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In the first part of this paper, we review old and new results about the influence of host population heterogeneity on (various characteristics of) epidemic outbreaks. In the second part we highlight a modelling issue that so far has…
We present a new method to obtain the generating functions for directed convex polyominoes according to several different statistics including: width, height, size of last column/row and number of corners. This method can be used to study…
In this article, we prove two results. First, we construct a dense subset in the space of polynomial foliations of degree $n$ such that each foliation from this subset has a leaf with at least $\frac{(n+1)(n+2)}2-4$ handles. Next, we prove…
Latest developments in leptogenesis are reviewed with a particular emphasis on the proposals to test leptogenesis. We discuss in particular the important role played by light and heavy flavour effects in the determination of the final…
In this paper we obtain the extended genus field of a finite abelian extension of a global rational function field. We first study the case of a cyclic extension of prime power degree. Next, we use that the extended genus fields of a…
Empirical exoplanet mass-radius relations have been used to study the demographics and compositions of small exoplanets for many years. However, the heterogeneous nature of these measurements hinders robust statistical analysis of this…
The generating function of the cumulants in random matrix models, as well as the cumulants themselves, can be expanded as asymptotic (divergent) series indexed by maps. While at fixed genus the sums over maps converge, the sums over genera…
Italian ryegrass is a grass weed commonly found in winter wheat fields that are competitive with winter wheat for moisture and nutrients. Ryegrass can cause substantial reductions in yield and grain quality if not properly controlled with…
Bio-inspired algorithms utilize natural processes such as evolution, swarm behavior, foraging, and plant growth to solve complex, nonlinear, high-dimensional optimization problems. However, a plethora of these algorithms require a more…
We present a survey of our recent research on varieties, generated by wreath products of groups. In particular, the full classification of all cases, when the (cartesian or direct) wreath product of any abelian groups $A$ and $B$ generates…
Uncovering the heterogeneous effects of particular policies or "treatments" is a key concern for researchers and policymakers. A common approach is to report average treatment effects across subgroups based on observable covariates.…
The Yule branching process is a classical model for the random generation of gene tree topologies in population genetics. It generates binary ranked trees -- also called "histories" -- with a finite number $n$ of leaves. We study the…
This paper addresses the enumeration of rooted and unrooted hypermaps of a given genus. For rooted hypermaps the enumeration method consists of considering the more general family of multirooted hypermaps, in which darts other than the root…
Lyme disease is an infectious disease transmitted to humans by a bite from an infected Ixodes species (blacklegged ticks). It is one of the fastest growing vector-borne illness in North America and is expanding its geographic footprint.…
Accurate identification of synergistic treatment combinations and their underlying biological mechanisms is critical across many disease domains, especially cancer. In translational oncology research, preclinical systems such as…
Neutral macroevolutionary models, such as the Yule model, give rise to a probability distribution on the set of discrete rooted binary trees over a given leaf set. Such models can provide a signal as to the approximate location of the root…
RNA sequencing allows one to study allelic imbalance of gene expression, which may be due to genetic factors or genomic imprinting. It is desirable to model both genetic and parent-of-origin effects simultaneously to avoid confounding and…
The host's odor serves as a critical biological tracking signal in the host-seeking process of mosquitoes, and its heterogeneity significantly influences the transmission of mosquito-borne diseases. In this study, we propose a…
Arabidopsis thaliana is a plant species widely utilized by scientists to estimate the impact of genetic differences in root morphological features. For this purpose, images of this plant after genetic modifications are taken to study…
Aphids are one of the main threats to crops, rural families, and global food security. Chemical pest control is a necessary component of crop production for maximizing yields, however, it is unnecessary to apply the chemical approaches to…