Abstract:
Two fundamental questions in the theory of Groebner bases are decision ("Is a basis G of a polynomial ideal a Groebner basis?") and transformation ("If it is not, how do we transform it into a Groebner basis?") This paper considers the first question. It is well-known that G is a Groebner basis if and only if a certain set of polynomials (the S-polynomials) satisfy a certain property. In general there are m(m-1)/2 of these, where m is the number of polynomials in G, but criteria due to Buchberger and others often allow one to consider a smaller number. This paper presents two original results. The first is a new characterization theorem for Groebner bases that makes use of a new criterion that extends Buchberger's Criteria. The second is the identification of a class of polynomial systems G for which the new criterion has dramatic impact, reducing the worst-case scenario from m(m-1)/2 S-polynomials to m-1.

Abstract:
Nurse practitioners have become an increasingly important part of the US medical workforce as they have gained greater practice authority through state-level regulatory changes. This study investigates one labor market impact of this large change in nurse practitioner regulation. Using data from the National Sample Survey of Registered Nurses and a dataset of state-level nurse practitioner prescribing authority, a multivariate estimation is performed analysing the impact of greater practice authority on the probability of a nurse practitioner moving from a state. The empirical results indicate that nurse practitioners in states that grant expanded practice are less likely to move from the state than nurse practitioners in states that have not granted expanded practice authority. The estimated effect is robust and is statistically and economically meaningful. This finding is in concert with and strengthens the wider literature which finds states that grant expanded practice authority to nurse practitioners tend to have larger nurse practitioner populations. 1. Introduction Nurse practitioners ( s) are, according to the International Council of Nurses, “a registered nurse who has acquired the expert knowledge base, complex decision-making skills, and clinical competencies for expanded practice, the characteristics of which are shaped by the context and/or country in which s/he is credentialed to practice” [1]. In the United States, s are typically masters-prepared registered nurses and have become an increasingly important part of the health care system. They have over time obtained greater practice authority through state-level regulatory changes which has fundamentally altered what an can do as a caregiver. This has, in turn, altered their role in the health care system. In particular, these changes have allowed s to take a more central, independent role in providing health care. While s were initially seen as “physician extenders” by the wider health care industry in the United States, they have become, in many respects, “physician replacers.” Today, in most U.S. states, s can see, diagnose, prescribe, and in general provide care for patients as a general practice physician would. As such, these regulatory changes in practice authority, and the “rise” of the they have ushered in, have fundamentally changed the labor market. As would be expected in an industry as important as health care, the “rise of the ” has been accompanied by a large body of research. In general, this research can be grouped into four broad categories: their rise as caregivers, the

Abstract:
The study investigates housing demolition and timber waste recovery – with the aim to identify ways of improving recovery. Using case studies the research focused on demolisher decision making, their onsite processes and the associated network of participants that influence timber recovery. From the data, a process model was developed that identifies and orders the drivers of demolition decision making. One aspect of the model identified the initiators of demolition and the waste created, including issues revolving around the demolition feedstock. Another aspect covers organisational business drivers and includes site safety, productivity, economies of scale, market value of waste and supply chain entrepreneurship. A third component deals with project specific drivers including the recurring cost versus income equation that impacts on the viability of project level decisions. The model includes a typology of the operational onsite response to the above drivers. Here, the deconstruction approach was found to provide high timber recovery mainly used where high-value timber waste was involved; the miscellaneous salvage approach provided some recovery of high and low-value timber; the crunch and dump approach provided low recovery or dumping at landfill and was used where low and no-value timber was involved. An expected increase in supply of these latter timber categories creates a significant need to increase the market value of currently low value timber groups. Designing for deconstruction is also posed as a long term strategy for this.

Abstract:
Faugere's F5 algorithm computes a Groebner basis incrementally, by computing a sequence of (non-reduced) Groebner bases. The authors describe a variant of F5, called F5C, that replaces each intermediate Groebner basis with its reduced Groebner basis. As a result, F5C considers fewer polynomials and performs substantially fewer polynomial reductions, so that it terminates more quickly. We also provide a generalization of Faugere's characterization theorem for Groebner bases.

