Global Gradients Research Articles

Macroevolutionary processes in turtles (Testudines): a view from biomic specialization and historical climatic changes

The resource-use hypothesis proposed by Elisabeth S. Vrba suggests that lineages display varying tendencies toward generalism or specialization in biome occupancy, with a tendency towards the accumulation of specialists due to their higher rate of speciation through vicariance. It also posits differences in biome occupancy patterns driven by the environmental characteristics of biomes, with a higher presence of biome specialist species in biomes that are placed in the extremes of the global climatic gradients. Here, we tested this hypothesis in turtles, a very ancient and morphologically stable lineage, representing a remarkable diversity with 357 species, many of which are threatened with extinction. We analyzed the resource-use hypothesis in a phylogenetic context within the Testudines lineage. For this purpose, a presence/absence matrix was compiled for all species across all 10 terrestrial biomes. Their distribution across biomes was contrasted with 10,000 Monte Carlo simulations. The relationship between diversification rates and both the biomic specialization index and the biomes occupied by specialists species was evaluated. The results demonstrate strong consistency with Vrba`s hypothesis, revealing a higher number of biome specialist species than expected by chance, with a significant accumulation of species in tropical ecosystems. These trends also were observed for ecological groups (terrestrial and freshwater species). In addition, higher diversification rates were observed for biome specialist species, although the particular biome occupied did not significantly influence their diversification rates.

FedFAIM: A Model Performance-Based Fair Incentive Mechanism for Federated Learning

Federated Learning (FL) has emerged as a privacy-preserving distributed machine learning paradigm. To motivate data owners to contribute towards FL, research on FL incentive mechanisms is gaining great interest. Existing monetary incentive mechanisms generally share the same FL model with all participants regardless of their contributions. Such an assumption can be unfair towards participants who contributed more and promote undesirable free-riding, especially when the final model is of great utility value to participants. In this paper, we propose a Fairness-Aware Incentive Mechanism for federated learning (FedFAIM) to address such problem. It satisfies two types of fairness notion: 1) aggregation fairness, which determines aggregation results according to data quality; 2) reward fairness, which assigns each participant a unique model with performance reflecting his contribution. Aggregation fairness is achieved through efficient gradient aggregation which examines local gradient quality and aggregates them based on data quality. Reward fairness is achieved through an efficient Shapley value-based contribution assessment method and a novel reward allocation method based on reputation and distribution of local and global gradients. We further prove reward fairness is theoretically guaranteed. Extensive experiments show that FedFAIM provides stronger incentives than similar non-monetary FL incentive mechanisms while achieving a high level of fairness.

Latitudinal gradients of biodiversity and ecosystem services in protected and non-protected oak forest areas can inform climate smart conservation

Adaptive governance of areas set aside for future protection of biodiversity, sustainable production, and recreation requires knowledge about whether and how effects of area protection are modulated by climate change and redistribution of species. To investigate this, we compare biodiversity of plants (assessed using vegetation plots) and arthropods (collected with Malaise traps, analyzed using metabarcoding) and productivity (tree growth, determined using dendrochronology) in protected and non-protected oak (Quercus spp.) forests along a latitudinal gradient (55.6 °N – 60.8 °N) in Sweden. We also compare historical, recent and projected future climate in the region. In contrast to established global latitudinal diversity gradients, species richness of plants and arthropods increased northwards, possibly reflecting recent climate-induced community redistributions, but neither was higher in protected than in non-protected areas, nor associated with contemporary ground temperature. Species composition of arthropods also did not differ between protected and non-protected areas. Arthropod biomass increased with latitude, suggesting that the magnitude of cascading effects mediated via their roles as pollinators, herbivores, and prey for other trophic levels, varies geographically and will change with a moving climate. Annual growth rate of oaks (an ecosystem service in the form of biomass increase and carbon sequestration) was independent of latitude and did not differ between protected and non-protected areas. Our findings question the efficacy of contemporary designation and management of protected oak forests, and emphasize that development and implementation of modified climate smart conservation strategies is needed to safeguard ecosystem functioning, biodiversity, and recreational values of protected forest areas against future challenges.

