The Complexity of Drawing Graphs on Few Lines and Few Planes

It is well known that any graph admits a crossing-free straight-line drawing in $\mathbb{R}^3$ and that any planar graph admits the same even in $\mathbb{R}^2$. For a graph $G$ and $d \in \{2,3\}$, let $\rho^1_d(G)$ denote the minimum number of lines in $\mathbb{R}^d$ that together can cover all edges of a drawing of $G$. For $d=2$, $G$ must be planar. We investigate the complexity of computing these parameters and obtain the following hardness and algorithmic results. - For $d\in\{2,3\}$, we prove that deciding whether $\rho^1_d(G)\le k$ for a given graph $G$ and integer $k$ is ${\exists\mathbb{R}}$-complete. - Since $\mathrm{NP}\subseteq{\exists\mathbb{R}}$, deciding $\rho^1_d(G)\le k$ is NP-hard for $d\in\{2,3\}$. On the positive side, we show that the problem is fixed-parameter tractable with respect to $k$. - Since ${\exists\mathbb{R}}\subseteq\mathrm{PSPACE}$, both $\rho^1_2(G)$ and $\rho^1_3(G)$ are computable in polynomial space. On the negative side, we show that drawings that are optimal with respect to $\rho^1_2$ or $\rho^1_3$ sometimes require irrational coordinates. - Let $\rho^2_3(G)$ be the minimum number of planes in $\mathbb{R}^3$ needed to cover a straight-line drawing of a graph $G$. We prove that deciding whether $\rho^2_3(G)\le k$ is NP-hard for any fixed $k \ge 2$. Hence, the problem is not fixed-parameter tractable with respect to $k$ unless $\mathrm{P}=\mathrm{NP}$

Recognizing hyperelliptic graphs in polynomial time

Recently, a new set of multigraph parameters was defined, called "gonalities". Gonality bears some similarity to treewidth, and is a relevant graph parameter for problems in number theory and multigraph algorithms. Multigraphs of gonality 1 are trees. We consider so-called "hyperelliptic graphs" (multigraphs of gonality 2) and provide a safe and complete sets of reduction rules for such multigraphs, showing that for three of the flavors of gonality, we can recognize hyperelliptic graphs in O(n log n+m) time, where n is the number of vertices and m the number of edges of the multigraph.Comment: 33 pages, 8 figure

A Unifying Model of Genome Evolution Under Parsimony

We present a data structure called a history graph that offers a practical basis for the analysis of genome evolution. It conceptually simplifies the study of parsimonious evolutionary histories by representing both substitutions and double cut and join (DCJ) rearrangements in the presence of duplications. The problem of constructing parsimonious history graphs thus subsumes related maximum parsimony problems in the fields of phylogenetic reconstruction and genome rearrangement. We show that tractable functions can be used to define upper and lower bounds on the minimum number of substitutions and DCJ rearrangements needed to explain any history graph. These bounds become tight for a special type of unambiguous history graph called an ancestral variation graph (AVG), which constrains in its combinatorial structure the number of operations required. We finally demonstrate that for a given history graph $G$, a finite set of AVGs describe all parsimonious interpretations of $G$, and this set can be explored with a few sampling moves.Comment: 52 pages, 24 figure

The history of degenerate (bipartite) extremal graph problems

This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe many important results, methods, problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version of our survey presented in Erdos 100. In this version 2 only a citation was complete

Measurement of νˉμ\bar{\nu}_{\mu} and νμ\nu_{\mu} charged current inclusive cross sections and their ratio with the T2K off-axis near detector

We report a measurement of cross section $\sigma(\nu_{\mu}+{\rm nucleus}\rightarrow\mu^{-}+X)$ and the first measurements of the cross section $\sigma(\bar{\nu}_{\mu}+{\rm nucleus}\rightarrow\mu^{+}+X)$ and their ratio $R(\frac{\sigma(\bar \nu)}{\sigma(\nu)})$ at (anti-)neutrino energies below 1.5 GeV. We determine the single momentum bin cross section measurements, averaged over the T2K $\bar{\nu}/\nu$-flux, for the detector target material (mainly Carbon, Oxygen, Hydrogen and Copper) with phase space restricted laboratory frame kinematics of $\theta_{\mu}$500 MeV/c. The results are $\sigma(\bar{\nu})=\left( 0.900\pm0.029{\rm (stat.)}\pm0.088{\rm (syst.)}\right)\times10^{-39}$ and $\sigma(\nu)=\left( 2.41\ \pm0.022{\rm{(stat.)}}\pm0.231{\rm (syst.)}\ \right)\times10^{-39}$in units of cm$^{2}$/nucleon and$R\left(\frac{\sigma(\bar{\nu})}{\sigma(\nu)}\right)= 0.373\pm0.012{\rm (stat.)}\pm0.015{\rm (syst.)}$.Comment: 18 pages, 8 figure

