Maximum gradient embeddings and monotone clustering

Let (X,d_X) be an n-point metric space. We show that there exists a distribution D over non-contractive embeddings into trees f:X-->T such that for every x in X, the expectation with respect to D of the maximum over y in X of the ratio d_T(f(x),f(y)) / d_X(x,y) is at most C (log n)^2, where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient embeddings, yield a framework for the design of approximation algorithms for a wide range of clustering problems with monotone costs, including fault-tolerant versions of k-median and facility location.Comment: 25 pages, 2 figures. Final version, minor revision of the previous one. To appear in "Combinatorica

The Relation of Contemporary Labour Market Skills and the Future Engineers’ Visions

The study describes a segment of an international research which was aimed to find answers what the future generations‘ (Gen Z) vision is concerning their career and the correlation between these visions and the expectations of labour market nowadays. The preferred competencies of the labour market are constantly altering: a prognosis from 2018 says that the five most important skills will be analytical thinking, innovation, active learning, creativity, and critical thinking in 2022. Keywords: career, competences, engineering education, future priorities, generation Z, labour market, STEM, top skill

The Traveling Salesman Problem: Low-Dimensionality Implies a Polynomial Time Approximation Scheme

The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1+eps)-approximation to the optimal tour, for any fixed eps>0, in TSP instances that form an arbitrary metric space with bounded intrinsic dimension. The celebrated results of Arora (A-98) and Mitchell (M-99) prove that the above result holds in the special case of TSP in a fixed-dimensional Euclidean space. Thus, our algorithm demonstrates that the algorithmic tractability of metric TSP depends on the dimensionality of the space and not on its specific geometry. This result resolves a problem that has been open since the quasi-polynomial time algorithm of Talwar (T-04)

Limitations to Frechet's Metric Embedding Method

Frechet's classical isometric embedding argument has evolved to become a major tool in the study of metric spaces. An important example of a Frechet embedding is Bourgain's embedding. The authors have recently shown that for every e>0 any n-point metric space contains a subset of size at least n^(1-e) which embeds into l_2 with distortion O(\log(2/e) /e). The embedding we used is non-Frechet, and the purpose of this note is to show that this is not coincidental. Specifically, for every e>0, we construct arbitrarily large n-point metric spaces, such that the distortion of any Frechet embedding into l_p on subsets of size at least n^{1/2 + e} is \Omega((\log n)^{1/p}).Comment: 10 pages, 1 figur

COPD and tobacco smoke

Chronic obstructive pulmonary disease (COPD) is a chronic inflammation of the airways, including the parenchyma and the pulmonary vasculature. The burden of COPD is increasing around the world in terms of morbidity and mortality in adult population. Active smoking is a major risk factor for COPD, although there is individual susceptibility to the effects of tobacco smoke. This variability could result from host as well as environmental factors. Even passive smoking in early childhood as well as intrauterine exposure could pave the way for COPD. Tobacco smoke induces a specific, persistent inflammation, different from that of asthma. Three other processes accompany and interact with inflammation: imbalance of both the proteases- antiproteases, the oxidants-antioxidants, and improper repair mechanisms. These processes respectively lead to mucus hypersecretion and alveol wall destruction, dysfunction and death of biological molecules, damage to the extracellular matrix and pulmonary fibrosis with adventitial, submucosal and smooth muscle thickening. The earlier the smoke exposure, the greater the level of decline in lung function. Combined mucus hypersecretion, reduced clearance, and impairment of the lung defence mechanisms explain why COPD patients even with stable condition, carry potential respiratory pathogens in significant concentration, paving the way for infection and acute exacerbations of COPD. Every additional exacerbation in a smoker deteriorate more the lung function. Fortunately, smoking cessation, which is a part of the respiratory rehabilitation could reduce the number of hospitalisations and the decline of lung function, and thus reduce the management cost of the disease and improve the quality of life. The earlier the quitting, the better the improvement of FEV1. “Smoking cessation is the single effective and cost effective way to reduce exposure to COPD risk factors” (GOLD, evidence A)

Utilizing AI and Social Media Analytics to Discover Adverse Side Effects of GLP-1 Receptor Agonists

Adverse side effects (ASEs) of drugs, revealed after FDA approval, pose a threat to patient safety. To promptly detect overlooked ASEs, we developed a digital health methodology capable of analyzing massive public data from social media, published clinical research, manufacturers' reports, and ChatGPT. We uncovered ASEs associated with the glucagon-like peptide 1 receptor agonists (GLP-1 RA), a market expected to grow exponentially to $133.5 billion USD by 2030. Using a Named Entity Recognition (NER) model, our method successfully detected 21 potential ASEs overlooked upon FDA approval, including irritability and numbness. Our data-analytic approach revolutionizes the detection of unreported ASEs associated with newly deployed drugs, leveraging cutting-edge AI-driven social media analytics. It can increase the safety of new drugs in the marketplace by unlocking the power of social media to support regulators and manufacturers in the rapid discovery of hidden ASE risks.Comment: 19 pages, 7 figures, 3 tables, 1 Appendix tabl

Nonlinear optics and light localization in periodic photonic lattices

We review the recent developments in the field of photonic lattices emphasizing their unique properties for controlling linear and nonlinear propagation of light. We draw some important links between optical lattices and photonic crystals pointing towards practical applications in optical communications and computing, beam shaping, and bio-sensing.Comment: to appear in Journal of Nonlinear Optical Physics & Materials (JNOPM

Exploiting disorder for perfect focusing

We demonstrate experimentally that disordered scattering can be used to improve, rather than deteriorate, the focusing resolution of a lens. By using wavefront shaping to compensate for scattering, light was focused to a spot as small as one tenth of the diffraction limit of the lens. We show both experimentally and theoretically that it is the scattering medium, rather than the lens, that determines the width of the focus. Despite the disordered propagation of the light, the profile of the focus was always exactly equal to the theoretical best focus that we derived.Comment: 4 pages, 4 figure