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We introduce a class of Laurent polynomials, called maximally mutable Laurent polynomials (MMLPs), that we believe correspond under mirror symmetry to Fano varieties. A subclass of these, called rigid, are expected to correspond to Fano varieties with terminal locally toric singularities. We prove that there are exactly 10 mutation classes of rigid MMLPs in two variables; under mirror symmetry these correspond one-to-one with the 10 deformation classes of smooth del~Pezzo surfaces. Furthermore we give a computer-assisted classification of rigid MMLPs in three variables with reflexive Newton polytope; under mirror symmetry these correspond one-to-one with the 98 deformation classes of three-dimensional Fano manifolds with very ample anticanonical bundle. We compare our proposal to previous approaches to constructing mirrors to Fano varieties, and explain why mirror symmetry in higher dimensions necessarily involves varieties with terminal singularities. Every known mirror to a Fano manifold, of any dimension, is a rigid MMLP., Comment: 21 pages, plus a 321 page appendix; 7 figures; 100 tables

The Partnership for Chemicals Risk Assessment (PARC) is currently under development as a joint research and innovation programme to strengthen the scientific basis for chemical risk assessment in the EU. The plan is to bring chemical risk assessors and managers together with scientists to accelerate method development and the production of necessary data and knowledge, and to facilitate the transition to next-generation evidence-based risk assessment, a non-toxic environment and the European Green Deal. The NORMAN Network is an independent, well-established and competent network of more than 80 organisations in the field of emerging substances and has enormous potential to contribute to the implementation of the PARC partnership. NORMAN stands ready to provide expert advice to PARC, drawing on its long experience in the development, harmonisation and testing of advanced tools in relation to chemicals of emerging concern and in support of a European Early Warning System to unravel the risks of contaminants of emerging concern (CECs) and close the gap between research and innovation and regulatory processes. In this commentary we highlight the tools developed by NORMAN that we consider most relevant to supporting the PARC initiative: (i) joint data space and cutting-edge research tools for risk assessment of contaminants of emerging concern; (ii) collaborative European framework to improve data quality and comparability; (iii) advanced data analysis tools for a European early warning system and (iv) support to national and European chemical risk assessment thanks to harnessing, combining and sharing evidence and expertise on CECs. By combining the extensive knowledge and experience of the NORMAN network with the financial and policy-related strengths of the PARC initiative, a large step towards the goal of a non-toxic environment can be taken. © 2020, The Author(s).

We study $${\mathbb {Q}}$$ -factorial terminal Fano 3-folds whose equations are modelled on those of the Segre embedding of . These lie in codimension 4 in their total anticanonical embedding and have Picard rank 2. They fit into the current state of classification in three different ways. Some families arise as unprojections of degenerations of complete intersections, where the generic unprojection is a known prime Fano 3-fold in codimension 3; these are new, and an analysis of their Gorenstein projections reveals yet other new families. Others represent the “second Tom” unprojection families already known in codimension 4, and we show that every such family contains one of our models. Yet others have no easy Gorenstein projection analysis at all, so prove the existence of Fano components on their Hilbert scheme.

Background Chronic spontaneous urticaria (CSU) is one of the commonest diseases in allergological and dermatological practice. It constitutes an interdisciplinary problem, and its pathogenesis is not always easily determined. It has been suggested that metabolic syndrome and hyperlipidaemia are more frequent in patients with CSU, but the influence of overweight and obesity on the development of CSU has not been thoroughly investigated. Aim To assess the association between body parameters and the development of CSU. Methods The study enrolled 85 patients with CSU, who were divided into three subgroups: patients whose only symptoms were weals, patients whose only symptom was angio-oedema, and patients with urticaria and accompanying angio-oedema. Mean weight, height, body mass index (BMI), body surface area, disease duration and age of disease onset were recorded RESULTS: There was a statistically significant association between CSU and heavier weight, higher BMI, greater affected body surface area and older age at disease onset. Subjects with higher BMI values had a tendency towards longer disease duration. There were no statistically significant differences between the three subgroups. Conclusions Our results suggest that CSU, especially if of long duration, may be associated with overweight and obesity, while increased body mass can result in later onset of urticaria symptoms. Further analyses to confirm the presented results and possible association between obesity and CSU occurrence are needed.

