Since the 1970s, twin birth rates have increased sharply in developed countries. In Africa, where the rate is the highest globally, its evolution and variation are poorly understood. This article aims to estimate the twinning rate in sub-Saharan African (SSA) countries throughout 1986–2016 and analyze its spatial, temporal, and ethnic variations. It also seeks to identify social and demographic factors associated with a high probability of twin births and outline a forecast of the twinning rate. We used data from 174 Demographic and Health Surveys from 42 countries. We supplemented them with the UN World Population Prospects (WPP). The twinning rate was calculated by reporting the number of twin births per thousand total births. We used logistic regression to analyze the factors associated with twin births. We projected the twinning rate based on WPP. The overall SSA twinning rate is 17.4 per 1000, but it has changed very little over time, and we expect it will grow a little between 2015 and 2050, increasing at most from 17.4 per 1000 to 18.4 per 1000. We also show significant differences in the twinning rate in SSA according to mother ethnicity. Most ethnic groups with high twinning rates belong to the large Bantu ethnic family. SSA remains the ‘land of twins’, with the twinning rate changing slowly. However, specific health policies must target twin births in SSA to address the public health challenges they present.

Central banks are increasingly communicating their economic outlook in an effort to manage the public and financial market participants’ expectations. We provide original causal evidence that the information communicated and the assumptions underlying a central bank’s projection can matter for expectation formation and aggregate stability. Using a between-subject design, we systematically vary the central bank’s projected forecasts in an experimental macroeconomy where subjects are incentivized to forecast the output gap and inflation. Without projections, subjects exhibit a wide range of heuristics, with the modal heuristic involving a significant backward-looking component. Ex-Ante Rational dual projections of the output gap and inflation significantly reduce the number of subjects’ using backward-looking heuristics and nudge expectations in the direction of the rational expectations equilibrium. Ex-Ante Rational interest rate projections are cognitively challenging to employ and have limited effects on the distribution of heuristics. Adaptive dual projections generate unintended inflation volatility by inducing boundedly-rational forecasters to employ the projection and model-consistent forecasters to utilize the projection as a proxy for aggregate expectations. All projections reduce output gap disagreement but increase inflation disagreement. Central bank credibility is significantly diminished when the central bank makes larger forecast errors when communicating a relatively more complex projection. Our findings suggest that inflation-targeting central banks should strategically ignore agents’ irrationalities when constructing their projections and communicate easy-to-process information.

Machines and mechanisms realize processes, from the shaping process of a milling machine and the motion process of an automotive system to the trajectory realization of a robot. The dynamics of a machine generated by a properly chosen set of constraints in combination with an appropriate drive system is designed to meet the prescribed requirements of the process, which is done by projecting the machine equations of motion on the process dynamics. We get a set of nonlinear relations, which represent the machine motion in terms of the required process motion. A well-known example is the projection of arbitrary many robot degrees of freedom (DOFs) on a given path resulting in a set of nonlinear equations with one DOF only, the path coordinate s. Application of this idea can be used to construct a mobility space $(\ddot{s}, \dot{s}, s)$ for any combination of coordinates and constraints. The paper presents a corresponding approach for n-link robots by applying multibody system theory. Method might be interesting for layout of machines and mechanisms. Practical aspects are discussed, and an example is given.

Several authors have pointed out that in the next few decades dementia will affect a considerably increasing number of the elderly. To our knowledge there exist no calculations of the number of demented persons for the whole European region. We made calculations on the number of dementia cases for the period 2000–2050 based on the population projections of the United Nations. For this purpose, we used the results of several meta-analyses of epidemiological studies. The number of prevalent dementia cases in the year 2000 was 7.1 million. Within the next 50 years, this number will rise to about 16.2 million dementia sufferers. The number of new dementia cases per year will increase from about 1.9 million in the year 2000 to about 4.1 million in the year 2050. Contrarily, the working-age population will considerably decrease during the next 50 years. In the year 2000, 7.1 million dementia cases faced 493 million persons in working-age. This equals a ratio of 69.4 persons in working-age per one demented person. Until the year 2050, this ratio will decrease to only 21.1. Thus, the financial and emotional burden placed by dementia on the working-age population will markedly rise.

This paper analyses the implications that demographic and economic projections have on public pension spending in the European Union (EU). Using some stylised facts, we study the aging trends of the population, as well as labour force and employment projections. Indices of both demographic and economic dependence are built. All of this is used to determine the impact on public pension spending in the EU. Although we detect substantial heterogeneity of circumstances, we show that the states in which aging of the population weights more in explaining public pension expenditure growth as a percentage of gross domestic product (GDP) are generally the ones that make greater efforts to control this spending. Given the limited capacity of policies to increase active population or employment to offset the effects of aging, measures aimed at diminishing the generosity of the public pension system and at promoting private schemes have gained relevance.

