Hasil untuk "math-ph"

Arkil Patel, S. Bhattamishra, Navin Goyal

The problem of designing NLP solvers for math word problems (MWP) has seen sustained research activity and steady gains in the test accuracy. Since existing solvers achieve high performance on the benchmark datasets for elementary level MWPs containing one-unknown arithmetic word problems, such problems are often considered “solved” with the bulk of research attention moving to more complex MWPs. In this paper, we restrict our attention to English MWPs taught in grades four and lower. We provide strong evidence that the existing MWP solvers rely on shallow heuristics to achieve high performance on the benchmark datasets. To this end, we show that MWP solvers that do not have access to the question asked in the MWP can still solve a large fraction of MWPs. Similarly, models that treat MWPs as bag-of-words can also achieve surprisingly high accuracy. Further, we introduce a challenge dataset, SVAMP, created by applying carefully chosen variations over examples sampled from existing datasets. The best accuracy achieved by state-of-the-art models is substantially lower on SVAMP, thus showing that much remains to be done even for the simplest of the MWPs.

Shikha Verma

A former Wall Street quant sounds an alarm on the mathematical models that pervade modern life and threaten to rip apart our social fabricWe live in the age of the algorithm. Increasingly, the decisions that affect our liveswhere we go to school, whether we get a car loan, how much we pay for health insuranceare being made not by humans, but by mathematical models. In theory, this should lead to greater fairness: Everyone is judged according to the same rules, and bias is eliminated. But as Cathy ONeil reveals in this urgent and necessary book, the opposite is true. The models being used today are opaque, unregulated, and uncontestable, even when theyre wrong. Most troubling, they reinforce discrimination: If a poor student cant get a loan because a lending model deems him too risky (by virtue of his zip code), hes then cut off from the kind of education that could pull him out of poverty, and a vicious spiral ensues. Models are propping up the lucky and punishing the downtrodden, creating a toxic cocktail for democracy. Welcome to the dark side of Big Data. Tracing the arc of a persons life, ONeil exposes the black box models that shape our future, both as individuals and as a society. These weapons of math destruction score teachers and students, sort rsums, grant (or deny) loans, evaluate workers, target voters, set parole, and monitor our health. ONeil calls on modelers to take more responsibility for their algorithms and on policy makers to regulate their use. But in the end, its up to us to become more savvy about the models that govern our lives. This important book empowers us to ask the tough questions, uncover the truth, and demand change.

Aida Amini, Saadia Gabriel, Shanchuan Lin et al.

We introduce a large-scale dataset of math word problems and an interpretable neural math problem solver by learning to map problems to their operation programs. Due to annotation challenges, current datasets in this domain have been either relatively small in scale or did not offer precise operational annotations over diverse problem types. We introduce a new representation language to model operation programs corresponding to each math problem that aim to improve both the performance and the interpretability of the learned models. Using this representation language, we significantly enhance the AQUA-RAT dataset with fully-specified operational programs. We additionally introduce a neural sequence-to-program model with automatic problem categorization. Our experiments show improvements over competitive baselines in our dataset as well as the AQUA-RAT dataset. The results are still lower than human performance indicating that the dataset poses new challenges for future research. Our dataset is available at https://math-qa.github.io/math-QA/

Xiang Yue, Xingwei Qu, Ge Zhang et al.

We introduce MAmmoTH, a series of open-source large language models (LLMs) specifically tailored for general math problem-solving. The MAmmoTH models are trained on MathInstruct, our meticulously curated instruction tuning dataset. MathInstruct is compiled from 13 math datasets with intermediate rationales, six of which have rationales newly curated by us. It presents a unique hybrid of chain-of-thought (CoT) and program-of-thought (PoT) rationales, and also ensures extensive coverage of diverse fields in math. The hybrid of CoT and PoT not only unleashes the potential of tool use but also allows different thought processes for different math problems. As a result, the MAmmoTH series substantially outperform existing open-source models on nine mathematical reasoning datasets across all scales with an average accuracy gain between 16% and 32%. Remarkably, our MAmmoTH-7B model reaches 33% on MATH (a competition-level dataset), which exceeds the best open-source 7B model (WizardMath) by 23%, and the MAmmoTH-34B model achieves 44% accuracy on MATH, even surpassing GPT-4's CoT result. Our work underscores the importance of diverse problem coverage and the use of hybrid rationales in developing superior math generalist models.

