The tensor notation used in several areas of mathematics is a useful one, but it is not widely available to the functional programming community. In a practical sense, the (embedded) domain-specific languages (dsls) that are currently in use for tensor algebra are either 1. array-oriented languages that do not enforce or take advantage of tensor properties and algebraic structure or 2. follow the categorical structure of tensors but require the programmer to manipulate tensors in an unwieldy point-free notation. A deeper issue is that for tensor calculus, the dominant pedagogical paradigm assumes an audience which is either comfortable with notational liberties which programmers cannot afford, or focus on the applied mathematics of tensors, largely leaving their linguistic aspects (behaviour of variable binding, syntax and semantics, etc.) for the reader to figure out by themselves. This state of affairs is hardly surprising, because, as we highlight, several properties of standard tensor notation are somewhat exotic from the perspective of lambda calculi. We bridge the gap by defining a dsl, embedded in Haskell, whose syntax closely captures the index notation for tensors in wide use in the literature. The semantics of this edsl is defined in terms of the algebraic structures which define tensors in their full generality. This way, we believe that our edsl can be used both as a tool for scientific computing, but also as a vehicle to express and present the theory and applications of tensors.

The Paleoproterozoic Stollberg Zn-Pb-Ag plus magnetite ore field contains SVALS-type stratabound, limestone-skarn hosted sulphide deposits within volcanic (bimodal felsic and mafic rocks)/volcaniclastic rocks metamorphosed to the amphibolite facies. The sulphide ores consist of semi-massive to disseminated to vein-network sphalerite-galena and pyrrhotite (with subordinate pyrite, chalcopyrite, arsenopyrite and magnetite). Thermochemical considerations and stabilities of minerals in the systems K-Al-Si-O-H and Fe-S-O and sulphur isotope values for sulphides of δ34SVCDT = +1.12 to +5.71 ‰ suggest that sulphur most likely formed by inorganic reduction of seawater sulphate that was carried in hydrothermally modified seawater fluid under the following approximate physicochemical conditions: T = 250o–350 oC, δ34SΣS = +3 ‰, I = ∼1 m NaCl and a total dissolved S content of ∼0.01 to 0.1 moles/kg H2O. However, a magmatic contribution of sulphur cannot be discounted. Carbon and oxygen isotope compositions of calcite in altered rocks spatially associated with mineralisation show values of δ13CVPDB = −2.3 to −0.8 ‰ and δ18OVSMOW = +9.5 to +11.2 ‰, with one anomalous sample exhibiting values of δ13CVPDB = −0.1 ‰ and δ18OVSMOW = +10.9 ‰. Most carbonates in ore show lighter C and O isotope values than those of Proterozoic (Orosirian) limestones and are likely the result of premetamorphic hydrothermal alteration involving modified seawater followed by decarbonation during regional metamorphism. The isotopically light C and O isotope values are consistent with those for carbonates spatially associated with other SVALS-type deposits in the Bergslagen ore district and suggest that such values may be used for exploration purposes.

When simulating runaway electron dynamics in tokamak disruptions, fluid models with lower numerical cost are often preferred to more accurate kinetic models. The aim of this work is to compare fluid and kinetic simulations of a large variety of different disruption scenarios in ITER. We consider both non-activated and activated scenarios; for the latter, we derive and implement kinetic sources for the Compton scattering and tritium beta decay runaway electron generation mechanisms in our simulation tool Dream (Hoppe et al., Comput. Phys. Commun., vol. 268, 2021, 108098). To achieve a diverse set of disruption scenarios, Bayesian optimization is used to explore a range of massive material injection densities for deuterium and neon. The cost function is designed to distinguish between successful and unsuccessful disruption mitigation based on the runaway current, current quench time and transported fraction of the heat loss. In the non-activated scenarios, we find that fluid and kinetic disruption simulations can have significantly different runaway electron dynamics, due to an overestimation of the runaway seed by the fluid model. The primary cause of this is that the fluid hot-tail generation model neglects superthermal electron transport losses during the thermal quench. In the activated scenarios, the fluid and kinetic models give similar predictions, which can be explained by the significant influence of the activated sources on the runaway dynamics and the seed.

