The Dynamics of Group Codes: Dual Abelian Group Codes and Systems

Fundamental results concerning the dynamics of abelian group codes (behaviors) and their duals are developed. Duals of sequence spaces over locally compact abelian groups may be defined via Pontryagin duality; dual group codes are orthogonal subgroups of dual sequence spaces. The dual of a complete code or system is finite, and the dual of a Laurent code or system is (anti-)Laurent. If C and C^\perp are dual codes, then the state spaces of C act as the character groups of the state spaces of C^\perp. The controllability properties of C are the observability properties of C^\perp. In particular, C is (strongly) controllable if and only if C^\perp is (strongly) observable, and the controller memory of C is the observer memory of C^\perp. The controller granules of C act as the character groups of the observer granules of C^\perp. Examples of minimal observer-form encoder and syndrome-former constructions are given. Finally, every observer granule of C is an "end-around" controller granule of C.Comment: 30 pages, 11 figures. To appear in IEEE Trans. Inform. Theory, 200

Rateless Coding for Gaussian Channels

A rateless code-i.e., a rate-compatible family of codes-has the property that codewords of the higher rate codes are prefixes of those of the lower rate ones. A perfect family of such codes is one in which each of the codes in the family is capacity-achieving. We show by construction that perfect rateless codes with low-complexity decoding algorithms exist for additive white Gaussian noise channels. Our construction involves the use of layered encoding and successive decoding, together with repetition using time-varying layer weights. As an illustration of our framework, we design a practical three-rate code family. We further construct rich sets of near-perfect rateless codes within our architecture that require either significantly fewer layers or lower complexity than their perfect counterparts. Variations of the basic construction are also developed, including one for time-varying channels in which there is no a priori stochastic model.Comment: 18 page

Defining Teacher

The author takes an etymological look at the term “teacher” to humanize the current post-modern teacher’s quarries as to what their purpose is as a teacher. The author explicates the two terms, didaskalōs and pedagogue, to address the competing ideas of the role of a teacher before asserting that success, or virtue, comes in the form of continued development, paideia, of both the teacher and their students. Concluding that the current teacher doesn’t need to be any kind of teacher other than the one who continues to improve

Elements of Convergence Approach Theory

We introduce two generalizations to convergence approach spaces of classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other. Characterizations are obtained for two alternative extensions of reg- ularity to convergence-approach spaces: regularity and strong regularity. Along the way, we give a brief overview of the theory of convergence spaces and of convergence approach spaces

The Phytoremediative Effects of Cilantro (Coriandrum sativum) in Lead Contaminated Soil

Environmental exposure to heavy metals such as lead pose a significant health threat. The goal of this project was to evaluate the effectiveness of Coriandrum sativum (Cilantro) as a potential lead (II), Pb2+, phytoremediator. C. sativumplants were allowed to grow for 43 days while exposed to with different amounts of lead nitrate, Pb(NO3)2. Lead exposure was accomplished by regular watering with a concentration series of lead nitrate solutions. The roots and shoots of these plants were separated and dried. Ground plant material was liquefied by nitric acid digestion. The amount of lead absorbed by each plant sample was determined by Flame Atomic Absorption Spectrometry (FAAS). A Kruskal-Wallis test found a significant difference between the amounts of lead detected in the plants of the four treatment groups. This difference existed both in the roots and shoots of the C. sativum. The results of this study show that greater lead exposure yielded greater lead absorption in C. sativum. This supports that C. sativum effectively absorbs lead from the environment. Further studies and refined exposure series are needed to increase statistical validity and confirm C. sativum’s phytoremediative potential

Soil Microbial Community Composition of White Oak Mountain, Tennessee

Abstract - Soil microbial communities are responsible for nutrient cycling in terrestrial ecosystems and have symbiotic and parasitic relationships with the plant community. However, little is known about the factors that determine the soil microbial community composition. In this study we examined how spring wildflower diversity and geographical factors influence the soil microbial community composition of the second growth oak hickory forests of White Oak Mountain in Southeast Tennessee. The characterization of the soil microbial community was completed with 16S/18S/ITS rDNA amplicon sequencing of total DNA extracted from soil samples that were normalized for each sample plot. Here we characterize the soil microbial community of White Oak Mountain, demonstrate that an increase in spring wildflower diversity significantly increases bacterial but not fungal or total eukaryotic soil diversity, that slope type is a major factor in the microbial community composition, and that geographical differences between plots are greater than seasonal differences

Isolation of Arabidopsis thaliana plants homozygous for an insertional inactivation mutation within atPRP4.

The AtPRP4 gene in Arabidopsis thaliana has been shown to function in several specific parts of the plant’s cell wall. It is shown to be expressed in the seeds, radicles, roots, leaves, inflorescences, and embryos of Arabidopsis thaliana. These patterns have suggested unique functions for ATPRP4 in determining cell-type-specific wall structure during the development of a plant as well as contributing to defense reactions against physical damage to the plant and pathogen infection within the plant. In this study, a simple DNA prep was performed on the true leaves of Arabidopsis thaliana. Subsequent PCR reactions were performed using AtPRP4F/4R, AtPRP4F/Lba1, and AtPRP4F/4R/Lba1 primer combinations. The PCR products were analyzed on 1% (w/v) agarose gels in TAE, visualized by ethidium bromide staining, and imaged with a UVP EC3 imaging system. We expected to identify homozygous plants for a T-DNA insertional mutation. This work is poised to help develop a tool that will grant us the ability to examine the function of AtPRP4 inside specific cell walls as well as uncover any potential phenotypes associated with the loss of this protein found in Arabidopsis thaliana