The g-formula is a foundational tool for identifying causal effects in observational data. This tool is based on the law of iterated expectation, a key mathematical identity in statistics. However, the notation with which the law of iterated expectation and the g-formula is expressed can be opaque to those with little background in statistics. We provide a primer introducing the law of iterated expectation, the integration notation used to express it, and its role for causal effect identification via the g-formula. Combined with the assumptions of causal consistency, positivity, and conditional exchangeability, the law of iterated expectation yields a causal standardization formula (the g-formula) in two nonparametrically equivalent forms: a non-iterative conditional expectation (NICE) form involving a single weighted average of conditional outcome means, and an iterative conditional expectation (ICE) form involving nested expectations. We illustrate both forms using three progressively complex numerical examples: a time-fixed example with a single binary confounder, a time-fixed example with discrete and continuous confounders, and a time-varying example with two timepoints. We provide clarity on what the law of iterated expectation is, how it is related to the g-formula, and how to gain intuition of its mathematical formulations in actual data examples that can be generalized to a range of settings.

The preservation of fish quality during post-harvest storage remains a major challenge for the aquaculture industry, particularly in Mediterranean countries where chilled storage is the most commonly used preservation method. This study evaluated, for the first time in Algeria, the effect of different ice-to-fish ratios on the quality and shelf life of farmed gilthead sea bream (Sparus aurata) during refrigerated storage. Fish were stored at three ice-to-fish ratios (1:2, 1:3, and 1:4) and monitored over 16 days. Sensory quality, total viable counts (TVC), H₂S-producing bacterial counts, pH, total volatile basic nitrogen (TVB-N), and trimethylamine (TMA) were determined at regular intervals. Storage time significantly affected all quality parameters (p < 0.05), with progressive sensory deterioration, microbial growth, and accumulation of spoilage metabolites observed in all treatments. However, the extent of quality loss depended on the ice-to-fish ratio. Fish stored at a ratio of 1:2 exhibited significantly lower TVC, H₂S-producing bacterial counts, TVB-N, TMA, and pH values than fish stored at ratios of 1:3 and 1:4 throughout storage. Pearson correlation analysis revealed strong positive relationships among all spoilage indicators, with the highest correlation observed between TVC and H₂S-producing bacterial counts (r = 0.997). Principal component analysis explained 98.9% of the total variance and clearly associated spoilage progression with increasing microbiological and biochemical deterioration. Shelf-life estimation based on the microbiological rejection limit (7 log CFU g⁻¹ TVC) indicated storage lives of 9.9, 7.6, and 5.6 days for fish stored at ice-to-fish ratios of 1:2, 1:3, and 1:4, respectively. Based on a TVB-N limit of 35 mg N 100 g⁻¹, estimated shelf life reached 17.3, 12.2, and 9.4 days, respectively. These findings demonstrate the importance of adequate icing for maintaining fish quality and provide the first scientific basis for optimising cold-chain management of farmed gilthead sea bream in Algeria.

Thwaites Glacier is a major contributor to Antarctic mass loss and a key source of uncertainty in future sea-level rise. Ocean-driven melting at its grounding line drives rapid retreat, yet most models treat the transition between grounded and floating ice as a sharp boundary, neglecting kilometer-scale seawater intrusions that develop as the grounding line migrates and forms a grounding zone. Here, we show that actively-melting grounding zones are required to reproduce nearly three decades of observed retreat, thinning, and acceleration of Thwaites Glacier in a calibrated ice-sheet model, with successful reconstruction occurring only when grounding zones are represented as 2-5 km wide regions. Extending this model forward, we show that grounding-zone processes govern glacier's detachment from stabilizing seafloor ridges, enabling unpinning as early as 2038 and producing up to 30 ± 6 mm of global mean sea-level rise by 2100 - approximately double previous projections even without additional climate warming.

