Formal Verification of Nonlinear Inequalities with Taylor Interval Approximations

We present a formal tool for verification of multivariate nonlinear inequalities. Our verification method is based on interval arithmetic with Taylor approximations. Our tool is implemented in the HOL Light proof assistant and it is capable to verify multivariate nonlinear polynomial and non-polynomial inequalities on rectangular domains. One of the main features of our work is an efficient implementation of the verification procedure which can prove non-trivial high-dimensional inequalities in several seconds. We developed the verification tool as a part of the Flyspeck project (a formal proof of the Kepler conjecture). The Flyspeck project includes about 1000 nonlinear inequalities. We successfully tested our method on more than 100 Flyspeck inequalities and estimated that the formal verification procedure is about 3000 times slower than an informal verification method implemented in C++. We also describe future work and prospective optimizations for our method.Comment: 15 page

Truth Table Invariant Cylindrical Algebraic Decomposition by Regular Chains

A new algorithm to compute cylindrical algebraic decompositions (CADs) is presented, building on two recent advances. Firstly, the output is truth table invariant (a TTICAD) meaning given formulae have constant truth value on each cell of the decomposition. Secondly, the computation uses regular chains theory to first build a cylindrical decomposition of complex space (CCD) incrementally by polynomial. Significant modification of the regular chains technology was used to achieve the more sophisticated invariance criteria. Experimental results on an implementation in the RegularChains Library for Maple verify that combining these advances gives an algorithm superior to its individual components and competitive with the state of the art

Problem formulation for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition

Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truth-table invariance, making the CAD invariant with respect to the truth of logical formulae rather than the signs of polynomials; and CAD construction by regular chains technology, where first a complex decomposition is constructed by refining a tree incrementally by constraint. We here consider how best to formulate problems for input to this algorithm. We focus on a choice (not relevant for other CAD algorithms) about the order in which constraints are presented. We develop new heuristics to help make this choice and thus allow the best use of the algorithm in practice. We also consider other choices of problem formulation for CAD, as discussed in CICM 2013, revisiting these in the context of the new algorithm

PAM50 molecular intrinsic subtypes in the nurses' health Study cohorts

Background: Modified median and subgroup-specific gene subtypes by PAM50 and IHC surrogates improved to fair centering are two essential preprocessing methods to assign when Luminal subtypes were grouped together. Using the breast cancer molecular subtypes by PAM50. We evaluated the modified median method, our study consisted of 46% PAM50 subtypes derived from both methods in a subset of Luminal A, 18% Luminal B, 14% HER2-enriched, 15% Nurses' Health Study (NHS) and NHSII participants; correlat-Basal-like, and 8% Normal-like subtypes; 53% of tumor-ed tumor subtypes by PAM50 with IHC surrogates; and adjacent tissues were Normal-like. Women with the Basal-characterized the PAM50 subtype distribution, proliferation like subtype had a higher rate of relapse within 5 years. scores, and risk of relapse with proliferation and tumor size HER2-enriched subtypes had poorer outcomes prior to weighted (ROR-PT) scores in the NHS/NHSII. 1999. Methods: PAM50 subtypes, proliferation scores, and Conclusions: Either preprocessing method may be uti-ROR-PT scores were calculated for 882 invasive breast tumors lized to derive PAM50 subtypes for future studies. The and 695 histologically normal tumor-adjacent tissues. Cox majority of NHS/NHSII tumor and tumor-adjacent tissues proportional hazards models evaluated the relationship were classified as Luminal A and Normal-like, respectively. between PAM50 subtypes or ROR-PT scores/groups with Impact: Preprocessing methods are important for the recurrence-free survival (RFS) or distant RFS. accurate assignment of PAM50 subtypes. These data provide Results: PAM50 subtypes were highly comparable evidence that either preprocessing method can be used in between the two methods. The agreement between tumor epidemiologic studies

‘What are you going to do, confiscate their passports?’ Professional perspectives on cross-border reproductive travel

