Bad semidefinite programs: they all look the same

Conic linear programs, among them semidefinite programs, often behave pathologically: the optimal values of the primal and dual programs may differ, and may not be attained. We present a novel analysis of these pathological behaviors. We call a conic linear system $Ax <= b$ {\em badly behaved} if the value of $\sup { | A x <= b }$ is finite but the dual program has no solution with the same value for {\em some} $c.$ We describe simple and intuitive geometric characterizations of badly behaved conic linear systems. Our main motivation is the striking similarity of badly behaved semidefinite systems in the literature; we characterize such systems by certain {\em excluded matrices}, which are easy to spot in all published examples. We show how to transform semidefinite systems into a canonical form, which allows us to easily verify whether they are badly behaved. We prove several other structural results about badly behaved semidefinite systems; for example, we show that they are in $NP \cap co-NP$ in the real number model of computing. As a byproduct, we prove that all linear maps that act on symmetric matrices can be brought into a canonical form; this canonical form allows us to easily check whether the image of the semidefinite cone under the given linear map is closed.Comment: For some reason, the intended changes between versions 4 and 5 did not take effect, so versions 4 and 5 are the same. So version 6 is the final version. The only difference between version 4 and version 6 is that 2 typos were fixed: in the last displayed formula on page 6, "7" was replaced by "1"; and in the 4th displayed formula on page 12 "A_1 - A_2 - A_3" was replaced by "A_3 - A_2 - A_1

Joint Stiffness Influence on the First-Order Seismic Capacity of Dry-Joint Masonry Structures: Numerical DEM Investigations

Heritage masonry structures are often modelled as dry-jointed structures. On the one hand, it may correspond to the reality where the initial mortar was weak, missing, or has disappeared through time because of erosion and lixiviation. On the other hand, this modelling approach reduces complexity to the studied problem, both from an experimental and theoretical/numerical point of views, while being conservative. Still, for modelling purposes, in addition to the joint friction, numerical approaches require a specific elastic parameter, the dry-joint stiffness, which is often hard to estimate experimentally. This work numerically investigates the effect of the joint stiffness on the collapse of scaled-down tilting test experiments carried out on perforated dry-joint masonry shear walls. It is found that geometrical imperfections of bricks and the absence of vertical precompression load can lead to very low equivalent dry-joint stiffness, which strongly affects the results, both in terms of collapse and damage limit state (DLS) loads, with practical implications for the engineering practice

3D fractal analysis of multi–scale morphology of sand particles with μCT and interferometer

The particle morphology of granular materials comprises different characteristic scales, including particle shape and surface texture. Different methods have been proposed to characterise the morphology using three-dimensional parameters, among which is the fractal method. These methods, however, are applied either at the scale of particle shape or surface texture. A framework unifying the multi-scale morphology obtained from different measuring instruments could advance the current understanding to this topic, but is still lacking. This paper proposes a novel methodology to characterise the morphology of sand particles across different scales based on results from two previously adopted instruments with different measuring capabilities – an X-ray micro-computed tomography (μCT) and a high-resolution optical microscope equipped with an interferometer. The methodology is applied to sand-sized particles of a crushed granitic rock and a natural quarzitic sand (Fujian sand). By using spectrum analysis on data from both μCT and interferometer measurements, a single fractal dimension is found linking the spectrum of the two measurements for the crushed granitic rock. For Fujian sand, two self-affine patterns are observed, which serves as a separation between particle shape and surface texture, and also indicates that the fractal dimension obtained at larger scale may not be simply extended to small scales. The translation of surface measurements into numerically reconstructed particle morphology at particle shape and surface texture scale is demonstrated by using spherical harmonic expansion and power spectral density functions

Traceability for Model Driven, Software Product Line Engineering

Traceability is an important challenge for software organizations. This is true for traditional software development and even more so in new approaches that introduce more variety of artefacts such as Model Driven development or Software Product Lines. In this paper we look at some aspect of the interaction of Traceability, Model Driven development and Software Product Line

