Dynamical Evolution Research Articles

Time/Event‐Triggered Exponential Stabilization for Stochastic Systems: Enhancing Nonlinearity Tolerance

ABSTRACTThis article seeks the enhancement of nonlinearity tolerance in time/event‐triggered stabilization for stochastic systems. In the related results, the controller functions are required to obey global Lipschitz condition for the suppression of sampling/execution error, and the drift and/or diffusion coefficients of the stochastic systems are restricted to polynomial or, even, linear growth. These limitations deserve overcoming for enlarged applications. To this end, a distinct framework of time/event‐triggered controls is established for stochastic systems, targeted at exponential stabilization. Specifically, inclusive Lyapunov‐type feasibility conditions are proposed by capturing the effect of sampling/execution error and distinguishing the role of system nonlinearities. Particularly, different from the related results, the evolution of sampling/execution error is subtly exploited via Lyapunov functions to reveal the dynamic interaction between the sampling/execution errors and system state. Then, time‐triggered exponential stabilization via sampled‐data controller is achieved not only in the moment sense but also in the almost sure sense. Accordingly, Lyapunov function based analysis is performed for the composite dynamics of system state and sampling error, confronted with the coupling of discontinuous and stochastic features. To further reduce execution, periodic event‐triggered control is exploited to achieve exponential stabilization for stochastic nonlinear systems, by virtue of the relation with the dynamic evolution under sampled‐data control. Through typical examples, we demonstrate the potential of our framework in handling the cases with the controller functions violating global Lipschitz condition and with the system nonlinearities beyond polynomial growth.

Distributive difference, dynamic evolution and spatial convergence of the supply capacity of ecological products in China

Distributive difference, dynamic evolution and spatial convergence of the supply capacity of ecological products in China

Merger of Single-Atom Catalysis and Photothermal Catalysis for Future Chemical Production.

Photothermal catalysis is an emerging field with significant potential for sustainable chemical production processes. The merger of single-atom catalysts (SACs) and photothermal catalysis has garnered widespread attention for its ability to achieve precise bond activation and superior catalytic performance. This review provides a comprehensive overview of the recent progress of SACs in photothermal catalysis, focusing on their underlying mechanisms and applications. The dynamic structural evolution of SACs during photothermal processes is highlighted, and the current advancements and future perspectives in the design, screening, and scaling up of SACs for photothermal processes are discussed. This review aims to provide insights into their continued development in this rapidly evolving field.

Modeling the potential public health and economic impact of different COVID-19 vaccination strategies with an adapted vaccine in the Kingdom of Saudi Arabia

ABSTRACT Background The dynamic evolution of the virus causing COVID-19 necessitates the development of adapted vaccines to protect against emerging variants. Research design and methods A combined Markov-decision tree model estimated the outcomes of alternative vaccination strategies. The Saudi Arabian population was stratified into standard-risk and high-risk subpopulations, defined as either the population comprising individuals aged ≥65 years and individuals with at least one comorbidity. The model estimated the health and economic outcomes of vaccination based on age-specific inputs taken from published sources and national surveillance data. Results The vaccination strategy targeting the elderly and high-risk subpopulation (was estimated to prevent 156,694 cases 12,800 hospitalizations, and 2,919 deaths and result in cost savings of SAR 1,239 million in direct costs and SAR 4,145 million in indirect costs. These gains increased with the vaccination strategies additionally targeting other subpopulations. Compared to the base case (aged ≥65 and those at high-risk), expanding vaccination coverage to 75% of the standard-risk population prevented more cases (323%), hospitalizations (154%), and deaths (60%) and increased the direct (232%) and indirect (270%) cost savings. Conclusions The adoption of broad vaccination strategies using a vaccine adapted to the dominant variant in circulation would yield substantial benefits in Saudi Arabia.

