Toric rings, inseparability and rigidity

This article provides the basic algebraic background on infinitesimal deformations and presents the proof of the well-known fact that the non-trivial infinitesimal deformations of a $K$-algebra $R$ are parameterized by the elements of cotangent module $T^1(R)$ of $R$. In this article we focus on deformations of toric rings, and give an explicit description of $T^1(R)$ in the case that $R$ is a toric ring. In particular, we are interested in unobstructed deformations which preserve the toric structure. Such deformations we call separations. Toric rings which do not admit any separation are called inseparable. We apply the theory to the edge ring of a finite graph. The coordinate ring of a convex polyomino may be viewed as the edge ring of a special class of bipartite graphs. It is shown that the coordinate ring of any convex polyomino is inseparable. We introduce the concept of semi-rigidity, and give a combinatorial description of the graphs whose edge ring is semi-rigid. The results are applied to show that for $m-k=k=3$, $G_{k,m-k}$ is not rigid while for $m-k\geq k\geq 4$, $G_{k,m-k}$ is rigid. Here $G_{k,m-k}$ is the complete bipartite graph $K_{m-k,k}$ with one edge removed.Comment: 33 pages, chapter 2 of the Book << Multigraded Algebra and Applications>> 2018, Springer International Publishing AG, part of Springer Natur

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

Towards an Energy-Aware Cloud Architecture for Smart Grids

Energy consumption in Cloud computing is a significant issue in regards to aspects such as the cost of energy, cooling in the data center and the environmental impact of cloud data centers. Smart grids offers the prospect of dynamic costs for a data center’s energy usage. These dynamic costs can be passed on to Cloud users providing incentives for users to moderate their load while also ensuring the Cloud providers are insulated from fluctuations in the cost of energy. The first step towards this is an architecture that focuses on energy monitoring and usage prediction. We provide such an architecture at both the PaaS and IaaS layers, resulting in energy metrics for applications, VMs and physical hosts, which is key to enabling active demand in cloud data centers. This architecture is demonstrated through our initial results utilising a generic use case, providing energy consumption information at the PaaS and IaaS layers. Such monitoring and prediction provides the groundwork for providers passing on energy consumption costs to end users. It is envisaged that the resulting varying price associated with energy consumption can help motivate the formation of methods and tools to support software developers aiming to optimise energy efficiency and minimise the carbon footprint of Cloud applications

Closed string tachyons, flips and conifolds

Following the analysis of tachyons and orbifold flips described in hep-th/0412337, we study nonsupersymmetric analogs of the supersymmetric conifold singularity and show using their toric geometry description that they are nonsupersymmetric orbifolds of the latter. Using linear sigma models, we see that these are unstable to localized closed string tachyon condensation and exhibit flip transitions between their two small resolutions (involving 2-cycles), in the process mediating mild dynamical topology change. Our analysis shows that the structure of these nonsupersymmetric conifolds as quotients of the supersymmetric conifold obstructs the 3-cycle deformation of such singularities, suggesting that these nonsupersymmetric conifolds decay by evolving towards their stable small resolutions.Comment: Latex, 22 pgs, 2 figs. v4: matches JHEP version, 29 pgs, 3 figures, more elaborate Introduction, various clarifications adde

On the classification of Kahler-Ricci solitons on Gorenstein del Pezzo surfaces

We give a classification of all pairs (X,v) of Gorenstein del Pezzo surfaces X and vector fields v which are K-stable in the sense of Berman-Nystrom and therefore are expected to admit a Kahler-Ricci solition. Moreover, we provide some new examples of Fano threefolds admitting a Kahler-Ricci soliton.Comment: 21 pages, ancillary files containing calculations in SageMath; minor correction

East Mediterr Health J

Background: The emergence and re-emergence of viral haemorrhagic fevers (VHFs) is a growing concern worldwide. They are associated with major epidemics with an estimated 51-101 million cases each year, of which around 67 000 are fatal. In 2007, 13 countries in the Eastern Mediterranean Region reported VHF cases. Aims: The main purpose of the study was to review the epidemiological situation in the Region vis-a-vis VHFs to obtain baseline epidemiological information for the establishment of the Emerging Dangerous Pathogen Laboratory Network (EDPLN). Methods: A literature search was performed using PubMed, ProMED-Mail and GIDEON databases. Reported data included disease burden (reported cases and deaths), human prevalence (general population, high-risk groups), vectors and reservoirs. A scoring method was employed to divide countries into 4 groups (very highly, highly, medium and low affected countries). Results: Very highly affected countries were Afghanistan, Egypt, Islamic Republic of Iran, Saudi Arabia and Sudan. Highly affected countries were Djibouti, Morocco, Oman, Pakistan, Tunisia and Yemen. Medium affected countries were Iraq, Somalia and United Arab Emirates. Low affected countries were Bahrain, Jordan, Lebanon, Libya, Palestine, Qatar and Syrian Arab Republic. Conclusions: This study contributes in prioritizing countries to be part of EDPLN and in addressing specific needs related to outbreak investigations, surveillance and research

Antisymmetric Higgs representation in SO(10) for neutrinos

A Model based on SO(10) grand unified theory (GUT) and supersymmetry is presented to describe observed phenomena for neutrinos. The large mixing angles among different generations, together with the small masses, are attributed to the Higgs boson structure at the GUT energy scale. Quantitative discussions for these observables are given, taking into account their energy evolution.Comment: 10 page