(Non-)existence of Polynomial Kernels for the Test Cover Problem

The input of the Test Cover problem consists of a set $V$ of vertices, and a collection ${\cal E}=\{E_1,..., E_m\}$ of distinct subsets of $V$, called tests. A test $E_q$ separates a pair $v_i,v_j$ of vertices if $|\{v_i,v_j\}\cap E_q|=1.$ A subcollection ${\cal T}\subseteq {\cal E}$ is a test cover if each pair $v_i,v_j$ of distinct vertices is separated by a test in ${\cal T}$. The objective is to find a test cover of minimum cardinality, if one exists. This problem is NP-hard. We consider two parameterizations the Test Cover problem with parameter $k$: (a) decide whether there is a test cover with at most $k$ tests, (b) decide whether there is a test cover with at most $|V|-k$ tests. Both parameterizations are known to be fixed-parameter tractable. We prove that none have a polynomial size kernel unless $NP\subseteq coNP/poly$. Our proofs use the cross-composition method recently introduced by Bodlaender et al. (2011) and parametric duality introduced by Chen et al. (2005). The result for the parameterization (a) was an open problem (private communications with Henning Fernau and Jiong Guo, Jan.-Feb. 2012). We also show that the parameterization (a) admits a polynomial size kernel if the size of each test is upper-bounded by a constant

Fast Spherical Harmonic Analysis: a quick algorithm for generating and/or inverting full sky, high resolution CMB Anisotropy maps

We present a fast algorithm for generating full sky, high resolution ($\sim 5'$) simulations of the CMB anisotropy pattern. We also discuss the inverse problem, that of evaluating from such a map the full set of $a_{\ell m}$'s and the spectral coefficients $C_\ell$. We show that using an Equidistant Cylindrical Projection of the sky substantially speeds up the calculations. Thus, generating and/or inverting a full sky, high resolution map can be easily achieved with present day computer technology.Comment: 13 pages, LaTex, 5 PostScript figures included, 1 colour plate available (PostScript version, 1.6 Mb) at http://itovf2.roma2.infn.it/natoli

Haunch retrofit of RC beam–column joints: Linear stress field analysis and Strut-and-Tie method application

This paper addresses the stress field of reinforced concrete (RC) beam–column joints retrofitted with haunches. Design of such solution currently assumes internal forces evaluated by the so called β-factor approach, which was originally conceived targeting the enhancement of steel moment-resisting frames. Extension to RC is subsequent as it emerges from the literature survey. The analytical model is first critically rediscussed. Inconsistencies of the adopted structural scheme, with respect to the actual mechanical behavior, may lie on the compatibility conditions which are imposed between the haunch and concrete beam (or column). In this regard, two-dimensional finite element models (FEM), using linear-elastic materials, are employed to study the stress field of two benchmark specimens derived from literature. A partial validation is carried out against experimentally derived internal forces. Results show that, for haunches with extended flat plates and stiff diagonals, compressive diffusion affects the entire haunch region. Consequently, beam's kinematic hypothesis of linear strains is no longer valid. The predicted joint shear demand resulted underestimated by β-factor approach by 50%. Since 2D FEM may be not efficient for many practical circumstances, an application of Strut-and-Tie is alternatively proposed. Finally, both the limitations and possible extensions of the proposed approaches are stated transparently

RC beam-column joints, discussion of the provisions in the second generation Eurocode 8

This paper reviews the provisions given in the draft of the second-generation Eurocode 8 (EC8) for the design and assessment of RC beam-column joint against seismic conditions. The analytical bases were recently published by Michael Fardis. A critical discussion of the analytical models, supported by a numerical example, is given. Validation against an independent database of exterior joints is made. A final comparison with respect to (i) current EC8 provisions and (ii) other Building Codes is presented

Comparative Assessment of Shear Demand for RC Beam-Column Joints under Earthquake Loading

This paper focuses on the evaluation of bi-axial shear demand for reinforced concrete (RC) beam-column joints assuming: (i) the SPEAR frame as a benchmark; and (ii) different structural analysis methods which share the same seismic input. A numerical model was implemented using lumped plasticity. The joints were modeled as rigid offsets of beams and columns. The shear demand at a joint is evaluated as a post-process of the beam's nodal moment. The discussion focuses on the differences between the estimated shear demand considering modal-response-spectrum analysis (MRSA), non-linear static analysis (NLSA) and non-linear time history (NLTH). Strength assessment of joints is discussed as well. Significant strength differences were recognized by using different building codes targeted to existing structures which, in general, behaved on the safe side. The elliptical shear strength domain resulted in being conservative when compared to NLTH shear demand orbits. NLSA, using modal combination, proved to estimate the larger shear demand with respect to MRSA and NLTH