Abstract:
We describe an algorithm to compute Gr\"obner bases which combines F4-style reduction with the F5 criteria. Both F4 and F5 originate in the work of Jean-Charles Faug\`ere, who has successfully computed many Gr\"obner bases that were previously considered intractable. Another description of a similar algorithm already exists in Gwenole Ars' dissertation; unfortunately, this is only available in French, and although an implementation exists, it is not made available for study. We not only describe the algorithm, we also direct the reader to a study implementation for the free and open source Sage computer algebra system. We conclude with a short discussion of how the approach described here compares and contrasts with that of Ars' dissertation.

Abstract:
The purpose of this work is to generalize part of the theory behind Faugere's "F5" algorithm. This is one of the fastest known algorithms to compute a Groebner basis of a polynomial ideal I generated by polynomials f_{1},...,f_{m}. A major reason for this is what Faugere called the algorithm's "new" criterion, and we call "the F5 criterion"; it provides a sufficient condition for a set of polynomials G to be a Groebner basis. However, the F5 algorithm is difficult to grasp, and there are unresolved questions regarding its termination. This paper introduces some new concepts that place the criterion in a more general setting: S-Groebner bases and primitive S-irreducible polynomials. We use these to propose a new, simple algorithm based on a revised F5 criterion. The new concepts also enable us to remove various restrictions, such as proving termination without the requirement that f_{1},...,f_{m} be a regular sequence.

Abstract:
This paper describes a Buchberger-style algorithm to compute a Groebner basis of a polynomial ideal, allowing for a selection strategy based on "signatures". We explain how three recent algorithms can be viewed as different strategies for the new algorithm, and how other selection strategies can be formulated. We describe a fourth as an example. We analyze the strategies both theoretically and empirically, leading to some surprising results.

Abstract:
The dynamic algorithm to compute a Gr\"obner basis is nearly twenty years old, yet it seems to have arrived stillborn; aside from two initial publications, there have been no published followups. One reason for this may be that, at first glance, the added overhead seems to outweigh the benefit; the algorithm must solve many linear programs with many linear constraints. This paper describes two methods of reducing the cost substantially, answering the problem effectively.

Abstract:
Background: Trigger finger is characterized by the inability to smoothly flex and extend the digit. Corticosteroids are an accepted non-surgical treatment option and can be delivered via two techniques. While the palmar approach is more commonly used, some have suggested that the mid-axial approach may be less painful for patients and yield higher intrasheath injection rates. The purpose of this study is to compare the accuracy of the palmar and midaxial approaches for delivery of corticosteroids into the flexor tendon sheath using radio-opaque dye in a cadaver model. Methods: A total of 50 injections were performed, 25 via midaxial technique and 25 via palmar technique. A one inch, 25-gauge needle was used to inject 1 mL of Isovue contrast dye into the flexor tendon sheath under live fluoroscopy. The fluoroscopic images were examined after injection to determine intrasheath versus extrasheath delivery of the dye, with visualization of contrast filling the sheath defining a successful injection. Results: The midaxial approach had a success rate of 52% compared to the conventional palmar approach success rate of 36%, p=0.5. The ring finger is the most common location of trigger finger and the rates of success were equal between groups for this digit (80%). Conclusions: Based on our findings, there is no statistical difference in the accuracy of intrasheath injection between the midaxial technique and palmar technique. The midaxial technique can be considered as an alternative to the palmar technique for trigger finger injection.

Abstract:
Dimensional reduction of a self-dual tensor gauge field in 6d gives an Abelian vector gauge field in 5d. We derive the conditions under which an interacting 5d theory of an Abelian vector gauge field is the dimensional reduction of a 6d Lorentz invariant interacting theory of a self-dual tensor. Then we specialize to the particular 6d theory that gives 5d Born-Infeld theory. The field equation and Lagrangian of this 6d theory are formulated with manifest 5d Lorentz invariance, while the remaining Lorentz symmetries are realized nontrivially. A string soliton with finite tension and self-dual charge is constructed.