This paper describes a purely functional library for computing level-p-complexity of Boolean functions and applies it to two-level iterated majority. Boolean functions are simply functions from n bits to one bit, and they can describe digital circuits, voting systems, etc. An example of a Boolean function is majority, which returns the value that has majority among the n input bits for odd n. The complexity of a Boolean function f measures the cost of evaluating it: how many bits of the input are needed to be certain about the result of f. There are many competing complexity measures, but we focus on level-p-complexity — a function of the probability p that a bit is 1. The level-p-complexity $D_p(f)$ is the minimum expected cost when the input bits are independent and identically distributed with Bernoulli(p) distribution. We specify the problem as choosing the minimum expected cost of all possible decision trees — which directly translates to a clearly correct, but very inefficient implementation. The library uses thinning and memoization for efficiency and type classes for separation of concerns. The complexity is represented using (sets of) polynomials, and the order relation used for thinning is implemented using polynomial factorization and root counting. Finally, we compute the complexity for two-level iterated majority and improve on an earlier result by J. Jansson.

A Bayesian optimization framework is used to investigate scenarios for disruptions mitigated with combined deuterium and neon injection in ITER. The optimization cost function takes into account limits on the maximum runaway current, the transported fraction of the heat loss and the current quench time. The aim is to explore the dependence of the cost function on injected densities, and provide insights into the behaviour of the disruption dynamics for representative scenarios. The simulations are conducted using the numerical framework Dream (Disruption Runaway Electron Analysis Model). We show that, irrespective of the quantities of the material deposition, multi-megaampere runaway currents will be produced in the deuterium–tritium phase of operations, even in the optimal scenarios. However, the severity of the outcome can be influenced by tailoring the radial profile of the injected material; in particular, if the injected neon is deposited at the edge region it leads to a significant reduction of both the final runaway current and the transported heat losses. The Bayesian approach allows us to map the parameter space efficiently, with more accuracy in favourable parameter regions, thereby providing us with information about the robustness of the optima.

Increased on-farm cow mortality (ie unassisted death and euthanasia) has been demonstrated in Swedish dairy herds during the last decade. Identifying risk factors associated with type of death is needed for future work in reducing cow mortality rates. The objectives of this case-control study were to quantify the relative proportion of unassisted dead cows among cows that die on-farm, and to identify risk factors associated with unassisted death (as opposed to euthanasia). In Sweden, cadavers and animal waste products are being processed into biofuel at destruction plants. Two destruction plants were visited three times in 2011-2012. All dairy cows (n = 556) entering the plants were examined. Farmers that had sent the cows were contacted by telephone to verify type of death. Of the 433 dairy cows included in the analysis, 30% had died unassisted. A stillbirth rate above or equal to the median in the study material (7%) increased the risk for unassisted death. The proportion of unassisted dead cows was lower than that found in other countries. The results indicate that it might be possible to study euthanasia and unassisted death as one group in Swedish dairy cows, because only one factor differentiating between the two types of death was identified. However, unidentified risk factors may still differ and, possibly more importantly, welfare implications may also differ between the two types of death which implies the need to separate them in future studies.

A strategy activated in one task may be transferred to subsequent tasks and prevent activation of other strategies that would otherwise come to mind, a mechanism referred to as procedural priming. In a novel application of procedural priming we show that it can make or break cognitive illusions. Our test case is the 1/k illusion, which is based on the same unwarranted mathematical shortcut as the MPG illusion and the time-saving bias. The task is to estimate distances between values of fractions on the form 1/k. Most people given this task intuitively base their estimates on the distances between the denominators (i.e., the reciprocals of the fractions), which may yield very poor estimations of the true distances between the fractions. As expected, the tendency to fall for this illusion is related to cognitive style (Study 1). In order to apply procedural priming we constructed versions of the task in which the illusion is weak, in the sense that most people do not fall for it anymore. We then gave participants both “strong illusion” and “weak illusion” versions of the task (Studies 2 and 3). Participants who first did the task in the weak illusion version would often persist with the correct strategy even in the strong illusion version, thus breaking the otherwise strong illusion in the latter task. Conversely, participants who took the strong illusion version first would then often fall for the illusion even in the weak illusion version, thus strengthening the otherwise weak illusion in the latter task.

