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Traditional signal processing and machine learning methods rely on mean square error, which becomes brittle when data contains heavy-tailed noise, impulsive disturbances, and outliers—conditions frequently encountered in real-world applications. This comprehensive guidebook introduces correntropy-based methods that demonstrate superior robustness across diverse engineering domains, progressing from foundational concepts to applications. Authored by pioneers in information theoretic learning, the book systematically covers correntropy fundamentals, adaptive filtering techniques, neural network training, feature learning, and applications including point set registration, matrix completion, and federated learning. Each chapter balances rigorous theory with practical algorithms and performance comparisons against conventional methods. With implementation guidelines and a unified framework connecting different robust learning criteria, this book addresses the critical gap between Gaussian-assumption theory and non-Gaussian reality, providing researchers and graduate students with applicable solutions for challenging real-world problems.
The concept of communicative competence has been rendered as context-abstracted code-bound knowledge for language teaching and assessment. This Element offers a different perspective on 'communication' and 'competence'. Section 1 offers the rationale for this re-orientation. Section 2 examines the conceptual and pedagogic affordances and delimitations of the prevailing approach to communicative competence; Section 3 describes a conceptual re-framing of language use as ecological languaging in terms of embodied, situation-sensitive action through which people coordinate with others, artefacts, and environments; Section 4 explores assessment approaches built on Bayesian principles for tracking learner development and progress by taking account of prior accomplishment, expert opinion, and emerging performance to create probabilistic trajectories; Section 5 focusses on professional developments related to conceptual refinement, curriculum design, teaching materials, and teacher education. Section 6 considers some key future challenges. This Element is also available as Open Access on Cambridge Core.
Neonates are highly susceptible to infection, a major cause of neonatal death, given their immature immune system. Comprehensive studies examining multiple immune-response-related proteins in relation to neonatal infection are scarce. We conducted a nested case-control study within the Shenzhen Baoan Birth and Twin (SZBBTwin) cohort, measuring 92 immune-response-related proteins in cord plasma of 149 twins (including 34 discordant twin pairs) with proximity extension assay. All twins were followed for clinical diagnoses of infection from birth until 27 days of age. Wilcoxon rank-sum test was used to determine differentially abundant proteins (DAPs) between infected and noninfected neonates, the predictive performance of which was evaluated by receiver operating characteristic curves, and their functions and pathways were annotated through enrichment analysis. Logistic regression was used to assess the associations between levels of proteins and risk of neonatal infection. Finally, five DAPs (ITGA11, FCRL6, DDX58, SH2D1A, and EDAR) were identified for neonatal infection, and the area under the curve of the five DAPs achieved 0.835 for infection prediction. Enrichment analysis indicated that five DAPs were mainly involved in immune function and cell binding, and they were mainly enriched in the nuclear factor kappa-B pathway. A higher level of ITGA11 was associated with an increased risk of neonatal infection in all twins (OR 3.00; 95% CI [1.33, 6.78]) and discordant twin pairs (OR 5.50; 95% CI [1.20, 25.23]). In conclusion, multiple immune-response-related proteins in cord plasma, particularly ITGA11, are associated with the risk of neonatal infection in twins.
It is well established that cytochrome P450 monooxygenases (P450s) play a crucial role in herbicide metabolism and resistance evolution in weeds. In most documented cases, P450-mediated resistance is primarily conferred through the overexpression of P450 enzymes. However, the regulatory mechanisms underlying this overexpression remain poorly understood. In insects, amino acid substitutions that enhance P450-mediated metabolic detoxification have been clearly demonstrated as a key mechanism of insecticide resistance. In contrast, their potential role in herbicide resistance in weeds remains unclear. In this study, two CYP96A146 variants from flixweed [Descurainia sophia (L.) Webb ex Prantl], designated CYP96A146-S and CYP96A146-R, were heterologously expressed in Saccharomyces cerevisiae. These variants, which differ by four amino acid residues, were examined for their ability to metabolize model substrates and herbicides. The results indicated that both variants exhibited catalytic activity toward model substrates of p-nitroanisole, methoxyresorufin, ethoxyresorufin, 7-ethoxycoumarin, and benzo[a]pyrene, as well as toward the herbicides tribenuron-methyl, bensulfuron-methyl, and carfentrazone-ethyl. Notably, CYP96A146-R showed significantly higher catalytic activity than CYP96A146-S to both the model substrates (p-nitroanisole, methoxyresorufin, ethoxyresorufin, and 7-ethoxycoumarin) and the herbicides (tribenuron-methyl and carfentrazone-ethyl). These findings suggest that the amino acid substitutions are likely responsible for the enhanced metabolic capability of CYP96A146-R. Such mutations may induce conformational changes of CYP96A146 enzyme, facilitating more frequent molecular collisions between CYP96A146 and the substrates or herbicides, thereby improving catalytic efficiency.