Exploring Sustainable Innovation Level, Spatial Inequities, and Convergence Trends in China’s Wood Industry

The importance of sustainable innovation in the wood industry is growing, but there is a lack of comprehensive analysis of its evolution, regional differences, and patterns of convergence in China. Based on the panel data of 31 provinces in China from 2011 to 2021, the sustainable innovation index of the wood industry is measured by the projection pursuit method. On this basis, the kernel density estimation method and Dagum Gini coefficient are used to study the dynamic evolution trend, regional differences, and sources of the index, and the convergence characteristics are examined using the coefficient of variation method. The study shows that (1) China’s overall wood industry sustainable innovation index shows a decreasing trend from 2011 to 2021. (2) The differences in the four regions mainly come from inter-regional differences. (3) The index shows significant nonequilibrium characteristics and progressive evolution patterns, and the spatial agglomeration is significant. The magnitude of the index deviation from the average did not decrease over time for the northern and southwestern forest regions. (4) The wood industry sustainable innovation index of the four major forest regions has obviously converged to the same level; under the condition of considering multifactors differentiation, the growth rate of the index of the lower regions is significantly higher than that of the higher regions. The study concludes that current regional imbalances in sustainable innovation in China impede progress and equitable distribution of benefits in the wood industry, and that the impact of regional differences on the β-convergence of sustainable innovation varies according to specific regional characteristics and conditions. These findings provide important theoretical contributions and practical guidance for the development of targeted innovation strategies for the sustainable development of the wood industry, as well as for the promotion of balanced regional development.

Revealing the Dynamic Evolution of Electrolyte Configuration on the Cathode-Electrolyte Interface by Visualizing (De) Solvation Processes.

Electrolyte engineering is crucial for improving cathode electrolyte interphase (CEI) to enhance the performance of lithium-ion batteries, especially at high charging cut-off voltages. However, typical electrolyte modification strategies always focus on the solvation structure in the bulk region, but consistently neglect the dynamic evolution of electrolyte solvation configuration at the cathode-electrolyte interface, which directly influences the CEI construction. Herein, we reveal an anti-synergy effect between Li+-solvation and interfacial electric field by visualizing the dynamic evolution of electrolyte solvation configuration at the cathode-electrolyte interface, which determines the concentration of interfacial solvated-Li+. The Li+ solvation in the charging process facilitates the construction of a concentrated (Li+-solvent/anion-rich) interface and anion-derived CEI, while the repulsive force derived from interfacial electric field induces the formation of a diluted (solvent-rich) interface and solvent-derived CEI. Modifying the electrochemical protocols and electrolyte formulation, we regulate the "inflection voltage" arising from the anti-synergy effect and prolong the lifetime of the concentrated interface, which further improves the functionality of CEI architecture.

Origin of fast charging in solid-state batteries revealed by Cryo-transmission X-ray microscopy

The interface issue poses a limitation on the fast charging of solid-state batteries (SSBs), with the high-impedance non-Faraday electric field serving as a pivotal factor. However, the mechanism of fast-charging capability degradation triggered by the dynamic evolution of non-Faraday electric fields remains unclear due to the lack of particle-scale nondestructive detection techniques. Here, we dissect the generation and elimination processes of non-Faradaic electric field in segments using the developed operando cryogenic transmission X-ray microscopy (Cryo-TXM). This method accurately tracks the ion self-balancing pathways in LiNi0.8Co0.1Mn0.1O2 (NCM811) post-fast-charging, elucidating the high polarization during late charging caused by exacerbated irreversible local electric field. By intermittently applying reverse potential during fast charging to alleviate the exacerbation of non-Faradaic electric field at the cathode interface, we achieved a roughly 400% reversible capacity increase of SSBs at 10 C. This insightful dynamic imaging method effectively captures and resolves the transient, opaque signals within SSBs, significantly enhancing their fast-charging performance.

Dynamic Scenario Simulation of Building Carbon Peak from the Perspective of Urbanization

With the rapid development of urbanization in China, the energy consumption and carbon emissions in the building sector will continue to grow. Therefore, the future dynamic evolution of building carbon emissions must be crucially investigated to achieve the "dual carbon" target in China. A system dynamics model of "urbanization-building carbon emissions" was constructed from the perspective of urbanization for revealing the mechanism of urbanization-related factors on building carbon emissions. On this basis, a dynamic simulation of the evolution trend and peak situation of building carbon emissions in the Beijing-Tianjin-Hebei （BTH） Region from 2000 to 2050 was carried out using multi-scenario analysis. The results showed that： ① Under the baseline scenario, the carbon emissions of rural residential buildings, urban residential buildings, and commercial buildings peak in 2027, 2028, and 2037, respectively, with peaks （in CO2） of 0.60×108, 0.99×108, and 1.95×108 tons. ② Under the low-carbon scenario, the peak （in CO2, the same below） time of carbon emissions of urban residential buildings was the most advanced, reaching the peak of 0.88×108 tons in 2024. ③ In the deep low-carbon scenario, the peak time of carbon emissions of the overall buildings occurred five years earlier than that in the low-carbon scenario. It was predicted to peak at 2.61×108 tons in 2028, reaching the 2030 carbon peak target. ④ The sensitivity analysis showed that the carbon emission factor of commercial buildings and the per capita commercial building space floor in the spatial dimension were the major factors influencing the building carbon emissions, followed by the percentage of the urban population in the population dimension. Finally, suggestions are made for the government of the Beijing-Tianjin-Hebei Region to carry out energy conservation and emission reduction planning.