Shen-Yun Miao, Chao-Chun Liang, Keh-Yih Su

We present ASDiv (Academia Sinica Diverse MWP Dataset), a diverse (in terms of both language patterns and problem types) English math word problem (MWP) corpus for evaluating the capability of various MWP solvers. Existing MWP corpora for studying AI progress remain limited either in language usage patterns or in problem types. We thus present a new English MWP corpus with 2,305 MWPs that cover more text patterns and most problem types taught in elementary school. Each MWP is annotated with its problem type and grade level (for indicating the level of difficulty). Furthermore, we propose a metric to measure the lexicon usage diversity of a given MWP corpus, and demonstrate that ASDiv is more diverse than existing corpora. Experiments show that our proposed corpus reflects the true capability of MWP solvers more faithfully.

E. Makarova, Belinda Aeschlimann, W. Herzog

Studies have repeatedly reported that math and science are perceived as male domains, and scientists as predominantly male. However, the impact of the gender image of school science subjects on young people’s career choice has not yet been analyzed. This paper investigates the impact of the masculinity image of three school subjects – chemistry, mathematics and physics – on secondary students’ career aspirations in STEM fields. The data originated from a cross-sectional study among 1’364 Swiss secondary school students who were close to obtaining their matriculation diploma. By means of a standardized survey, data on students’ perception of masculinity of science school subjects were collected using semantic differentials. The results indicate that for both sexes, math has the strongest masculinity attribution, followed by physics as second, and, finally, chemistry with the lowest masculinity attribution. With respect to gender differences, our findings have shown that among female students, the attribution of masculinity to the three school subjects does not differ significantly, meaning that female students rated all subjects similarly strongly as masculine. Within the group of male students however, the attribution of masculinity to math compared to chemistry and physics differs significantly, whereas the attribution of masculinity to chemistry and physics does not. Our findings also suggest that gender-science stereotypes of math and science can potentially influence young women’s and men’s aspirations to enroll in a STEM major at university by showing that a less pronounced masculine image of science has the potential to increase the likelihood of STEM career aspirations. Finally, the paper discusses ways of changing the image of math and science in the context of secondary education in order to overcome the disparities between females and males in STEM.

Gerardo Ramirez, S. Shaw, Erin A. Maloney

Joy He-Yueya, Gabriel Poesia, Rose E. Wang et al.

Automatically generating high-quality step-by-step solutions to math word problems has many applications in education. Recently, combining large language models (LLMs) with external tools to perform complex reasoning and calculation has emerged as a promising direction for solving math word problems, but prior approaches such as Program-Aided Language model (PAL) are biased towards simple procedural problems and less effective for problems that require declarative reasoning. We propose an approach that combines an LLM that can incrementally formalize word problems as a set of variables and equations with an external symbolic solver that can solve the equations. Our approach achieves comparable accuracy to the original PAL on the GSM8K benchmark of math word problems and outperforms PAL by an absolute 20% on ALGEBRA, a new dataset of more challenging word problems extracted from Algebra textbooks. Our work highlights the benefits of using declarative and incremental representations when interfacing with an external tool for solving complex math word problems. Our data and prompts are publicly available at https://github.com/joyheyueya/declarative-math-word-problem.

Jing Zhang, Nan Zhao, Qiping Kong

Math anxiety (MA) has been suggested to decrease the math performance of students. However, it remains unclear what factors moderate this relationship. The aim of this research was to explore the link between MA and math performance. Studies that explored the math anxiety-performance link, conducted from 2000 to 2019 (84 samples, N = 8680), were identified and statistically integrated with a meta-analysis method. The results indicated a robust negative math anxiety-performance link. Furthermore, regarding the analysis of moderator variables, this negative link was stronger in the studies that involved Asian students, but this link was the weakest in the studies that involved European students. Moreover, this negative link was stronger in the studies within a senior high school group, whereas it was the weakest in the studies within an elementary group. Finally, this negative link was strongest among studies that used a custom test and studies that assessed problem-solving skills. Potential explanations and implications for research and practice are discussed.