Human milk oligosaccharides (HMOs) are the third most abundant biomolecules in breast milk, with over 200 structural variants, mainly fucosylated, sialylated, and neutral core types. Key HMOs include 2′-fucosyllactose (2′-FL), and 3′/6′-sialyllactose (3′/6′-SL), which enhance brain development in animal models(1). Lactoferrin (Lf), a sialylated glycoprotein, also supports neurodevelopment by promoting neurogenesis and reducing neuroinflammation(2). However, the combined effects of HMOs and Lf on brain metabolism remain unknown. We therefore investigated their synergy on brain metabolites and neurotransmitters in neonatal piglets using in vivo ¹H-MRS. Three-day-old male domestic piglets (Sus scrofa – Large White × Duroc × Belgian Landrace) were randomly assigned to one of three groups and fed a standard pig milk replacer with the following supplements: control (methyl cellulose at 1.8 g/L; n = 14), combined HMOs (70% 2′-FL and 30% 3′-SL:6′-SL in a 1:2.5 ratio at 1.8 g/L; n = 16), or cHMOs + Lf (cHMOs at 1.8 g/L + lactoferrin at 0.5 g/L; n = 14). In vivo ¹H-MRS was performed on postnatal day 38/39 using a 3T scanner (TE = 30 ms) to assess regional brain metabolite profiles. The research protocol was approved by the ACECs of Charles Sturt University (A23566) and Monash University (38776). Our results demonstrated that the group received combined HMOs and Lf exhibited significantly higher absolute levels of total lipids and macromolecules, along with increased relative concentrations of glutathione (Glth), total creatine (TCr), total choline (TCh), and total lipids and macromolecules at 2.0 ppm (TLM20) (p < 0.05). In contrast, the cHMOs group were observed to have significantly increased levels of absolute total N-acetylaspartate (TNAA) (p < 0.05). Collectively, these findings suggest that combined HMOs and lactoferrin supplementation may synergistically support neurodevelopment by enhancing lipid mobilization, energy metabolism, and antioxidant capacity, while cHMOs alone promotes brain development by improving neuronal integrity and synaptic activity in piglets—a translational model for human infants. To our knowledge, these findings have not been previously reported.
Human milk oligosaccharides (HMOs) are the third most abundant carbohydrates in human milk after lactose and lipids(1). While HMOs are known for various health benefits, their effects on cognitive function and brain development remain debated. This study investigates whether individual or combined supplementation of HMOs improves cognitive behaviours and stress responses in piglets, an ideal animal model for human infants. Sixty-four domestic male piglets, 3 days old, were randomly assigned to 1 of 4 groups and received pig milk replacer supplemented with different HMOs from postnatal day (PND) 3 to 38. Treatment groups included: Group 1: 2′-Fucosyllactose (2′-FL, 1.8 g/L; n = 14); Group 2: 3′/6′-Sialyllactose (3′/6′-SL in a 1:2.5 ratio, 1.8 g/L, n = 16); Group 3: combined HMOs (cHMOs, 70% 2′-FL and 30% 3’/6’-SL in a 1:2.5 ratio, at 1.8 g/L, n = 16), and Control (methyl cellulose, 1.8 g/L; n = 14). Cognitive performances were assessed using our published 8-arm radial maze(2), incorporating easy task (PND 23–27) and difficult task (PND 29–33) visual cues. Stress responses were assessed by measuring serum cortisol concentrations via ELISA. All data were analysed using SPSS (SPSS Inc., Chicago, IL) with significance set at *p < 0.05. The research protocol was approved by the ACECs of Charles Sturt University (A23566). Results showed that on the third day of behaviour testing, piglets in the cHMO group made significantly fewer total mistakes than the controls in the easy task (p < 0.05), whereas the 2′-FL group exhibited significantly fewer total mistakes in the difficult task (p < 0.05). Serum cortisol levels were not significantly different between the groups (p > 0.05). The findings suggest that HMOs supplementation may enhance cognitive function under both challenging and non-challenging conditions without affecting physiological stress markers, highlighting their potential role in supporting brain development during early life.
