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

Wettability influences cell behavior on superhydrophobic surfaces with different topographies

Surface wettability and topography are recognized as critical factors influencing cell behavior on biomaterials. So far only few works have reported cell responses on surfaces exhibiting extreme wettability in combination with surface topography. The goal of this work is to study whether cell behavior on superhydrophobic surfaces is influenced by surface topography and polymer type. Biomimetic superhydrophobic rough surfaces of polystyrene and poly(l-lactic acid) with different micro/nanotopographies were obtained from smooth surfaces using a simple phase-separation based method. Total protein was quantified and showed a less adsorption of bovine serum albumin onto rough surfaces as compared to smooth surfaces of the same material. The mouse osteoblastic MC3T3-E1 cell line and primary bovine articular chondrocytes were used to study cell attachment and proliferation. Cells attached and proliferate better in the smooth surfaces. The superhydrophobic surfaces allowed cells to adhere but inhibited their proliferation. This study indicates that surface wettability, rather than polymer type or the topography of the superhydrophobic surfaces, is a critical factor in determining cell behavior

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

Using Preferred Outcome Distributions to estimate Value and Probability Weighting Functions in Decisions under Risk

In this paper we propose the use of preferred outcome distributions as a new method to elicit individuals' value and probability weighting functions in decisions under risk. Extant approaches for the elicitation of these two key ingredients of individuals' risk attitude typically rely on a long, chained sequence of lottery choices. In contrast, preferred outcome distributions can be elicited through an intuitive graphical interface, and, as we show, the information contained in two preferred outcome distributions is sufficient to identify non-parametrically both the value function and the probability weighting function in rank-dependent utility models. To illustrate our method and its advantages, we run an incentive-compatible lab study in which participants use a simple graphical interface - the Distribution Builder (Goldstein et al. 2008) - to construct their preferred outcome distributions, subject to a budget constraint. Results show that estimates of the value function are in line with previous research but that probability weighting biases are diminished, thus favoring our proposed approach based on preferred outcome distributions

Non Linearity of the Ball/Rubber Impact in Table Tennis: Experiments and Modeling

AbstractAlong with comfort, the speed is a key metric used to qualify the performance of a table tennis racket. The restitution coefficient which corresponds to the ratio between the velocities of the ball right before and after normally impacting the racket relates to the speed performance: the higher the restitution coefficient, the greater the speed. Thus, understanding the normal impact problem is key and suggests investigating the effects of the intrinsic properties and architectures of the constituents of the racket. In this work, both experimental and numerical studies were pursued. Experimentally, normal impact tests were performed for varying launching velocities on samples made of isolated or associated constituents of a table tennis racket and the restitution coefficients calculated. Numerically, 3D finite elements simulations were conducted to replicate the normal impact conditions while incorporating the time-dependent constitutive behavior of the polymeric elements contributing during the impact: the racket constituents (the foam and the compact) and the ball. The restitution coefficients are seen to decrease with increasing launching velocity, while being minimum when the two racket polymeric constituents are associated. A fair agreement is obtained with the FE simulations in which the sample/ball contact zone is identified as a ring with its mean radius increasing till the maximum crushing. Ultimately, additional FE calculations confirm that the friction plays a key role in the energy dissipation process, alongside with the rate-dependent behavior and architecture of the polymeric constituents