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National levels of personal health-care access and quality can be approximated by measuring mortality rates from causes that should not be fatal in the presence of effective medical care (ie, amenable mortality). Previous analyses of mortality amenable to health care only focused on high-income countries and faced several methodological challenges. In the present analysis, we use the highly standardised cause of death and risk factor estimates generated through the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) to improve and expand the quantification of personal health-care access and quality for 195 countries and territories from 1990 to 2015. We mapped the most widely used list of causes amenable to personal health care developed by Nolte and McKee to 32 GBD causes. We accounted for variations in cause of death certification and misclassifications through the extensive data standardisation processes and redistribution algorithms developed for GBD. To isolate the effects of personal health-care access and quality, we risk-standardised cause-specific mortality rates for each geography-year by removing the joint effects of local environmental and behavioural risks, and adding back the global levels of risk exposure as estimated for GBD 2015. We employed principal component analysis to create a single, interpretable summary measure–the Healthcare Quality and Access (HAQ) Index–on a scale of 0 to 100. The HAQ Index showed strong convergence validity as compared with other health-system indicators, including health expenditure per capita (r=0·88), an index of 11 universal health coverage interventions (r=0·83), and human resources for health per 1000 (r=0·77). We used free disposal hull analysis with bootstrapping to produce a frontier based on the relationship between the HAQ Index and the Socio-demographic Index (SDI), a measure of overall development consisting of income per capita, average years of education, and total fertility rates. This frontier allowed us to better quantify the maximum levels of personal health-care access and quality achieved across the development spectrum, and pinpoint geographies where gaps between observed and potential levels have narrowed or widened over time. Between 1990 and 2015, nearly all countries and territories saw their HAQ Index values improve; nonetheless, the difference between the highest and lowest observed HAQ Index was larger in 2015 than in 1990, ranging from 28·6 to 94·6. Of 195 geographies, 167 had statistically significant increases in HAQ Index levels since 1990, with South Korea, Turkey, Peru, China, and the Maldives recording among the largest gains by 2015. Performance on the HAQ Index and individual causes showed distinct patterns by region and level of development, yet substantial heterogeneities emerged for several causes, including cancers in highest-SDI countries; chronic kidney disease, diabetes, diarrhoeal diseases, and lower respiratory infections among middle-SDI countries; and measles and tetanus among lowest-SDI countries. While the global HAQ Index average rose from 40·7 (95% uncertainty interval, 39·0–42·8) in 1990 to 53·7 (52·2–55·4) in 2015, far less progress occurred in narrowing the gap between observed HAQ Index values and maximum levels achieved; at the global level, the difference between the observed and frontier HAQ Index only decreased from 21·2 in 1990 to 20·1 in 2015. If every country and territory had achieved the highest observed HAQ Index by their corresponding level of SDI, the global average would have been 73·8 in 2015. Several countries, particularly in eastern and western sub-Saharan Africa, reached HAQ Index values similar to or beyond their development levels, whereas others, namely in southern sub-Saharan Africa, the Middle East, and south Asia, lagged behind what geographies of similar development attained between 1990 and 2015. This novel extension of the GBD Study shows the untapped potential for personal health-care access and quality improvement across the development spectrum. Amid substantive advances in personal health care at the national level, heterogeneous patterns for individual causes in given countries or territories suggest that few places have consistently achieved optimal health-care access and quality across health-system functions and therapeutic areas. This is especially evident in middle-SDI countries, many of which have recently undergone or are currently experiencing epidemiological transitions. The HAQ Index, if paired with other measures of health-system characteristics such as intervention coverage, could provide a robust avenue for tracking progress on universal health coverage and identifying local priorities for strengthening personal health-care quality and access throughout the world. Bill & Melinda Gates Foundation.

We prove that on a closed surface, a Lagrangian system defined by a Tonelli Lagrangian LL possesses a periodic orbit that is a local minimizer of the free-period action functional on every energy level belonging to the low range of energies (e0(L),cu(L))(e_0(L),c_{\\mathrm {u}}(L)). We also prove that almost every energy level in (e0(L),cu(L))(e_0(L),c_{\\mathrm {u}}(L)) possesses infinitely many periodic orbits. These statements extend two results, respectively due to Taimanov and Abbondandolo–Macarini–Mazzucchelli–Paternain, valid for the special case of electromagnetic Lagrangians.

