How Ordinary Elimination Became Gaussian Elimination

Newton, in notes that he would rather not have seen published, described a process for solving simultaneous equations that later authors applied specifically to linear equations. This method that Euler did not recommend, that Legendre called "ordinary," and that Gauss called "common" - is now named after Gauss: "Gaussian" elimination. Gauss's name became associated with elimination through the adoption, by professional computers, of a specialized notation that Gauss devised for his own least squares calculations. The notation allowed elimination to be viewed as a sequence of arithmetic operations that were repeatedly optimized for hand computing and eventually were described by matrices.Comment: 56 pages, 21 figures, 1 tabl

Partial Quantifier Elimination

We consider the problem of Partial Quantifier Elimination (PQE). Given formula exists(X)[F(X,Y) & G(X,Y)], where F, G are in conjunctive normal form, the PQE problem is to find a formula F*(Y) such that F* & exists(X)[G] is logically equivalent to exists(X)[F & G]. We solve the PQE problem by generating and adding to F clauses over the free variables that make the clauses of F with quantified variables redundant. The traditional Quantifier Elimination problem (QE) is a special case of PQE where G is empty so all clauses of the input formula with quantified variables need to be made redundant. The importance of PQE is twofold. First, many problems are more naturally formulated in terms of PQE rather than QE. Second, in many cases PQE can be solved more efficiently than QE. We describe a PQE algorithm based on the machinery of dependency sequents and give experimental results showing the promise of PQE

Towards Measles elimination

In many European countries measles is still a cause of great public health concern. Outbreaks of the disease are still occurring because the degree of vaccination coverage required to interrupt transmission has not yet been achieved. Many countries have started to implement measles elimination strategies. These are primarily based on attaining a very high coverage of measles vaccination and strengthening measles surveillance systems.peer-reviewe

Universal Leakage Elimination

``Leakage'' errors are particularly serious errors which couple states within a code subspace to states outside of that subspace thus destroying the error protection benefit afforded by an encoded state. We generalize an earlier method for producing leakage elimination decoupling operations and examine the effects of the leakage eliminating operations on decoherence-free or noiseless subsystems which encode one logical, or protected qubit into three or four qubits. We find that by eliminating the large class of leakage errors, under some circumstances, we can create the conditions for a decoherence free evolution. In other cases we identify a combination decoherence-free and quantum error correcting code which could eliminate errors in solid-state qubits with anisotropic exchange interaction Hamiltonians and enable universal quantum computing with only these interactions.Comment: 14 pages, no figures, new version has references updated/fixe

