Computing GCRDs of Approximate Differential Polynomials

Differential (Ore) type polynomials with approximate polynomial coefficients are introduced. These provide a useful representation of approximate differential operators with a strong algebraic structure, which has been used successfully in the exact, symbolic, setting. We then present an algorithm for the approximate Greatest Common Right Divisor (GCRD) of two approximate differential polynomials, which intuitively is the differential operator whose solutions are those common to the two inputs operators. More formally, given approximate differential polynomials $f$ and $g$, we show how to find "nearby" polynomials $\widetilde f$ and $\widetilde g$ which have a non-trivial GCRD. Here "nearby" is under a suitably defined norm. The algorithm is a generalization of the SVD-based method of Corless et al. (1995) for the approximate GCD of regular polynomials. We work on an appropriately "linearized" differential Sylvester matrix, to which we apply a block SVD. The algorithm has been implemented in Maple and a demonstration of its robustness is presented.Comment: To appear, Workshop on Symbolic-Numeric Computing (SNC'14) July 201

Comparing the Online Learning Capabilities of Gaussian ARTMAP and Fuzzy ARTMAP for Building Energy Management Systems

Recently, there has been a growing interest in the application of Fuzzy ARTMAP for use in building energy management systems or EMS. However, a number of papers have indicated that there are important weaknesses to the Fuzzy ARTMAP approach, such as sensitivity to noisy data and category proliferation. Gaussian ARTMAP was developed to help overcome these weaknesses, raising the question of whether Gaussian ARTMAP could be a more effective approach for building energy management systems? This paper aims to answer this question. In particular, our results show that Gaussian ARTMAP not only has the capability to address the weaknesses of Fuzzy ARTMAP but, by doing this, provides better and more efficient EMS controls with online learning capabilities

Design, Evaluation and Experimental Effort Toward Development of a High Strain Composite Wing for Navy Aircraft

This design development effort addressed significant technical issues concerning the use and benefits of high strain composite wing structures (Epsilon(sub ult) = 6000 micro-in/in) for future Navy aircraft. These issues were concerned primarily with the structural integrity and durability of the innovative design concepts and manufacturing techniques which permitted a 50 percent increase in design ultimate strain level (while maintaining the same fiber/resin system) as well as damage tolerance and survivability requirements. An extensive test effort consisting of a progressive series of coupon and major element tests was an integral part of this development effort, and culminated in the design, fabrication and test of a major full-scale wing box component. The successful completion of the tests demonstrated the structural integrity, durability and benefits of the design. Low energy impact testing followed by fatigue cycling verified the damage tolerance concepts incorporated within the structure. Finally, live fire ballistic testing confirmed the survivability of the design. The potential benefits of combining newer/emerging composite materials and new or previously developed high strain wing design to maximize structural efficiency and reduce fabrication costs was the subject of subsequent preliminary design and experimental evaluation effort

A North American Record for \u3ci\u3eValgus Hemipterus\u3c/i\u3e (Coleoptera: Scarabaeidae) and Information on its Life Cycle

A rotting American elm log containing adults of Valgus hemipterus (L.) was discovered on 6 May 1980, at the Rose Lake Wildlife Experiment Station, Shiawassee County, Michigan. This appears to be the first record of this European species in North America. Larvae were collected in the summer, and pupae and teneral adults in the early fall suggesting a univoltine life cycle with the adults overwintering

Multiscale modelling of cancer progression and treatment control : the role of intracellular heterogeneities in chemotherapy treatment

Cancer is a complex, multiscale process involving interactions at intracellular, intercellular and tissue scales that are in turn susceptible to microenvironmental changes. Each individual cancer cell within a cancer cell mass is unique, with its own internal cellular pathways and biochemical interactions. These interactions contribute to the functional changes at the cellular and tissue scale, creating a heterogenous cancer cell population. Anticancer drugs are effective in controlling cancer growth by inflicting damage to various target molecules and thereby triggering multiple cellular and intracellular pathways, leading to cell death or cell-cycle arrest. One of the major impediments in the chemotherapy treatment of cancer is drug resistance driven by multiple mechanisms, including multi-drug and cell-cycle mediated resistance to chemotherapy drugs. In this article, we discuss two hybrid multiscale modelling approaches, incorporating multiple interactions involved in the sub-cellular, cellular and microenvironmental levels to study the effects of cell-cycle, phase-specific chemotherapy on the growth and progression of cancer cells.PostprintPeer reviewe

Tracking internet interest in anabolic-androgenic steroids using Google Trends

Background: There is a perception that the prevalence of anabolic-androgenic steroid (AAS) use is increasing in the UK, with consequent individual and public health risks. Nevertheless, there is a lack of real-time surveillance data to support the development of effective policy. This paper explores the potential of Google Trends to complement existing surveillance methods by analysing user generated search term data. Methods: The Google Trends web tool was used to identify patterns of UK online interest in 15 AAS from January 2011 to December 2015, with 10 ultimately suitable for further analysis. Time series analysis was applied to the data. Results: 10 steroids were ranked from most to least popular. All compounds had peaks in interest between April to July, potentially indicating a consumer driven desire to attain a desired physique in time for summer. Oral steroids were among the most searched for drugs which may have relevance for current service provision to steroid users. Conclusion: Alternative data sources such Google Trends may provide useful additional information to supplement existing surveillance data. The limitations of this method however makes cautious interpretation and triangulation with other data sources essential