Roots of the affine Cremona group

Let k[x_1,...,x_n] be the polynomial algebra in n variables and let A^n=Spec k[x_1,...,x_n]. In this note we show that the root vectors of the affine Cremona group Aut(A^n) with respect to the diagonal torus are exactly the locally nilpotent derivations x^a\times d/dx_i, where x^a is any monomial not depending on x_i. This answers a question due to Popov.Comment: 4 page

Calogero-Sutherland Approach to Defect Blocks

Extended objects such as line or surface operators, interfaces or boundaries play an important role in conformal field theory. Here we propose a systematic approach to the relevant conformal blocks which are argued to coincide with the wave functions of an integrable multi-particle Calogero-Sutherland problem. This generalizes a recent observation in 1602.01858 and makes extensive mathematical results from the modern theory of multi-variable hypergeometric functions available for studies of conformal defects. Applications range from several new relations with scalar four-point blocks to a Euclidean inversion formula for defect correlators.Comment: v2: changes for clarit

Torus invariant divisors

Using the language of polyhedral divisors and divisorial fans we describe invariant divisors on normal varieties X which admit an effective codimension one torus action. In this picture X is given by a divisorial fan on a smooth projective curve Y. Cartier divisors on X can be described by piecewise affine functions h on the divisorial fan S whereas Weil divisors correspond to certain zero and one dimensional faces of it. Furthermore we provide descriptions of the divisor class group and the canonical divisor. Global sections of line bundles O(D_h) will be determined by a subset of a weight polytope associated to h, and global sections of specific line bundles on the underlying curve Y.Comment: 16 pages; 5 pictures; small changes in the layout, further typos remove

Affine T-varieties of complexity one and locally nilpotent derivations

Let X=spec A be a normal affine variety over an algebraically closed field k of characteristic 0 endowed with an effective action of a torus T of dimension n. Let also D be a homogeneous locally nilpotent derivation on the normal affine Z^n-graded domain A, so that D generates a k_+-action on X that is normalized by the T-action. We provide a complete classification of pairs (X,D) in two cases: for toric varieties (n=\dim X) and in the case where n=\dim X-1. This generalizes previously known results for surfaces due to Flenner and Zaidenberg. As an application we compute the homogeneous Makar-Limanov invariant of such varieties. In particular we exhibit a family of non-rational varieties with trivial Makar-Limanov invariant.Comment: 31 pages. Minor changes in the structure. Fixed some typo

Evaluation of the mechanical properties of cements with fillers derived from the CO2 reduction of cement plants

This work introduces a novel method for the development of CO2 recovery systems derived from the production process of cement in order to obtain CaCO3 nanofiller in cement-based composites. Research was carried out in collaboration between the Department of Applied Science and Technology (DISAT) and the Department of Structural, Construction and Geotechnical Engineering (DISEG) of Politecnico di Torino. The objective of this method was dual. Firstly, it aimed to obtain a precipitated calcium carbonate - nanoCaCO3 - with a high degree of purity. Secondly, it aimed to optimize the characteristics of these nanoparticles e.g. additional percentages, morphology, particle size distribution or crystal phase, according to their use in cement-based composites. The synthesized nanoCaCO3 particles were subsequently added into the cementitious composites in different percentages according to the weight of the cement, in order to understand their behaviour within the cement matrix. The mechanical properties were also evaluated, both at 7 and 28 days, through three point bending and compression tests. The results of the mechanical tests showed a promising improvement in strength and toughness. This study is a first step towards developing a CO2 circular economy

Nano CaCO3 particles in cement mortars towards developing a circular economy in the cement industry