Zhipeng Xie, Shichao Sun

Most existing neural models for math word problems exploit Seq2Seq model to generate solution expressions sequentially from left to right, whose results are far from satisfactory due to the lack of goal-driven mechanism commonly seen in human problem solving. This paper proposes a tree-structured neural model to generate expression tree in a goal-driven manner. Given a math word problem, the model first identifies and encodes its goal to achieve, and then the goal gets decomposed into sub-goals combined by an operator in a top-down recursive way. The whole process is repeated until the goal is simple enough to be realized by a known quantity as leaf node. During the process, two-layer gated-feedforward networks are designed to implement each step of goal decomposition, and a recursive neural network is used to encode fulfilled subtrees into subtree embeddings, which provides a better representation of subtrees than the simple goals of subtrees. Experimental results on the dataset Math23K have shown that our tree-structured model outperforms significantly several state-of-the-art models.

M. Daucourt, Amy R. Napoli, Jamie M. Quinn et al.

Mathematical thinking is in high demand in the global market, but approximately 6 percent of school-age children across the globe experience math difficulties (Shalev et al., 2000). The home math environment (HME), which includes all math-related activities, attitudes, beliefs, expectations, and utterances in the home, may be associated with children's math development. To examine the relation between the HME and children's math abilities, a preregistered meta-analysis was conducted to estimate the average weighted correlation coefficient (r) between the HME and children's math achievement and how potential moderators (i.e., assessment, study, and sample features) might contribute to study heterogeneity. A multilevel correlated effects model using 631 effect sizes from 64 quantitative studies comprising 68 independent samples found a positive, statistically significant average weighted correlation of r = .13 (SE = .02, p < .001). Our combined sensitivity analyses showed that the present findings were robust and that the sample of studies has evidential value. A number of assessment, study, and sample characteristics contributed to study heterogeneity, showing that no single feature of HME research was driving the large between-study differences found for the association between the HME and children's math achievement. These findings indicate that children's environments and interactions related to their learning are supported in the specific context of math learning. Our results also show that the HME represents a setting in which children learn about math through social interactions with their caregivers (Vygotsky, 1978) and what they learn depends on the influence of many levels of environmental input (Bronfenbrenner, 1979) and the specificity of input children receive (Bornstein, 2002). (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Adam Dahlgren Lindström, Savitha Sam Abraham

We introduce CLEVR-Math, a multi-modal math word problems dataset consisting of simple math word problems involving addition/subtraction, represented partly by a textual description and partly by an image illustrating the scenario. The text describes actions performed on the scene that is depicted in the image. Since the question posed may not be about the scene in the image, but about the state of the scene before or after the actions are applied, the solver envision or imagine the state changes due to these actions. Solving these word problems requires a combination of language, visual and mathematical reasoning. We apply state-of-the-art neural and neuro-symbolic models for visual question answering on CLEVR-Math and empirically evaluate their performances. Our results show how neither method generalise to chains of operations. We discuss the limitations of the two in addressing the task of multi-modal word problem solving.

Yu-ching Chen

Motivation and math anxiety are crucial in performance and satisfaction, and augmented reality (AR) may be a useful tool in enhancing these factors because it provides users with interesting visual experiences. Since related empirical research is limited in investigating the effects of using free mobile AR apps integrating Keller’s ARCS (attention-relevance-confidence-satisfaction) motivation model on learning motivation, anxiety, and outcomes between students with different levels of anxiety in primary math education, this study investigated whether mobile AR differently affected learning, motivation, and math anxiety between students with high and low anxiety. The results showed that the AR group performed better than the non-AR group, and high-anxiety learners in the AR group outperformed in algebra and geometry. The AR group had higher motivation based on Keller’s ARCS model. The high-anxiety learners had higher confidence and satisfaction and lower anxiety when learning using mobile AR. The AR users were satisfied with ease of use, usefulness, playfulness, and benefit from exploration and hands-on experiences. Moreover, high-anxiety users in the AR group had higher perceptions of exploration, hands-on experiences, and playfulness. This study includes the participants’ experience in adopting mobile AR for their learning and discusses its constraints.