As drones and unmanned aerial vehicles (UAVs) are used in different scenarios, a variety of potential risks and safety challenges have arisen. One of the threats is that an increasing number of UAV encounter events are found near the airport in recent years, which pose significant dangers to manned aircraft and result in accidents. However, only a few studies examine the impacts of these events and propose effective countermeasures to enhance safety. To unveil the risks of UAV risk events (incidents or accidents) and examine the mechanism with risk factors, this study uses a tree-augmented naive Bayes network (TAN-BN). This method analyses the relationships among risk factors and UAV accidents/incidents to assess the efficacy of risk mitigation measures. Environmental, technological and human factors are simultaneously considered in constructing the Bayesian network. The analysis results reveal 12 specific risk factors that are significantly associated with UAV accidents/incidents in UAV operation scenarios, among which flight control system failure (the most critical factor), remote communication failure, other aircraft approaching, loss of electrical power, adverse weather, electromagnetic interference, operational errors, violations and risk factors leading to loss-of-control in flight are recognised as the most prominent factors. Based on these, five targeted risk mitigation measures are comprehensively implemented and evaluated. Moreover, a case study using UAV operation data near the Guanghan airport is introduced to justify the generalisability of the proposed TAN-BN model and the effectiveness of risk mitigation measures.
Autistic people are at an elevated risk of premature mortality; however, few studies have identified factors that explain this association. Co-occurring psychiatric conditions are a strong candidate, given that autistic people are at a high risk of such conditions and these conditions are broadly associated with premature mortality.
Aims
We aimed to investigate the degree to which co-occurring psychiatric conditions are associated with premature mortality in autistic people. We explored these associations across sex and co-occurring other neurodevelopmental conditions.
Method
We conducted a cohort study based on registry linkage. We identified 2 958 317 individuals born in Sweden from 1974 to 2004, including 70 546 (2.38%) individuals with an autism diagnosis. We identified diagnoses of 13 psychiatric conditions. The cohort was followed up from age 16 to age 46 at the oldest. We compared the risk of mortality (from all-causes, suicide, other external causes and natural causes) across autistic people with psychiatric conditions and (a) non-autistic people without psychiatric diagnoses; (b) autistic people without psychiatric diagnoses; and (c) non-autistic people with psychiatric diagnoses. We conducted separate analyses by sex and co-occurring neurodevelopmental conditions.
Results
The mortality rate in autistic people with psychiatric conditions was 3.2 deaths per 1000 person-years, which was higher than that observed in non-autistic (0.27 deaths per 1000 person-years) and autistic people without psychiatric conditions (0.96 deaths per 1000 person-years). The relative risk of premature mortality was higher in autistic people with psychiatric conditions compared with both non-autistic (hazard ratio 13.85, 12.86–14.91) and autistic people (hazard ratio 3.44, 2.94–4.02) without psychiatric conditions and also exceeded the risk of premature mortality in individuals with psychiatric conditions alone (hazard ratio 1.47, 1.37–1.58). Similar patterns emerged across sex, intellectual disability and attention-deficit hyperactivity disorder.
Conclusions
Co-occurring psychiatric conditions are a risk factor for premature mortality in autistic people. Timely detection and treatment of such conditions in autistic people may facilitate healthier, lengthier lives for autistic people.
The olive weevil Pimelocerus perforatus (Roelofs, 1873) is a destructive wood-boring pest of Oleaceae plants, which has caused serious damage to Fraxinus pennsylvanica Marshall and Olea europaea L. in China and Japan. This study evaluated the feeding preference, nutritional indices, and oviposition performance of olive weevil adults feeding on five Oleaceae plants, F. pennsylvanica, O. europaea, Osmanthus fragrans Lour., Syringa oblata Lindl., and Ligustrum × vicaryi Rehder. The results showed that adult olive weevils preferred to feed on O. fragrans, with a selection rate of 56.25 ± 6.91%, followed by F. pennsylvanica and O. europaea. No feeding preference was observed on L. × vicaryi. The nutritional index F values for female adult weevils feeding on F. pennsylvanica and S. oblata were the highest, 0.37 ± 0.02 g and 0.37 ± 0.01 g, respectively. For both female and male adults, F values were lowest on O. europaea for both sexes, while ECD, ECI, and GR were highest on this host. Although adult olive weevils preferred O. fragrans, the female adults did not exhibit oviposition behaviour after feeding on O. fragrans. After feeding on F. pennsylvanica and S. oblata, the maximum number of eggs laid by female adults was 19.20 ± 3.90 and 18.80 ± 3.11, respectively. Therefore, we believe that F. pennsylvanica and S. oblata may be the plants with the most serious harm caused by adult olive weevils, while O. fragrans could be used as a trap plant to attract female adult olive weevils.
