| 1. |
- Afshin, Ashkan, et al.
(författare)
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Health Effects of Overweight and Obesity in 195 Countries over 25 Years
- 2017
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Ingår i: New England Journal of Medicine. - : MASSACHUSETTS MEDICAL SOC. - 0028-4793 .- 1533-4406. ; 377:1, s. 13-27
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Tidskriftsartikel (refereegranskat)abstract
- BACKGROUND Although the rising pandemic of obesity has received major attention in many countries, the effects of this attention on trends and the disease burden of obesity remain uncertain. METHODS We analyzed data from 68.5 million persons to assess the trends in the prevalence of overweight and obesity among children and adults between 1980 and 2015. Using the Global Burden of Disease study data and methods, we also quantified the burden of disease related to high body-mass index (BMI), according to age, sex, cause, and BMI in 195 countries between 1990 and 2015. RESULTS In 2015, a total of 107.7 million children and 603.7 million adults were obese. Since 1980, the prevalence of obesity has doubled in more than 70 countries and has continuously increased in most other countries. Although the prevalence of obesity among children has been lower than that among adults, the rate of increase in childhood obesity in many countries has been greater than the rate of increase in adult obesity. High BMI accounted for 4.0 million deaths globally, nearly 40% of which occurred in persons who were not obese. More than two thirds of deaths related to high BMI were due to cardiovascular disease. The disease burden related to high BMI has increased since 1990; however, the rate of this increase has been attenuated owing to decreases in underlying rates of death from cardiovascular disease. CONCLUSIONS The rapid increase in the prevalence and disease burden of elevated BMI highlights the need for continued focus on surveillance of BMI and identification, implementation, and evaluation of evidence-based interventions to address this problem.
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| 2. |
- Amini, Nima
(författare)
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Combinatorics and zeros of multivariate polynomials
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis consists of five papers in algebraic and enumerative combinatorics. The objects at the heart of the thesis are combinatorial polynomials in one or more variables. We study their zeros, coefficients and special evaluations. Hyperbolic polynomials may be viewed as multivariate generalizations of real-rooted polynomials in one variable. To each hyperbolic polynomial one may associate a convex cone from which a matroid can be derived - a so called hyperbolic matroid. In Paper A we prove the existence of an infinite family of non-representable hyperbolic matroids parametrized by hypergraphs. We further use special members of our family to investigate consequences to a central conjecture around hyperbolic polynomials, namely the generalized Lax conjecture. Along the way we strengthen and generalize several symmetric function inequalities in the literature, such as the Laguerre-Tur\'an inequality and an inequality due to Jensen. In Paper B we affirm the generalized Lax conjecture for two related classes of combinatorial polynomials: multivariate matching polynomials over arbitrary graphs and multivariate independence polynomials over simplicial graphs. In Paper C we prove that the multivariate $d$-matching polynomial is hyperbolic for arbitrary multigraphs, in particular answering a question by Hall, Puder and Sawin. We also provide a hypergraphic generalization of a classical theorem by Heilmann and Lieb regarding the real-rootedness of the matching polynomial of a graph. In Paper D we establish a number of equidistributions between Mahonian statistics which are given by conic combinations of vincular pattern functions of length at most three, over permutations avoiding a single classical pattern of length three. In Paper E we find necessary and sufficient conditions for a candidate polynomial to be complemented to a cyclic sieving phenomenon (without regards to combinatorial context). We further take a geometric perspective on the phenomenon by associating a convex rational polyhedral cone which has integer lattice points in correspondence with cyclic sieving phenomena. We find the half-space description of this cone and investigate its properties.
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| 3. |
- Amini, Nima
(författare)
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Equidistributions of mahonian statistics over pattern avoiding permutations
- 2018
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Ingår i: The Electronic Journal of Combinatorics. - : Australian National University Press. - 1097-1440 .- 1077-8926. ; 25:1
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Tidskriftsartikel (refereegranskat)abstract
- A Mahonian d-function is a Mahonian statistic that can be expressed as a linear combination of vincular pattern functions of length at most d. Babson and Ste- ingrímsson classified all Mahonian 3-functions up to trivial bijections and identified many of them with well-known Mahonian statistics in the literature. We prove a host of Mahonian 3-function equidistributions over permutations in Sn avoiding a single classical pattern in S3. Tools used include block decomposition, Dyck paths and generating functions.
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| 4. |
- Amini, Nima, et al.