V. L. D. L. Melo, T. L. A. C. D. Araújo, P. D. O. Lima et al.

<p>The antibacterial, antifungal, and anti-inflammatory properties of refined wood vinegar make it a promising product for ruminant nutrition. This study aimed to evaluate the effect of increasing oral doses (0, 10, 20, 30, and 40 mL d<span class="inline-formula">⁻¹</span>) of wood vinegar (WV) on the intake, apparent digestibility, ingestive behavior, water balance, ruminal parameters, serum biochemistry, nitrogen balance, and physiology of sheep fed with high levels of concentrate. We used five castrated male sheep, <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M2" display="inline" overflow="scroll" dspmath="mathml"><mrow><mn mathvariant="normal">1</mn><mo>/</mo><mn mathvariant="normal">2</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="20pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="31e2b84ce41f6d9f34e4e2702e1af4f3"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="aab-68-619-2025-ie00001.svg" width="20pt" height="14pt" src="aab-68-619-2025-ie00001.png"/></svg:svg></span></span> Dorper <span class="inline-formula">×</span> <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M4" display="inline" overflow="scroll" dspmath="mathml"><mrow><mn mathvariant="normal">1</mn><mo>/</mo><mn mathvariant="normal">2</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="20pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="3c8990878d180267826a36f4c2b239d2"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="aab-68-619-2025-ie00002.svg" width="20pt" height="14pt" src="aab-68-619-2025-ie00002.png"/></svg:svg></span></span> Santa Inês, with an average age of 36 months and an average weight of <span class="inline-formula">59.34±5.73</span> kg, in a Latin-square design. The animals were provided a total mixed ration formulated at a roughage-to-concentrate ratio of <span class="inline-formula">20:80</span>, which was offered twice daily following the delivery of half the daily dose of WV. There was no effect (<span class="inline-formula"><i>P</i>&gt;0.05</span>) of WV on dry-matter intake. Increasing WV levels linearly increased (<span class="inline-formula"><i>P</i>&lt;0.05</span>) the neutral-detergent fiber intake and apparent digestibility of crude protein in the sheep's diet. Feeding time was increased (<span class="inline-formula"><i>P</i>&lt;0.05</span>) by increasing the supply of WV to the sheep; pH values decreased (<span class="inline-formula"><i>P</i>&lt;0.05</span>), and ruminal ammonia nitrogen increased (<span class="inline-formula"><i>P</i>&lt;0.05</span>) with an increasing dose of WV. The increase in the WV supplied did not influence the water absorbed and nitrogen retained by the lambs (<span class="inline-formula"><i>P</i>&gt;0.05</span>). The supply of WV to lambs altered the concentrations of total protein, globulin, urea, and gamma-glutamyltransferase (<span class="inline-formula"><i>P</i>&lt;0.05</span>). It may be advisable to offer up to 40 mL d<span class="inline-formula">⁻¹</span> of WV to sheep fed high-concentrate diets.</p>

Cláudia Ferreira, Fiona Barry, Miomir Todorović et al.

This study aims to develop and validate a novel fast-detection electrochemical sensing platform to enhance portable electrochemical sensor solutions. The research focuses on optimising analogue front-end circuits, developing data analysis algorithms, and validating the device through experiments to enhance measurement accuracy and detection speed, enabling on-site measurements across diverse applications. This work successfully designed a Portable Unit for Lab-on-Site Electrochemistry (PULSE) system with dimensions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>78</mn><mo>×</mo><mn>100</mn><mo>×</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula> <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>mm</mi><mn>3</mn></msup></semantics></math></inline-formula>. The device’s implementation was complemented by robust firmware that performed desired electrochemical measurements, including open circuit potentiometry (OCP), chronoamperometry (CA), and cyclic voltammetry (CV). To assess its reliability, the PULSE was benchmarked against a well-established benchtop potentiostat. The results obtained highlight the system’s rapid sensing capabilities, achieving pH detection in 2 s and performing CA in 20 s. The pH calibration curve exhibited Nernstian behaviour with an accuracy of 97.58%. A correlation analysis comparing the calibration curve datasets across all electrochemical techniques from both systems revealed high correlation coefficients (>0.99), confirming the strong agreement between the two systems.