Wetland CH4 and CO2 emissions show opposite temperature dependencies along global climate gradients

Methane (CH4) and carbon dioxide (CO2) are the two largest contributors to the anthropogenically-driven greenhouse effect, which are the dominant gaseous end-products of wetland C decomposition. However, given our limited understanding of the spatial heterogeneity of wetland CH4 and CO2 emissions, it is uncertain how future warming may impact the emissions of these dangerous emissions. Here, we show opposite temperature dependencies of CH4 and CO2 emissions along global climate gradients using data from 45 widely distributed wetlands in the FLUXNET-CH4 database. Specifically, the temperature dependence of CH4 emissions increased as mean annual temperature (MAT) rose, while the dependence of CO2 emissions decreased, suggesting that in warmer areas, there is a greater risk for increased wetland CH4 emissions accompanying lower CO2 emissions in response to global warming. The ratio of wetland CH4 to CO2 emissions increased linearly with increasing temperature only when MAT and mean annual precipitation (MAP) are greater than 4.7 °C and 483 mm, respectively. This response indicates that, compared with those in cold and dry climates, wetland ecosystems in warmer and wetter climates are more prone to methanogenesis as temperatures rise. Our results suggest that neglecting spatial variation of temperature dependencies in models may underestimate wetland CH4 and CO2 emissions compared to the use of a static and consistent temperature dependence parameter when only considering temperature effects. These findings highlight the importance of incorporating climate-related variation in the temperature dependencies of CH4 and CO2 emissions into models to improve predictions of wetland C-climate change feedbacks in the Anthropocene.

Functional gradient dysfunction in drug-naïve first-episode schizophrenia and its correlation with specific transcriptional patterns and treatment predictions

Abstract Background First-episode schizophrenia (FES) is a progressive psychiatric disorder influenced by genetics, environmental factors, and brain function. The functional gradient deficits of drug-naïve FES and its relationship to gene expression profiles and treatment outcomes are unknown. Methods In this study, we engaged a cohort of 116 FES and 100 healthy controls (HC), aged 7 to 30 years, including 15 FES over an 8-week antipsychotic medication regimen. Our examination focused on primary-to-transmodal alterations in voxel-based connection gradients in FES. Then, we employed network topology, Neurosynth, postmortem gene expression, and support vector regression to evaluate integration and segregation functions, meta-analytic cognitive terms, transcriptional patterns, and treatment predictions. Results FES displayed diminished global connectome gradients (Cohen's d = 0.32–0.57) correlated with compensatory integration and segregation functions (Cohen's d = 0.31–0.36). Predominant alterations were observed in the default (67.6%) and sensorimotor (21.9%) network, related to high-order cognitive functions. Furthermore, we identified notable overlaps between partial least squares (PLS1) weighted genes and dysregulated genes in other psychiatric conditions. Genes linked with gradient alterations were enriched in synaptic signaling, neurodevelopment process, specific astrocytes, cortical layers (layer II and IV), and developmental phases from late/mid fetal to young adulthood. Additionally, the onset age influenced the severity of FES, with discernible differences in connection gradients between minor- and adult-FES. Moreover, the connectivity gradients of FES at baseline significantly predicted treatment outcomes. Conclusions These results offer significant theoretical foundations for elucidating the intricate interplay between macroscopic functional connection gradient changes and microscopic transcriptional patterns during the onset and progression of FES.

Emergence of planar cell polarity from the interplay of local interactions and global gradients.