Randomized Trial of Anticoagulation Strategies for Noncritically Ill Patients Hospitalized With COVID-19.

BACKGROUND Prior studies of therapeutic-dose anticoagulation in patients with COVID-19 have reported conflicting results. OBJECTIVES We sought to determine the safety and effectiveness of therapeutic-dose anticoagulation in noncritically ill patients with COVID-19. METHODS Patients hospitalized with COVID-19 not requiring intensive care unit treatment were randomized to prophylactic-dose enoxaparin, therapeutic-dose enoxaparin, or therapeutic-dose apixaban. The primary outcome was the 30-day composite of all-cause mortality, requirement for intensive care unit-level of care, systemic thromboembolism, or ischemic stroke assessed in the combined therapeutic-dose groups compared with the prophylactic-dose group. RESULTS Between August 26, 2020, and September 19, 2022, 3,398 noncritically ill patients hospitalized with COVID-19 were randomized to prophylactic-dose enoxaparin (n = 1,141), therapeutic-dose enoxaparin (n = 1,136), or therapeutic-dose apixaban (n = 1,121) at 76 centers in 10 countries. The 30-day primary outcome occurred in 13.2% of patients in the prophylactic-dose group and 11.3% of patients in the combined therapeutic-dose groups (HR: 0.85; 95% CI: 0.69-1.04; P = 0.11). All-cause mortality occurred in 7.0% of patients treated with prophylactic-dose enoxaparin and 4.9% of patients treated with therapeutic-dose anticoagulation (HR: 0.70; 95% CI: 0.52-0.93; P = 0.01), and intubation was required in 8.4% vs 6.4% of patients, respectively (HR: 0.75; 95% CI: 0.58-0.98; P = 0.03). Results were similar in the 2 therapeutic-dose groups, and major bleeding in all 3 groups was infrequent. CONCLUSIONS Among noncritically ill patients hospitalized with COVID-19, the 30-day primary composite outcome was not significantly reduced with therapeutic-dose anticoagulation compared with prophylactic-dose anticoagulation. However, fewer patients who were treated with therapeutic-dose anticoagulation required intubation and fewer died (FREEDOM COVID [FREEDOM COVID Anticoagulation Strategy]; NCT04512079).Dr Stone has received speaker honoraria from Medtronic, Pulnovo, Infraredx, Abiomed, and Abbott; has served as a consultant to Daiichi-Sankyo, Valfix, TherOx, Robocath, HeartFlow, Ablative Solutions, Vectorious, Miracor, Neovasc, Ancora, Elucid Bio, Occlutech, CorFlow, Apollo Therapeutics, Impulse Dynamics, Cardiomech, Gore, Amgen, Adona Medical, and Millennia Biopharma; and has equity/ options from Ancora, Cagent, Applied Therapeutics, Biostar family of funds, SpectraWave, Orchestra Biomed, Aria, Cardiac Success, Valfix, and Xenter; his daughter is an employee at IQVIA; and his employer, Mount Sinai Hospital, receives research support from Abbott, Abiomed, Bioventrix, Cardiovascular Systems Inc, Phillips, BiosenseWebster, Shockwave, Vascular Dynamics, Pulnovo, and V-wave. Dr Farkouh has received institutional research grants from Amgen, AstraZeneca, Novo Nordisk, and Novartis; has received consulting fees from Otitopic; and has received honoraria from Novo Nordisk. Dr Lala has received consulting fees from Merck and Bioventrix; has received honoraria from Zoll Medical and Novartis; has served on an advisory board for Sequana Medical; and is the Deputy Editor for the Journal of Cardiac Failure. Dr Moreno has received honoraria from Amgen, Cuquerela Medical, and Gafney; has received payment for expert testimony from Koskoff, Koskoff & Dominus, Dallas W. Hartman, and Riscassi & Davis PC; and has stock options in Provisio. Dr Goodman has received institutional research grants from Bristol Myers Squibb/Pfizer Alliance, Bayer, and Boehringer Ingelheim; has received consulting fees from Amgen, Anthos Therapeutics, AstraZeneca, Bayer, Boehringer