(författare)
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Non-representable hyperbolic matroids
- 2018
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Ingår i: Advances in Mathematics. - : Academic Press. - 0001-8708 .- 1090-2082. ; 334, s. 417-449
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Tidskriftsartikel (refereegranskat)abstract
- The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. Hyperbolic polynomials give rise to a class of (hyperbolic) matroids which properly contains the class of matroids representable over the complex numbers. This connection was used by the second author to construct counterexamples to algebraic (stronger) versions of the generalized Lax conjecture by considering a non-representable hyperbolic matroid. The Vamos matroid and a generalization of it are, prior to this work, the only known instances of non-representable hyperbolic matroids. We prove that the Non-Pappus and Non-Desargues matroids are non-representable hyperbolic matroids by exploiting a connection between Euclidean Jordan algebras and projective geometries. We further identify a large class of hyperbolic matroids which contains the Vamos matroid and the generalized Vamos matroids recently studied by Burton, Vinzant and Youm. This proves a conjecture of Burton et al. We also prove that many of the matroids considered here are non representable. The proof of hyperbolicity for the matroids in the class depends on proving nonnegativity of certain symmetric polynomials. In particular we generalize and strengthen several inequalities in the literature, such as the Laguerre Turan inequality and an inequality due to Jensen. Finally we explore consequences to algebraic versions of the generalized Lax conjecture.
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| 5. |
- Amini, Nima, et al.
(författare)
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Non-representable hyperbolic matroids
- 2016
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Ingår i: Discrete Mathematics and Theoretical Computer Science. - : Discrete Mathematics and Theoretical Computer Science. ; , s. 37-48
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Konferensbidrag (refereegranskat)abstract
- The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positivesemidefinite matrices. Hyperbolic polynomials give rise to a class of (hyperbolic) matroids which properly containsthe class of matroids representable over the complex numbers. This connection was used by the first author toconstruct counterexamples to algebraic (stronger) versions of the generalized Lax conjecture by considering a nonrepresentable hyperbolic matroid. The Vamos matroid and a generalization of it are to this day the only known ´instances of non-representable hyperbolic matroids. We prove that the Non-Pappus and Non-Desargues matroids arenon-representable hyperbolic matroids by exploiting a connection, due to Jordan, between Euclidean Jordan algebrasand projective geometries. We further identify a large class of hyperbolic matroids that are parametrized by uniformhypergraphs and prove that many of them are non-representable. Finally we explore consequences to algebraicversions of the generalized Lax conjecture.
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| 6. |
- Amini, Nima
(författare)
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Spectrahedrality of hyperbolicity cones of multivariate matching polynomials
- 2019
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Ingår i: Journal of Algebraic Combinatorics. - : SPRINGER. - 0925-9899 .- 1572-9192. ; 50:2, s. 165-190
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Tidskriftsartikel (refereegranskat)abstract
- The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. We prove the conjecture for a multivariate generalization of the matching polynomial. This is further extended (albeit in a weaker sense) to a multivariate version of the independence polynomial for simplicial graphs. As an application, we give a new proof of the conjecture for elementary symmetric polynomials (originally due to Branden). Finally, we consider a hyperbolic convolution of determinant polynomials generalizing an identity of Godsil and Gutman.
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| 7. |
- Amini, Nima
(författare)
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Spectrahedrality of hyperbolicity cones of multivariate matching polynomials
- 2018
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Ingår i: Journal of Algebraic Combinatorics. - : Springer. - 0925-9899 .- 1572-9192.
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Tidskriftsartikel (refereegranskat)abstract
- The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. We prove the conjecture for a multivariate generalization of the matching polynomial. This is further extended (albeit in a weaker sense) to a multivariate version of the independence polynomial for simplicial graphs. As an application we give a new proof of the conjecture for elementary symmetric polynomials (originally due to Brändén). Finally we consider a hyperbolic convolution of determinant polynomials generalizing an identity of Godsil and Gutman.
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| 8. |
- Amini, Nima
(författare)
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Stable multivariate generalizations of matching polynomials
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- The first part of this note concerns stable averages of multivariate matching polynomials. In proving the existence of infinite families of bipartite Ramanujan d-coverings, Hall, Puder and Sawin introduced the d-matching polynomial of a graph G, defined as the uniform average of matching polynomials over the set of d-sheeted covering graphs of G. We prove that a natural multivariate version of the d-matching polynomial is stable, consequently giving a short direct proof of the real-rootedness of the d-matching polynomial. Our theorem also includes graphs with loops, thus answering a question of said authors. Furthermore we define a weaker notion of matchings for hypergraphs and prove that a family of natural polynomials associated to such matchings are stable. In particular this provides a hypergraphic generalization of the classical Heilmann-Lieb theorem.
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| 9. |
- Amini, Nima, et al.
