Locally recurrent functions, density topologies and algebraic genericity

We study the algebraic and topological genericity of certain subsets of locally recurrent functions, obtaining (among other results) algebrability and spaceability within these classes.

Aspects of Motives: Finite-dimensionality, Chow-Kunneth Decompositions and Intersections of Cycles

This thesis analyzes the Chow motives of 3 types of smooth projective varieties: the desingularized elliptic self fiber product, the Fano surface of lines on a cubic threefold and an ample hypersurface of an Abelian variety. For the desingularized elliptic self fiber product, we use an isotypic decomposition of the motive to deduce the Murre conjectures. We also prove a result about the intersection product. For the Fano surface of lines, we prove the finite-dimensionality of the Chow motive. Finally, we prove that an ample hypersurface on an Abelian variety possesses a Chow-Kunneth decomposition for which a motivic version of the Lefschetz hyperplane theorem holds.

A monoidal algebraic model for rational SO(2)-spectra

The category of rational SO(2)--equivariant spectra admits an algebraic model. That is, there is an abelian category A(SO(2)) whose derived category is equivalent to the homotopy category of rational$SO(2)--equivariant spectra. An important question is: does this algebraic model capture the smash product of spectra? The category A(SO(2)) is known as Greenlees' standard model, it is an abelian category that has no projective objects and is constructed from modules over a non--Noetherian ring. As a consequence, the standard techniques for constructing a monoidal model structure cannot be applied. In this paper a monoidal model structure on A(SO(2)) is constructed and the derived tensor product on the homotopy category is shown to be compatible with the smash product of spectra. The method used is related to techniques developed by the author in earlier joint work with Roitzheim. That work constructed a monoidal model structure on Franke's exotic model for the K_(p)--local stable homotopy category. A monoidal Quillen equivalence to a simpler monoidal model category that has explicit generating sets is also given. Having monoidal model structures on the two categories removes a serious obstruction to constructing a series of monoidal Quillen equivalences between the algebraic model and rational SO(2)--equivariant spectra.

Problems in Algebraic Vision

Thesis (Ph.D.)--University of Washington, 2016-08

Behavioral equivalence of hidden k-logics: an abstract algebraic approach

This work advances a research agenda which has as its main aim the application of Abstract Algebraic Logic (AAL) methods and tools to the specification and verification of software systems. It uses a generalization of the notion of an abstract deductive system to handle multi-sorted deductive systems which differentiate visible and hidden sorts. Two main results of the paper are obtained by generalizing properties of the Leibniz congruence — the central notion in AAL. In this paper we discuss a question we posed in [1] about the relationship between the behavioral equivalences of equivalent hidden logics. We also present a necessary and sufficient intrinsic condition for two hidden logics to be equivalent.

Improving income and livelihood of poor farming household in Bangladesh through adoption of improved aquaculture technologies and varieties

Fish are an important part of Bangladeshi culture and diet. Bangladesh ranks among the top five freshwater fish producers in the world. Fish are abundant in the thousands of rivers, ponds, lakes and seasonal floodplains across the country. They are a major source of protein for people living near these water bodies. In Bangladesh, many households depend on fish farming for their livelihood. By growing fish in homestead ponds, households have a consistent supply of nutritious fish and can sell the surplus for an income. The USAID-funded Cereal Systems Initiative for South Asia in Bangladesh (CSISA-BD) aimed to increase the income of farming households through increased productivity of aquaculture systems. Key activities of the project included developing and disseminating appropriate improved agricultural technology and quality fish seeds to improve livelihoods, food security and nutrition.

Transcriptomic comparison between two Vitis vinifera L. varieties (Trincadeira and Touriga Nacional) in abiotic stress conditions

Predicted climate changes announce an increase of extreme environmental conditions including drought and excessive heat and light in classical viticultural regions. Thus, understanding how grapevine responds to these conditions and how different genotypes can adapt, is crucial for informed decisions on accurate viticultural actions. Global transcriptome analyses are useful for this purpose as the response to these abiotic stresses involves the interplay of complex and diverse cascades of physiological, cellular and molecular events. The main goal of the present work was to evaluate the response to diverse imposed abiotic stresses at the transcriptome level and to compare the response of two grapevine varieties with contrasting physiological trends, Trincadeira (TR) and Touriga Nacional (TN).

