A New Perspective on Clustered Planarity as a Combinatorial Embedding Problem

The clustered planarity problem (c-planarity) asks whether a hierarchically clustered graph admits a planar drawing such that the clusters can be nicely represented by regions. We introduce the cd-tree data structure and give a new characterization of c-planarity. It leads to efficient algorithms for c-planarity testing in the following cases. (i) Every cluster and every co-cluster (complement of a cluster) has at most two connected components. (ii) Every cluster has at most five outgoing edges. Moreover, the cd-tree reveals interesting connections between c-planarity and planarity with constraints on the order of edges around vertices. On one hand, this gives rise to a bunch of new open problems related to c-planarity, on the other hand it provides a new perspective on previous results.Comment: 17 pages, 2 figure

Advances on Testing C-Planarity of Embedded Flat Clustered Graphs

We show a polynomial-time algorithm for testing c-planarity of embedded flat clustered graphs with at most two vertices per cluster on each face.Comment: Accepted at GD '1

Deformed Superspace, N=1/2 Supersymmetry and (Non)Renormalization Theorems

We consider a deformed superspace in which the coordinates \theta do not anticommute, but satisfy a Clifford algebra. We present results on the properties of N=1/2 supersymmetric theories of chiral superfields in deformed superspace, taking the Wess-Zumino model as the prototype. We prove new (non)renormalization theorems: the F-term is radiatively corrected and becomes indistinguishable from the D-term, while the Fbar-term is not renormalized. Supersymmetric vacua are critical points of the antiholomorphic superpotential. The vacuum energy is zero to all orders in perturbation theory. We illustrate these results with several examples.Comment: 21 pages, 5 figures and one table; V2: references adde

Multigluon tree amplitudes with a pair of massive fermions

We consider the calculation of n-point multigluon tree amplitudes with a pair of massive fermions in QCD. We give the explicit transformation rules of this kind of massive fermion-pair amplitudes with respect to different reference momenta and check the correctness of them by SUSY Ward identities. Using these rules and onshell BCFW recursion relation, we calculate the analytic results of several n-point multigluon amplitudes.Comment: 15page

Splitting Clusters To Get C-Planarity

In this paper we introduce a generalization of the c-planarity testing problem for clustered graphs. Namely, given a clustered graph, the goal of the S PLIT-C-P LANARITY problem is to split as few clusters as possible in order to make the graph c-planar. Determining whether zero splits are enough coincides with testing c-planarity. We show that S PLIT-C-P LANARITY is NP-complete for c-connected clustered triangulations and for non-c-connected clustered paths and cycles. On the other hand, we present a polynomial-time algorithm for flat c-connected clustered graphs whose underlying graph is a biconnected seriesparallel graph, both in the fixed and in the variable embedding setting, when the splits are assumed to maintain the c-connectivity of the clusters

Dark Matter attempts for CoGeNT and DAMA

Recently, the CoGeNT collaboration presented a positive signal for an annual modulation in their data set. In light of the long standing annual modulation signal in DAMA/LIBRA, we analyze the compatibility of both of these signal within the hypothesis of dark matter (DM) scattering on nuclei, taking into account existing experimental constraints. We consider the cases of elastic and inelastic scattering with either spin-dependent or spin-independent coupling to nucleons. We allow for isospin violating interactions as well as for light mediators. We find that there is some tension between the size of the modulation signal and the time-integrated event excess in CoGeNT, making it difficult to explain both simultaneously. Moreover, within the wide range of DM interaction models considered, we do not find a simultaneous explanation of CoGeNT and DAMA/LIBRA compatible with constraints from other experiments. However, in certain cases part of the data can be made consistent. For example, the modulation signal from CoGeNT becomes consistent with the total rate and with limits from other DM searches at 90% CL (but not with the DAMA/LIBRA signal) if DM scattering is inelastic spin-independent with just the right couplings to protons and neutrons to reduce the scattering rate on xenon. Conversely the DAMA/LIBRA signal (but not CoGeNT) can be explained by spin-dependent inelastic DM scattering.Comment: 20 pages, 9 figure