In previous work by Coates, Galkin, and the authors, the notion of mutation between lattice polytopes was introduced. Such a mutation gives rise to a deformation between the corresponding toric varieties. In this paper we study one-step mutations that correspond to deformations between weighted projective planes, giving a complete characterisation of such mutations in terms of T-singularities. We show also that the weights involved satisfy Diophantine equations, generalising results of Hacking-Prokhorov., 14 pages, 2 figures

The quantum period of a variety X is a generating function for certain Gromov-Witten invariants of X which plays an important role in mirror symmetry. In this paper we compute the quantum periods of all 3-dimensional Fano manifolds. In particular we show that 3-dimensional Fano manifolds with very ample anticanonical bundle have mirrors given by a collection of Laurent polynomials called Minkowski polynomials. This was conjectured in joint work with Golyshev. It suggests a new approach to the classification of Fano manifolds: by proving an appropriate mirror theorem and then classifying Fano mirrors. Our methods are likely to be of independent interest. We rework the Mori-Mukai classification of 3-dimensional Fano manifolds, showing that each of them can be expressed as the zero locus of a section of a homogeneous vector bundle over a GIT quotient V/G, where G is a product of groups of the form GL_n(C) and V is a representation of G. When G=GL_1(C)^r, this expresses the Fano 3-fold as a toric complete intersection; in the remaining cases, it expresses the Fano 3-fold as a tautological subvariety of a Grassmannian, partial flag manifold, or projective bundle thereon. We then compute the quantum periods using the Quantum Lefschetz Hyperplane Theorem of Coates-Givental and the Abelian/non-Abelian correspondence of Bertram-Ciocan-Fontanine-Kim-Sabbah., 104 pages. v2: references updated, minor changes to presentation. v3: some changes to exposition and minor mathematical corrections, plus much improved hyperlinking

We classify four-dimensional quasismooth weighted hypersurfaces with small canonical class, and verify a conjecture of Johnson and Kollar on infinite series of quasismooth hypersurfaces with anticanonical hyperplane section in the case of fourfolds. By considering the quotient singularities that arise, we classify those weighted hypersurfaces that are canonical, Calabi-Yau, and Fano fourfolds. We also consider other classes of hypersurfaces, including Fano hypersurfaces of index greater than 1 in dimensions 3 and 4., Comment: 25 pages

We introduce a concept of minimality for Fano polygons. We show that, up to mutation, there are only finitely many Fano polygons with given singularity content, and give an algorithm to determine the mutation-equivalence classes of such polygons. This is a key step in a program to classify orbifold del Pezzo surfaces using mirror symmetry. As an application, we classify all Fano polygons such that the corresponding toric surface is qG-deformation-equivalent to either (i) a smooth surface; or (ii) a surface with only singularities of type 1/3(1,1)., 29 pages

We find at least 527 new four-dimensional Fano manifolds, each of which is a complete intersection in a smooth toric Fano manifold., Comment: 12 pages plus a 60 page Appendix. Includes results of computer algebra calculations and full source code: see the Appendix and the ancillary files. v2: included missing ancillary file. v3: bibliography updated, typos corrected, other minor improvements, new figure added, now includes Euler numbers

Recent work has focused on the roots z of the Ehrhart polynomial of a lattice polytope P. The case when Re(z) = -1/2 is of particular interest: these polytopes satisfy Golyshev's "canonical line hypothesis". We characterise such polytopes when dim(P), 20 pages, 1 figure

We state a number of conjectures that together allow one to classify a broad class of del Pezzo surfaces with cyclic quotient singularities using mirror symmetry. We prove our conjectures in the simplest cases. The conjectures relate mutation-equivalence classes of Fano polygons with Q-Gorenstein deformation classes of del Pezzo surfaces., Comment: 14 pages. v2: references updated

This paper classifies all toric Fano 3-folds with terminal singularities. This is achieved by solving the equivalent combinatorial problem; that of finding, up to the action of $GL(3,\Z)$, all convex polytopes in $\Z^3$ which contain the origin as the only non-vertex lattice point. We obtain, up to isomorphism, 233 toric Fano 3-folds possessing at worst $\Q$-factorial singularities (of which 18 are known to be smooth) and 401 toric Fano 3-folds with terminal singularities that are not $\Q$-factorial.

We collect a list of known four-dimensional Fano manifolds and compute their quantum periods. This list includes all four-dimensional Fano manifolds of index greater than one, all four-dimensional toric Fano manifolds, all four-dimensional products of lower-dimensional Fano manifolds, and certain complete intersections in projective bundles., Comment: 44 pages. Includes results of computer algebra calculations and full source code: see the Appendices and the ancillary files. v2: typos corrected, explained connections to the work of Batyrev--Ciocan-Fontanine--Kim--van Straten. v3: fixed strange problem with PDF generation

The paper presents some basic physical properties (static electric permittivities, refraction indices, density and viscosity) of 2-chloro-4-n’-alkylphenyl esters of 4-n-alkylbicyclo[2,2,2] octane-1-carboxylic acids (n’=7, n = 5 and 7) which are, at room temperature, nematics with a negative dielectric an-isotropy. On the basis of temperature dependence of the principal static permittivities ε‖(T) and e⊥(T) of the nematics, using the Maier-Meier equations, the angle between the dipole moment vector and the long axis of mesogenic molecules, the apparent molecular dipole moment square pl μ2 app(T), and the nematic order parameter S(T) were determined.