Shrinking the Malaria Map: A Prospectus on Malaria Elimination

\ud Thirty-nine countries across the world are making progress toward malaria elimination. Some are committed to nationwide elimination, while others are pursuing spatially progressive elimination within their borders. Influential donor and multilateral organizations are supporting their goals of achieving malaria-free status. With elimination back on the global agenda, countries face a myriad of questions. Should they change their programs to eliminate rather than control malaria? What tools are available? What policies need to be put into place? How will they benefit from elimination? Unfortunately, answers to these questions, and resources for agencies and country program managers considering or pursuing elimination, are scarce. The 39 eliminating countries are all positioned along the endemic margins of the disease, yet they naturally experience a variety of country characteristics and epidemiologies that make their malaria situations different from one another. The Malaria Elimination Group (MEG) and this Prospectus recognize\ud that there is no single solution, strategy, or time line that will be appropriate for every country, and each is encouraged to initiate a comprehensive evaluation of its readiness and strategy for elimination. The Prospectus is designed to guide countries in conducting these assessments. The Prospectus provides detailed and informed discussion on the practical means of achieving and sustaining zero transmission. It is designed as a road map, providing direction and options from which to choose an appropriate path. As on all maps, the destination is clearly marked, but the possible routes to reach it are numerous. The Prospectus is divided into two sections: Section 1 Eliminating Malaria comprises four chapters covering the strategic components important to the periods before, during, and after an elimination program. Section 2 Tools for the Job, comprises six chapters that outline basic information about how interventions in an elimination program will be different from those in a control setting. Chapter 1, Making the Decision, evaluates the issues that a country should consider when deciding whether or not to eliminate malaria. The chapter begins with a discussion about the quantitative and qualitative benefits that a country could expect from eliminating malaria and then recommends a thorough feasibility assessment. The feasibility assessment is based on three major components: operational, technical, and financial feasibility. Cross-border and regional collaboration is a key subject in this chapter. Chapter 2, Getting to Zero, describes changes that programs must consider when moving from sustained control to an elimination goal. The key strategic issues that must be addressed are considered, including supply chains, surveillance systems, intersectoral collaboration, political will, and legislative framework. Cross-border collaboration is again a key component in Getting to Zero. Chapter 3, Holding the Line, provides recommendations on how to conduct an assessment of two key factors that will affect preventing the reemergence of malaria once transmission is interrupted: outbreak risk and importation risk. The chapter emphasizes the need for a strong surveillance system in order to prevent and, if necessary, respond to imported cases. Chapter 4, Financing Elimination, reviews the cost-effectiveness of elimination as compared with sustained control and then presents the costs of selected elimination programs as examples. It evaluates four innovative financing mechanisms that must support elimination, emphasizing the need for predictable and stable financing. Case studies from Swaziland and two provinces in China are provided. Chapter 5, Understanding Malaria, considers malaria from the point of view of elimination and provides a concise overview of the current burden of the disease, malaria transmission, and the available interventions that can be used in an elimination program. Chapter 6, Learning from History, extracts important lessons from the Global Malaria Eradication Program and analyzes some elimination efforts that were successful and some that were unsuccessful. The chapter also reviews how the malaria map has been shrinking since 1900. xiv A Prosp ectus on Mala ria Elimi natio n\ud Chapter 7, Measuring Malaria for Elimination, provides a precise language for discussing malaria and gives the elimination discussion a quantitative structure. The chapter also describes the role of epidemiological theory and mathematical modeling in defining and updating an elimination agenda for malaria. Chapter 8, Killing the Parasite, outlines the importance of case detection and management in an elimination setting. Options for diagnosis, the hidden challenge of Plasmodium vivax in an elimination setting, and the impact of immunity are all discussed. Chapter 9, Suppressing the Vector, explores vector control, a necessary element of any malaria program. It considers optimal methods available to interrupt transmission and discusses potential changes, such as insecticide resistance, that may affect elimination efforts. Chapter 10, Identifying the Gaps — What We Need to Know, reviews the gaps in our understanding of what is required for elimination. The chapter outlines a short-term research agenda with a focus on the operational needs that countries are facing today. The Prospectus reviews the operational, technical, and financial feasibility for those working on the front lines and considers whether, when, and how to eliminate malaria. A companion document, A Guide on Malaria Elimination for Policy Makers, is provided for those countries or agencies whose responsibility is primarily to make the policy decisions on whether to pursue or support a malaria elimination strategy. The Guide is available at www.malaria eliminationgroup.org

A note on perfect partial elimination

In Gaussian elimination it is often desirable to preserve existing zeros (sparsity). This is closely related to perfect elimination schemes on graphs. Such schemes can be found in polynomial time. Gaussian elimination uses a pivot for each column, so opportunities for preserving sparsity can be missed. In this paper we consider a more flexible process that selects a pivot for each nonzero to be eliminated and show that recognizing matrices that allow such perfect partial elimination schemes is NP-hard

Diverse Sequences within Tlr Elements Target Programmed DNA Elimination in \u3cem\u3eTetrahymena Thermophila\u3c/em\u3e

Tlr elements are a novel family of ~30 putative mobile genetic elements that are confined to the germ line micronuclear genome in Tetrahymena thermophila. Thousands of diverse germ line-limited sequences, including the Tlr elements, are specifically eliminated from the differentiating somatic macronucleus. Macronucleusretained sequences flanking deleted regions are known to contain cis-acting signals that delineate elimination boundaries. It is unclear whether sequences within deleted DNA also play a regulatory role in the elimination process. In the current study, an in vivo DNA rearrangement assay was used to identify internal sequences required in cis for the elimination of Tlr elements. Multiple, nonoverlapping regions from the ~23-kb Tlr elements were independently sufficient to stimulate developmentally regulated DNA elimination when placed within the context of flanking sequences from the most thoroughly characterized family member, Tlr1. Replacement of element DNA with macronuclear or foreign DNA abolished elimination activity. Thus, diverse sequences dispersed throughout Tlr DNA contain cis-acting signals that target these elements for programmed elimination. Surprisingly, Tlr DNA was also efficiently deleted when Tlr1 flanking sequences were replaced with DNA from a region of the genome that is not normally associated with rearrangement, suggesting that specific flanking sequences are not required for the elimination of Tlr element DNA

Mechanism of C−F Reductive Elimination from Palladium(IV) Fluorides

The first systematic mechanism study of C−F reductive elimination from a transition metal complex is described. C−F bond formation from three different Pd(IV) fluoride complexes was mechanistically evaluated. The experimental data suggest that reductive elimination occurs from cationic Pd(IV) fluoride complexes via a dissociative mechanism. The ancillary pyridyl-sulfonamide ligand plays a crucial role for C−F reductive elimination, likely due to a κ^3 coordination mode, in which an oxygen atom of the sulfonyl group coordinates to Pd. The pyridyl-sulfonamide can support Pd(IV) and has the appropriate geometry and electronic structure to induce reductive elimination