The auto-Igusa zeta function of a plane curve singularity is rational

It is shown that the auto-Igusa zeta function of a plane curve singularity is rational. This gives a new criterion for a plane curve over an algebraically closed field of characteristic zero to be smooth at a point.Comment: 9 page

Decision Tree Analysis as a Supplementary Tool to Enhance Histomorphological Differentiation when Distinguishing Human from Non-human Cranial Bone in both Burnt and Unburnt States: A feasibility study

This feasibility study was undertaken to describe and record the histological characteristics of burnt and unburnt cranial bone fragments from human and non-human bones. Reference series of fully mineralised, transverse sections of cranial bone, from all variables and specimen states were prepared by manual cutting and semi-automated grinding and polishing methods. A photomicrograph catalogue reflecting differences in burnt and unburnt bone from human and non-humans was recorded and qualitative analysis was performed using an established classification system based on primary bone characteristics. The histomorphology associated with human and non-human samples was, for the main part, preserved following burning at high temperature. Clearly, fibro-lamellar complex tissue subtypes, such as plexiform or laminar primary bone, were only present in non-human bones. A decision tree analysis based on histological features provided a definitive identification key for distinguishing human from non-human bone, with an accuracy of 100%. The decision tree for samples where burning was unknown was 96% accurate, and multi-step classification to taxon was possible with 100% accuracy. The results of this feasibility study, strongly suggest that histology remains a viable alternative technique if fragments of cranial bone require forensic examination in both burnt and unburnt states. The decision tree analysis may provide an additional, but vital tool to enhance data interpretation. Further studies are needed to assess variation in histomorphology taking into account other cranial bones, ontogeny, species and burning conditions

Formal deformations of algebraic spaces and generalizations of the motivic Igusa zeta function

We generalize the notion of the auto-Igusa zeta function to formal deformations of algebraic spaces. By incorporating data from all algebraic transformations of local coordinates, this function can be viewed as a generalization of the traditional motivic Igusa zeta function. Furthermore, we introduce a new series, which we term the canonical auto-Igusa zeta function, whose coefficients are given by the quotient stacks formed from the coefficients of the auto-Igusa zeta function modulo change of coordinates. We indicate the current state of the literature on these generalized Igusa-zeta functions and offer directions for future research.Comment: 8 page

Effects on a Harsh Environment on the Life History Patterns of Two Species of Tropical Aquatic Hemiptera (Family: Naucoridae)

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/119071/1/ecy198263175.pd

Auto-Arcs of Complete Intersection Varieties

We systematically study the so-called auto-arc spaces. Auto-arc spaces were originally introduced by Schoutens in 2012 and later generalized and studied by the author in his PhD Thesis and subsequent work. In that aforementioned work, only results concerning trivial deformations were explicitly considered because even in that case auto-arc spaces being a subset of generalized jet schemes are difficult to understand. The major advance in this work is obtained by considering auto arc spaces of complete intersections. It is shown that over $k[t]/(t^{n+1})$, these spaces can be viewed as global flat deformations over $\mathbb{A}_k^n$ of the classical jet scheme of order $n$. We propose the project in general of investigating the flat locus of this naturally induced morphism as a type of relativized version of previous results by Mustata on jet schemes a local complete intersections. We also introduce the study of so-called strong/weak deformations of curves in this context, and we show that a motivic volume can be defined in this case.Comment: 20 page