Objective: This article reports findings from a UK-based study which explored the phenomenon of overseas travel for fertility treatment. The first phase of this project aimed to explore how infertility clinicians and others professionally involved in fertility treatment understand the nature and consequences of cross-border reproductive travel. Background: There are indications that, for a variety of reasons, people from the UK are increasingly travelling across national borders to access assisted reproductive technologies. While research with patients is growing, little is known about how ‘fertility tourism’ is perceived by health professionals and others with a close association with infertility patients. Methods: Using an interpretivist approach, this exploratory research included focussed discussions with 20 people professionally knowledgeable about patients who had either been abroad or were considering having treatment outside the UK. Semi-structured interviews were recorded, transcribed verbatim and subjected to a thematic analysis. Results: Three conceptual categories are developed from the data: ‘the autonomous patient’; ‘cross-border travel as risk’, and ‘professional responsibilities in harm minimisation’. Professionals construct nuanced, complex and sometimes contradictory narratives of the ‘fertility traveller’, as vulnerable and knowledgeable; as engaged in risky behaviour and in its active minimisation. Conclusions: There is little support for the suggestion that states should seek to prevent cross-border treatment. Rather, an argument is made for less direct strategies to safeguard patient interests. Further research is required to assess the impact of professional views and actions on patient choices and patient experiences of treatment, before, during and after travelling abroad

Excluded Volume Effects in the Quark Meson Coupling Model

Excluded volume effects are incorporated in the quark meson coupling model to take into account in a phenomenological way the hard core repulsion of the nuclear force. The formalism employed is thermodynamically consistent and does not violate causality. The effects of the excluded volume on in-medium nucleon properties and the nuclear matter equation of state are investigated as a function of the size of the hard core. It is found that in-medium nucleon properties are not altered significantly by the excluded volume, even for large hard core radii, and the equation of state becomes stiffer as the size of the hard core increases.Comment: 14 pages, revtex, 6 figure

IKKγ mimetic peptides block the resistance to apoptosis associated with KSHV infection

Primary effusion lymphoma (PEL) is a lymphogenic disorder associated with KSHV infection. Key to the survival and proliferation of PEL is the canonical NF-kB pathway that becomes constitutively activated following overexpression of the viral oncoprotein ks-vFLIP. This arises from its capacity to form a complex with the modulatory subunit of the IKK kinase, IKKgamma (or NEMO) resulting in the overproduction of proteins that promote cellular survival and prevent apoptosis; both of which are important drivers of tumourigenesis. Using a combination of cell based and biophysical assays together with structural techniques, we show that the observed resistance to cell death is largely independent of autophagy or major death receptor signalling pathways and demonstrate that direct targeting of the ks-vFLIP-IKKgamma interaction both in cells and in vitro can be achieved using IKKgamma mimetic peptides. Our results further reveal that these peptides not only induce cell killing, but potently sensitise PEL to the pro-apoptotic agents tumour necrosis factor alpha and etoposide and are the first to confirm ks-vFLIP as a tractable target for the treatment of PEL and related disorders

eta-prime photoproduction on the proton for photon energies from 1.527 to 2.227 GeV

Differential cross sections for the reaction gamma p -> eta-prime p have been measured with the CLAS spectrometer and a tagged photon beam with energies from 1.527 to 2.227 GeV. The results reported here possess much greater accuracy than previous measurements. Analyses of these data indicate for the first time the coupling of the etaprime N channel to both the S_11(1535) and P_11(1710) resonances, known to couple strongly to the eta N channel in photoproduction on the proton, and the importance of j=3/2 resonances in the process.Comment: 6 pages, 3 figure

Impact of pre-existing dengue immunity on human antibody and memory B cell responses to Zika

Little is known about enduring memory B cell (MBC) responses to Zika virus (ZIKV) and their relationship with circulating antibodies. Here we comprehensively assess MBC frequency and specificity alongside serum binding and neutralizing antibody responses to ZIKV ~2 weeks and ~8 months postinfection in 31 pediatric subjects with 0, 1 or >1 prior infections with the related dengue virus (DENV). ZIKV infection elicits a robust type-specific MBC response, and the majority of late convalescent anti-ZIKV serum neutralizing activity is attributable to ZIKV-specific antibodies. The number of prior DENV infections does not influence type-specific or cross-reactive MBC responses, although ZIKV has the highest cross-reactivity with DENV3. DENV cross-reactive MBCs expanded by ZIKV infection decline in number and proportion by late convalescence. Finally, ZIKV induces greater cross-reactivity in the MBC pool than in serum antibodies. Our data suggest immunity to DENV only modestly shapes breadth and magnitude of enduring ZIKV antibody responses

A Bayesian analysis of pentaquark signals from CLAS data

We examine the results of two measurements by the CLAS collaboration, one of which claimed evidence for a $\Theta^{+}$ pentaquark, whilst the other found no such evidence. The unique feature of these two experiments was that they were performed with the same experimental setup. Using a Bayesian analysis we find that the results of the two experiments are in fact compatible with each other, but that the first measurement did not contain sufficient information to determine unambiguously the existence of a $\Theta^{+}$. Further, we suggest a means by which the existence of a new candidate particle can be tested in a rigorous manner.Comment: 5 pages, 3 figure