Lower bound for the maximal number of facets of a 0/1 polytope

We show that there exist 0/1 polytopes in R^n with as many as (cn / (log n)^2)^(n/2) facets (or more), where c>0 is an absolute constant.Comment: 19 page

Asymptotic formulas for the diameter of sections of symmetric convex bodies

AbstractSharpening work of the first two authors, for every proportion λ∈(0,1) we provide exact quantitative relations between global parameters of n-dimensional symmetric convex bodies and the diameter of their random ⌊λn⌋-dimensional sections. Using recent results of Gromov and Vershynin, we obtain an “asymptotic formula” for the diameter of random proportional sections

Estimation in high dimensions: a geometric perspective

This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of asymptotic convex geometry, and demonstrates connections between geometric results and estimation problems. The theory is illustrated with applications to sparse recovery, matrix completion, quantization, linear and logistic regression and generalized linear models.Comment: 56 pages, 9 figures. Multiple minor change

Linking healthcare and societal resilience during the Covid-19 pandemic

Coronavirus disease 2019 (Covid-19) has highlighted the link between public healthcare and the broader context of operational response to complex crises. Data are needed to support the work of the emergency services and enhance governance. This study develops a Europe-wide analysis of perceptions, needs and priorities of the public affected by the Covid-19 emergency. An online multilingual survey was conducted from mid-May until mid-July 2020. The questionnaire investigates perceptions of public healthcare, emergency management and societal resilience. In total, N = 3029 valid answers were collected. They were analysed both as a whole and focusing on the most represented countries (Italy, Romania, Spain and the United Kingdom). Our findings highlight some perceived weaknesses in emergency management that are associated with the underlying vulnerability of the global interconnected society and public healthcare systems. The spreading of the epidemic in Italy represented a ‘tipping point’ for perceiving Covid-19 as an ‘emergency’ in the surveyed countries. The respondents uniformly suggested a preference for gradually restarting activities. We observed a tendency to ignore the cascading effects of Covid-19 and possible concurrence of threats. Our study highlights the need for practices designed to address the next phases of the Covid-19 crisis and prepare for future systemic shocks. Cascading effects that could compromise operational capacity need to be considered more carefully. We make the case for the reinforcement of cross-border coordination of public health initiatives, for standardization in business continuity management, and for dealing with the recovery at the European level

The Complexity of Separating Points in the Plane

We study the following separation problem: given n connected curves and two points s and t in the plane, compute the minimum number of curves one needs to retain so that any path connecting s to t intersects some of the retained curves. We give the first polynomial (O(n3)) time algorithm for the problem, assuming that the curves have reasonable computational properties. The algorithm is based on considering the intersection graph of the curves, defining an appropriate family of closed walks in the intersection graph that satisfies the 3-path-condition, and arguing that a shortest cycle in the family gives an optimal solution. The 3-path-condition has been used mainly in topological graph theory, and thus its use here makes the connection to topology clear. We also show that the generalized version, where several input points are to be separated, is NP-hard for natural families of curves, like segments in two directions or unit circles

The parameterized complexity of some geometric problems in unbounded dimension

We study the parameterized complexity of the following fundamental geometric problems with respect to the dimension $d$: i) Given $n$ points in \Rd, compute their minimum enclosing cylinder. ii) Given two $n$-point sets in \Rd, decide whether they can be separated by two hyperplanes. iii) Given a system of $n$ linear inequalities with $d$ variables, find a maximum-size feasible subsystem. We show that (the decision versions of) all these problems are W[1]-hard when parameterized by the dimension $d$. %and hence not solvable in ${O}(f(d)n^c)$ time, for any computable function $f$ and constant $c$ %(unless FPT=W[1]). Our reductions also give a $n^{\Omega(d)}$-time lower bound (under the Exponential Time Hypothesis)

Discrete element modelling of masonry infilled steel frames with multiple window openings subjected to lateral load variations

Steel framed structures are routinely infilled with masonry or concrete walls. The infill offers in-plane shear resistance that adds to the one from the steel frame. However, the stiffness effect on the entire frame's response is usually neglected. In recent years, researchers have recognised the lack of in-depth understanding on infilled steel frames; hence specialised computational tools have been developed to provide an easy way of assessing these interactive structural systems and aid practising engineers in evaluating the overall behaviour. A computational model to study the behaviour of masonry infilled steel frames for the non-standard case of variable potential positions of openings and their interaction, when subjected to in-plane monotonic loading, is herein developed. Using the Discrete Element Method (DEM) and the software UDEC, the masonry wall is modelled as an assemblage of distinct deformable blocks while the mortar joints as zero thickness interfaces. The numerical model validated against full scale experimental tests found in the literature and a good agreement obtained. In addition, a series of parametric studies were performed to draw the significance of the size and location of the openings on the lateral load capacity, as well as the stiffness and failure mechanisms of the infilled steel frames. From the results analyses, it was found that the inclusion of multiple openings significantly reduces the strength and stiffness of the system. In particular, placing an opening close to the point of application of the lateral load will result to further reduction of masonry infill's stiffness

Taxonomic corpus-based concept summary generation for document annotation.

Semantic annotation is an enabling technology which links documents to concepts that unambiguously describe their content. Annotation improves access to document contents for both humans and software agents. However, the annotation process is a challenging task as annotators often have to select from thousands of potentially relevant concepts from controlled vocabularies. The best approaches to assist in this task rely on reusing the annotations of an annotated corpus. In the absence of a pre-annotated corpus, alternative approaches suffer due to insufficient descriptive texts for concepts in most vocabularies. In this paper, we propose an unsupervised method for recommending document annotations based on generating node descriptors from an external corpus. We exploit knowledge of the taxonomic structure of a thesaurus to ensure that effective descriptors (concept summaries) are generated for concepts. Our evaluation on recommending annotations show that the content that we generate effectively represents the concepts. Also, our approach outperforms those which rely on information from a thesaurus alone and is comparable with supervised approaches