As artificial intelligence (AI) systems rapidly develop in biomedical research, bioethical frameworks focused on human subjects research are often limited in their capacity to address ethical concerns related to data-driven and black-boxed AI algorithms. Calls to embed Ethical, Legal and Social Implications research into large research consortia focused on AI seek to address the challenges of applying models developed in the context of genomics research to AI projects. Foundational questions related to the conduct of such embedded ethics work include: what are the goals of this work, what counts as “ethics,” who qualifies as an ethics expert and what mechanisms, including organizational structures, can ensure success in achieving ethics goals alongside scientific goals by multidisciplinary research teams? We draw on empirical case studies (including semi-structured interviews and document analysis) of large, federally funded AI research projects in the US that required embedded ethics. Notable findings include the lack of consensus among key players regarding the definition of AI ethics and conflict over the scope of ethics work, which impedes the implementation of ethics-related goals in research practices. These conflicts highlight the differences in disciplinary cultures, contentious boundaries between technical and ethical expertise and the lack of power and impact of the ethics team. Our findings underscore that effective ethics integration depends on trust and respect for ethics scholarship through leadership and relationship-building. We argue that building long-lasting, equitable relationships requires institutional commitment through organizational frameworks and funding mechanisms that prioritize deliberation about ethical concerns, shared values and shared power, as well as co-developing ethics goals alongside science goals. A horizontal approach is needed to nurture joint relationships for fostering ethical and just biomedical AI research and development.
Whether the Lambert–Amery glacial system (LAGS) will remain near mass balance this century while adjusting to geometric change remains an open question. We couple the ice-flow model Úa to the PICO sub-shelf melt parameterization for 2020–2100 under ten high-emissions scenarios, two control experiments and targeted pinning-point perturbations. By 2100, unperturbed absolute trajectories across the twelve applied forcings contribute $-11.4$ to $1.9$ mm to sea level relative to the common 2020-relaxed state; member-specific transient-minus-2020-constant diagnostics isolate the response to post-2020 forcing evolution, which spans $-3.84$ to $+4.66$ mm. With SMB held time-invariant over the model domain, using time-evolving rather than time-invariant 2020 basin-mean ocean conditions increases the 2100 contribution by $1.50$ mm. Minimizing the dynamic buttressing contribution of all pinning points adds an almost forcing-invariant $0.82$ mm. Across ten single-point experiments, the 2100 sea-level response is proportional to grounding-area loss. Paired perturbed–unperturbed simulations have nearly identical shelf-integrated basal melt but distinct sea-level contributions, showing that the additional response is driven primarily by reduced buttressing rather than melt-forcing changes. Overall, LAGS remains close to mass balance under the applied forcing protocol, while time-evolving ocean forcing and pinning-point weakening modulate the magnitude of the 2100 sea-level response. Dynamically important pinning points are priorities for long-term monitoring.