A Tricky Diagnosis of Poncet?s Disease

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Fragility Functions for Tall URM Buildings around Early 20th Century in Lisbon, Part 2: Application to Different Classes of Buildings

This article describes the application of the procedure for the derivation of fragility functions presented in the companion article entitled Fragility functions for tall URM buildings around early 20th century in Lisbon. Part 1: methodology and application at building level. The procedure, based on the execution of non-linear analyses, was developed to be applied to unreinforced masonry buildings considering both the in-plane and out-of-plane response. Different sources of uncertainty, both epistemic and aleatory, affecting the behaviour of these unreinforced masonry buildings are discussed and treated with a probabilistic procedure. The fragility curves determined for the different classes of buildings are compared and then combined to define the final fragility curves for these unreinforced masonry buildings. The results put in evidence the high seismic vulnerability of these buildings and the urgent need for the structural intervention and for the design of retrofitting measures in order to reduce potential losses due to future earthquakes

Seismic vulnerability assessment of historical urban centres: The case study of campi alto di norcia, Italy

Seismic damage assessment is a valuable opportunity to evaluate the accuracy of vulnerability and risk methodologies applied to historic masonry buildings, giving the possibility of enhancing and optimizing mitigation and retrofit strategies. Vulnerability index methodologies are flexible and powerful tools for the seismic assessment at urban scale, able to provide a first screening of the critical issues present in masonry structural aggregates. The different structural features of the buildings, directly and indirectly influencing their structural behaviour, are measured through different weights and scores finally achieving a vulnerability indicator. In the present paper, four different vulnerability index methodologies are applied to the medieval city of Campi Alto di Norcia in Valnerina, Umbria, recently stroke by the 2016 Central Italy earthquakes. The accuracy of the adopted Iv methods is assessed based on the real damages' analysis performed in the surrounding area, comparing results achieved from the application of considered methodologies to direct in-situ observations. Data collected during the 2016 post-earthquake damage surveys and usability assessment, together with the external visual inspections carried out and with the information coming from retrofitting design interventions performed between 1979 and 1997, are used

An early sex difference in the relation between mental rotation and object preference

Accumulating evidence suggests that males outperform females on mental rotation tasks as early as infancy. Sex differences in object preference have also been shown to emerge early in development and precede sex-typed play in childhood. Although research with adults and older children is suggestive of a relationship between play preferences and visuospatial abilities, including mental rotation, little is known about the developmental origins of this relationship. The present study compared mental rotation ability and object preference in 6- to 13-month-old infants. We used a novel paradigm to examine individual differences in infants’ mental rotation abilities as well as their differential preference for one of two sex-typed objects. A sex difference was found on both tasks, with boys showing an advantage in performance on the mental rotation task and exhibiting greater visual attention to the male-typed object (i.e., a toy truck) than to the female-typed object (i.e., a doll) in comparison to girls. Moreover, we found a relation between mental rotation and object preference that varied by sex. Greater visual interest in the male-typed object was related to greater mental rotation performance in boys, but not in girls. Possible explanations related to perceptual biases, prenatal androgen exposure, and experiential influences for this sex difference are discussed

Formation of misfit dislocations in strained-layer GaAs/In_xGa_1–xAs/GaAs heterostructures during postfabrication thermal processing

It is demonstrated that relaxation of GaAs/InxGa1–xAs/GaAs strained-layer heterostructures can be brought about by postfabrication thermal processing. Misfit dislocations are introduced into the structure during thermal processing, even though the thickness of the strained layer is well below the critical value predicted by the Matthews–Blakeslee model. The misfit dislocations are observed to be of both 60° mixed type and 90° pure edge type. As no relaxation occurs at the lower temperatures encountered during fabrication by molecular-beam epitaxy, it can be inferred that the critical condition for the formation of misfit dislocations is not only a function of strained-layer thickness and composition, but also of temperature. This observation cannot be accounted for by differential thermal expansion or diffusion across the strained-layer interfaces, but the temperature-dependent Peierls force may offer an explanation. The high temperature required to produce relaxation of these structures suggests that they are sufficiently thermally stable for most practical applications