Reducing the size and number of linear programs in a dynamic Gr\"obner basis algorithm

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.Comment: 11 figures, of which half are algorithms; submitted to journal for refereeing, December 201

Toward characterization and definition of fibromyalgia severity

<p>Abstract</p> <p>Background</p> <p>There are no standard criteria for defining or assessing severity of fibromyalgia (FM) as a condition as fibromyalgia is associated with multiple symptom domains. The objective of this study was to evaluate whether patient self-reported severity of FM is associated with severity of pain and sleep interference and the presence of core co-morbidities.</p> <p>Methods</p> <p>We recruited individuals ≥ 18 years of age with a clinician-confirmed diagnosis of FM ≥ 3 months and a current pain rating >2 on a 0-10 numeric rating scale (NRS). Patients completed a questionnaire by mail in which they self-rated their FM severity (very mild, mild, moderate, and severe), their current pain severity and extent of sleep interference (NRS; mild, 0-3; moderate, 4-6, severe, 7-10), and provided information (yes/no) on the presence of core comorbidities (symptoms of depression, anxiety, sleep problems, back pain, neck pain) and medication use for FM. The core symptoms of FM were stratified to assist with patient characterization. Analysis of variance (ANOVA) was used to explore the relationship between self-reported FM severity and continuous variables (pain severity and sleep interference), and Mantel-Haenszel chi-square analysis was used to evaluate the trend in the proportions of patients reporting use of medications and core symptoms of FM by severity of FM. To complement patient-reported FM severity and to understand physicians' perspectives, a survey was performed among 28 physician specialists (rheumatology, neurology, anesthesiology/pain management, family practice, internal medicine, and psychiatry) to determine what they assessed when evaluating FM severity in clinical practice.</p> <p>Results</p> <p>The population (N = 129) of FM patients was predominantly female (89.1%), with a mean age of 49.4 ± 11.0 years, and 81.4% reported duration ≥ 2 years. Self-reported FM severity was moderate/severe in 86.0% of patients; mean current pain score was 6.40 ± 2.19 (moderate), and mean sleep interference score was 7.28 ± 2.23 (severe). Greater FM severity was significantly associated with higher levels of current pain and sleep interference (p < 0.0001), the proportion of patients reporting FM medication use (p = 0.0001), and the presence of core comorbidities (p < 0.05). Pain, functional disability, and fatigue severity were ranked as the top three criteria by the highest proportion of physicians when evaluating FM severity.</p> <p>Conclusion</p> <p>With higher self-reported FM severity, patients have greater pain and sleep interference as well as increased frequency of core comorbidities. Further investigation into understanding FM severity is warranted.</p

Identification of symptom and functional domains that fibromyalgia patients would like to see improved: a cluster analysis

<p>Abstract</p> <p>Background</p> <p>The purpose of this study was to determine whether some of the clinical features of fibromyalgia (FM) that patients would like to see improved aggregate into definable clusters.</p> <p>Methods</p> <p>Seven hundred and eighty-eight patients with clinically confirmed FM and baseline pain ≥40 mm on a 100 mm visual analogue scale ranked 5 FM clinical features that the subjects would most like to see improved after treatment (one for each priority quintile) from a list of 20 developed during focus groups. For each subject, clinical features were transformed into vectors with rankings assigned values 1-5 (lowest to highest ranking). Logistic analysis was used to create a distance matrix and hierarchical cluster analysis was applied to identify cluster structure. The frequency of cluster selection was determined, and cluster importance was ranked using cluster scores derived from rankings of the clinical features. Multidimensional scaling was used to visualize and conceptualize cluster relationships.</p> <p>Results</p> <p>Six clinical features clusters were identified and named based on their key characteristics. In order of selection frequency, the clusters were Pain (90%; 4 clinical features), Fatigue (89%; 4 clinical features), Domestic (42%; 4 clinical features), Impairment (29%; 3 functions), Affective (21%; 3 clinical features), and Social (9%; 2 functional). The "Pain Cluster" was ranked of greatest importance by 54% of subjects, followed by Fatigue, which was given the highest ranking by 28% of subjects. Multidimensional scaling mapped these clusters to two dimensions: Status (bounded by Physical and Emotional domains), and Setting (bounded by Individual and Group interactions).</p> <p>Conclusion</p> <p>Common clinical features of FM could be grouped into 6 clusters (Pain, Fatigue, Domestic, Impairment, Affective, and Social) based on patient perception of relevance to treatment. Furthermore, these 6 clusters could be charted in the 2 dimensions of Status and Setting, thus providing a unique perspective for interpretation of FM symptomatology.</p

CocoaLib

CocoaLib is a C++ library for computations in commutative algebra; it consists of more than 4MB of code. All the basic ideal/module theoretic operations are provided

CoCoA 4

Cocoa4 is a C software for computations in commutative algebra; it consists of more than 1MB of code. All the basic ideal/module theoretic operations are provided, together with a programming language and a basic environment

CoCoa 5

Cocoa 5 is a C++ frontend for the CocoaLib, and it consists of more than 2MB of code. It provides the libary with a programming language and an advanced environment