Spatial and Temporal Evolution of Regional Energy Efficiency in China and Its Influencing Factors

Finding ways to improve regional energy efficiency is important for the Chinese government to achieve its dual carbon target. This paper aims to explore ways to improve regional energy efficiency by studying the spatial–temporal dynamic evolution of energy efficiency. To scientifically study the evolution trend in regional energy efficiency in China, this study uses convergence analysis, a spatial Gini coefficient decomposition model (no spatial consideration), and a spatial Markov chain model and spatial measurement model (spatial consideration). The results show the following: from 2008 to 2019, the mean value of regional single-factor energy efficiency (RS) showed an obvious trend of continuous increase, while the mean value of regional green total-factor energy efficiency (RT) changed from a trend of continuous decline to a relatively stable trend. The overall Gini coefficient of RS showed a trend of “steady–rising–steady”, and the overall Gini coefficient of RT showed a trend of “steady–small increase–sharp increase–fall”. There was club convergence in the two types of regional energy efficiency, and both of them achieved certain “leapfrog” changes. The factors that had a significant impact on RS include human capital, industrialization, openness, urbanization, financial development, and innovation environment. The significant factors for RT included governance structure, industrialization, openness, policy support, and financial development. The limitation of this paper is that only provincial data were used. In the future, city-level data can be mined and more detailed policy suggestions can be put forward for city-level differences. The research method used in this paper to study regional energy efficiency evolution trends is also applicable to other countries.

Dilemma and sustainable development strategy of sharing teaching resources for big data majors in universities based on game theory

In the process of sharing teaching resources for big data majors in universities, the competition and cooperation between universities are complex, and there are problems such as unfair resource allocation and information asymmetry. Resource sharing faces many difficulties. In response to these issues, this article constructed a dynamic information evolution game model based on game theory, which integrated three sub models: static game, incomplete information game, and evolutionary game. The static game model was used to analyze the strategic choices of universities in a certain environment; the incomplete information game model revealed the game behavior under information asymmetry; the evolutionary game model simulated the dynamic evolution process of university strategies. This article combined a simulation case of the teaching resource sharing project for big data majors in university alliances, and used this model to identify and analyze the practical difficulties of resource sharing in universities, revealing the deep-seated reasons why resource sharing is difficult to achieve in competitive and cooperative relationships. On this basis, this article proposed a series of sustainable development strategies, including optimizing resource allocation mechanisms, improving information transparency, etc., providing theoretical support and practical reference for the effective sharing of teaching resources in big data majors in universities. Experimental data showed that in the resource sharing simulation process of five universities (A, B, C, D, E), the strategy adjustment values of each university decreased from around 0.8 to below 0.2.

The Current Situation and Trend of Sino-US Trade Development in the Context of Economic Globalization

The evolution of trade and commercial relations between China and the US is particularly noteworthy, given the significant impact of economic globalization and its role as a fundamental pillar of global economic stability and progress. The trade volume between China and the US is steadily increasing, and this is happening at the same time as the trade structure is changing significantly. The process of commerce between China and the US is not without its difficulties, though, as seen by the US's gradual growth in trade protectionism, the frequency of trade disputes, and the imbalance in trade relations. This paper provides an in-depth analysis of the dynamic evolution trend of China-US trade in the context of economic globalization and discusses the current status and challenges of China-US trade relations, as well as the future trend based on global economic, political, and technological development trends. In addition, the paper forecasts how China-US trade relations will develop in the future in light of new technological advancements, policy adjustments, and shifts in the global economic landscape. It also offers policy recommendations and strategic adjustment guidelines to encourage collaboration between the two sides and produce win-win outcomes.