We consider a local minimizer, in the sense of the W1,m norm (m≥1), of the classical problem of the calculus of variations PMinimizeI(x):=∫abΛ(t,x(t),x′(t))dt+Ψ(x(a),x(b))subject to:x∈W1,m([a,b];Rn),x′(t)∈Ca.e.,x(t)∈Σ∀t∈[a,b].where Λ:[a,b]×Rn×Rn→R∪{+∞} is just Borel measurable, C is a cone, Σ is a nonempty subset of Rn and Ψ is an arbitrary possibly extended valued function. When Λ is real valued, we merely assume a local Lipschitz condition on Λ with respect to t, allowing Λ(t,x,ξ) to be discontinuous and nonconvex in x or ξ. In the case of an extended valued Lagrangian, we impose the lower semicontinuity of Λ(·,x,·), and a condition on the effective domain of Λ(t,x,·). We use a recent variational Weierstrass type inequality to show that the minimizers satisfy a relaxation result and an Erdmann – Du Bois-Reymond convex inclusion which, remarkably, holds whenever Λ(x,ξ) is autonomous and just Borel. Under a growth condition, weaker than superlinearity, we infer the Lipschitz continuity of minimizers.

In this paper, we proved that for generic Tonelli Lagrangian, there always exists a residual set G⊂H1(M,R)\\mathcal {G}\\subset H^1(M,\\mathbb {R}) such that \\[ M~(c)=A~(c)=N~(c),∀c∈G,\\widetilde {\\mathcal {M}}(c)=\\widetilde {\\mathcal {A}}(c)=\\widetilde {\\mathcal {N}}(c),\\quad \\forall c\\in \\mathcal {G}, \\] with M~(c)\\widetilde {\\mathcal {M}}(c) supports on a uniquely ergodic measure.

John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical mechanics. His novel approach—known as Aubry-Mather theory—singles out the existence of special orbits and invariant measures of the system, which possess a very rich dynamical and geometric structure. In particular, the associated invariant sets play a leading role in determining the global dynamics of the system. This book provides a comprehensive introduction to Mather’s theory, and can serve as an interdisciplinary bridge for researchers and students from different fields seeking to acquaint themselves with the topic.Starting with the mathematical background from which Mather’s theory was born, Alfonso Sorrentino first focuses on the core questions the theory aims to answer—notably the destiny of broken invariant KAM tori and the onset of chaos—and describes how it can be viewed as a natural counterpart of KAM theory. He achieves this by guiding readers through a detailed illustrative example, which also provides the basis for introducing the main ideas and concepts of the general theory. Sorrentino then describes the whole theory and its subsequent developments and applications in their full generality.Shedding new light on John Mather’s revolutionary ideas, this book is certain to become a foundational text in the modern study of Hamiltonian systems.

We discuss a space of Young measures in connection with some variational problems. We use it to present a proof of the Theorem of Tonelli on the existence of minimizing curves. We generalize a recent result of Ambrosio, Gigli and Savaré on the decomposition of the weak solutions of the transport equation. We also prove, in the context of Mather theory, the equality between Closed measures and Holonomic measures.

We consider the Cauchy problem for a loaded partial differential equation arising in coefficient inverse problem. The convergence of Tonelli's and weak approximation methods for this problem is previously proved. In the article we will prove linear rate of convergence of given methods.

Purpose - This paper is a conversation with Maria José Tonelli, conducted by Santiago Ibarreche, about her career as an Iberoamerican scholar.Design methodology approach - Interview.Findings - The interview explores Tonelli's career, her achievements and continued search for excellence in her institution, the IAM, and her country Brazil, as well as the way she has coped with life's demands.Originality value - The interview in this special section, A Life in Research, brings out an individual scholar's experience and history, not only as recognition of scholarly impact, but also as recognition of the person.

[Annalena Tonelli] trained as a lawyer in Italy, but went to work in east Africa in 1969. In the 1970s, in Wajir, Kenya, she established the tuberculosis manyatta (huts) system. Wajir is just across the border from Somalia, and most of Tonelli's patients were ethnic Somalis who would not stay in hospitals, so Tonelli brought the hospitals to them, treating them in locally made huts. The manyatta system laid the foundation of DOTS strategies now in place around the world, Emanuele Capobianco, Polio Officer for UNICEF in Somalia, told The Lancet. In 1984, Tonelli saved hundreds of Somalis from the Wagalla massacre, carried out by the Kenyan government, by sending pictures of the slaughter to the press. During that time, she was the only person to care for the injured and bury the dead, Capobianco said. Tonelli's actions earned her the admiration of many Somali Muslims, but led the Kenyan government to force her out of the country, so she went to Merka, Somalia, where she remained until 1995. She was often the only humanitarian worker left in a region after others had heeded security warnings. \"During the Somalia famine, she saved the lives of thousands of Somalis who would have otherwise starved\", Capobianco said.