(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

Introduction of the IFRS 10: an analysis of the reaction of italian groups

ope

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

Bond in RC structures at high temperature and in fire: lessons from the past and hot issues still open to investigation

High temperatures and fire are definitely among the various exceptional load situations RC structures are required to resist, as demonstrated by the extensive research activity performed so far, from the behavior of cementitious materials to that of single members and entire structures. Reinforcement-concrete bond, however, has become a hot issue at a relatively late stage, with an acceleration in the new millennium. The objective of this paper is to recall some of the major issues treated in the literature since the last conference “Bond in Concrete” (Brescia, Italy, 2012) and still open to investigation, such as: (1) bond micromechanics in fire; (2) bond stress-slip law as a function of the temperature; (3) the role of polypropylene, steel and hybrid fibers; (4) tension stiffening in fire; and (5) bonded fasteners in fire. This reexamination takes advantage of the tests performed in Milan in the last decade on bond-stress distribution along anchored bars in fire, pull-out vs. splitting failures, in-fire capacity of postinstalled fasteners and tension stiffening at high temperature. Only by improving the knowledge – and the modelling - of the basic resisting mechanisms, bond included, today’s refined FE codes will provide rational structural responses based on clearly-recognizable contributions

Lap splice connection of new-to-existing rebars: a numerical study based on literature data

Bond between steel reinforcement and concrete is the basic and fundamental mechanism which assures load transfer between the two materials in reinforced concrete elements. Even though bond has been widely investigated during the last decades, the number of parameters involved in the mechanism, as well as the number of possible geometrical configurations of the final element, are such that both models for the local bond-slip law and for anchorages or lap splices still need further investigation. As evidence of this, design-oriented documents, such as the fib Model Code, are constantly updated. Significant modifications of the bond models and the methods for the calculation of the anchorage length are foreseen in the next generation of codes. The use of post-installed reinforcement offers a reliable solution for the connections in concrete structures, the strength and the stiffness being similar to traditional cast-in rebars. Many applications may be found in the rehabilitation and strengthening of existing structures. Nonetheless, post-installed rebars are becoming popular also in new constructions to make easier building and flexibility in design. Within this framework, structural designers often face the need of overlapping existing and new rebars, with a lack of design recommendations. This paper aims to investigate the load transfer of the new-to-existing lap splices. Numerical simulations were carried out with a commercial code, particularly an experiment from the literature was reviewed and numerically revaluated, also simulating the effects of different splice lengths, not counted in the original study. Inverse analysis was used to calibrate a local bond-slip law, which was the input for the following simulations. Failure mode and crack pattern are discussed showing that splitting is the dominant failure mode for short lap splices