Probing chiral-symmetric higher-order topological insulators with multipole winding number

The interplay between crystalline symmetry and band topology gives rise to unprecedented lower-dimensional boundary states in higher-order topological insulators (HOTIs). However, the measurement of the topological invariants of HOTIs remains a significant challenge. Here, we define a multipole winding number (MWN) for chiral-symmetric HOTIs by applying a corner twisted boundary condition. The MWN, arising from both bulk and boundary states, accurately captures the bulk-corner correspondence including boundary-obstructed topological phases. To address the measurement challenge, we leverage the perturbative nature of the corner twisted boundary condition and develop a real-space approach for determining the MWN in both two-dimensional and three-dimensional systems. The real-space formula provides an experimentally viable strategy for directly probing the topology of chiral-symmetric HOTIs through dynamical evolution. Our findings not only highlight the twisted boundary condition as a powerful tool for investigating HOTIs, but also establish a paradigm for exploring real-space formulas for the topological invariants of HOTIs.

Framework Construction and Dynamic Characteristics of Spring Low-Temperature Disasters Affecting Winter Wheat in the Huang-Huai-Hai Region, China

The accurate and sub-daily identification of agricultural low-temperature disasters (LTDs) facilitates the understanding of their dynamic evolution, the evaluation of the characteristics of disaster events, and informs effective strategies aimed at disaster prevention and mitigation. In order to ensure the timely, precise, and comprehensive capture of disaster processes, we have developed a dynamic evaluation framework for winter wheat spring LTD in the Huang-Huai-Hai (HHH) region, driven by meteorological data. This framework consists of two primary components: a disaster classification module and a dynamic simulation-assessment module. Through disaster mechanisms and comprehensive statistical analysis, we have established the input features and structural framework of the classification module using a decision tree algorithm. The dynamic simulation evaluation module is based on our newly developed index for the cumulative hourly intensity of low-temperature stress (CHI) and its grade indicators. This index integrates the interaction between cold stress (low-temperature intensity, cooling amplitude, and duration) and mitigating conditions (air humidity) during the evolution process of LTD. Based on CHI, we found that as the intensity of low temperatures and the amplitude of cooling rise, along with an extended duration of stress and a reduction in relative humidity, the severity of spring LTDs in winter wheat get worse. The overall validation accuracy of the evaluation framework is 92.6%. High validation accuracy indicates that our newly established framework demonstrates significant efficacy in identifying LTDs and assessing grade. Through the analysis of the characteristics of the disaster process, spring LTDs affecting winter wheat are mainly mild, with frost identified as the primary category of LTD. The duration of freeze injury typically exceeds 24 h, while the duration of frost damage and cold damage is less than 24 h. From 1980 to 2022 in the HHH region, the frequency of spring freeze injury and frost damage on winter wheat showed an overall decreasing trend, with a particularly significant decrease in frost damage occurrences. Conversely, cold damage occurrences are on the rise. In addition, the duration of individual disaster events for the three categories of spring LTDs is decreasing, while both the average intensity and extremity of these events show increasing trends. This study has important practical value for the sub-daily scale evaluation of the spring LTD affecting winter wheat in the HHH region and serves as an effective guide for agricultural disaster prevention and mitigation, as well as for the formulation of planting strategies.

Assessment of hypoxia and its dynamic evolution in glioblastoma via qBOLD MRI: a comparative study with metformin treatment