Branes, Anti-Branes and Brauer Algebras in Gauge-Gravity duality

We propose gauge theory operators built using a complex Matrix scalar which are dual to brane-anti-brane systems in $AdS_5 \times S^5$, in the zero coupling limit of the dual Yang-Mills. The branes involved are half-BPS giant gravitons. The proposed operators dual to giant-anti-giant configurations satisfy the appropriate orthogonality properties. Projection operators in Brauer algebras are used to construct the relevant multi-trace Matrix operators. These are related to the ``coupled representations'' which appear in 2D Yang-Mills theory. We discuss the implications of these results for the quantum mechanics of a complex matrix model, the counting of non-supersymmetric operators and the physics of brane-anti-brane systems. The stringy exclusion principle known from the properties of half-BPS giant gravitons, has a new incarnation in this context. It involves a qualitative change in the map between brane-anti-brane states to gauge theory operators. In the case of a pair of sphere giant and anti-giant this change occurs when the sum of the magnitudes of their angular momenta reaches $N$.Comment: 52 pages, 10 figure

Integrated computer-aided working-fluid design and thermoeconomic ORC system optimisation

The successful commercialisation of organic Rankine cycle (ORC) systems across a range of power outputs and heat-source temperatures demands step-changes in both improved thermodynamic performance and reduced investment costs. The former can be achieved through high-performance components and optimised system architectures operating with novel working-fluids, whilst the latter requires careful component-technology selection, economies of scale, learning curves and a proper selection of materials and cycle configurations. In this context, thermoeconomic optimisation of the whole power-system should be completed aimed at maximising profitability. This paper couples the computer-aided molecular design (CAMD) of the working-fluid with ORC thermodynamic models, including recuperated and other alternative (e.g., partial evaporation or trilateral) cycles, and a thermoeconomic system assessment. The developed CAMD-ORC framework integrates an advanced molecular-based group-contribution equation of state, SAFT-γ Mie, with a thermodynamic description of the system, and is capable of simultaneously optimising the working-fluid structure, and the thermodynamic system. The advantage of the proposed CAMD-ORC methodology is that it removes subjective and pre-emptive screening criteria that would otherwise exist in conventional working-fluid selection studies. The framework is used to optimise hydrocarbon working-fluids for three different heat sources (150, 250 and 350 °C, each with mcp = 4.2 kW/K). In each case, the optimal combination of working-fluid and ORC system architecture is identified, and system investment costs are evaluated through component sizing models. It is observed that optimal working fluids that minimise the specific investment cost (SIC) are not the same as those that maximise power output. For the three heat sources the optimal working-fluids that minimise the SIC are isobutane, 2-pentene and 2-heptene, with SICs of 4.03, 2.22 and 1.84 £/W respectively

U(N) Instantons on N=1/2 superspace -- exact solution & geometry of moduli space

We construct the exact solution of one (anti)instanton in N=1/2 super Yang-Mills theory defined on non(anti)commutative superspace. We first identify N = 1/2 superconformal invariance as maximal spacetime symmetry. For gauge group U(2), SU(2) part of the solution is given by the standard (anti)instanton, but U(1) field strength also turns out nonzero. The solution is SO(4) rotationally symmetric. For gauge group U(N), in contrast to the U(2) case, we show that the entire U(N) part of the solution is deformed by non(anti)commutativity and fermion zero-modes. The solution is no longer rotationally symmetric; it is polarized into an axially symmetric configuration because of the underlying non(anti)commutativity. We compute the `information metric' of one (anti) instanton. We find that moduli space geometry is deformed from hyperbolic space (Euclidean anti-de Sitter space) in a way anticipated from reduced spacetime symmetry. Remarkably, the volume measure of the moduli space turns out to be independent of the non(anti)commutativity. Implications to D-branes in Ramond- Ramond flux background and Maldacena's gauge-gravity correspondence are discussed.Comment: 39 pages, 3 figures, JHEP style; v2. typos corrected + a paragraph adde