Climate warming accelerates glacier retreat, creating glacier forefields that serve as critical chronosequences for studying nitrogen cycling succession. Ammonia-oxidizing microorganisms (AOMs) play key roles in regulating nitrogen availability for organic carbon accumulation and plant colonization. However, the underlying metabolic mechanisms governing these successional shifts and their functional consequences for nitrification potential remain poorly understood. Here, we integrated soil physicochemical and nitrification potential measurements with a multi-omics approach (qPCR, amplicon and metagenomic sequencing) across four successional stages at the Kuoqionggangri Glacier forefield, Tibetan Plateau. Results revealed a shift from ammonia-oxidizing bacteria (AOB, primarily Nitrosospira) dominance in barren ground to ammonia-oxidizing archaea (AOA, Nitrososphaerales) dominance in meadows, driven by environmental filtering (lowered pH, increased moisture, carbon, nitrogen). Additionally, metagenomic binning showed that AOA possessed broad metabolic capacities for cycling carbon, nitrogen, sulphur and phosphorus. This metabolic versatility conferred a superior adaptive advantage, driving AOA dominance and a corresponding increase in nitrification potential. Furthermore, elevated nitrification potential was jointly driven by shifts in the AOM community and environmental variables. These findings suggest that environmental filtering and AOA metabolic versatility contribute to AOA success in late-successional soils, establishing a dual-mechanism framework for nitrification dynamics during proglacial ecosystem succession.

Documenting distributional shifts in populations is critical for understanding ecosystem function and developing effective conservation strategies, particularly for rare and understudied species. The Critically Endangered eastern population of North Pacific right whale (NPRW) was driven to near extinction by commercial whaling and has not recovered (N < 35). We analyzed passive acoustic data from seven sites along the eastern Bering Sea shelf (2012-2019) to investigate spatial and environmental associations of NPRW calling patterns on a rapidly warming primary foraging ground. Generalized additive models were used to relate acoustic metrics summarized by ecological year (March-February) to environmental conditions at two scales: (1) cold pool extent (CPE), a shelf-scale hydrographic feature derived from seasonal sea ice meltwater that structures right whale prey, and (2) site-specific mean fall bottom temperature (BT), a local thermal expression of cold pool conditions and fall mixing. NPRW phenology, specifically spring arrival and fall departure, was modeled against sea ice retreat and formation dates. NPRW calls occurred at all sites but were most consistently detected within Critical Habitat in the southeastern Bering Sea (SEBS). Calling activity expanded northward during consecutive years of lower CPE (2014-2016), whereas overall few detections occurred during record-low CPE years (2018 and 2019), suggesting a redistribution associated with environmental conditions. While spatial structure explained much of the observed variation, models incorporating CPE and BT received greater and comparable support, suggesting that NPRW calling patterns are associated with habitat conditions generated by cold pool processes rather than single metrics. The strength of environmental effects implied greater sensitivity of calling intensity to environmental variability than calling occurrence. Significant environmental relationships were restricted to the SEBS, where detections increased with CPE and decreased with warming BTs, consistent with known prey-temperature associations. These results, combined with no significant trends between whale phenology and sea ice timing, suggest that NPRW calling patterns are associated with trophically mediated effects of sea-ice-driven oceanography rather than direct responses to ice timing. More broadly, this study demonstrates how long-term passive acoustic monitoring can reveal climate-associated changes in marine predator calling patterns and link detected calling to ecosystem processes operating across spatial scales.

Natural polysaccharides have gained considerable attention in food, pharmaceutical and biomedical applications due to their inherent renewability, biodegradability, biocompatibility, structural and functional diversity. Recently, increasing evidence has demonstrated that polysaccharides can serve as effective freeze-drying protectants for microorganisms, cells, proteins and other bioactive substances. Therefore, preparation and characterization of natural polysaccharides, and clarifying the mechanism of their freeze-drying protective effects are of great significance. This review systematically summarizes the extraction, purification and structural characterization of natural polysaccharides from plant and microbial sources. It particularly emphasizes the freeze-drying protective activity of polysaccharides and the underlying mechanism. Various extraction techniques including acid/alkali extraction, ultrasonic-assisted extraction, microwave-assisted extraction, ultrahigh pressure extraction, subcritical water extraction and enzymatic extraction have been developed to improve polysaccharide yield and quality. Property characterization is mainly achieved through analyses of molecular weight, monosaccharide composition, glycosidic linkage and morphology. In addition, polysaccharides possess freeze-drying protective property mainly through inhibition of ice crystal growth and ice recrystallization, vitrification and water replacement hypothesis. This review may provide theoretical guidance for the development of efficient, sustainable and multifunctional natural polysaccharides as lyoprotectants.

