In this paper, we revisit the Nested Stochastic Simulation Algorithm (NSSA) for stochastic chemical reacting networks by first proving its strong convergence. We then study a speed up of the algorithm by using the explicit Tau-Leaping method as the Inner solver to approximate invariant measures of fast processes, for which strong error estimates can also be obtained. Numerical experiments are p...

Interactive Evolutionary Algorithms (IEAs) are a powerful explorative search technique that utilizes human input to make subjective decisions on potential problem solutions. But humans are much slower than computers and get bored and tired easily, limiting the usefulness of IEAs. Here two variations of a user-modeling approach are compared to determine if this approach can accelerate IEA search...

The Box-Cox power exponential (BCPE) distribution, developed in this paper, provides a model for a dependent variable Y exhibiting both skewness and kurtosis (leptokurtosis or platykurtosis). The distribution is defined by a power transformation Y(nu) having a shifted and scaled (truncated) standard power exponential distribution with parameter tau. The distribution has four parameters and is d...

Tau-leaping is a popular discretization method for generating approximate paths of continuous time, discrete space, Markov chains, notably for biochemical reaction systems. To compute expected values in this context, an appropriate multilevel Monte Carlo form of tau-leaping has been shown to improve efficiency dramatically. In this work we derive new analytic results concerning the computationa...

This note is concerned with the spectral properties of matrices associated with linear smoothers. We derive analytical results on the eigenvalues and eigenvectors of smoothing matrices by interpreting the latter as perturbations of matrices belonging to algebras with known spectral properties, such as the Circulant and the generalised Tau. These results are used to characterise the properties o...

We give three applications of a recently-proven "Decomposition Lemma," which allows one to count preimages certain sets permutations under West's stack-sorting map $s$. first enumerate the permutation class $s^{-1}(\text{Av}(231,321))=\text{Av}(2341,3241,45231)$, finding new example an unbalanced Wilf equivalence. This result is equivalent enumeration sortable by ${\bf B}\circ s$, where B}$ bub...

Objective(s):Breast cancer is an important leading cause of death from cancer. Stathmin and tau proteins are regulators of cell motility, and their overexpression is associated with the progression and bad prognosis of breast cancer. Memantine, an N-methyl-D-aspartate (NMDA) receptor antagonist, is the potential inhibitor of tau protein in neurons. This study determines the effect of memantine ...

Objective(s):Alzheimer's disease (AD) is the most common age-related neurodegenerative disorder. One of the hallmarks of AD is an abnormal accumulation of fibril forms of tau protein which is known as a microtubule associated protein. In this regard, inhibition of tau aggregation has been documented to be a potent therapeutic approach in AD and tauopathies. Unfortunately, the available syntheti...

When examining the robustness of systems that take ranked lists as input, we can induce noise, measured in terms of Kendall’s tau rank correlation, by applying a set number of random adjacent transpositions. The set number of random transpositions ensures that any ranked lists, induced with this noise, has a specific expected Kendall’s tau. However, if we have ranked lists of varying length, it...