Understanding vortex-induced vibrations (VIV) of long flexible structures with curvature such as catenary-type risers (CTRs) is essential for offshore engineering, where such structures are widely deployed. Here, we perform numerical simulations of the VIV responses of CTRs in uniform flow over a range of incoming velocities and initial configurations, revealing pronounced spanwise zoning characteristics. First, modal-group switching is identified as the mechanism governing the transition between mono- and multi-frequency responses. Within modal group, mono-frequency dominates, organising a monotonic phase angle and single travelling-wave direction. At the modal-transition region, drifting mono-frequency events constitute multi-frequency response, resulting in non-monotonic phase behaviour and travelling-wave reflection. A mixed standing–travelling-wave pattern emerges as a unifying feature. Furthermore, we find that the spanwise response distribution is governed by two intrinsic length scales: lower-span standing wavelength $\lambda _s$, scaling inversely with mode number $({\sim} n^{-1.0})$ and critical detuning length $\lambda _d$, a scale-dependent measure of natural frequency damping. By comparing the spanwise responses, three distinct regimes are identified: (i) flow-induced lock-in regime $(z/L\gt \lambda _d)$, where the vibration frequency locks in the vortex-shedding frequency and the energy transfer sustains positive ($C_{lv}\gt 0$), with predominantly counter-clockwise trajectories; (ii) non-lock-in regime $(\lambda _s\lt z/L\lt \lambda _d)$, where the local Strouhal frequency surpasses the vibration frequency, generating a discontinuous cellular pattern, with $C_{lv}\lt 0$ and predominantly clockwise trajectories; and (iii) structural resonance regime $(z/L\lt \lambda _s)$, where the frequency lock-in reoccurs but $C_{lv}\lt 0$ indicates flow-damped vibrations and the response is dominated by standing waves. These findings establish a new framework for spanwise zoning in CTRs, providing guidance for VIV prediction, suppression and control in catenary-type risers.
This work presents an integrated modelling study of fast-proton distributions generated by ion cyclotron range of frequency (ICRF) minority heating in the Experimental Advanced Superconducting Tokamak (EAST). Using a series of high-confinement (H-mode) discharges with increasing ICRF power levels from 0.8 to 2.4 MW, fast protons were produced via minority heating mechanisms and analysed through simulations using the ASCOT code. The results reveal that the fast protons are primarily concentrated near the fundamental cyclotron resonance layer and exhibit strong power-dependent behaviour in both real-space (R–Z) distribution and velocity space, where R is the major radius and Z is the vertical coordinate. As the ICRF power increases, the energetic proton population shows significant spatial broadening and energy enhancement, reaching up to 1 MeV. The fast-ion pitch-angle distribution becomes increasingly anisotropic, with high-energy ions concentrated around $|\textit{v}_{\|}/\textit{v}| \lt 0.5$, where $\nu$ is the magnitude (speed) of the full velocity vector of the particle. Furthermore, the energy density of fast ions aligns well with the ICRF power deposition profile, confirming efficient central-core heating. These findings, which provide insight into fast-ion behaviour and ICRF heating characteristics in EAST plasmas, also support future fast-ion diagnostics and performance control strategies in EAST and similar experimental conditions.
Cognitive impairment is a major determinant of disability in bipolar disorder (BD) and a defining feature of both mild cognitive impairment (MCI) and Alzheimer’s disease (AD). Lithium, a first-line maintenance treatment for BD, is implicated in neuroprotective mechanisms including glycogen synthase kinase-3β inhibition, amyloid and tau modulation, and neurogenesis promotion. The overarching aim of this systematic review is to evaluate the long-term effects of lithium on cognition across BD, MCI, and early-to-moderate AD using randomized controlled trial (RCT) evidence. Online databases were searched from inception through May 2025 for RCTs reporting lithium’s effect on cognitive outcomes in BD, MCI, or early-to-moderate AD with ≥8 weeks of follow-up. Risk of bias was assessed using the Cochrane RoB 2 tool. Eight RCTs met the inclusion criteria, ranging from 10 weeks to 3 years in duration. Across four BD trials, lithium did not exhibit consistent improvement or worsening on composite cognitive scores. Three of four MCI/AD trials reported attenuated global cognitive deterioration with low-dose lithium, especially when exposure was ≥12 months. Methodological limitations included small sample sizes, exploratory endpoints, and variable measures for cognitive function as well as lithium strategies. Lithium demonstrates preliminary signals of slower cognitive decline in MCI/AD. Available evidence suggests lithium has neutral effects on cognitive impairment in BD. Future adequately powered RCTs with cognition as a primary endpoint, functional measures, and biomarker outcomes are warranted to clarify lithium’s role as a maintenance treatment in psychiatric disorders and its potential neuroprotective effects in neurodegenerative diseases.