Strong shift equivalence, algebraic K-theory, and isolating zero-dimensional dynamics on manifolds

We study the relations of shift equivalence and strong shift equivalence for matrices over a ring $\mathcal{R}$, and establish a connection between these relations and algebraic K-theory. We utilize this connection to obtain results in two areas where the shift and strong shift equivalence relations play an important role: the study of finite group extensions of shifts of finite type, and the Generalized Spectral Conjectures of Boyle and Handelman for nonnegative matrices over subrings of the real numbers. We show the refinement of the shift equivalence class of a matrix $A$ over a ring $\mathcal{R}$ by strong shift equivalence classes over the ring is classified by a quotient $NK_{1}(\mathcal{R}) / E(A,\mathcal{R})$ of the algebraic K-group $NK_{1}(\calR)$. We use the K-theory of non-commutative localizations to show that in certain cases the subgroup $E(A,\mathcal{R})$ must vanish, including the case $A$ is invertible over $\mathcal{R}$. We use the K-theory connection to clarify the structure of algebraic invariants for finite group extensions of shifts of finite type. In particular, we give a strong negative answer to a question of Parry, who asked whether the dynamical zeta function determines up to finitely many topological conjugacy classes the extensions by $G$ of a fixed mixing shift of finite type. We apply the K-theory connection to prove the equivalence of a strong and weak form of the Generalized Spectral Conjecture of Boyle and Handelman for primitive matrices over subrings of $\mathbb{R}$. We construct explicit matrices whose class in the algebraic K-group $NK_{1}(\mathcal{R})$ is non-zero for certain rings $\mathcal{R}$ motivated by applications. We study the possible dynamics of the restriction of a homeomorphism of a compact manifold to an isolated zero-dimensional set. We prove that for $n \ge 3$ every compact zero-dimensional system can arise as an isolated invariant set for a homeomorphism of a compact $n$-manifold. In dimension two, we provide obstructions and examples.

The Real-Quaternionic Indicator of Irreducible Self-Conjugate Representations of Real Reductive Algebraic Groups and A Comment on the Local Langlands Correspondence of GL(2, F )

The real-quaternionic indicator, also called the $\delta$ indicator, indicates if a self-conjugate representation is of real or quaternionic type. It is closely related to the Frobenius-Schur indicator, which we call the $\varepsilon$ indicator. The Frobenius-Schur indicator $\varepsilon(\pi)$ is known to be given by a particular value of the central character. We would like a similar result for the $\delta$ indicator. When $G$ is compact, $\delta(\pi)$ and $\varepsilon(\pi)$ coincide. In general, they are not necessarily the same. In this thesis, we will give a relation between the two indicators when $G$ is a real reductive algebraic group. This relation also leads to a formula for $\delta(\pi)$ in terms of the central character. For the second part, we consider the construction of the local Langlands correspondence of $GL(2,F)$ when $F$ is a non-Archimedean local field with odd residual characteristics. By re-examining the construction, we provide new proofs to some important properties of the correspondence. Namely, the construction is independent of the choice of additive character in the theta correspondence.

Algebraic geometric codes over rings

The techniques of algebraic geometry have been widely and successfully applied to the study of linear codes over finite fields since the early 1980's. Recently, there has been an increased interest in the study of linear codes over finite rings. In this thesis, we combine these two approaches to coding theory by introducing and studying algebraic geometric codes over rings.