This study reports the first national intercomparison of environmental gamma radiation dose rate in China where each device's response to the ubiquitous cosmic rays was measured on top of a frozen lake ice surface. A total of 78 ambient gamma dose rate instruments from 38 institutions were tested at four typical sites, including a low-terrestrial-background site on the ice surface of the Bosten Lake to measure the detector-specific cosmic ray responses, and wilderness, road, indoor sites nearby. The measured dose rates on the ice surface show significant variations for different detector types but exhibit good consistency within the same model. The cosmic ray responses were then subtracted from the measured dose rates at the other three environmental sites, and the corrected terrestrial gamma radiation dose rates are generally very similar for all instruments. A robust Z-score analysis was applied to evaluate proficiency and identify outliers. This work demonstrates the feasibility of ice-based measurement of the detector-specific apparent cosmic-ray response, and offers a practical technical reference for future intercomparison activities and quality assurance in environmental gamma radiation measurements.

Simulations of the ocean wave climate are critical for assessment of coastal processes and hazards in observation sparse regions such as the Arctic. While the multidecade wind and ice datasets necessary for driving long-term wave simulations have proven reliable for such efforts, the presence of landfast ice along shorelines at scales not represented by these data has been a persistent uncertainty impeding accurate analysis of impacts to Arctic coasts. Here, we explore this uncertainty by producing a historical high-resolution wave simulation and combining simulation outputs with landfast ice data for the Alaskan Arctic. The resulting dataset yields an improved assessment of coastal waves and identifies stark contrasts in the seasonal wave exposure of the Chukchi and Beaufort regions. Notably, analysis shows that absent supplemented landfast ice, coastal ice cover is broadly underestimated by 10 to 25 d, resulting in wave energy being overestimated by 5 to 10% in shallow depths nearshore. Notably, these figures can reach up to 70 d of underestimation for ice cover and 48% overestimation of wave energy in certain locations. The persistent overestimation and potential for extreme positive biases in coastal wave assessment highlight the need for representation of landfast ice in Arctic coastal analysis efforts and our analysis reveals the spatial and temporal biases for related research.

Estimating longitudinal treatment effects is essential for sequential decision-making but is challenging due to treatment-confounder feedback. While Iterative Conditional Expectation (ICE) G-computation offers a principled approach, its recursive structure suffers from error propagation, corrupting the learned outcome regression models. We propose D [3] -Net, a framework that mitigates error propagation in ICE training and then applies a robust final correction. First, to interrupt error propagation during learning, we train the ICE sequence using Sequential Doubly Robust (SDR) pseudo-outcomes, which provide bias-corrected targets for each regression. Second, we employ a multi-task transformer with a covariate simulator head for auxiliary supervision, regularizing representation learning, and a target network to stabilize training dynamics. For the final estimate, we discard the SDR correction and instead use the uncorrected nuisance models to perform Longitudinal Targeted Minimum Loss-Based Estimation (LTMLE) on the original outcomes. This second-stage, targeted debiasing ensures robustness and optimal finite-sample properties. Comprehensive experiments demonstrate that our model, D 3 -Net, robustly reduces bias and variance across different horizons, counterfactuals, and time-varying confoundings, compared to existing state-of-the-art ICE-based estimators.

The visual strategies underpinning performance in the high-velocity invasion sports so far remain unexamined during live play. This study provides the first in-situ analysis of scanning and gaze behaviour in ice hockey. The participants were 16 elite junior players (Mage = 16.5 years; SDage = 0.6 years) from the USA Hockey National Team Development Program. The data were collected during game-representative scrimmage play with mobile eye-tracking technology. Gaze behaviour was quantified using fixation frequencies and viewing times per area of interest (AOI), scan complexity (single- and multi-fixation scans) and possession status (5-s prior to possession). Chi-Square tests were used to analyse the distribution of fixations across these variables, while Markov chain models were constructed to map the transition probabilities of gaze between AOIs. Results revealed that 58.1% of scans contained only one fixation between puck anchors. Mean fixation duration was 134.52 ms. Scans prior to puck reception were shorter and less complex than non-possession scans. Markov chain analysis indicated that the first fixations were largely directed toward space, particularly for forwards (47-53%). The findings of this study may inform training design and future research in visual perception in ice hockey and other team sports.