Anxiety disorders are highly prevalent mental health conditions and are closely associated with early-life adversity. Although research on childhood adversity and anxiety disorders has expanded rapidly, the overall knowledge structure and emerging trends remain unclear. This bibliometric study systematically searched English-language publications from Web of Science Core Collection, Scopus and PubMed. Bibliometrix was used to analyze annual publication trends, countries, institutions, authors and journals. VOSviewer was applied to construct keyword co-occurrence and institutional collaboration networks, and CiteSpace was used to visualize thematic evolution and keyword bursts. A total of 4,481 eligible publications were included. The annual number of publications increased steadily since 2000, with marked acceleration after 2010. Research output and influence were mainly concentrated in the United States and Western Europe. High-frequency keywords included anxiety disorders, depression, childhood abuse, adverse childhood experiences and post-traumatic stress responses. Keyword analyses indicated a thematic shift from specific trauma types and diagnostic categories toward cumulative adversity, cross-diagnostic risk factors, emotional regulation, psychological resilience and symptom networks. This field has evolved from descriptive correlational studies to an interdisciplinary area integrating multilayered and mechanistic perspectives. Future studies should strengthen longitudinal designs, cross-cultural samples and multimodal data integration.
Despite the rapid development of the digital economy, its impact on corporate environmental responsibility remains unclear. Drawing on stakeholder theory, we suggest that city digitalization enhances regulatory and social stakeholder governance and, in turn, facilitates local firms’ corporate environmental investment (CEI). Utilizing data from 2,358 Chinese listed firms operating in environmentally sensitive industries from 2014 through 2019, our findings indicate that city digitalization positively affects CEI. Moreover, such positive impact is more pronounced in regions where environmental regulatory or social salience is high, and for firms with high levels of state share or top management team ownership. Our study sheds light on the governance function of digital development and provides valuable insights into how city digitalization helps address environmental challenges in emerging markets.
The Eulerian–Lagrangian approach is employed to simulate a compressible turbulent boundary layer laden with inertial particles at Mach numbers 0.95, 2, 6 and 7. The governing equations for the five-species reacting compressible fluid are solved using the direct numerical simulations method. The particle motion equations involve thermophoretic force besides the drag force because thermal effects become significant. Results show that the thermal effects significantly alter the near-wall particle accumulation. Specifically, a distinct peak in particle concentration emerges at $y^+\approx 3$, which is absent when thermal effects are neglected and particle wall-normal transport is controlled by turbophoresis. This phenomenon is attributed to the alternating positive and negative structures in the near-wall region. In the outer layer, particles tend to accumulate on the turbulent side of the turbulent/non-turbulent interface (TNTI) due to the centrifugal effect of large-scale vortices and the combined barrier effect of potential flow. Meanwhile, particles also accumulate in the lower downstream region of the bubbles generated by the engulfment of the TNTI. As the Mach number increases, the near-wall particle concentration peak becomes clear, but the particle accumulation near the TNTI becomes less pronounced. On the horizontal plane, particles tend to distribute in the low-speed streaks near the wall, while accumulating at the inward cusps near the TNTI. The tendency for near-wall preferential distribution is weakened by the particle up/down transport induced by the alternating positive and negative structures. However, the distribution area seen by the TNTI becomes larger because the TNTI is less wrinkled as the Mach number increases.
We provide a theoretical model for foam-driven fracturing of an elastic solid. Based on recent experimental observations, we take into consideration the influence of foam rheology and compressibility. We arrive at a nonlinear non-local system that couples the dynamics of one-dimensional compressible plug flow of foam and elastic deformation of the infinite solid. The model leads to time-dependent solutions for the evolution of the fracture’s profile shape and the pressure distribution in the film of foam. The solutions are affected by a dimensionless control parameter $\varPi _c$, which measures the influence of foam compressibility. An increase in $\varPi _c$ leads to more significant expansion of the gas phase in the fracture, and the spreading of the film of foam is enhanced. Asymptotic efforts were also made in the weakly compressible regime. The profile now admits a linear asymptote $h \propto \chi$ as $\chi \equiv x_f - x \to 0^+$, compared with the standard viscous asymptote $h \propto \chi ^{2/3}$ for hydraulic fracturing using incompressible Newtonian fluids. The pressure singularity now follows $p \propto \mbox{ln}\, \chi$, which is weaker than the standard $p \propto \chi ^{-1/3}$ singularity in the viscous regime. It is also observed that the profile shape and pressure distribution can be rescaled appropriately to collapse onto universal curves at intermediate times, with the length and pressure scales following the $x \propto t^{5/9}$, $h \propto t^{4/9}$ and $p \propto t^{-1/9}$ scaling laws. Using foam as the fracturing fluid may save water in practical applications such as enhanced gas recovery from shale rocks.