BackgroundTo investigate the accuracy of quantitative blood oxygen level-dependent (qBOLD) magnetic resonance imaging (MRI) in identifying hypoxia within glioblastoma and explore dynamic changes in oxygenation status of glioblastoma with and without metformin administration.MethodsThree healthy and seven C6-bearing rats underwent 7-T qBOLD MRI. Oxygen extraction fraction (OEF) and cerebral metabolism rate of O2 (CMRO2) were calculated from qBOLD data. Tumor tissues were stained using hypoxia-inducible factor-1α (HIF-1α) and pimonidazole. The correlation between the hypoxia markers and corresponding qBOLD-based parameters was analyzed. Six C6-bearing rats were divided into metformin-treated and control groups for a longitudinal study of qBOLD imaging changes, with scans conducted on the 12th, 15th, and 18th day post-tumor implantation.ResultsIn healthy rats, gray matter showed higher values than white matter in T2, T2*, cerebral blood volume (CBV), and cerebral blood flow (CBF), whereas OEF was lower. Glioblastoma tissues exhibited elevated T2, T2*, CBV, and CBF but decreased OEF and CMRO2 relative to normal-appearing white matter. No significant correlation was found between staining scores from HIF-1α and pimonidazole. T2* and T2 values were negatively correlated with pimonidazole scores in tumor regions. As the tumor progressed, OEF values increased with intra-tissue variations, whereas CMRO2 decreased. Metformin delayed the reduction of T2 and T2* values, with significant differences in OEF and CMRO2 values compared to controls on day 18.ConclusionT2* and T2 values were significantly associated with the hypoxia status in glioma. Metformin could potentially mitigate the progression of hypoxia in glioblastoma, which can be tracked by qBOLD parameters.Relevance statementThis study demonstrates the potential of qBOLD parameters in assessing glioma dynamic oxygen metabolism and the efficacy of metformin as an anti-hypoxic agent, providing insights into improving glioblastoma treatment strategies.Key PointsThe study investigated qBOLD imaging’s accuracy in identifying hypoxia status within glioblastoma.qBOLD effectively assesses hypoxia and its dynamic evolution in glioblastoma.qBOLD parameters assist in identifying a suitable patient demographic for metformin treatment.Graphical

Long-range four-body interactions in structured nonlinear photonic waveguides

Multiphoton dynamics beyond linear optical materials are of significant fundamental and technological importance in quantum information processing. However, it remains largely unexplored in nonlinear waveguide QED. In this work, we theoretically propose a structured nonlinear waveguide in the presence of staggered photon-photon interactions, which supports two branches of gaped bands for doublons (i.e., spatially bound-photon-pair states). In contrast to linear waveguide QED systems, we identify two important contributions to its dynamical evolution, i.e., single-photon bound states (SPBSs) and doublon bound states (DBSs). Most remarkably, the nonlinear waveguide can mediate the long-range four-body interactions between two emitter pairs, even in the presence of disturbance from SPBSs. By appropriately designing system's parameters, we can achieve high-fidelity four-body Rabi oscillations mediated only by virtual doublons in DBSs. Our findings pave the way for applying structured nonlinear waveguide QED in multi-body quantum information processing and quantum simulations among remote sites. Published by the American Physical Society 2024

Domain wall networks from first-order phase transitions and gravitational waves

In the first-order phase transitions (PTs) colliding bubble is an important gravitational wave (GW) source. Following bubble collision, domain walls can be formed when degenerate vacua occur as a result of the spontaneous breaking of a discrete symmetry relevant to new physics at electroweak or higher scales. Using lattice simulations, we study the dynamical evolution of domain walls and find that the networks of the domain wall are formed around the completion of PTs and quickly collapse before entering into the scaling regime provide that the degeneracy of true vacua is broken. Our numerical results indicate that domain wall networks continue to produce GWs in the aftermath of PTs, leading to dramatically changing the spectral shape and enhancing the magnitude by about one order. The resulting GW power spectra are peaked at kR*≃π as predicted by the envelop approximation model, above the peak wave number it has a decaying power law close to k−1.2 followed by a slowly decreasing plateau with the UV cutoff at kR*∼O(102). Published by the American Physical Society 2024

A global dynamic evolution snow ablation optimizer for unmanned aerial vehicle path planning under space obstacle threat

In this paper, an improved Global Dynamic Evolution Snow Ablation Optimizer (GDSAO) is proposed in order to solve the problem of global optimization and Unmanned Aerial Vehicle (UAV) path planning in 3D space with obstacle threats. Three improvement schemes are proposed in GDSAO: (1) Population initialization is carried out using the theory of the best point set to obtain a more diverse initial population; (2) A dynamic snowmelt ratio using the global evolutionary dispersion is proposed to adapt the exploitation process of the original SAO to the evolutionary process of population fitness; (3) A neighborhood dimensional search scheme is proposed to update the locations of all searched individuals outside the elite pool to obtain better population fitness. The algorithm was tested on 30 10-dimensional problems at CEC 2017 and performed better than a series of joint and leading optimization algorithms. The path planning problem of UAV was solved, and the path satisfying all obstacle avoidance threats and corner constraints was obtained. By comparison, GDSAO is superior to the existing algorithms in terms of reliability and stability of optimization.