Planar cell polarity (PCP) - tissue-scale alignment of the direction of asymmetric localization of proteins at the cell-cell interface - is essential for embryonic development and physiological functions. Abnormalities in PCP can result in developmental imperfections, including neural tube closure defects and misaligned hair follicles. Decoding the mechanisms responsible for PCP establishment and maintenance remains a fundamental open question. While the roles of various molecules - broadly classified into "global" and "local" modules - have been well-studied, their necessity and sufficiency in explaining PCP and connecting their perturbations to experimentally observed patterns have not been examined. Here, we develop a minimal model that captures the proposed features of PCP establishment - a global tissue-level gradient and local asymmetric distribution of protein complexes. The proposed model suggests that while polarity can emerge without a gradient, the gradient not only acts as a global cue but also increases the robustness of PCP against stochastic perturbations. We also recapitulated and quantified the experimentally observed features of swirling patterns and domineering non-autonomy, using only three free model parameters - the rate of protein binding to membrane, the concentration of PCP proteins, and the gradient steepness. We explain how self-stabilizing asymmetric protein localizations in the presence of tissue-level gradient can lead to robust PCP patterns and reveal minimal design principles for a polarized system.

Parasite Abundance‐Occupancy Relationships Across Biogeographic Regions: Joint Effects of Niche Breadth, Host Availability and Climate

ABSTRACTAimChanging biodiversity and environmental conditions may allow multi‐host pathogens to spread among host species and affect prevalence. There are several widely acknowledged theories about mechanisms that may influence variation in pathogen prevalence, including the controversially debated dilution effect and abundance‐occupancy relationship hypotheses. Here, we explore such abundance‐occupancy relationships for unique lineages of three vector‐borne avian blood parasite genera (the avian malaria parasite Plasmodium and the related haemosporidian parasites Parahaemoproteus and Leucocytozoon) across biogeographical regions.LocationNearctic‐Neotropical and Palearctic‐Afrotropical regions.MethodsWe compiled a cross‐continental dataset of 17,116 bird individuals surveyed from 46 bird assemblages across the Nearctic‐Neotropical and Palearctic‐Afrotropical regions and explored relationships between local parasite lineage prevalence and host assemblage metrics in a Bayesian random regression framework.ResultsMost lineages from these three genera infected ≥ 5 host species and exhibited clear phylogenetic or functional host specificity. Lineage prevalence from all three genera increased with host range, but also with higher degrees of specialisation to phylogenetically or functionally related host species. Local avian community features were also found to be important drivers of prevalence. For example, bird species richness was positively correlated with lineage prevalence for Plasmodium and Leucocytozoon, whereas higher relative abundances of the main host species were associated with lower prevalence for Plasmodium and Parahaemoproteus but higher prevalence for Leucocytozoon.ConclusionsOur results broadly support several of the leading hypotheses about mechanisms that influence pathogen prevalence, including the niche breadth hypothesis in that higher avian host species diversity and broader host range amplify prevalence through increasing ecological opportunities and the trade‐off hypotheses in that specialisation among subsets of available host species may increase prevalence. Furthermore, the three studied avian haemosporidian genera exhibited different abundance‐occupancy relationships across the major global climate gradients and in relation to host availability, emphasising that these relationships do not strictly follow common rules for vector‐borne parasites with different life histories.

The genomics and physiology of abiotic stressors associated with global elevational gradients in Arabidopsis thaliana.

Phenotypic and genomic diversity in Arabidopsis thaliana may be associated with adaptation along its wide elevational range, but it is unclear whether elevational clines are consistent among different mountain ranges. We took a multi-regional view of selection associated with elevation. In a diverse panel of ecotypes, we measured plant traits under alpine stressors (low CO2 partial pressure, high light, and night freezing) and conducted genome-wide association studies. We found evidence of contrasting locally adaptive regional clines. Western Mediterranean ecotypes showed low water use efficiency (WUE)/early flowering at low elevations to high WUE/late flowering at high elevations. Central Asian ecotypes showed the opposite pattern. We mapped different candidate genes for each region, and some quantitative trait loci (QTL) showed elevational and climatic clines likely maintained by selection. Consistent with regional heterogeneity, trait and QTL clines were evident at regional scales (c. 2000 km) but disappeared globally. Antioxidants and pigmentation rarely showed elevational clines. High elevation east African ecotypes might have higher antioxidant activity under night freezing. Physiological and genomic elevational clines in different regions can be unique, underlining the complexity of local adaptation in widely distributed species, while hindering global trait-environment or genome-environment associations. To tackle the mechanisms of range-wide local adaptation, regional approaches are thus warranted.

