flexibility; however, nonparametric models often provide trends too complex to interpret. Other existing methods use interpretable but restrictive models. Since model interpretability and flexibility are both indispensable for understanding biological processes, the single-cell field needs a model that improves the interpretability and largely maintains the flexibility of nonparametric regression models. Results: Here, we propose the single-cell generalized trend model (scGTM) for capturing a gene's expression trend, which may be monotone, hill-shaped or valley-shaped, along cell pseudotime. The scGTM has three advantages: (i) it can capture non-monotonic trends that are easy to interpret, (ii) its parameters are biologically interpretable and trend informative, and (iii) it can flexibly accommodate common distributions for modeling gene expression counts. To tackle the complex optimization problems, we use the particle swarm optimization algorithm to find the constrained maximum likelihood estimates for the scGTM parameters. As an application, we analyze several single-cell gene expression datasets using the scGTM and show that scGTM can capture interpretable gene expression trends along cell pseudotime and reveal molecular insights underlying biological processes.

The aim of this paper is to model COVID-19 based on Markov chains. First, we introduce basic concepts of Markov chains with examples from different disciplines. Second, we use different types of Markov chains to model COVID-19, including confirmed cases, death and recovered cases and forecasting future confirmed cases. Third, we give conclusions based on these models and ideas for future work. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This study did not receive any funding. ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: The study used ONLY simulated data. I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable. Yes All data produced in the present study are available upon reasonable request to the authors.

The aim of paper is to apply two types of particle swarm optimization, global best and local best PSO to a constrained maximum likelihood estimation problem in pseudotime analysis, a sub-field in bioinformatics. The results have shown that particle swarm optimization is extremely useful and efficient when the optimization problem is non-differentiable and nonconvex so that analytical solution can not be derived and gradient-based methods can not be applied.

Learning novel classes from a very few labeled samples has attracted increasing attention in machine learning areas. Recent research on either meta-learning based or transfer-learning based paradigm demonstrates that gaining information on a good feature space can be an effective solution to achieve favorable performance on few-shot tasks. In this paper, we propose a simple but effective paradigm that decouples the tasks of learning feature representations and classifiers and only learns the feature embedding architecture from base classes via the typical transfer-learning training strategy. To maintain both the generalization ability across base and novel classes and discrimination ability within each class, we propose a dual path feature learning scheme that effectively combines structural similarity with contrastive feature construction. In this way, both inner-class alignment and inter-class uniformity can be well balanced, and result in improved performance. Experiments on three popular benchmarks show that when incorporated with a simple prototype based classifier, our method can still achieve promising results for both standard and generalized few-shot problems in either an inductive or transductive inference setting.

In this paper, we explore the limitations of PCA as a dimension reduction technique and study its extension, projection pursuit (PP), which is a broad class of linear dimension reduction methods. We first discuss the relevant concepts and theorems and then apply PCA and PP (with negative standardized Shannon's entropy as the projection index) on single cell RNA sequencing data.