Need Polynomial Systems Be Doubly-Exponential?

Polynomial Systems, or at least their algorithms, have the reputation of being doubly-exponential in the number of variables [Mayr and Mayer, 1982], [Davenport and Heintz, 1988]. Nevertheless, the Bezout bound tells us that that number of zeros of a zero-dimensional system is singly-exponential in the number of variables. How should this contradiction be reconciled? We first note that [Mayr and Ritscher, 2013] shows that the doubly exponential nature of Gr\"{o}bner bases is with respect to the dimension of the ideal, not the number of variables. This inspires us to consider what can be done for Cylindrical Algebraic Decomposition which produces a doubly-exponential number of polynomials of doubly-exponential degree. We review work from ISSAC 2015 which showed the number of polynomials could be restricted to doubly-exponential in the (complex) dimension using McCallum's theory of reduced projection in the presence of equational constraints. We then discuss preliminary results showing the same for the degree of those polynomials. The results are under primitivity assumptions whose importance we illustrate.Comment: Extended Abstract for ICMS 2016 Presentation. arXiv admin note: text overlap with arXiv:1605.0249

Chemerin Elicits Potent Constrictor Actions via Chemokine-Like Receptor 1 (CMKLR1), not G-Protein-Coupled Receptor 1 (GPR1), in Human and Rat Vasculature

BACKGROUND: Circulating levels of chemerin are significantly higher in hypertensive patients and positively correlate with blood pressure. Chemerin activates chemokine-like receptor 1 (CMKLR1 or ChemR23) and is proposed to activate the "orphan" G-protein-coupled receptor 1 (GPR1), which has been linked with hypertension. Our aim was to localize chemerin, CMKLR1, and GPR1 in the human vasculature and determine whether 1 or both of these receptors mediate vasoconstriction. METHODS AND RESULTS: Using immunohistochemistry and molecular biology in conduit arteries and veins and resistance vessels, we localized chemerin to endothelium, smooth muscle, and adventitia and found that CMKLR1 and GPR1 were widely expressed in smooth muscle. C9 (chemerin149-157) contracted human saphenous vein (pD2=7.30±0.31) and resistance arteries (pD2=7.05±0.54) and increased blood pressure in rats by 9.1±1.0 mm Hg at 200 nmol. Crucially, these in vitro and in vivo vascular actions were blocked by CCX832, which we confirmed to be highly selective for CMKLR1 over GPR1. C9 inhibited cAMP accumulation in human aortic smooth muscle cells and preconstricted rat aorta, consistent with the observed vasoconstrictor action. Downstream signaling was explored further and, compared to chemerin, C9 showed a bias factor=≈5000 for the Gi protein pathway, suggesting that CMKLR1 exhibits biased agonism. CONCLUSIONS: Our data suggest that chemerin acts at CMKLR1, but not GPR1, to increase blood pressure. Chemerin has an established detrimental role in metabolic syndrome, and these direct vascular actions may contribute to hypertension, an additional risk factor for cardiovascular disease. This study provides proof of principle for the therapeutic potential of selective CMKLR1 antagonists.This work was supported by the British Heart Foundation (FS/12/64/30001 [to AJK], FS/14/59/31282 [to CR], and PG/09/050/27734); Wellcome Trust (100780/Z/12/Z [to LY], 101844 [to CWT], 107715/Z/15/Z [to APD and JJM], and 096822/Z/11/Z [to APD and PY]); the Raymond and Beverley Sackler Fellowship (to LY), and the Medical Research Council (MRC MC_PC_14116; to APD) and by the Pulmonary Hypertension Association and the Cambridge Biomedical Research Centre. Biomedical Resources (grant 099156/Z/12/Z)

Anticipatory nausea in cyclical vomiting

BACKGROUND: Cyclical Vomiting Syndrome (CVS) is characterised by discrete, unexplained episodes of intense nausea and vomiting, and mainly affects children and adolescents. Comprehending Cyclical Vomiting Syndrome requires awareness of the severity of nausea experienced by patients. As a subjective symptom, nausea is easily overlooked, yet is the most distressing symptom for patients and causes many behavioural changes during attacks. CASE PRESENTATION: This first-hand account of one patient's experience of Cyclical Vomiting Syndrome shows how severe nausea contributed to the development of anticipatory nausea and vomiting (ANV), a conditioned response frequently observed in chemotherapy patients. This conditioning apparently worsened the course of the patient's disease. Anticipatory nausea and vomiting has not previously been recognised in Cyclical Vomiting Syndrome, however predictors of its occurrence in oncology patients indicate that it could complicate many cases. CONCLUSION: We suggest a model whereby untreated severe and prolonged nausea provokes anxiety about further cyclical vomiting attacks. This anxiety facilitates conditioning, thus increasing the range of triggers in a self-perpetuating manner. Effective management of the nausea-anxiety feedback loop can reduce the likelihood of anticipatory nausea and vomiting developing in other patients

