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The Einstein evolution equations may be written in a variety of equivalent analytical forms, but numerical solutions of these different formulations display a wide range of growth rates for constraint violations. For symmetric hyperbolic…
Obtaining high certainty in predictive models is crucial for making informed and trustworthy decisions in many scientific and engineering domains. However, extensive experimentation required for model accuracy can be both costly and…
A novel numerical method for the estimation of large time-varying parameter (TVP) models is proposed. The updating and smoothing estimates of the TVP model are derived within the context of generalised linear least squares and through…
Computer model calibration is a crucial step in building a reliable computer model. In the face of massive physical observations, a fast estimation for the calibration parameters is urgently needed. To alleviate the computational burden, we…
Providing diagnostic feedback about growth is crucial to formative decisions such as targeted remedial instructions or interventions. This paper proposed a longitudinal higher-order diagnostic classification modeling approach for measuring…
Individual-based models are complex and they have usually an elevated number of input parameters which must be tuned for reproducing the observed population data or the experimental results as accurately as possible. Thus, one of the…
Differential equations are pivotal in modeling and understanding the dynamics of various systems, offering insights into their future states through parameter estimation fitted to time series data. In fields such as economy, politics, and…
We consider two minimal mathematical models for cancer dynamics and self-adaptation. We aim to capture the interplay between the rapid progression of cancer growth and the possibility to leverage and enhance self-adaptive defense mechanisms…
When mathematical biology models are used to make quantitative predictions for clinical or industrial use, it is important that these predictions come with a reliable estimate of their accuracy (uncertainty quantification). Because models…
Most human protein-coding genes can be transcribed into multiple possible distinct mRNA isoforms. These alternative splicing patterns encourage molecular diversity and dysregulation of isoform expression plays an important role in disease…
For biological experiments aiming at calibrating models with unknown parameters, a good experimental design is crucial, especially for those subject to various constraints, such as financial limitations, time consumption and physical…
An individualized treatment rule (ITR) is a decision rule that aims to improve individual patients health outcomes by recommending optimal treatments according to patients specific information. In observational studies, collected data may…
The paper deals with the estimation of a signal model in the form of the output of a continuous linear time-invariant system driven by a sequence of instantaneous impulses, i.e. an impulsive time series. This modeling concept arises in,…
RNA-seq has become a de facto standard for measuring gene expression. Traditionally, RNA-seq experiments are mathematically averaged -- they sequence the mRNA of individuals from different treatment groups, hoping to correlate phenotype…
To promote precision medicine, individualized treatment regimes (ITRs) are crucial for optimizing the expected clinical outcome based on patient-specific characteristics. However, existing ITR research has primarily focused on scenarios…
The paper concerns the problem of minimization of the compliance of linear elastic structures made of an isotropic material. The bulk and shear moduli are the design variables, both viewed as non-negative fields on the design domain. The…
During the last decade, incremental sampling-based motion planning algorithms, such as the Rapidly-exploring Random Trees (RRTs) have been shown to work well in practice and to possess theoretical guarantees such as probabilistic…
Statistical learning evolves quickly with more and more sophisticated models proposed to incorporate the complicated data structure from modern scientific and business problems. Varying index coefficient models extend varying coefficient…
The circadian rhythm plays a crucial role in regulating biological processes, and its disruption is linked to various health issues. Identifying small molecules that influence the circadian period is essential for developing targeted…
Chirp signal models and their generalizations have been used to model many natural and man-made phenomena in signal processing and time series literature. In recent times, several methods have been proposed for parameter estimation of these…