This paper calls into question the effects of incorporating nano calcium carbonate (CaCO3) particles in cement mortars, as they are interesting additive materials already successfully tested as cement nanofiller. These nanoparticles could potentially be prepared through the carbonation route using CO2 from combustion gases from the cement industry. This could enable a circular-economy approach for carbon capture and its re-use within the cement industry, in a sustainable and synergistic manner. In this study, part of the cement content was substituted with commercial nano CaCO3 particles to investigate their effects on the flexural and compressive strength of the resulting cement mortars, after curing for 7 and 28 days. Decreasing the cement content could lead to a reduction in the carbon footprint of cement, which is responsible for approximately 8% of global carbon dioxide emissions. Preliminary results using synthesized CaCO3 particles as nanofillers showed that, after 7 days of curing, mechanical properties of cement mortars improved. This indicates that hydration reaction was accelerated since CaCO3 acts as seeding for this reaction. By contrast, after 28 days of curing, no major improvement was observed. A higher content of calcium carbonate nanoparticles may have reduced the filler effect of these particles due to aggregation phenomena. In the present work, the effects of commercial nano CaCO3 particles on cement hydration were investigated. Mechanical tests showed promising results both after 7 and 28 days of curing. This could lead to the reduction of the carbon footprint of cement manufacturing and produce increasingly better performing building materials. Thus, the development of a circular economy in the cement industry could be achieved

High prevalence of clustered tuberculosis cases in peruvian migrants in Florence, Italy.

Tuberculosis is a leading cause of morbidity for Peruvian migrants in Florence, Italy, where they account for about 20% of yearly diagnosed cases. A retrospective study on cases notified in Peruvian residents in Florence in the period 2001-2010 was carried out and available Mycobacterium tuberculosis strains were genotyped (MIRU-VNTR-24 and Spoligotyping). One hundred thirty eight cases were retrieved. Genotyping performed in 87 strains revealed that 39 (44.8%) belonged to 12 clusters. Assuming that in each cluster the transmission of tuberculosis from the index case took place in Florence, a large proportion of cases could be preventable by improving early diagnosis of contagious cases and contact tracing

From Scattering Amplitudes to the Dilatation Generator in N=4 SYM

The complete spin chain representation of the planar N=4 SYM dilatation generator has long been known at one loop, where it involves leading nearest-neighbor 2 -> 2 interactions. In this work we use superconformal symmetry to derive the unique solution for the leading L -> 2 interactions of the planar dilatation generator for arbitrarily large L. We then propose that these interactions are given by the scattering operator that has N=4 SYM tree-level scattering amplitudes as matrix elements. We provide compelling evidence for this proposal, including explicit checks for L=2,3 and a proof of consistency with superconformal symmetry.Comment: 39 pages, v2: reference added and minor changes, published versio

Chromatin condensation and recruitment of PHD finger proteins to histone H3K4me3 are mutually exclusive

Histone post-translational modifications, and specific combinations they create, mediate a wide range of nuclear events. However, the mechanistic bases for recognition of these combinations have not been elucidated. Here, we characterize crosstalk between H3T3 and H3T6 phosphorylation, occurring in mitosis, and H3K4me3, a mark associated with active transcription. We detail the molecular mechanisms by which H3T3ph/K4me3/T6ph switches mediate activities of H3K4me3-binding proteins, including those containing plant homeodomain (PHD) and double Tudor reader domains. Our results derived from nuclear magnetic resonance chemical shift perturbation analysis, orthogonal binding assays and cell fluorescence microscopy studies reveal a strong anti-correlation between histone H3T3/T6 phosphorylation and retention of PHD finger proteins in chromatin during mitosis. Together, our findings uncover the mechanistic rules of chromatin engagement for H3K4me3-specific readers during cell division

On the order of an automorphism of a smooth hypersurface

In this paper we give an effective criterion as to when a positive integer q is the order of an automorphism of a smooth hypersurface of dimension n and degree d, for every d>2, n>1, (n,d)\neq (2,4), and \gcd(q,d)=\gcd(q,d-1)=1. This allows us to give a complete criterion in the case where q=p is a prime number. In particular, we show the following result: If X is a smooth hypersurface of dimension n and degree d admitting an automorphism of prime order p then p(d-1)^n then X is isomorphic to the Klein hypersurface, n=2 or n+2 is prime, and p=\Phi_{n+2}(1-d) where \Phi_{n+2} is the (n+2)-th cyclotomic polynomial. Finally, we provide some applications to intermediate jacobians of Klein hypersurfaces