The neuron mixer and its impact on human brain dynamics.

A signal mixer facilitates rich computation, which has been the building block of modern telecommunication. This frequency mixing produces new signals at the sum and difference frequencies of input signals, enabling powerful operations such as heterodyning and multiplexing. Here, we report that a neuron is a signal mixer. We found through ex vivo and in vivo whole-cell measurements that neurons mix exogenous (controlled) and endogenous (spontaneous) subthreshold membrane potential oscillations, producing new oscillation frequencies, and that neural mixing originates in voltage-gated ion channels. Furthermore, we demonstrate that mixing is evident in human brain activity and is associated with cognitive functions. We found that the human electroencephalogram displays distinct clusters of local and inter-region mixing and that conversion of the salient posterior alpha-beta oscillations into gamma-band oscillations regulates visual attention. Signal mixing may enable individual neurons to sculpt the spectrum of neural circuit oscillations and utilize them for computational operations.

Kernel-Based Independence Tests for Causal Structure Learning on Functional Data.

Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering. Such measurements can be viewed as realisations of an underlying smooth process sampled over the continuum. However, traditional methods for independence testing and causal learning are not directly applicable to such data, as they do not take into account the dependence along the functional dimension. By using specifically designed kernels, we introduce statistical tests for bivariate, joint, and conditional independence for functional variables. Our method not only extends the applicability to functional data of the Hilbert-Schmidt independence criterion (hsic) and its d-variate version (d-hsic), but also allows us to introduce a test for conditional independence by defining a novel statistic for the conditional permutation test (cpt) based on the Hilbert-Schmidt conditional independence criterion (hscic), with optimised regularisation strength estimated through an evaluation rejection rate. Our empirical results of the size and power of these tests on synthetic functional data show good performance, and we then exemplify their application to several constraint- and regression-based causal structure learning problems, including both synthetic examples and real socioeconomic data.

Kernel-based joint independence tests for multivariate stationary and non-stationary time series.

Multivariate time-series data that capture the temporal evolution of interconnected systems are ubiquitous in diverse areas. Understanding the complex relationships and potential dependencies among co-observed variables is crucial for the accurate statistical modelling and analysis of such systems. Here, we introduce kernel-based statistical tests of joint independence in multivariate time series by extending the d-variable Hilbert-Schmidt independence criterion to encompass both stationary and non-stationary processes, thus allowing broader real-world applications. By leveraging resampling techniques tailored for both single- and multiple-realization time series, we show how the method robustly uncovers significant higher-order dependencies in synthetic examples, including frequency mixing data and logic gates, as well as real-world climate, neuroscience and socio-economic data. Our method adds to the mathematical toolbox for the analysis of multivariate time series and can aid in uncovering high-order interactions in data.

Complex interlinkages, key objectives, and nexuses among the Sustainable Development Goals and climate change: a network analysis.

BACKGROUND: Global sustainability is an enmeshed system of complex socioeconomic, climatological, and ecological interactions. The numerous objectives of the UN's Sustainable Development Goals (SDGs) and the Paris Agreement have various levels of interdependence, making it difficult to ascertain the influence of changes to particular indicators across the whole system. In this analysis, we aimed to detect and rank the complex interlinkages between objectives of sustainability agendas. METHODS: We developed a method to find interlinkages among the 17 SDGs and climate change, including non-linear and non-monotonic dependences. We used time series of indicators defined by the World Bank, consisting of 400 indicators that measure progress towards the 17 SDGs and an 18th variable (annual average temperatures), representing progress in the response to the climate crisis, from 2000 to 2019. This method detects significant dependencies among the time evolution of the objectives by using partial distance correlations, a non-linear measure of conditional dependence that also discounts spurious correlations originating from lurking variables. We then used a network representation to identify the most important objectives (using network centrality) and to obtain nexuses of objectives (defined as highly interconnected clusters in the network). FINDINGS: Using temporal data from 181 countries spanning 20 years, we analysed dependencies among SDGs and climate for 35 country groupings based on region, development, and income level. The observed significant interlinkages, central objectives, and nexuses identified varied greatly across country groupings; however, SDG 17 (partnerships for the goals) and climate change ranked as highly important across many country groupings. Temperature rise was strongly linked to urbanisation, air pollution, and slum expansion (SDG 11), especially in country groupings likely to be worst affected by climate breakdown, such as Africa. In several country groupings composed of developing nations, we observed a consistent nexus of strongly interconnected objectives formed by SDG 1 (poverty reduction), SDG 4 (education), and SDG 8 (economic growth), sometimes incorporating SDG 5 (gender equality), and SDG 16 (peace and justice). INTERPRETATION: The differences across groupings emphasise the need to define goals in accordance with local circumstances and priorities. Our analysis highlights global partnerships (SDG 17) as a pivot in global sustainability efforts, which have been strongly linked to economic growth (SDG 8). However, if economic growth and trade expansion were repositioned as a means instead of an end goal of development, our analysis showed that education (SDG 4) and poverty reduction (SDG 1) become more central, thus suggesting that these could be prioritised in global partnerships. Urban livelihoods (SDG 11) were also flagged as important to avoid replicating unsustainable patterns of the past. FUNDING: Engineering and Physical Sciences Research Council, UK Research and Innovation.

A hybrid approach to identifying and assessing interactions between climate action (SDG13) policies and a range of SDGs in a UK context.

In 2015 the United Nations drafted the Paris Agreement and established the Sustainable Development Goals (SDGs) for all nations. A question of increasing relevance is the extent to which the pursuit of climate action (SDG 13) interacts both positively and negatively with other SDGs. We tackle this question through a two-pronged approach: a novel, automated keyword search to identify linkages between SDGs and UK climate-relevant policies; and a detailed expert survey to evaluate these linkages through specific examples. We consider a particular subset of SDGs relating to health, economic growth, affordable and clean energy and sustainable cities and communities. Overall, we find that of the 89 UK climate-relevant policies assessed, most are particularly interlinked with the delivery of SDG 7 (Affordable and Clean Energy) and SDG 11 (Sustainable Cities and Communities) and that certain UK policies, like the Industrial Strategy and 25-Year Environment Plan, interlink with a wide range of SDGs. Focusing on these climate-relevant policies is therefore likely to deliver a wide range of synergies across SDGs 3 (Good Health and Well-being), 7, 8 (Decent Work and Economic Growth), 9 (Industry, Innovation and Infrastructure), 11, 14 (Life Below Water) and 15 (Life on Land). The expert survey demonstrates that in addition to the range of mostly synergistic interlinkages identified in the keyword search, there are also important potential trade-offs to consider. Our analysis provides an important new toolkit for the research and policy communities to consider interactions between SDGs, which can be employed across a range of national and international contexts. Supplementary Information: The online version contains supplementary material available at 10.1007/s43621-021-00051-w.