Icing threatens the safe operation of aircraft, power facilities, wind turbine blades, and other engineering surfaces. Although existing superhydrophobic, photothermal, electrothermal, and drainage surfaces can individually delay freezing, actively melt ice, or transport liquids, most of them are static designs and therefore cannot simultaneously meet the conflicting requirements of water-repellent anti-icing before freezing and rapid drainage after ice melting. Here, we propose a slippery-pore-based photo-electro dual-mode gated anti-/de-icing surface, termed the porous epoxy actuated electrothermal superhydrophobic (PEAES) surface. In the closed state, the surface maintains superhydrophobic anti-icing properties. Under photothermal or electrothermal stimulation, the PI/graphene scales undergo thermally induced bending and expose the underlying slippery pores, enabling low-residue meltwater drainage. When the pores are blocked by ice, the embedded multiwalled carbon nanotube electrothermal layer can further restore the drainage pathway. The PEAES scales achieved reversible opening within 11 s under 1 sun irradiation and within 8 s under a 5 V electrothermal input. At -10 and -20 °C, PEAES exhibited prolonged freezing delay and a low ice adhesion strength of approximately 6 kPa. Under photothermal, electrothermal, and photo-electro synergistic modes, ice melting was completed within 11, 6, and 3 s, respectively. More importantly, PEAES reduced the residual meltwater after ice melting to nearly zero and decreased the secondary icing area ratio to 0%. This work coordinates anti-icing, de-icing, drainage, and recovery through gated state switching, providing a new structural strategy for adaptive anti-/de-icing and meltwater management across multiple energy-input conditions and successive icing stages.

Antibiotic resistance is a growing environmental and public-health threat, yet its seasonal dynamics in cold-region freshwater ecosystems remain poorly understood. Using year-round observations, metagenomic sequencing, and machine learning, we investigated antibiotic resistance genes (ARGs) across ice, water, and sediment in an ice-covered lake. Winter ice contained significantly higher abundances of ARGs, mobile genetic elements (MGEs), and microbial hosts than water and sediments. Driver analysis based on explainable machine learning showed that ARG dynamics in ice were primarily associated with MGEs, whereas ARGs in water and sediments were associated with host-related ecological processes and environmental conditions. During spring, ice-associated ARGs, MGEs, and their microbial hosts showed potential contribution to the water column, expanding resistance-risk hotspots and reorganizing associations among ARGs, MGEs, hosts, and virulence factors. These findings indicate that winter ice acts as a seasonal reservoir of antibiotic resistance, regulating spring antibiotic resistance dynamics and potential health risks.

This study investigated the protective effects of gamma-irradiated ice-nucleating Pseudomonas syringae, known as P. syringae parabiotics (PBs), on the freezing behavior, physicochemical quality, and microstructural integrity of rainbow trout mince during six freeze-thaw (F-T) cycles. PBs were added to the mince at levels of 2 × 10[2] to 2 × 10[4] inactivated cells/g and compared with the viable cell treatment (2 × 10[3] CFU/g). The results demonstrated a pronounced protective effect of 2 × 10[2] inactivated cells/g (PBs-2) and 2 × 10[3] inactivated cells/g (PBs-3) during repeated F-T cycles. PBs-2 exhibited the lowest thawing loss, delayed color deterioration, reduced particle size, and the highest absolute negative zeta potential (-32.45 mV). While PBs-3 reduced loss of total sulfhydryl groups (35.10%), mitigated formation of protein carbonyls (1.92 nmol/mg protein), and decreased centrifugal loss (39.00%). The use of P. syringae PBs may be a non-viable biotic-based strategy for protecting fish myofibrillar proteins from freeze-thaw-induced damage.

Cryoablation, which induces rapid intracellular ice crystal formation, has been widely used in clinics for treating various tumors, yet monotherapy yields limited efficacy due to inadequate elimination of tumor cells. Here, we proposed an effective synergistic strategy with intelligent biomaterials to overcome the limitation of conventional cryo-thermal therapy that requires two separate devices, integrating cryo-thermal ablation, mechanical destruction, and drug release to improve therapeutic efficacy. A sodium alginate (SA) modified iron-containing liquid metal microdroplet (FLMM@DOX@SA) was fabricated with diverse intelligent merits under stimulation. Under cooling, FLMM@SA would go through a multi-phase transition process and present a unique "bomb-explosion-like" behavior, leading to fierce mechanical destruction (more than 6.3 MPa) to surrounding ice crystals. Then, FLMM@SA was demonstrated as a powerful magnetocaloric agent when subject to an alternating magnetic field. In addition, this intelligent biomaterial exhibited stimulus-enhanced drug release across multiple cues, including cryo-stimulation, magnetothermal activation, and pH changes, thereby driving synergistic antitumor efficacy with the highest fraction of necrotic cells. The mechano-thermal-chemo-freezing synergistic therapy further verified the effective destructive performance with robust tumor growth suppression and a 100% animal survival rate. Collectively, this work highlights the integration of intelligent biomaterials into cryoablation, thereby forging a novel modality for highly effective combination therapy.