We study large sample properties of likelihood ratio tests of the unit-root hypothesis in an autoregressive model of arbitrary order. Earlier research on this testing problem has developed likelihood ratio tests in the autoregressive model of order 1, but resorted to a plug-in approach when dealing with higher-order models. In contrast, we consider the full model and derive the relevant large sample properties of likelihood ratio tests under a local-to-unity asymptotic framework. As in the simpler model, we show that the full likelihood ratio tests are nearly efficient, in the sense that their asymptotic local power functions are virtually indistinguishable from the Gaussian power envelopes. Extensions to sieve-type approximations and different classes of alternatives are also considered.

Magnetite is a common mineral in the Paleoproterozoic Stollberg Zn–Pb–Ag plus magnetite ore field (~6.6 Mt of production), which occurs in 1.9 Ga metamorphosed felsic and mafic rocks. Mineralisation at Stollberg consists of magnetite bodies and massive to semi-massive sphalerite–galena and pyrrhotite (with subordinate pyrite, chalcopyrite, arsenopyrite and magnetite) hosted by metavolcanic rocks and skarn. Magnetite occurs in sulfides, skarn, amphibolite and altered metamorphosed rhyolitic ash–siltstone that consists of garnet–biotite, quartz–garnet–pyroxene, gedrite–albite, and sericitic rocks. Magnetite probably formed from hydrothermal ore-bearing fluids (~250–400°C) that replaced limestone and rhyolitic ash–siltstone, and subsequently recrystallised during metamorphism. The composition of magnetite from these rock types was measured using electron microprobe analysis and LA–ICP–MS. Utilisation of discrimination plots (Ca+Al+Mn vs. Ti+V, Ni/(Cr+Mn) vs. Ti+V, and trace-element variation diagrams (median concentration of Mg, Al, Ti, V, Co, Mn, Zn and Ga) suggest that the composition of magnetite in sulfides from the Stollberg ore field more closely resembles that from skarns found elsewhere rather than previously published compositions of magnetite in metamorphosed volcanogenic massive sulfide deposits. Although the variation diagrams show that magnetite compositions from various rock types have similar patterns, principal component analyses and element–element variation diagrams indicate that its composition from the same rock type in different sulfide deposits can be distinguished. This suggests that bulk-rock composition also has a strong influence on magnetite composition. Principal component analyses also show that magnetite in sulfides has a distinctive compositional signature which allows it to be a prospective pathfinder mineral for sulfide deposits in the Stollberg ore field.

Loneliness has proved to be common in long-term care facilities (LTCF) and is associated with adverse health outcomes. Although older residents have expressed their experiences of loneliness in previous studies in various ways, researchers have rarely distinguished or explored the three dimensions of loneliness: social, emotional and existential. Furthermore, descriptions of existential loneliness in LTCF is still a neglected area of research. The aim of this study was to explore how the experiences of loneliness of older people in LTCF are manifested and divided into these dimensions. We used an ethnographic multi-method approach. The analysis leaned on abductive reasoning. In terms of social loneliness, the respondents missed company and lacked peer support, but also felt lonely in a crowd. Emotional loneliness felt miserable and could not be shared with anyone. It was related to a feeling of meaninglessness of life and a lack of meaningful others. Existential loneliness was characterised by waiting and a feeling of emptiness. It reflected the fundamental issues of humanity. The present study is one of the first to explore the dimensions of the experiences of loneliness among frail and cognitively impaired older people in LTCF. According to the voices of the lonely respondents, loneliness has many social, emotional and existential aspects. These features of loneliness should be recognised in studies, care practices and interventions.

This paper highlights a tension between semiparametric efficiency and bootstrap consistency in the context of a canonical semiparametric estimation problem, namely the problem of estimating the average density. It is shown that although simple plug-in estimators suffer from bias problems preventing them from achieving semiparametric efficiency under minimal smoothness conditions, the nonparametric bootstrap automatically corrects for this bias and that, as a result, these seemingly inferior estimators achieve bootstrap consistency under minimal smoothness conditions. In contrast, several “debiased” estimators that achieve semiparametric efficiency under minimal smoothness conditions do not achieve bootstrap consistency under those same conditions.