A. Cromartie, C. De Jonge, G. Ménot et al.

<p>Branched glycerol dialkyl glycerol tetraethers (brGDGTs) are critical molecular biomarkers for the quantitative reconstruction of past environments, ambient temperature, and pH across various archives. However, numerous issues persist that limit their application. The distribution of brGDGTs varies significantly based on provenance, resulting in biases in environmental reconstructions that rely on fractional abundances and derived indices, such as MBT<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi/><mrow><mn mathvariant="normal">5</mn><mi mathvariant="normal">ME</mi></mrow><mo>′</mo></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="19pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="44319adb42b61fed78d465fbd8084fb4"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="bg-22-7687-2025-ie00001.svg" width="19pt" height="15pt" src="bg-22-7687-2025-ie00001.png"/></svg:svg></span></span>. This issue is especially significant in shallow lakes, wetlands, and peatlands, where ecosystems are sensitive to diverse environmental and climatic factors. Recent advancements, such as machine learning techniques, have been developed to identify changes in provenance; however, these techniques are insufficient for detecting mixed environments. The probability estimates derived from five machine learning algorithms are employed here to detect provenance changes in brGDGT downcore records and to identify periods of mixed provenance. A new global modern database (<span class="inline-formula"><i>n</i>=2031</span>) was compiled to train, validate, test, and apply these algorithms to two sedimentary records. Our findings are corroborated by pollen, non-pollen palynomorphs, and X-ray fluorescence (XRF) obtained from the same sedimentary core sequence. These microfossil and geochemical proxies are utilized to discuss changes in provenance, hydrology, and ecology that influence brGDGT provenance. Probability estimates derived from random forest with a sigmoid calibration are most effective in detecting changes in brGDGT provenance. Minor changes in the relative contributions of brGDGT provenance can significantly influence the distribution of brGDGT, especially regarding the MBT<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M3" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi/><mrow><mn mathvariant="normal">5</mn><mi mathvariant="normal">ME</mi></mrow><mo>′</mo></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="19pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="69a3f4f20c51bb988be2dcfc66f76c5a"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="bg-22-7687-2025-ie00002.svg" width="19pt" height="15pt" src="bg-22-7687-2025-ie00002.png"/></svg:svg></span></span> index.</p>

Jue Zhang, Guangxin Xu, Zhiwei Yi et al.

Keratin is a fibrous structural protein found in various natural materials such as hair, feathers, and nails. Its high stability and cross-linked structure make it resistant to degradation by common proteases, leading to the accumulation of keratinous waste in various industries. In this study, we developed and validated an effective bioinformatics-driven strategy for mining novel keratinase genes from the Esmatlas (ESM Metagenomic Atlas) macrogenomic database. Two candidate genes, <i>ker820</i> and <i>ker907</i>, were identified through sequence alignment, structural modeling, and phylogenetic analysis, and were subsequently heterologously expressed in <i>Escherichia coli</i> Rosetta (DE3) with the assistance of a solubility-enhancing chaperone system. Both enzymes belong to the Peptidase S8 family. Enzymatic characterization revealed that GST-tagged ker820 and ker907 exhibited strong keratinolytic activity, with optimal conditions at pH 9.0 and temperatures of 60 °C and 50 °C, respectively. Both enzymes showed significant degradation of feather and cat-hair keratin. Kinetic analysis showed favorable catalytic parameters, including <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mi>m</mi></msub></semantics></math></inline-formula> values of 9.81 mg/mL (ker820) and 5.25 mg/mL (ker907), and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>V</mi><mo movablelimits="true" form="prefix">max</mo></msub></semantics></math></inline-formula> values of 120.99 U/mg (ker820) and 89.52 U/mg (ker907). Stability tests indicated that GST-ker820 retained 70% activity at 60 °C for 120 min, while both enzymes remained stable at 4 °C for up to 10 days. These results demonstrate the high catalytic capacity, thermal stability, and substrate specificity of the enzymes, supporting their classification as active keratinases. This study introduces a promising strategy for efficiently discovering novel functional enzymes using an integrated computational and experimental approach. Beyond keratinases, this methodology could be extended to screen for enzymes with potential applications in environmental remediation.

Natalia Levashova, Pavel Levashov, Dmitry Erofeev et al.