Ingelheim, Bristol Myers Squibb, CSL Behring, Ferring Pharmaceuticals, HLS Therapeutics, Novartis, Pendopharm/Pharmascience, Pfizer, Regeneron, and Sanofi; has received honoraria from Amgen, AstraZeneca, Bayer, Boehringer Ingelheim, Bristol Myers Squibb, Eli Lilly, Ferring Pharmaceuticals, HLS Therapeutics, JAMP Pharma, Merck, Novartis, Pendopharm/Pharmascience, Pfizer, Regeneron, Sanofi, and Servier; has served on Data Safety and Monitoring boards for Daiichi-Sankyo/American Regent and Novo Nordisk A/C; has served on advisory boards for Amgen, AstraZeneca, Bayer, Boehringer Ingelheim, Bristol Myers Squibb, CSL Behring, Eli Lilly, Ferring Pharmaceuticals, HLS Therapeutics, JAMP Pharma, Merck, Novartis, Pendopharm/Pharmascience, Pfizer, Regeneron, Sanofi, Servier, and Tolmar Pharmaceuticals; has a leadership role in the Novartis Council for Heart Health (unpaid); and otherwise has received salary support or honoraria from the Heart and Stroke Foundation of Ontario/University of Toronto (Polo) Chair, Canadian Heart Failure Society, Canadian Heart Research Centre and MD Primer, Canadian VIGOUR Centre, Cleveland Clinic Coordinating Centre for Clinical Research, Duke Clinical Research Institute, New York University Clinical Coordinating Centre, PERFUSE Research Institute, and the TIMI Study Group (Brigham Health). Dr Ricalde has received consulting fees from Medtronic, Servier, and Boston Scientific; has received honoraria from Medtronic, Pfizer, Merck, Boston Scientific, Biosensors, and Bayer; has served on an advisory board for Medtronic; and has leadership roles in SOLACI and Kardiologen. Dr Payro has received consulting fees from Bayer Mexico; has received honoraria from Bayer, Merck, AstraZeneca, Medtronic, and Viatris; has received payments for expert testimony from Bayer; has received travel support from AstraZeneca; has served on an advisory board for Bayer; and his institution has received equipment donated from AstraZeneca. Dr Castellano has received consulting fees and honoraria from Ferrer International, Servier, and Daiichi-Sankyo; and has received travel support from Ferrer International. Dr Hung has served as an advisory board member for Pfizer, Merck, AstraZeneca, Fosun, and Gilead. Dr Nadkarni has received consulting fees from Renalytix, Variant Bio, Qiming Capital, Menarini Health, Daiichi-Sankyo, BioVie, and Cambridge Health; has received honoraria from Daiichi-Sankyo and Menarini Health; has patents for automatic disease diagnoses using longitudinal medical record data, methods, and apparatus for diagnosis of progressive kidney function decline using a machine learning model, electronic phenotyping technique for diagnosing chronic kidney disease, deep learning to identify biventricular structure and function, fusion models for identification of pulmonary embolism, and SparTeN: a novel spatio-temporal deep learning model; has served on a Data Safety and Monitoring Board for CRIC OSMB; has leadership roles for Renalytix scientific advisory board, Pensive Health scientific advisory board, and ASN Augmented Intelligence and Digital Health Committee; has ownership interests in Renalytix, Data2Wisdom LLC, Verici Dx, Nexus I Connect, and Pensieve Health; and his institution receives royalties from Renalytix. Dr Goday has received the Frederick Banting and Charles Best Canada Graduate Scholarship (Doctoral Research Award) from the Canadian Institutes of Health Research. Dr Furtado has received institutional research grants from AstraZeneca, CytoDin, Pfizer, Servier, Amgen, Alliar Diagnostics, and the Brazilian Ministry of Health; has received consulting fees from Biomm and Bayer; has received honoraria from AstraZeneca, Bayer, Servier, and Pfizer; and has received travel support from Servier, AstraZeneca, and Bayer. Dr Granada has received