Analysis on Innovation Efficiency of High-tech Industries in the Three Coastal Economic Zones in Eastern China

The high-tech industry is an important force in promoting the upgrading of traditional industries and the transformation of economic growth mode. Its technological innovation directly affects the innovation efficiency and economic development level of the region. The three major economic zones of Bohai Rim, Yangtze River Delta, and Pan Pearl River Delta are the most active areas for China's economic development and independent innovation, with a level of technological development far exceeding the average level of China, becoming the three growth poles driving China's economic growth. This article first uses the three-stage DEA Windows method to measure the innovation efficiency of high-tech industries in China's Yangtze River Delta, Pan Pearl River Delta, and Bohai Rim economic zones from 2016 to 2022, and considers the dynamic evolution characteristics of innovation efficiency in each region over time. Secondly, the impact of environmental variables on the redundancy of input variables in high-tech industries in the three major economic zones was studied. Finally, the differences of innovation efficiency values among the three major economic zones were examined. Research has found that after controlling for environmental factors and random errors, the overall innovation efficiency values of the three major regions have not reached the forefront of production, and have shown an increasing trend year by year. Low scale efficiency is the main factor affecting the R&D efficiency of the three regions, and further coordinated planning is urgently needed.

Dynamic critical factors identification: A novel fuzzy DEMATEL method considering heterogeneous information

Identifying the critical factors and their interrelationships plays a critical role in system analysis. Fuzzy DEMATEL method is one of the popular techniques widely applied to identify the critical factors and analyze the interrelationship among them under fuzzy and uncertain environment. Different information types are often used to describe given problems in the real world, similar to how experts express their assessments due to their diverse knowledge backgrounds or individual preferences. However, in existing fuzzy DEMATEL studies, experts are allowed to use only a single information type to express their assessments, which can not reflect the real-world situations. Additionally, dynamic evolution is a typical feature of practical problems. Factors associated with these problems, including critical factors, might change and update alongside this dynamic evolution. Nevertheless, such dynamic evolution has not been considered in existing fuzzy DEMATEL studies. To address the issues of heterogeneous information and dynamic evolution, this study proposes a novel method based on fuzzy DEMATEL that considers both dynamic evolution and heterogeneous information. The dynamic evolution is described not only from the perspective of time changes, but also information updates. The heterogeneous information includes numerical values, interval values, linguistic information, and hesitant fuzzy linguistic term information. The proposed method consists of five parts including problem definition, information gathering, information transformation, information aggregation, and dynamic critical factors identification. A reasonable way based on alpha-level sets is employed to handle the aggregated fuzzy information, and dynamic degrees of different factors at each moment are calculated for critical factors identification. A numerical example, related discussions, and comparison analysis are provided to demonstrate the novelty and superiority of the proposed method.

Evolution of Rapid Clonal Dynamics and Non-Cross-Resistance in Response to Alternating Targeted Therapy and Chemotherapy in BRAF-V600E-Mutant Colon Cancer.

Combined BRAF, MEK, and EGFR inhibition can induce clinical responses in BRAF-V600E-mutant colon cancer, but rapid resistance often occurs. We use serial monitoring of circulating tumor DNA cell-free plasma DNA (cfDNA) in a patient case study in addition to organoids derived from mouse models of BRAF-V600E-mutant intestinal cancer, which emulated the patient's mutational profile to assess drug treatment efficacy. We demonstrate dynamic evolution of resistance to combined EGFR/BRAF/MEK inhibition in a pediatric patient with metastatic BRAF-V600E-mutant, mismatch repair-stable colon cancer. Initial resistance to targeted therapy was associated with development of MET amplification. Sequential treatment with chemotherapy and targeted therapy resulted in clearing of the resistant MET-amplified clone. Rechallenge with combined BRAF/EGFR inhibition resulted in clinical and radiographic response, demonstrating these treatments may be non-cross-resistant. Tumor organoids were used to model clinical findings and demonstrated effectiveness of combined targeted therapy and chemotherapy. These findings suggest rational strategies for combining sequential chemotherapy and BRAF-/EGFR-directed therapy in BRAF-V600E-mutant colon cancer to prevent resistance and improve outcome. The data demonstrate rapid clonal dynamics in response to effective therapies in BRAF-V600E-mutant colon cancer that can be monitored by serial cfDNA analysis. Moreover, in mismatch repair-proficient BRAF-V600E-mutant colon cancers, combined EGFR and BRAF/MEK therapy is not cross-resistant with standard chemotherapy, suggesting new rational combination treatment strategies.