In the context of the current global transition toward low-carbon energy, the issue of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><msub><mi>O</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> utilization has become increasingly important. One of the most promising natural targets for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><msub><mi>O</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> sequestration is the terrigenous sedimentary formations found in oil, gas, and coal basins. It is generally assumed that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><msub><mi>O</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> injected into such formations can be stored indefinitely in a stable form. However, the dissolution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><msub><mi>O</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> into subsurface water leads to a reduction in pH, which may cause partial dissolution of the host formation, altering the structure of the subsurface in the injection zone. This process is relatively slow, potentially unfolding over decades or even centuries, and its long-term consequences require careful investigation through mathematical modeling. The geological formation is treated as a partially soluble porous medium, where the dissolution rate is governed by surface chemical reactions occurring at the pore boundaries. In this study, we present an applied mathematical model that captures the coupled processes of mass transport, surface chemical reactions, and the resulting microscopic changes in the pore structure of the formation. To ensure the model remains grounded in realistic geological conditions, we based it on exploration data characterizing the composition and microstructure of the pore space typical of the Cenomanian suite in northern Western Siberia. The model incorporates the dominant geochemical reactions involving calcium carbonate (calcite, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><mi>a</mi><mi>C</mi><msub><mi>O</mi><mn>3</mn></msub></mrow></semantics></math></inline-formula>), characteristic of Cenomanian reservoir rocks. It describes the dissolution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><msub><mi>O</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> in the pore fluid and the associated evolution of ion concentrations, specifically <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>H</mi><mo>+</mo></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><msup><mi>a</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mi>C</mi><msubsup><mi>O</mi><mn>3</mn><mo>−</mo></msubsup></mrow></semantics></math></inline-formula>. The input parameters are derived from experimental data. While the model focuses on calcite-based formations, the algorithm can be adapted to other mineralogies with appropriate modifications to the reaction terms. The simulation domain is defined as a cubic region with a side length of 1 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">μ</mi></semantics></math></inline-formula>m, representing a fragment of the geological formation with a porosity of 0.33. The pore space is initially filled with a mixture of liquid <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><msub><mi>O</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> and water at known saturation levels. The mathematical framework consists of a system of diffusion–reaction equations describing the dissolution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><msub><mi>O</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> in water and the subsequent mineral dissolution, coupled with a model for surface evolution of the solid phase. This model enables calculation of surface reaction rates within the porous medium and estimates the timescales over which significant changes in pore structure may occur, depending on the relative saturations of water and liquid <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><msub><mi>O</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula>.