consulting fees, travel support, and stock from Cogent Technologies Corp; and has received stock from Kutai. Dr Contreras has served as a consultant for Merck, CVRx, Novodisk, and Boehringer Ingelheim; and has received educational grants from Alnylam Pharmaceuticals and AstraZeneca. Dr Bhatt has received research funding from Abbott, Acesion Pharma, Afimmune, Aker Biomarine, Amarin, Amgen, AstraZeneca, Bayer, Beren, Boehringer Ingelheim, Boston Scientific, Bristol Myers Squibb, Cardax, CellProthera, Cereno Scientific, Chiesi, Cincor, CSL Behring, Eisai, Ethicon, Faraday Pharmaceuticals, Ferring Pharmaceuticals, Forest Laboratories, Fractyl, Garmin, HLS Therapeutics, Idorsia, Ironwood, Ischemix, Janssen, Javelin, Lexicon, Lilly, Medtronic, Merck, Moderna, MyoKardia, NirvaMed, Novartis, Novo Nordisk, Owkin, Pfizer Inc, PhaseBio, PLx Pharma, Recardio, Regeneron, Reid Hoffman Foundation, Roche, Sanofi, Stasys, Synaptic, The Medicines Company, Youngene, and 89bio; has received royalties from Elsevier; has received consultant fees from Broadview Ventures and McKinsey; has received honoraria from the American College of Cardiology, Baim Institute for Clinical Research, Belvoir Publications, Boston Scientific, Cleveland Clinic, Duke Clinical Research Institute, Mayo Clinic, Mount Sinai School of Medicine, Novartis, Population Health Research Institute, Rutgers University, Canadian Medical and Surgical Knowledge Translation Research Group, Cowen and Company, HMP Global, Journal of the American College of Cardiology, K2P, Level Ex, Medtelligence/ReachMD, MJH Life Sciences, Oakstone CME, Piper Sandler, Population Health Research Institute, Slack Publications, WebMD, Wiley, Society of Cardiovascular Patient Care; has received fees from expert testimony from the Arnold and Porter law firm; has received travel support from the American College of Cardiology, Society of Cardiovascular Patient Care, American Heart Association; has a patent for otagliflozin assigned to Brigham and Women’s Hospital who assigned to Lexicon; has participated on a data safety monitoring board or advisory board for Acesion Pharma, Assistance Publique-Hôpitaux de Paris, AngioWave, Baim Institute, Bayer, Boehringer Ingelheim, Boston Scientific, Cardax, CellProthera, Cereno Scientific, Cleveland Clinic, Contego Medical, Duke Clinical Research Institute, Elsevier Practice Update Cardiology, Janssen, Level Ex, Mayo Clinic, Medscape Cardiology, Merck, Mount Sinai School of Medicine, MyoKardia, NirvaMed, Novartis, Novo Nordisk, PhaseBio, PLx Pharma, Regado Biosciences, Population Health Research Institute, and Stasys; serves as a trustee or director for American College of Cardiology, AngioWave, Boston VA Research Institute, Bristol Myers Squibb, DRS.LINQ, High Enroll, Society of Cardiovascular Patient Care, and TobeSoft; has ownership interests in AngioWave, Bristol Myers Squibb, DRS.LINQ, and High Enroll; has other interests in Clinical Cardiology, the NCDR-ACTION Registry Steering Committee; has conducted unfunded research with FlowCo and Takeda, Contego Medical, American Heart Association Quality Oversight Committee, Inaugural Chair, VA CART Research and Publications Committee; and has been a site co-investigator for Abbott, Biotronik, Boston Scientific, CSI, St Jude Medical (now Abbott), Phillips SpectraWAVE, Svelte, and Vascular Solutions. Dr Fuster declares that he raised $7 million from patients for this study granted to Mount Sinai Heart, unrelated to industry. All other authors have reported that they have no relationships relevant to the contents of this paper to disclose.S

Large-scale unit commitment under uncertainty: an updated literature survey

The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115--171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject