Abstract In this paper, we prove that a classical theorem by McAdam about the analytic spread of an ideal in Noetherian local ring continues to be true for divisorial filtrations on two-dimensional normal excellent R , and Hilbert polynomial fiber cone filtration has function which is sum linear bounded function. We these theorems first studying asymptotic properties divisors resolution singula...

This writeup is intended to be an early draft showing progress in analytical models of the spread of an infectious disease through a population with non-negligible partnership duration and demographic turnover. We assume that individuals in the population form long-lasting (but not permanent) partnerships with others. New individuals enter the population at a constant rate, while others leave. ...

While the spread of some neurodegenerative disease-associated proteinopathies, such as tau and α-synuclein, is well studied and clearly implicates transsynaptic pathology transmission, research into the progressive spread of amyloid-β pathology has been less clear. In fact, prior analyses of transregional amyloid-β pathology spread have implicated both transsynaptic and other intracellular- as ...

Volumetric light transport effects are significant for many materials like skin, smoke, clouds, snow or water. In particular, one must consider the multiple scattering of light within the volume. While it is possible to simulate such media using volumetric Monte Carlo or finite element techniques, those methods are very computationally expensive. On the other hand, simple analytic models have s...

The effects of anisoplanatism on the adaptive optics point-spread function are investigated. A model is derived that combines observations of the guide star with an analytic formulation of anisoplanatism in order to generate predictions for the adaptive optics point-spread function at arbitrary locations within the field of view. The analytic formulation captures the dependencies of anisoplanat...

Epidemic spread in single-host systems strongly depends on the population's transmission network. However, little is known regarding the spread of epidemics across networks representing populations of multiple hosts. We explored cross-species transmission in a multilayer network where layers represent populations of two distinct hosts, and disease can spread across intralayer (within-host) and ...