Experimental study on backward erosion piping of a double-layer dike foundation under variable exit geometries

Double-layer dike foundation is composed of a weakly permeable overlying clay layer and a highly permeable underlying sand layer, which is one of the most common stratum types in dike engineering with the highest probability of catastrophic damage, and the main danger is backward erosion piping. Existing research on backward erosion piping of double-layer dike foundation has not fully considered the influence of the exit on the erosion process. Therefore, a self-designed test device is used to assess the influences of the size, position and type of different exits, and the circular exit is connected with the slot exit via the exit area to explore the critical identification conditions and the pipe development mechanism toward the upstream direction under different exit geometry conditions. The results show that both the local and global hydraulic gradients borne by the exit are inversely proportional to the exit area and are less notably affected by the location of the exit. The development process of slot exit pipes differs from that of circular exit pipes, and pipes are usually developed alternately at the two corners of the exit near the upstream end and then converge into one pipe. The average pipe depth and width are proportional to the exit size and the seepage length. With increasing average pipe area of the slot exit, pipes develop more rapidly after head enhancement, and the damage to the dike foundation increases.

Positional Information-Based Organization of Surfactant Droplet Swarms Emerging from Competition Between Local and Global Marangoni Effects.

Positional information is key for particles to adapt their behavior based on their position in external concentration gradients, and thereby self-organize into complex patterns. Here, position-dependent behavior of floating surfactant droplets that self-organize in a pH gradient is demonstrated, using the Marangoni effect to translate gradients of surface-active molecules into motion. First,fields of surfactant microliter-droplets are generated, in which droplets floating on water drive local, outbound Marangoni flows upon dissolution of surfactantand concomitantly grow myelin filaments. Next, a competing surfactant based on a hydrolysable amide is introduced, which is more surface active than the myelin surfactant and thereby inhibits the local Marangoni flows and myelin growth from the droplets. Upon introducing a pH gradient, the amide surfactant hydrolyses in the acidic region, so that the local Marangoni flows and myelin growth are reestablished. The resulting combination of local and global surface tension gradients produces a region of myelin-growing droplets and a region where myelin growth is suppressed, separated by a wave front of closely packed droplets, of which the position can be controlled by the pH gradient. Thereby, it is shown how "French flag"-patterns, in synthetic settings typically emerging from reaction-diffusion systems, can also be established via surfactant droplet systems.

The global distribution and climate resilience of marine heterotrophic prokaryotes

Heterotrophic Bacteria and Archaea (prokaryotes) are a major component of marine food webs and global biogeochemical cycles. Yet, there is limited understanding about how prokaryotes vary across global environmental gradients, and how their global abundance and metabolic activity (production and respiration) may be affected by climate change. Using global datasets of prokaryotic abundance, cell carbon and metabolic activity we reveal that mean prokaryotic biomass varies by just under 3-fold across the global surface ocean, while total prokaryotic metabolic activity increases by more than one order of magnitude from polar to tropical coastal and upwelling regions. Under climate change, global prokaryotic biomass in surface waters is projected to decline ~1.5% per °C of warming, while prokaryotic respiration will increase ~3.5% ( ~ 0.85 Pg C yr−1). The rate of prokaryotic biomass decline is one-third that of zooplankton and fish, while the rate of increase in prokaryotic respiration is double. This suggests that future, warmer oceans could be increasingly dominated by prokaryotes, diverting a growing proportion of primary production into microbial food webs and away from higher trophic levels as well as reducing the capacity of the deep ocean to sequester carbon, all else being equal.