We exhibit seven linear codes exceeding the current best known minimum distance d for their dimension k and block length n. Each code is defined over F_8, and their invariants [n,k,d] are given by [49,13,27], [49,14,26], [49,16,24], [49,17,23], [49,19,21], [49,25,16] and [49,26,15]. Our method includes an exhaustive search of all monomial evaluation codes generated by points in the [0,5]x[0,5] lattice square., Comment: 10 pages, 4 figures

Fano polytopes are the convex-geometric objects corresponding to toric Fano varieties. We give a brief survey of classification results for different classes of Fano polytopes.

We introduce reflexive polytopes of index l as a natural generalisation of the notion of a reflexive polytope of index 1. These l-reflexive polytopes also appear as dual pairs. In dimension two we show that they arise from reflexive polygons via a change of the underlying lattice. This allows us to efficiently classify all isomorphism classes of l-reflexive polygons up to index 200. As another application, we show that any reflexive polygon of arbitrary index satisfies the famous "number 12" property. This is a new, infinite class of lattice polygons possessing this property, and extends the previously known sixteen instances. The number 12 property also holds more generally for l-reflexive non-convex or self-intersecting polygonal loops. We conclude by discussing higher-dimensional examples and open questions., Dedicated to the memory of Maximilian Kreuzer. 23 pages, 4 figures, 4 tables, an appendix containing Magma source code

V. Golyshev conjectured that for any smooth polytope P of dimension at most five, the roots $z\in\C$ of the Ehrhart polynomial for P have real part equal to -1/2. An elementary proof is given, and in each dimension the roots are described explicitly. We also present examples which demonstrate that this result cannot be extended to dimension six., Comment: 10 pages

For a d-dimensional convex lattice polytope P, a formula for the boundary volume is derived in terms of the number of boundary lattice points on the first $\floor{d/2}$ dilations of P. As an application we give a necessary and sufficient condition for a polytope to be reflexive, and derive formulae for the f-vector of a smooth polytope in dimensions 3, 4, and 5. We also give applications to reflexive order polytopes, and to the Birkhoff polytope., Comment: 21 pages; subsumes arXiv:1002.1908 [math.CO]; to appear in the Bulletin of the Australian Mathematical Society

Toric log del Pezzo surfaces correspond to convex lattice polygons containing the origin in their interior and having only primitive vertices. An upper bound on the volume and on the number of boundary lattice points of these polygons is derived in terms of the index l. Techniques for classifying these polygons are also described: a direct classification for index two is given, and a classification for all l, 16 pages

A fake weighted projective space X is a Q-factorial toric variety with Picard number one. As with weighted projective space, X comes equipped with a set of weights (\lambda_0,...,\lambda_n). We see how the singularities of P(\lambda_0,...,\lambda_n) influence the singularities of X, and how the weights bound the number of possible fake weighted projective spaces for a fixed dimension. Finally, we present an upper bound on the ratios \lambda_j/\sum\lambda_i if we wish X to have only terminal (or canonical) singularities., Comment: 12 pages

Let P be a convex polytope containing the origin, whose dual is a lattice polytope. Hibi's Palindromic Theorem tells us that if P is also a lattice polytope then the Ehrhart $\delta$-vector of P is palindromic. Perhaps less well-known is that a similar result holds when P is rational. We present an elementary lattice-point proof of this fact., Comment: 4 pages

An inductive approach to classifying toric Fano varieties is given. As an application of this technique, we present a classification of the toric Fano threefolds with at worst canonical singularities. Up to isomorphism, there are 674,688 such varieties., Comment: 21 pages, 1 figure

Background. Total hip arthroplasty (THA) is today one of the most frequently performed major surgical operations in orthopedics. Although it is the standard method of treatment for advanced degenerative changes in the joint, the operation is accompanied by a high risk of thromboembolic complications. Material and methods. The present study is a retrospective analysis of two groups of THA patients. Group I consisted of 80 patients (average age 62) operated 1980-1983, for whom no prophylaxis was applied. In Group II, low molecular weight heparin (LMWH) was applied pre- and postoperatively. This group consisted of 94 patients (average age 63.5) operated in the year 1998. Thromboembolic complications were diagnosed on the basis of reported symptoms, physical examinations and additional tests (chest x-ray, EKG, gasometry). Results. In Group I there were 11 complications (13.75%), including 10 cases (91%) of deep venous thromboembolic disease of the lower extremities (DVT) and 1 case (9%) of pulmonary embolism (PE), while in Group II there were only 2 complications (2.1%), 1 DVT and 1 PE. The difference between groups was statistically significant. The risk factors for venous thromboembolic disease were analyzed. In both study groups, the predominant risk factors were prolonged duration of surgery and diabetes accompanied by venous insufficiency. Conclusions. The results of our analysis showed that the use of DVT prophylaxis with low-molecular heparin in the preoperative and postoperative period reduced the occurrence of thromboembolic complications.