Effect of ambient levels of ozone on photosynthetic components and radical scavenging system in leaves of African cowpea varieties

Tropospheric ozone (O3), a main component of photochemical oxidants, adversely affects not only human health but also vegetation. To clarify the long-term effects of ambient levels of tropospheric ozone (O3) on photosynthetic components and radical scavenging system in the leaves of cowpea ( Vigna unguiculata L.), two African varieties, Blackeye and Asontem, were grown in open-top chambers and exposed to filtered air (FA), non-filtered air (NF) or non-filtered air with additional O3 of approximately 50 nl l-1. Ambient levels of O3 significantly reduced chlorophyll concentration, quantum yield and activity of ribulose 1,5-bisphosphate carboxylase/oxygenase (Rubisco), thus contributing to the reduction in net photosynthetic rate at the reproductive growth stage of both varieties; with no significant variety difference in the sensitivity to O3. The O3-induced significant reduction in catalase activity was observed in Blackeye at vegetative and reproductive growth stages; and in Asontem at reproductive growth stage. On the other hand, exposure to O3 significantly increased ascorbate peroxidase activity in Blackeye at reproductive stage and did not significantly affect that in Blackeye at vegetative growth stage and that in Asontem at both growth stages. At reproductive growth stage, activities of monodehydroascorbate reductase and glutathione reductase were significantly increased by the exposure to O3 in both varieties. The results obtained in this study suggest that, although ascorbate peroxidase, monodehydroascorbate reductase and glutathione reductase played important roles in scavenging O3-induced reactive oxygen species in the leaves, radical scavenging ability of these enzymes is not sufficient to avoid detrimental effects of ambient levels of O3 on photosynthesis in both African cowpea varieties.

GENETIC EVALUATION OF SEED TRAITS FROM INTRASPECIFIC CROSSING OF GENETICALLY DISTINCT WATERMELON VARIETIES

Citrullus lanatus (Thunb.) Matsumura and Nakai (Cucurbitaceae) is an important cucurbit crop worldwide. Global production of watermelon is about 90 million metric tonnes per annum, making it among the top five most consumed fresh fruits. The objective of this study was to evaluate seed variability in different segregating populations, and determine heritability of traits of watermelon. Interspecific crosses were made between two cultivars of C. lanatus (Bebu and Wlêwlê Small Seeds (WSS) were performed at Research Station of Nangui Abrogoua University in Abidjan, Côte d’Ivoire. There was wide variability between parental, F1, BC1 (first generation of back-crossing) and F2 seeds. Seeds of all hybrid populations were intermediate versus those of the parents. Also, crossing did not affect F1 and F2 seed characters, but affected those of BC1 because of maternal effects. Thus, back-crossing on Bebu cultivar produced seeds which looked like those of Bebu; while back-crossing on WSS cultivar produced seeds similar to those of WSS. Principal Component Analysis (PCA) and individuals repartitioning revealed that Bebu and WSS cultivars were genetically distinct and showed three main groups: two groups from each parental line and one from a recombinant line (hybrids). F2 population had a wide individual’s dispersion, and contained seeds of all other populations. High heritability was observed for all evaluated characters.

FIELD TOLERANCE OF SELECTED VARIETIES TO AND FUNGICIDE EFFICACY AGAINST ALTERNARIA BLIGHT OF SWEET POTATO

Alternaria blight (AB) of sweet potato ( Ipomoea batatas L. ), caused by Alternaria spp., was recently reported in South Africa, but is common in southern and eastern Africa. Elsewhere in the world, AB is controlled primarily using resistant varieties. Twenty-five sweet potato varieties/breeding lines, from different origins were assessed for tolerance to AB. The materials were planted in fields having a history of AB disease and rated for tolerance based on a General Disease Index (GDI), with the lowest scores representing tolerance, and the higher scores representing susceptibility. Variety 199062-1 had the lowest GDI value, and was the most tolerant to AB; while W119 had the highest GDI value and was the most susceptible to the disease. Other varieties/breeding lines showed a variation in GDI values between most tolerant and most susceptible. Among the fungicides tested under field conditions, the mixture azoxystrobin-difenoconazole was the most effective in reducing AB intensity. Fungicides pyraclostrobin-boscalid, unizeb, azoxystrobin-chlorothalonil and cymoxanil-mancozeb were also effective against the disease.