In verified generic programming, one cannot exploit the structure of concrete data types but has to rely on well chosen sets of specifications or abstract data types (ADTs). Functors and monads are at the core of many applications of functional programming. This raises the question of what useful ADTs for verified functors and monads could look like. The functorial map of many important monads preserves extensional equality. For instance, if $$f,g \, : \, A \, \to \, B$$ are extensionally equal, that is, $$\forall x \in A$$, $$f \, x = g \, x$$, then $$map \, f \, : \, List \, A \to List \, B$$ and $$map \, g$$ are also extensionally equal. This suggests that preservation of extensional equality could be a useful principle in verified generic programming. We explore this possibility with a minimalist approach: we deal with (the lack of) extensional equality in Martin-Löf’s intensional type theories without extending the theories or using full-fledged setoids. Perhaps surprisingly, this minimal approach turns out to be extremely useful. It allows one to derive simple generic proofs of monadic laws but also verified, generic results in dynamical systems and control theory. In turn, these results avoid tedious code duplication and ad-hoc proofs. Thus, our work is a contribution toward pragmatic, verified generic programming.

The Northern Rocky Mountain Front (hereafter Northern Front) is a prominent geographic feature in archaeological models of human dispersal in the terminal Pleistocene and Early Holocene of North America. Testing those models has been arduous because of local geomorphological factors that tend to obliterate or otherwise limit access to archaeological finds of relevant age. In this paper, we present well-stratified archaeological and environmental records dating back to 14,000–13,000 cal yr BP from the site of Billy Big Spring (Blackfeet Indian Reservation, Montana), located on a glacial kettle, a type of landform that has been largely ignored by regional archaeological research to date. Findings from Billy Big Spring show the continuous use of the Northern Front foothills throughout the major climatic and environmental disturbances of the Early Holocene, and possibly the terminal Pleistocene as well. As such, Billy Big Spring contributes to refining several archaeological models of early settlement of the Northern Front, particularly those that posit differential use of foothills versus plains settings during the midst of the Holocene Thermal Maximum. The record at Billy Big Spring also suggests that kettles, regardless of physiographic setting, provide a yet unsuspected and unsampled potential for preserving high-quality and easily accessible early archaeological and paleoenvironmental records.

Public health emergencies, including the coronavirus disease 2019 (COVID-19) pandemic, highlight disproportionate impacts faced by populations with existing disparities. Concepts and terms used to describe populations disproportionately impacted in emergencies vary over time and across disciplines, but United States (US) federal guidance and law require equal access to our nation’s emergency resources. At all levels of emergency planning, public health and their partners must be accountable to populations with existing inequities, which requires a conceptual shift toward using the data-driven social determinants of health (SDOH). SDOH are conditions in which people are born, live, learn, work, play, worship, and age that affect a wide range of health, functioning, and quality of life outcomes and risks. This article reviews the historic use of concepts and terms to describe populations disproportionately impacted by emergencies. It also recommends a shift in emergency activities toward interventions that target the SDOH to adequately address long-standing systemic health disparities and socioeconomic inequities in the United States.

In recent decades, the Swedish economy has been characterized by rather fast economic growth. At the same time, income inequality has increased substantially. In the present study, I investigated who has gained and who has been left behind during this period—how disposable personal income has changed for men and women, as well as for those in different positions in the income distribution. Register data for the total population (aged 20 to 80 years old) from 1983 to 2010 were used and three different positions in the income distribution were investigated: percentile 10, the median, and percentile 99. Five years were selected: 1983, 1991, 2000, 2006, and 2010. Each selected year represents a snapshot and describes the general trend. Results show that women in the 10th percentile have increased their income quite well, a result of increased female labor force participation during the period. This has led to a decrease of the income gap between genders within this group. But results also show a masculinization of low income and poverty, as the male incomes in this group have not increased to the same extent as for males in the other income groups. At the median, both men and women experienced a steady increase of incomes, but the gender gap for ages younger than 50 widened between 2000 and 2010. At the very top, percentile 99, the increase in disposable personal income was enormous; however, the gender gap in income did not decrease.