Low-Dimensional Reality-Based Algebras

In this paper we introduce the definition of a reality-based algebra (RBA) as well as a subclass of reality-based algebras, table algebras. Using sesquilinear forms, we prove that a reality-based algebra is semisimple. We look at a specific reality-based algebra of dimension 5 and provide formulas for the structure constants of this algebra. We determine by looking at these structure constants and setting conditions on specific structural components when this particular reality-based algebra is a table algebra. In fact, this will be a noncommutative table algebra of dimension 5

Macroscopic Model of a Cilium Appendage

The goal of this project is to develop a macroscopic model of the cilia appendage and a realistic testing environment for the model. The model should be created with materials that effectively replicate the material and mechanical properties of the appendage in the human body. Additionally, the testing environment should mimic the viscous fluid that surrounds cilia in the human body to allow for more accurate testing. The fluid’s flow should be parallel to the model and induce instability in the system. This instability should force the cilia model to oscillate like a flag in the wind. Upon completion of this project, our model should allow testers to gain a deeper understanding of cilia\u27s motion by observing and measuring these oscillations. Ideally, our model and testing environment will be transportable and easy to set up. This project is important because cilia malfunction can lead to many different diseases in the human body

Recognizing algebraically constructed graphs which are wreath products.

It is known that a Cayley digraph of an abelian group A is isomorphic to a nontrivial wreath product if and only if there is a proper nontrivial subgroup B of A such that the connection set without B is a union of cosets of B in A. We generalize this result to Cayley digraphs of nonabelian groups G by showing that such a digraph is isomorphic to a nontrivial wreath product if and only if there is a proper nontrivial subgroup H of G such that S without H is a union of double cosets of H in G. This result is proven in the more general situation of a double coset digraph (also known as a Sabidussi coset digraph.) We then give applications of this result which include obtaining a graph theoretic definition of double coset digraphs, and determining the relationship between a double coset digraph and its corresponding Cayley digraph. We further expand the result obtained for double coset digraphs to a collection of bipartite graphs called bi-coset graphs and the bipartite equivalent to Cayley graphs called Haar graphs. Instead of considering when this collection of graphs is a wreath product, we consider the more general graph product known as an X-join by showing that a connected bi-coset graph of a group G with respect to some subgroups L and R of G is isomorphic to an X-join of a collection of empty graphs if and only if the connection set is a union of double cosets of some subgroups N containing L and M containing R in G. The automorphism group of such -joins is also found. We also prove that disconnected bi-coset graphs are always isomorphic to a wreath product of an empty graph with a bi-coset graph

Using the Reliable Change Index Statistic to Analyze Developmental Changes in Infants at Risk for Autism Spectrum Disorder

Longitudinal studies of the development of autism spectrum disorders (ASD) provide an understanding of which variables may be important predictors of an ASD. The objective of the current study is to apply the reliable change index (RCI) statistic to examine whether the Parent Observation of Early Markers Scale (POEMS) is sensitive to developmental change, and whether these changes can be quantified along a child’s developmental trajectory. Ninety-six children with older siblings with autism were followed from 1-36 months of age. Group-based RCI analysis confirms that the POEMS is capable of detecting significant changes within pre-defined diagnostic groups. Within-subject analysis suggests that ongoing monitoring of a child at-risk for an ASD requires interpretation of both significant intervals identified by the RCI statistic, as well as the presence of repeated high (i.e., >70) scores. This study provides preliminary evidence for a reasonably sensitive and specific means by which individual change can be clinically monitored via parent report

Investigating the prevalence and causes of prescribing errors in general practice : the PRACtICe Study

Report prepared by the University of Nottingham, University of Reading and University of Hertfordshir

Disruption of the autoinhibited state primes the E3 ligase parkin for activation and catalysis

The PARK2 gene is mutated in 50% of autosomal recessive juvenile parkinsonism (ARJP) cases. It encodes parkin, an E3 ubiquitin ligase of the RBR family. Parkin exists in an autoinhibited state that is activated by phosphorylation of its N‐terminal ubiquitin‐like (Ubl) domain and binding of phosphoubiquitin. We describe the 1.8 Å crystal structure of human parkin in its fully inhibited state and identify the key interfaces to maintain parkin inhibition. We identify the phosphoubiquitin‐binding interface, provide a model for the phosphoubiquitin–parkin complex and show how phosphorylation of the Ubl domain primes parkin for optimal phosphoubiquitin binding. Furthermore, we demonstrate that the addition of phosphoubiquitin leads to displacement of the Ubl domain through loss of structure, unveiling a ubiquitin‐binding site used by the E2~Ub conjugate, thus leading to active parkin. We find the role of the Ubl domain is to prevent parkin activity in the absence of the phosphorylation signals, and propose a model for parkin inhibition, optimization for phosphoubiquitin recruitment, release of inhibition by the Ubl domain and engagement with an E2~Ub conjugate. Taken together, this model provides a mechanistic framework for activating parkin