If $f,\,g:\,{{\mathbb{R}}^{n}}\,\to \,{{\mathbb{R}}_{\ge 0}}$ are non-negative measurable functions, then the Prékopa–Leindler inequality asserts that the integral of the Asplund sum (provided that it is measurable) is greater than or equal to the 0-mean of the integrals of $f$ and $g$. In this paper we prove that under the sole assumption that $f$ and $g$ have a common projection onto a hyperplane, the Prékopa–Leindler inequality admits a linear refinement. Moreover, the same inequality can be obtained when assuming that both projections (not necessarily equal as functions) have the same integral. An analogous approach may be also carried out for the so-called Borell-Brascamp-Lieb inequality.

The supertree construction problem is about combining several phylogenetic trees with possibly conflicting information into a single tree that has all the leaves of the source trees as its leaves and the relationships between the leaves are as consistent with the source trees as possible. This leads to an optimization problem that is computationally challenging and typically heuristic methods, such as matrix representation with parsimony (MRP), are used. In this paper we consider the use of answer set programming to solve the supertree construction problem in terms of two alternative encodings. The first is based on an existing encoding of trees using substructures known as quartets, while the other novel encoding captures the relationships present in trees through direct projections. We use these encodings to compute a genus-level supertree for the family of cats (Felidae). Furthermore, we compare our results to recent supertrees obtained by the MRP method.

The forest and agriculture sectors are linked by having a portion of their land bases suitable for use in either sector. A substantial part of the southern land base is suitable for either forestry or agriculture use, with most of forestation on U.S. agriculture land in the South. We examine how land exchanges between forestry and agriculture are influenced by specific federal conservation and farm support policies, including changes in the Conservation Reserve Program. Reallocation of land is a significant part of the sectors' responses to the policies, along with intensification of timber management on existing southern forests.

We study the reflexivity and transitivity of a double triangle lattice of subspaces in a Hilbert space. We show that the double triangle lattice is neither reflexive nor transitive when some invertibility condition is satisfied (by the restriction of a projection under another). In this case, we show that the reflexive lattice determined by the double triangle lattice contains infinitely many projections, which partially answers a problem of Halmos on small lattices of subspaces in Hilbert spaces.

A key feature of population ageing in Europe and other more economically developed countries is the projected unprecedented rise in need for long-term care in the next two decades. There is, however, considerable uncertainty over the future supply of unpaid care for older people by their adult children. The future of family care is particularly important in countries planning to reform their long-term care systems, as is the case in England. This article makes new projections of the supply of intense unpaid care for parents aged 65 and over in England to 2032, and compares these projections with existing projections of demand for unpaid care by older people with disabilities from their children. The results show that the supply of unpaid care to older people with disabilities by their adult children in England is unlikely to keep pace with demand in future. By 2032, there is projected to be a shortfall of 160,000 care-givers in England. Demand for unpaid care will begin to exceed supply by 2017 and the unpaid ‘care gap’ will grow rapidly from then onwards. The article concludes by examining how far this unpaid ‘care gap’ is likely to be met by other sources of unpaid care or by developments in new technology and examines the implications of the findings for long-term care policy.

We review recent stability and separation results in volume comparison problems and usethem to prove several hyperplane inequalities for intersection and projection bodies.

This paper addresses the process of estimating loss reserves for a company or syndicate writing in the London Market. Particular emphasis is placed on insurers maximising the value of the process, and ensuring that the process is not simply a series of mathematical calculations. The use of sophisticated mathematical techniques should not distract from the importance of understanding the business and ensuring that data are correct. Sophisticated mathematical techniques can give rise to misleading impressions of confidence and accuracy to estimates, which are often subject to considerable uncertainty. The principles (rather than the detailed techniques) are illustrated by a case study based on a hypothetical London Market writer. Many of these principles are relevant to other markets.

Canada's demographic situation in the future will differ substantially from what we have known in the past. Unless there is an early return to high fertility the average age of both the population and the labour force will increase substantially, while the overall dependency ratio will be low by historical standards. Our analysis suggests that up to about 2010 population change will have less of an impact on the real (i.e., constant—price) level of aggregate government expenditures than on the size of the real gross national product However, we can anticipate compositional changes in government expenditures as a result of population change: very large increases in the real social security costs, lesser (but still large) increases in health costs, and a reduction in education costs. Finally, a relatively large portion of the aggregate expenditure increases will be at the federal government level.