Single-tooth replacement: factors affecting different prosthetic treatment modalities

<p>Abstract</p> <p>Background</p> <p>The choice between several treatment options for replacing a single missing tooth is influenced by clinical, dentist- and patient-immanent factors. This study aimed to determine the patient factors that would affect the treatment decision to replace a single missing tooth and to assess the satisfaction with several options.</p> <p>Method</p> <p>200 volunteers involved (121 females and 79 males) divided into four groups, Group A: consisted of patients with conventional fixed partial dentures or patients with resin bonded fixed partial dentures. Group B: consisted of patients who received removable partial dentures while Group C: consisted of patients who received a single implant supported crown, and a control group D: consisted of patients who received no treatment. Data were collected using a questionnaire.</p> <p>Results</p> <p>The highest percentage of males within groups (58%) was within the removable prostheses category. The majority of the subjects in the study reported that the main reason for replacing a missing tooth was for esthetic and function. Most important factor affecting the choice between treatment modalities was damaging the neighboring teeth. Pain, post operative sensitivity and dental phobia were important factors in choosing the prosthesis type and affected the control group patients not to have any treatment. The highest satisfaction percentage among groups studied was recorded for dental implants then FPD groups, while the least percentage were in both the control and RPD groups, for all aspects of function, esthetic and speech efficiency.</p> <p>Conclusions</p> <p>The final choice between FPD, RPD and implant depended on several factors which affected the decision making; among these is cost and patients' awareness of the different treatment options.</p

Recent advances in real geometric reasoning

In the 1930s Tarski showed that real quantifier elimination was possible, and in 1975 Collins gave a remotely practicable method, albeit with doubly-exponential complexity, which was later shown to be inherent. We discuss some of the recent major advances in Collins method: such as an alternative approach based on passing via the complexes, and advances which come closer to "solving the question asked" rather than "solving all problems to do with these polynomials"

Satisfiability Checking and Symbolic Computation

Symbolic Computation and Satisfiability Checking are viewed as individual research areas, but they share common interests in the development, implementation and application of decision procedures for arithmetic theories. Despite these commonalities, the two communities are currently only weakly connected. We introduce a new project SC-square to build a joint community in this area, supported by a newly accepted EU (H2020-FETOPEN-CSA) project of the same name. We aim to strengthen the connection between these communities by creating common platforms, initiating interaction and exchange, identifying common challenges, and developing a common roadmap. This abstract and accompanying poster describes the motivation and aims for the project, and reports on the first activities.Comment: 3 page Extended Abstract to accompany an ISSAC 2016 poster. Poster available at http://www.sc-square.org/SC2-AnnouncementPoster.pd

Knowledge Management and Organisational Culture

This international Handbook provides a comprehensive overview of key topics, debates and issues within the now well-established field of Knowledge Management (KM)

Genetic dissection of heterosis using epistatic association mapping in a partial NCII mating design

Heterosis refers to the phenomenon in which an F1 hybrid exhibits enhanced growth or agronomic performance. However, previous theoretical studies on heterosis have been based on bi-parental segregating populations instead of F1 hybrids. To understand the genetic basis of heterosis, here we used a subset of F1 hybrids, named a partial North Carolina II design, to perform association mapping for dependent variables: original trait value, general combining ability (GCA), specific combining ability (SCA) and mid-parental heterosis (MPH). Our models jointly fitted all the additive, dominance and epistatic effects. The analyses resulted in several important findings: 1) Main components are additive and additive-by-additive effects for GCA and dominance-related effects for SCA and MPH, and additive-by-dominant effect for MPH was partly identified as additive effect; 2) the ranking of factors affecting heterosis was dominance > dominance-by-dominance > over-dominance > complete dominance; and 3) increasing the proportion of F1 hybrids in the population could significantly increase the power to detect dominance-related effects, and slightly reduce the power to detect additive and additive-by-additive effects. Analyses of cotton and rapeseed datasets showed that more additive-by-additive QTL were detected from GCA than from trait phenotype, and fewer QTL were from MPH than from other dependent variables