Efficient Generic Quotients Using Exact Arithmetic

The usual formulation of efficient division uses Newton iteration to compute an inverse in a related domain where multiplicative inverses exist. On one hand, Newton iteration allows quotients to be calculated using an efficient multiplication method. On the other hand, working in another domain is not always desirable and can lead to a library structure where arithmetic domains are interdependent. This paper uses the concept of a whole shifted inverse and modified Newton iteration to compute quotients efficiently without leaving the original domain. The iteration is generic to domains having a suitable shift operation, such as integers or polynomials with coefficients that do not necessarily commute

Efficient Quotients of Non-Commutative Polynomials

It is shown how to compute quotients efficiently in non-commutative univariate polynomial rings. This expands on earlier work where generic efficient quotients were introduced with a primary focus on commutative domains. Asymptotically fast algorithms are given for left and right quotients when the polynomial variable commutes with coefficients. These algorithms are based on the concept of the ``whole shifted inverse'', which is a specialized quotient where the dividend is a power of the polynomial variable. When the variable does not commute with coefficients, that is for skew polynomials, left and right whole shifted inverses are defined and the left whole shifted inverse may be used to compute the right quotient, although not with asymptotically fast complexity. Examples are shown of polynomials with matrix coefficients and differential operators and a proof-of-concept Maple implementation is given

Performance Rights for Software

As we use software in increasingly varied contexts, the concept of a software license has become progressively more complex. Software is embedded in devices that do not obviously resemble computers. Web services make software on one computer available to anyone with internet access. An individual may use several computers over the course of the day so the concept of a node locked or individual license is no longer clear. How should time based and single use and consumptive licenses be governed and interact? This paper examines how these and other issues in software licensing can be seen as instances of the general concept of performance rights, rather than simply reproduction rights. Licenses involving finely specified performance rights are common in the entertainment industry for music, film, stage and television. We describe how, as software and our use of it becomes more sophisticated, we see performance rights as becoming an apt basis for software licensing

Hybrid Intervals and Symbolic Block Matrices

Structured matrices with symbolic sizes appear frequently in the literature, especially in the description of algorithms for linear algebra. Recent work has treated these symbolic structured matrices themselves as computational objects, showing how to add matrices with blocks of different symbolic sizes in a general way while avoiding a combinatorial explosion of cases. The present article introduces the concept of hybrid intervals, in which points may have negative multiplicity. Various operations on hybrid intervals have compact and elegant formulations that do not require cases to handle different orders of the end points. This makes them useful to represent symbolic block matrix structures and to express arithmetic on symbolic block matrices compactly. We use these ideas to formulate symbolic block matrix addition and multiplication in a compact and uniform way

The Inverse of the Complex Gamma Function

We consider the functional inverse of the Gamma function in the complex plane, where it is multi-valued, and define a set of suitable branches by proposing a natural extension from the real case

06271 Abstracts Collection -- Challenges in Symbolic Computation Software

From 02.07.06 to 07.07.06, the Dagstuhl Seminar 06271 ``Challenges in Symbolic Computation Software\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Initial Conditions for Models of Dynamical Systems

The long-time behaviour of many dynamical systems may be effectively predicted by a low-dimensional model that describes the evolution of a reduced set of variables. We consider the question of how to equip such a low-dimensional model with appropriate initial conditions, so that it faithfully reproduces the long-term behaviour of the original high-dimensional dynamical system. Our method involves putting the dynamical system into normal form, which not only generates the low-dimensional model, but also provides the correct initial conditions for the model. We illustrate the method with several examples. Keywords: normal form, isochrons, initialisation, centre manifoldComment: 24 pages in standard LaTeX, 66K, no figure

What is the 'problem' that outreach work seeks to address and how might it be tackled? Seeking theory in a primary health prevention programme

<b>Background</b> Preventive approaches to health are disproportionately accessed by the more affluent and recent health improvement policy advocates the use of targeted preventive primary care to reduce risk factors in poorer individuals and communities. Outreach has become part of the health service response. Outreach has a long history of engaging those who do not otherwise access services. It has, however, been described as eclectic in its purpose, clientele and mode of practice; its effectiveness is unproven. Using a primary prevention programme in the UK as a case, this paper addresses two research questions: what are the perceived problems of non-engagement that outreach aims to address; and, what specific mechanisms of outreach are hypothesised to tackle these.<p></p> <b>Methods</b> Drawing on a wider programme evaluation, the study undertook qualitative interviews with strategically selected health-care professionals. The analysis was thematically guided by the concept of 'candidacy' which theorises the dynamic process through which services and individuals negotiate appropriate service use.<p></p> <b>Results</b> The study identified seven types of engagement 'problem' and corresponding solutions. These 'problems' lie on a continuum of complexity in terms of the challenges they present to primary care. Reasons for non-engagement are congruent with the concept of 'candidacy' but point to ways in which it can be expanded.<p></p> <b>Conclusions</b> The paper draws conclusions about the role of outreach in contributing to the implementation of inequalities focused primary prevention and identifies further research needed in the theoretical development of both outreach as an approach and candidacy as a conceptual framework

FRMD4A Upregulation in Human Squamous Cell Carcinoma Promotes Tumor Growth and Metastasis and Is Associated with Poor Prognosis

New therapeutic strategies are needed to improve treatment of head and neck squamous cell carcinoma (HNSCC), an aggressive tumor with poor survival rates. FRMD4A is a human epidermal stem cell marker implicated previously in epithelial polarity that is upregulated in SCC cells. Here, we report that FRMD4A upregulation occurs in primary human HNSCCs where high expression levels correlate with increased risks of relapse. FRMD4A silencing decreased growth and metastasis of human SCC xenografts in skin and tongue, reduced SCC proliferation and intercellular adhesion, and stimulated caspase-3 activity and expression of terminal differentiation markers. Notably, FRMD4A attenuation caused nuclear accumulation of YAP, suggesting a potential role for FRMD4A in Hippo signaling. Treatment with the HSP90 inhibitor 17-DMAG or ligation of CD44 with hyaluronan caused nuclear depletion of FRMD4A, nuclear accumulation of YAP and reduced SCC growth and metastasis. Together, our findings suggest FRMD4A as a novel candidate therapeutic target in HNSCC based on the key role in metastatic growth we have identified