The aim of the study was to assess the early and late results of extended pneumonectomies in lung cancer patients with T3 and T4 disease. Between Jan. 1995 and Dec. 1999--445 pneumonectomies were performed in patients with lung cancer. In 37 patients without preoperative N2 involvement a standard pneumonectomy was extended to include the following additional resections: chest wall (10), pericardium (9), diaphragm (5), VCS (3), descending aorta (2), left atrium (5), esophagus (1) and tracheal bifurcation (2). The effect of various factors on general mortality and morbidity was analyzed with the use of binary logistic regression. There were two early postoperative deaths (6.8%). Major complications occurred in 10 patients (29%). Overall survival rates at 1, 2, and 3 years were 43, 30 and 24%, respectively. The survival rates for the subgroup with chest involvement only were 50, 42 and 30%, respectively. Eight patients survived beyond the 36 month follow-up. The only factor significantly affecting mortality was incomplete resection, as revealed by postoperative microscopic examination (R1, p0.05). Extended operations are justified by a relatively low mortality rate and low number of severe postoperative complications, specially in patients with chest wall involvement only. The result of this treatment predominantly depends upon the completeness of the resection.

The aim of our study was the assessment of the ploidia and its influence on the remission time and the survival of surgically treated patients with squamous cell lung cancer. The results were then related to the clinical staging, grading, size and localization of the tumor. The tissue samples (n = 60) of squamous cell lung carcinoma resected between 1995-1996 at the Department of Thoracic Surgery at University of Medical Sciences in Poznań were prepared using modified Hedley's method. The measurement was done in Cytoron Absolute flow cytometer. The abnormal DNA (aneuploid) was found in 40% of tumors. In two-year observation period more patients died with aneuploid tumors (54.6% deaths) than with diploid tumors (35.2% deaths). No significant correlation was found between the ploidy and frequency of metastasis to regional lymph nodes, tumor size, localization and grading. The estimation of the DNA content in the cancer cells seems to be a significant and valuable prognostic factor. The measurement of the DNA content can be useful in patients to estimate risk of recurrence after surgery.

The aim of the paper is to present modelling of abrasive wear and grinding wheel durability by means of probabilistic description of abrasion and crush dressing of grinding wheels. Relations describing distributions of active grain age and its change during of grinding are determined. A practical application of the models proposed in the paper, using empirical data, makes it possible to determine other quantities which are very difficult to estimate in an experimental way.

Particularly good results in micro-smoothing of steel work-pieces surfaces by means of imperial micro-finishing films, and difficulties in obtaining proper machining effects for aluminium and its alloys and also for other high plasticity materials in surrounding temperature, have caused examining of this process in extra low temperatures. Carrying out the process in extra low temperature, and at the same time in vacuum, makes it possible to obtain extra smooth surfaces of elements made from aluminium. The paper presents the experimental stand which is adapted for operations in extra low temperatures and results of micro-smoothing processes.

ObjectivesThe purpose of the study was to evaluate the frequency of abnormal DNA content in squamous cancer cells (SCLC) and analyze its correlation with late survival rates after surgical treatment. Many previous studies included attempts to associate DNA quantification with prognosis for lung cancer. However, there is still considerable divergence of opinion about its prognostic value.MethodsA group of 110 patients surgically treated because of SCC was analyzed. Paraffin-embedded pathologic material underwent cytometric analysis. Post-operative follow-up was performed with standard follow-up visits. The 2 tests to χ statistical analysis was carried out using Mann-Whitney's and compare the following parameters in both groups: clinical staging, grading, tumor size, distant and local metastasis, tumor location, type of surgical procedure, local recurrence and survival time. The survival curves were drawn using the Kaplan-Meier method and two and five years survival rate were assessed. Clinical staging, regional metastasis and ploidy, having a great impact on survival rates, were analyzed with multivariational analysis.Results50 (45%) tumors were DNA aneuploid. There were no significance between the ploidy groups in clinical staging, grading, tumor size and location and type of surgical procedure. The two years survival rate in patients with aneuploid cancers (16,7%) was significantly worse than in those with diploid tumors (50%)(p