M. Casetta, S. Philippe, L. Courcot et al.

<p>In urban and industrialized areas, soil contamination and degradation caused by industrial dust deposition may pose significant health and environmental risks. Generally, the mobility and thus bioavailability of potentially toxic elements (PTEs) are key factors in these issues. In the Dunkerque agglomeration, one of the most industrialized regions in France, the soils are periodically exposed to metallurgical dust fallout, rich in PTEs. However, no study has reported on the behavior of these PTEs once integrated into the soils. The aim of this study is therefore to assess the fate of PTEs in the urban soils of Dunkerque in terms of vertical migration and potential bioavailability.</p> <p>Four soil short cores were collected in the city of Gravelines (Dunkerque agglomeration) along a gradient from industrial emitters to deposition sites. Each soil core was cut into discrete 1 cm sections for PTE concentration analyses (ICP-AES/MS). Single HCl extractions were performed to evaluate PTE mobility in soils and their behavior according to the current soil parameters. For this purpose, key soil properties were identified, including grain-size distribution, mineralogy, pH, cation exchange capacity (CEC), TOC (total organic carbon), calcium carbonates and water contents in addition to the soil chemical composition (XRF, ICP-AES/MS).</p> <p>The studied soils revealed globally low absorbent capacities for pollutants (CEC averaging <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1" display="inline" overflow="scroll" dspmath="mathml"><mrow><mn mathvariant="normal">5.3</mn><mspace width="0.125em" linebreak="nobreak"/><mrow class="unit"><mi mathvariant="normal">meq</mi></mrow><mo>/</mo><mn mathvariant="normal">100</mn><mspace width="0.125em" linebreak="nobreak"/><mrow class="unit"><mi mathvariant="normal">g</mi></mrow></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="72pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="ef58d05657810ef851f83467cbb5a845"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="soil-11-467-2025-ie00001.svg" width="72pt" height="14pt" src="soil-11-467-2025-ie00001.png"/></svg:svg></span></span>), partially counterbalanced by the buffering effect of calcium carbonates (contents ranging from 8 %–30 %). Near the industrial emitters, minor (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M2" display="inline" overflow="scroll" dspmath="mathml"><mrow><mn mathvariant="normal">1</mn><mo>&lt;</mo><mtext>EF</mtext><mo>&lt;</mo><mn mathvariant="normal">3</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="53pt" height="10pt" class="svg-formula" dspmath="mathimg" md5hash="44920e9be68d7e11b3400a053e6246ca"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="soil-11-467-2025-ie00002.svg" width="53pt" height="10pt" src="soil-11-467-2025-ie00002.png"/></svg:svg></span></span>) to moderately severe (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M3" display="inline" overflow="scroll" dspmath="mathml"><mrow><mn mathvariant="normal">5</mn><mo>&lt;</mo><mtext>EF</mtext><mo>&lt;</mo><mn mathvariant="normal">10</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="59pt" height="10pt" class="svg-formula" dspmath="mathimg" md5hash="27348bad55eabbcb44c65cd7a960ed7b"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="soil-11-467-2025-ie00003.svg" width="59pt" height="10pt" src="soil-11-467-2025-ie00003.png"/></svg:svg></span></span>) enrichment factors (EFs) were highlighted for industrial PTE (Cr, Ni, Mo, Mn, Cd and Zn) in the top 3 cm of soils near the industrial emitters. The contamination profiles of these soils are assigned to atmospheric inputs of metallurgical dust. Using a relatively strong leaching reagent (1 <span class="inline-formula">M</span> HCl), we estimated a low vertical mobility for Cr, Ni and Mo (average leached <span class="inline-formula">ratios&lt;25 <i>%</i></span>) in soils, suggesting their association with refractory phases (natural or anthropogenic). In contrast, Mn, Cd and Zn, which are related to industrial and/or urban sources, present a higher mobility (average leached <span class="inline-formula">ratios&gt;60 <i>%</i></span> for Mn and Cd and about 44 % for Zn).</p> <p>Our study points out the stability of industrial PTEs in soils under the current physicochemical conditions (calcareous soils with a slightly basic pH of 7.8). In this context, the monitoring of industrial PTEs in these urban soils is highly recommended, considering (1) the presence of allotment gardens in the vicinity of emitters and (2) the potential evolution of soil conditions due to increasing flood events.</p>

X. Duan, X. Duan, G. Zheng et al.

<p>Aerosol acidity (or pH) plays a crucial role in atmospheric chemistry, influencing the interaction of air pollutants with ecosystems and climate. Aerosol pH shows large temporal variations, while the driving factors of chemical profiles versus meteorological conditions are not fully understood due to their intrinsic complexity. Here, we propose a new framework to quantify factor importance, which incorporated an interpretive structural modeling (ISM) approach and time series analysis. In particular, a hierarchical influencing factor relationship is established based on the multiphase buffer theory with ISM. A long-term (2018–2023) observation dataset in Changzhou, China, is analyzed with this framework. We found the pH temporal variation is dominated by the seasonal and random variations, while the long-term pH trend varies little despite the large emission changes. This is an overall effect of decreasing <span class="inline-formula">PM_2.5</span>, increasing temperature and increased alkali-to-acid ratios. Temperature is the controlling factor of pH seasonal variations, through influencing the multiphase effective acid dissociation constant <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M2" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi>K</mi><mi mathvariant="normal">a</mi><mo>∗</mo></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="15pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="709dd69d0c1f0cca492ff1fd1e71ad09"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-25-3919-2025-ie00001.svg" width="15pt" height="14pt" src="acp-25-3919-2025-ie00001.png"/></svg:svg></span></span>, non-ideality <span class="inline-formula"><i>c</i>_ni</span> and gas–particle partitioning. Random variations are dominated by the aerosol water contents through <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M4" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi>K</mi><mi mathvariant="normal">a</mi><mo>∗</mo></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="15pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="7760512a7270fa80c4540f5cfaf2978e"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-25-3919-2025-ie00002.svg" width="15pt" height="14pt" src="acp-25-3919-2025-ie00002.png"/></svg:svg></span></span> and chemical profiles through <span class="inline-formula"><i>c</i>_ni</span>. This framework provides quantitative understanding of the driving factors of aerosol acidity at different levels, which is important in acidity-related process studies and policy-making.</p>