(författare)
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The cone of cyclic sieving phenomena
- 2019
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Ingår i: Discrete Mathematics. - : Elsevier. - 0012-365X .- 1872-681X. ; 342:6, s. 1581-1601
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Tidskriftsartikel (refereegranskat)abstract
- We study cyclic sieving phenomena (CSP) on combinatorial objects from an abstract point of view by considering a rational polyhedral cone determined by the linear equations that define such phenomena. Each lattice point in the cone corresponds to a non-negative integer matrix which jointly records the statistic and cyclic order distribution associated with the set of objects realizing the CSP. In particular we consider a universal subcone onto which every CSP matrix linearly projects such that the projection realizes a CSP with the same cyclic orbit structure, but via a universal statistic that has even distribution on the orbits.Reiner et.al. showed that every cyclic action gives rise to a unique polynomial (mod q^n-1) complementing the action to a CSP. We give a necessary and sufficient criterion for the converse to hold. This characterization allows one to determine if a combinatorial set with a statistic gives rise (in principle) to a CSP without having a combinatorial realization of the cyclic action. We apply the criterion to conjecture a new CSP involving stretched Schur polynomials and prove our conjecture for certain rectangular tableaux. Finally we study some geometric properties of the CSP cone. We explicitly determine its half-space description and in the prime order case we determine its extreme rays.
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| 10. |
- Forouzanfar, Mohammad H, et al.
(författare)
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Global, regional, and national comparative risk assessment of 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks in 188 countries, 1990-2013 : a systematic analysis for the Global Burden of Disease Study 2013.
- 2015
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Ingår i: The Lancet. - 0140-6736 .- 1474-547X. ; 386:10010, s. 2287-2323
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Tidskriftsartikel (refereegranskat)abstract
- BACKGROUND: The Global Burden of Disease, Injuries, and Risk Factor study 2013 (GBD 2013) is the first of a series of annual updates of the GBD. Risk factor quantification, particularly of modifiable risk factors, can help to identify emerging threats to population health and opportunities for prevention. The GBD 2013 provides a timely opportunity to update the comparative risk assessment with new data for exposure, relative risks, and evidence on the appropriate counterfactual risk distribution.METHODS: Attributable deaths, years of life lost, years lived with disability, and disability-adjusted life-years (DALYs) have been estimated for 79 risks or clusters of risks using the GBD 2010 methods. Risk-outcome pairs meeting explicit evidence criteria were assessed for 188 countries for the period 1990-2013 by age and sex using three inputs: risk exposure, relative risks, and the theoretical minimum risk exposure level (TMREL). Risks are organised into a hierarchy with blocks of behavioural, environmental and occupational, and metabolic risks at the first level of the hierarchy. The next level in the hierarchy includes nine clusters of related risks and two individual risks, with more detail provided at levels 3 and 4 of the hierarchy. Compared with GBD 2010, six new risk factors have been added: handwashing practices, occupational exposure to trichloroethylene, childhood wasting, childhood stunting, unsafe sex, and low glomerular filtration rate. For most risks, data for exposure were synthesised with a Bayesian meta-regression method, DisMod-MR 2.0, or spatial-temporal Gaussian process regression. Relative risks were based on meta-regressions of published cohort and intervention studies. Attributable burden for clusters of risks and all risks combined took into account evidence on the mediation of some risks such as high body-mass index (BMI) through other risks such as high systolic blood pressure and high cholesterol.FINDINGS: All risks combined account for 57·2% (95% uncertainty interval [UI] 55·8-58·5) of deaths and 41·6% (40·1-43·0) of DALYs. Risks quantified account for 87·9% (86·5-89·3) of cardiovascular disease DALYs, ranging to a low of 0% for neonatal disorders and neglected tropical diseases and malaria. In terms of global DALYs in 2013, six risks or clusters of risks each caused more than 5% of DALYs: dietary risks accounting for 11·3 million deaths and 241·4 million DALYs, high systolic blood pressure for 10·4 million deaths and 208·1 million DALYs, child and maternal malnutrition for 1·7 million deaths and 176·9 million DALYs, tobacco smoke for 6·1 million deaths and 143·5 million DALYs, air pollution for 5·5 million deaths and 141·5 million DALYs, and high BMI for 4·4 million deaths and 134·0 million DALYs. Risk factor patterns vary across regions and countries and with time. In sub-Saharan Africa, the leading risk factors are child and maternal malnutrition, unsafe sex, and unsafe water, sanitation, and handwashing. In women, in nearly all countries in the Americas, north Africa, and the Middle East, and in many other high-income countries, high BMI is the leading risk factor, with high systolic blood pressure as the leading risk in most of Central and Eastern Europe and south and east Asia. For men, high systolic blood pressure or tobacco use are the leading risks in nearly all high-income countries, in north Africa and the Middle East, Europe, and Asia. For men and women, unsafe sex is the leading risk in a corridor from Kenya to South Africa.INTERPRETATION: Behavioural, environmental and occupational, and metabolic risks can explain half of global mortality and more than one-third of global DALYs providing many opportunities for prevention. Of the larger risks, the attributable burden of high BMI has increased in the past 23 years. In view of the prominence of behavioural risk factors, behavioural and social science research on interventions for these risks should be strengthened. Many prevention and primary care policy options are available now to act on key risks.FUNDING: Bill & Melinda Gates Foundation.
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