The Distribution of the Irreducibles in an Algebraic Number Field

The objective of this thesis is to study the distribution of the number of principal ideals generated by an irreducible element in an algebraic number field, namely in the non-unique factorization ring of integers of such a field. In particular we are investigating the size of M(x), defined as M ( x ) =∑ (α) α irred.|N (α)|≤≠ 1, where x is any positive real number and N (α) is the norm of α. We finally obtain asymptotic results for hl(x).

Pathway Semantics: An Algebraic Data Driven Algorithm to Generate Hypotheses about Molecular Patterns Underlying Disease Progression

The overarching goal of the Pathway Semantics Algorithm (PSA) is to improve the in silico identification of clinically useful hypotheses about molecular patterns in disease progression. By framing biomedical questions within a variety of matrix representations, PSA has the flexibility to analyze combined quantitative and qualitative data over a wide range of stratifications. The resulting hypothetical answers can then move to in vitro and in vivo verification, research assay optimization, clinical validation, and commercialization. Herein PSA is shown to generate novel hypotheses about the significant biological pathways in two disease domains: shock / trauma and hemophilia A, and validated experimentally in the latter. The PSA matrix algebra approach identified differential molecular patterns in biological networks over time and outcome that would not be easily found through direct assays, literature or database searches. In this dissertation, Chapter 1 provides a broad overview of the background and motivation for the study, followed by Chapter 2 with a literature review of relevant computational methods. Chapters 3 and 4 describe PSA for node and edge analysis respectively, and apply the method to disease progression in shock / trauma. Chapter 5 demonstrates the application of PSA to hemophilia A and the validation with experimental results. The work is summarized in Chapter 6, followed by extensive references and an Appendix with additional material.

The algebraic density property for affine toric varieties

In this paper we generalize the algebraic density property to not necessarily smooth affine varieties relative to some closed subvariety containing the singular locus. This property implies the remarkable approximation results for holomorphic automorphisms of the Andersén–Lempert theory. We show that an affine toric variety X satisfies this algebraic density property relative to a closed T-invariant subvariety Y if and only if X∖Y≠TX∖Y≠T. For toric surfaces we are able to classify those which possess a strong version of the algebraic density property (relative to the singular locus). The main ingredient in this classification is our proof of an equivariant version of Brunella's famous classification of complete algebraic vector fields in the affine plane.

Decoding urban landscapes through the analysis of place names and imaginaries at a local scale.

Toponomastics is increasingly interested in the subjective role of place names in quotidian life. In the frame of Urban Geography, the interest in this matter is currently growing, as the recently change in modes of habitation has urged our discipline to find new ways of exploring the cities. In this context, the study of how name's significance is connected to a urban society constitutes a very interesting approach. We believe in the importance of place names as tools for decoding urban areas and societies at a local-scale. This consideration has been frequently taken into account in the analysis of exonyms, although in their case they are not exempt of political and practical implications that prevail over the tool function. The study of toponomastic processes helps us understanding how the city works, by analyzing the liaison between urban landscape, imaginaries and toponyms which is reflected in the scarcity of some names, in the biased creation of new toponyms and in the pressure exercised over every place name by tourists, residents and local government for changing, maintaining or eliminating them. Our study-case, Toledo, is one of the oldest cities in Spain, full of myths, stories and histories that can only be understood combined with processes of internal evolution of the city linked to the arrival of new residents and the more and more notorious change of its historical landscape. At a local scale, we are willing to decode the information which is contained in its toponyms about its landscape and its society.

On the approximate parametrization problem of algebraic curves.

The problem of parameterizing approximately algebraic curves and surfaces is an active research field, with many implications in practical applications. The problem can be treated locally or globally. We formally state the problem, in its global version for the case of algebraic curves (planar or spatial), and we report on some algorithms approaching it, as well as on the associated error distance analysis.

Systematic analysis of the decoding delay on MVC decoders

We present a framework for the analysis of the decoding delay and communication latency in Multiview Video Coding. The application of this framework on MVC decoders allows minimizing the overall delay in immersive video-conference systems.

Systematic analysis of the decoding delay in multiview video

We present a framework for the analysis of the decoding delay in multiview video coding (MVC). We show that in real-time applications, an accurate estimation of the decoding delay is essential to achieve a minimum communication latency. As opposed to single-view codecs, the complexity of the multiview prediction structure and the parallel decoding of several views requires a systematic analysis of this decoding delay, which we solve using graph theory and a model of the decoder hardware architecture. Our framework assumes a decoder implementation in general purpose multi-core processors with multi-threading capabilities. For this hardware model, we show that frame processing times depend on the computational load of the decoder and we provide an iterative algorithm to compute jointly frame processing times and decoding delay. Finally, we show that decoding delay analysis can be applied to design decoders with the objective of minimizing the communication latency of the MVC system.

Decoding temporally encoded sensory input by cortical oscillations and thalamic phase comparators

The temporally encoded information obtained by vibrissal touch could be decoded “passively,” involving only input-driven elements, or “actively,” utilizing intrinsically driven oscillators. A previous study suggested that the trigeminal somatosensory system of rats does not obey the bottom-up order of activation predicted by passive decoding. Thus, we have tested whether this system obeys the predictions of active decoding. We have studied cortical single units in the somatosensory cortices of anesthetized rats and guinea pigs and found that about a quarter of them exhibit clear spontaneous oscillations, many of them around whisking frequencies (≈10 Hz). The frequencies of these oscillations could be controlled locally by glutamate. These oscillations could be forced to track the frequency of induced rhythmic whisker movements at a stable, frequency-dependent, phase difference. During these stimulations, the response intensities of multiunits at the thalamic recipient layers of the cortex decreased, and their latencies increased, with increasing input frequency. These observations are consistent with thalamocortical loops implementing phase-locked loops, circuits that are most efficient in decoding temporally encoded information like that obtained by active vibrissal touch. According to this model, and consistent with our results, populations of thalamic “relay” neurons function as phase “comparators” that compare cortical timing expectations with the actual input timing and represent the difference by their population output rate.

Glu-tRNAGln amidotransferase: A novel heterotrimeric enzyme required for correct decoding of glutamine codons during translation

The three genes, gatC, gatA, and gatB, which constitute the transcriptional unit of the Bacillus subtilis glutamyl-tRNAGln amidotransferase have been cloned. Expression of this transcriptional unit results in the production of a heterotrimeric protein that has been purified to homogeneity. The enzyme furnishes a means for formation of correctly charged Gln-tRNAGln through the transamidation of misacylated Glu-tRNAGln, functionally replacing the lack of glutaminyl-tRNA synthetase activity in Gram-positive eubacteria, cyanobacteria, Archaea, and organelles. Disruption of this operon is lethal. This demonstrates that transamidation is the only pathway to Gln-tRNAGln in B. subtilis and that glutamyl-tRNAGln amidotransferase is a novel and essential component of the translational apparatus.

Nonlinearity in genetic decoding: Homologous DNA replicase genes use alternatives of transcriptional slippage or translational frameshifting

The τ and γ subunits of DNA polymerase III are both encoded by a single gene in Escherichia coli and Thermus thermophilus. γ is two-thirds the size of τ and shares virtually all its amino acid sequence with τ. E. coli and T. thermophilus have evolved very different mechanisms for setting the approximate 1:1 ratio between τ and γ. Both mechanisms put ribosomes into alternate reading frames so that stop codons in the new frame serve to make the smaller γ protein. In E. coli, ≈50% of initiating ribosomes translate the dnaX mRNA conventionally to give τ, but the other 50% shift into the −1 reading frame at a specific site (A AAA AAG) in the mRNA to produce γ. In T. thermophilus ribosomal frameshifting is not required: the dnaX mRNA is a heterogeneous population of molecules with different numbers of A residues arising from transcriptional slippage on a run of nine T residues in the DNA template. Translation of the subpopulation containing nine As (or +/− multiples of three As) yields τ. The rest of the population of mRNAs (containing nine +/− nonmultiples of three As) puts ribosomes into the alternate reading frames to produce the γ protein(s). It is surprising that two rather similar dnaX sequences in E. coli and T. thermophilus lead to very different mechanisms of expression.

Algebraic derivative estimation applied to nonlinear control of magnetic levitation.

The subject of this thesis is the real-time implementation of algebraic derivative estimators as observers in nonlinear control of magnetic levitation systems. These estimators are based on operational calculus and implemented as FIR filters, resulting on a feasible real-time implementation. The algebraic method provide a fast, non-asymptotic state estimation. For the magnetic levitation systems, the algebraic estimators may replace the standard asymptotic observers assuring very good performance and robustness. To validate the estimators as observers in closed-loop control, several nonlinear controllers are proposed and implemented in a experimental magnetic levitation prototype. The results show an excellent performance of the proposed control laws together with the algebraic estimators.

Modern algebraic theories,

Mode of access: Internet.

Algebraic topology.

Mode of access: Internet.

Selected topics in algebraic geometry; report of the Committee on rational transformations:

Bibliography at end of each chapter.