Li and Poon proved that every real square matrix is a real linear combination of four real orthogonal matrices. The resulting question, recorded by Zhan, asks whether four terms are necessary. We prove that three real orthogonal matrices always suffice.
Up to one in five or six recognised pregnancies ends in an involuntary loss, yet what follows for women's working lives is largely undocumented. In fifteen waves of the UK panel Understanding Society, this event study follows 2654 women whose first reported pregnancy ends in a live birth or a loss, each against her own pre-pregnancy baseline. After a loss, the hourly wage declines by 6 to 7% in the first year, with no detectable change in employment or hours. Employment and hours fall from the second year, and earnings decline by about 760 pound per month after five years, concentrated among the women who later become mothers, unlike the wage decline. Human capital, subsequent childbearing, career characteristics, and health account for only part of these gaps. Women whose pregnancy ends in a live birth show the well-documented child penalty. A pregnancy loss, then, carries labour-market costs in its own right.
Ecological Macroeconomic Integrated Assessment Models (EM-IAMs) have emerged as tools for exploring post-growth narratives and challenging the dominant discourse of continuous economic growth. Their use may be strategically advantageous: by employing modelling approaches that are epistemically legitimate within economics, EM-IAMs can contest the growth paradigm with their own tools. Yet, the framing of socio-ecological processes in EM-IAMs, through quantification and evaluative logics, risks interfering with the other goal of EM-IAMs; to address social inequality and injustices. As such, EM-IAMs risk operating as what ecologist Langdon Winner coined as ‘conceptual Trojan horse’. We question whether EM-IAMs may truly provide “robust modelling tools to explore alternative future scenarios, enabling the ex-ante evaluation of direct and indirect effects of policies on well-being, employment, and the ecosystem” (Ecological Economics, 2025). Our doubts rest upon complexity that does not reduce uncertainty, the politics of model simplification, the limitations of EM-IAM models for aspects that resist quantification, the reinforcement of historical power imbalances, and, ultimately, the performative effects of models themselves. We suggest that, rather than extending EM-IAMs to incorporate well-being analysis, we should adopt a different approach to modelling, learning from ecological values; appreciating diversity, variability in space and time, self-regulation, and entanglements.
ABSTRACT Background Intervertebral disc degeneration (IDD) reflects a poorly characterized shift from anabolic matrix renewal to catabolic breakdown. Fragmentary experimental and modeling efforts leave many signaling routes unresolved; a consolidated map is required to guide hypothesis‐driven studies. Methods A literature‐curated regulatory network model (RNM) for human nucleus pulposus (NP) cells was assembled from PubMed and enriched with interactions from STRING, KEGG and R&D Systems. The static graph was converted to a semi‐quantitative dynamical system. Simulations examined responses to interleukin‐1β (IL‐1β) and the Toll‐like receptor (TLR) and were benchmarked against time‐resolved proteomics from 2D NP monolayers and 3D alginate cultures representing healthy and degenerated discs. Single‐node perturbations assessed the impact of targeted inhibition on catabolic output. Results The final network contains 82 proteins and 193 directed edges; 41.4% of supporting evidence derives from NP‐specific studies, the highest for any cell type. Baseline activity depicts a non‐degenerate disc, with high expression of anabolic mediators and low expression of catabolic enzymes. Both IL‐1β and TLR elicited strong c‐Jun and p65 NF‐κB activation in silico and in vitro. The model simulated IκBα depletion, whereas its increase in the experimental study shows the biological agreement among in silico and in vitro simulations. Conclusions This RNM unifies scattered IDD data into a validated dynamic framework that mirrors NP signaling. The publicly available model provides a foundation for multiscale studies linking molecular events to disc mechanics and for prioritizing therapeutic interventions.
Recent advancements in data-driven approaches for remote photoplethysmography (rPPG) have significantly improved the accuracy of remote heart rate estimation. However, the performance of such approaches worsens considerably under video compression, which is nevertheless necessary to store and transmit video data efficiently. In this paper, we investigate the impact of video compression on the recovery of physiological signals from camera-based recordings. To mitigate the negative effects of compression on rPPG estimation, we propose a novel two-stage training strategy. This approach incorporates a pulse-signal magnification transformation, which adapts compressed video data into an uncompressed domain, where the rPPG signal is amplified. We validate the effectiveness of our model through comprehensive evaluations on two publicly available datasets, UCLArPPG and UBFC-rPPG, assessing both intra-and cross-database performance across various compression rates. Additionally, we assess the robustness of our approach on two additional highly compressed and widely-used datasets, MAHNOB-HCI and COHFACE, which reveal outstanding heart rate estimation results.