A coupled thermal-analytical and mechanical approach to investigate the behavior of bonded anchors cured at sub-zero temperatures

In post-installed connection in reinforced concrete structures, bonded anchors are commonly adopted when elevated mechanical performances are required. Such performances may be significantly impaired by adverse service conditions, above all temperature variations with respect to room ambient one. It is also generally acknowledged that the curing temperature may impact on the anchor performances, to the extent that all the main existing qualification procedures assess the anchor behavior when cured at different temperatures, in particular below zero Celsius degree. However, among the few investigations focusing on the impact of a low curing temperature on the long term behavior of an anchor, a low effort exists in addressing the relationship between the anchor mechanical behavior and the thermal properties of the bonding agent. The paper proposes a coupled thermal-analytical and mechanical approach to detect potential critical issues in the long term mechanical behavior of the anchor as a function of the adhesive behavior, as investigated by thermal or thermo-mechanical analyses. To the scope, a wide investigation on two adhesives is carried out comprising MDSC, DMA, pull-out and sustained load tests. On the basis of the obtained results, it is concluded that some thresholds in the variations of degree of conversion and phase transition temperatures may indicate a negligible impact of a low curing temperature on the anchor mechanical behavior, but also that existing qualification procedures are not able to capture the anchor behavior, when cured at low temperatures and subjected, during its service life, to temperatures higher than room ambient one

A semi-coherent analysis method to search for continuous gravitational waves emitted by ultra-light boson clouds around spinning black holes

As a consequence of superradiant instability induced in Kerr black holes, ultra-light boson clouds can be a source of persistent gravitational waves, potentially detectable by current and future gravitational-wave detectors. These signals have been predicted to be nearly monochromatic, with a small steady frequency increase (spin-up), but given the several assumptions and simplifications done at theoretical level, it is wise to consider, from the data analysis point of view, a broader class of gravitational signals in which the phase (or the frequency) slightly wander in time. Also other types of sources, e.g. neutron stars in which a torque balance equilibrium exists between matter accretion and emission of persistent gravitational waves, would fit in this category. In this paper we present a robust and computationally cheap analysis pipeline devoted to the search of such kind of signals. We provide a full characterization of the method, through both a theoretical sensitivity estimation and through the analysis of syntethic data in which simulated signals have been injected. The search setup for both all-sky searches and higher sensitivity directed searches is discussed.Comment: 13 pages, 13 figure

{Polynomial Kernels for λ\lambda-extendible Properties Parameterized Above the {Poljak--Turz{\'{i}}k} Bound}

Poljak and Turzik (Discrete Mathematics 1986) introduced the notion of {\lambda}-extendible properties of graphs as a generalization of the property of being bipartite. They showed that for any 0 < {\lambda} < 1 and {\lambda}-extendible property {\Pi}, any connected graph G on n vertices and m edges contains a spanning subgraph H in {\Pi} with at least {\lambda}m + (1-{\lambda})(n-1)/2 edges. The property of being bipartite is {\lambda}-extendible for {\lambda} = 1/2, and so the Poljak-Turzik bound generalizes the well-known Edwards-Erdos bound for Max-Cut. Other examples of {\lambda}-extendible properties include: being an acyclic oriented graph, a balanced signed graph, or a q-colorable graph for some integer q. Mnich et. al. (FSTTCS 2012) defined the closely related notion of strong {\lambda}-extendibility. They showed that the problem of finding a subgraph satisfying a given strongly {\lambda}-extendible property {\Pi} is fixed-parameter tractable (FPT) when parameterized above the Poljak-Turzik bound - does there exist a spanning subgraph H of a connected graph G such that H in {\Pi} and H has at least {\lambda}m + (1-{\lambda})(n-1)/2 + k edges? - subject to the condition that the problem is FPT on a certain simple class of graphs called almost-forests of cliques. In this paper we settle the kernelization complexity of nearly all problems parameterized above Poljak-Turzik bounds, in the affirmative. We show that these problems admit quadratic kernels (cubic when {\lambda} = 1/2), without using the assumption that the problem is FPT on almost-forests of cliques. Thus our results not only remove the technical condition of being FPT on almost-forests of cliques from previous results, but also unify and extend previously known kernelization results in this direction. Our results add to the select list of generic kernelization results known in the literature