Artificial chemotaxis under electrodiffusiophoresis

HypothesisThrough a large parameter space, electric fields can tune colloidal interactions and forces leading to diverse static and dynamical structures. So far, however, field-driven interactions have been limited to dipole-dipole and hydrodynamic contributions. Nonetheless, in this work, we propose that under the right conditions, electric fields can also induce interactions based on local chemical fields and diffusiophoretic flows. ExperimentsHerein, we present a strategy to generate and measure 3D chemical gradients under electric fields. In this approach, faradaic reactions at electrodes induce global pH gradients that drive long-range transport through electrodiffusiophoresis. Simultaneously, the electric field induces local pH gradients by driving the particle's double layer far from equilibrium. FindingsAs a result, while global pH gradients lead to 2D focusing away from electrodes, local pH gradients induce aggregation in the third dimension. Evidence points to a mechanism of interaction based on diffusiophoresis. Interparticle interactions display a strong dependence on surface chemistry, zeta potential and diameter of particles. Furthermore, pH gradients can be readily tuned by adjusting the voltage and frequency of the electric field. For large Péclet numbers, we observed a collective chemotactic-like collapse of particles. Remarkably, such collapse occurs without reactions at a particle's surface. By mixing particles with different sizes, we also demonstrate, through experiments and Brownian dynamics simulations, the emergence of non-reciprocal interactions, where small particles are more drawn towards large ones.

Multiple focal pulvinar projection fields in the macaque cortex

Abstract The pulvinar, the largest nucleus of the thalamus, is functionally heterogeneous and involved in multiple cognitive functions. It has been proposed to act as a functional hub of cortical processes due to its extensive reciprocal connectivity with the cortex. However, its role in cognition is not fully understood yet. Here, we posit that an improved understanding of its functional connectivity with the cortex is needed to better capture the cognitive functions of this nucleus. To address this question, we characterize the pulvino-cortical functional connectivity along the ventro-dorsal, antero-posterior, and medio-lateral axes, using awake resting-state data from 10 adult macaques. We first report two global cortical functional connectivity gradients along the antero-posterior and ventro-dorsal pulvinar gradients that match remarkably well the structural connectivity gradients described by anatomical approaches. In addition to these global gradients, multiple local cortical pulvinar projection fields can be identified at the sulci level such as in the lateral sulcus (LS), the intraparietal sulcus (IPS), the principal sulci (PS), and the anterior cingulate cortex (ACC). For most sulci, we show that functional pulvino-cortical projection fields follow the major anatomical axis of these different sulci (e.g., the ventro-dorsal axis for the LS and the antero-posterior axis for the IPS). Other sulci, such as the superior temporal sulcus, the posterior cingulate cortex, or the central sulcus, display multiple projection fields from the pulvinar. Although substantial inter-individual differences exist, the general functional connectivity patterns are remarkably consistent across hemispheres and individuals. Overall, we propose that these multiple pulvinar projection fields correspond to a fundamental principle of pulvino-cortical connectivity and that a better understanding of this connectional organization will shed light on the function of pulvino-cortical interactions and the role of the pulvinar in cognition at large.

The Clock and Wavefront Self-Organizing model recreates the dynamics of mouse somitogenesis in vivo and in vitro.

During mouse development, presomitic mesoderm cells synchronize Wnt and Notch oscillations, creating sequential phase waves that pattern somites. Traditional somitogenesis models attribute phase waves to a global modulation of the oscillation frequency. However, increasing evidence suggests that they could arise in a self-organizing manner. Here, we introduce the Sevilletor, a novel reaction-diffusion system that serves as a framework to compare different somitogenesis patterning hypotheses. Using this framework, we propose the Clock and Wavefront Self-Organizing model that considers an excitable self-organizing region where phase waves form independent of global frequency gradients. The model recapitulates the change in relative phase of Wnt and Notch observed during mouse somitogenesis and provides a theoretical basis for understanding the excitability of mouse presomitic mesoderm cells in vitro.

Global arthropod beta-diversity is spatially and temporally structured by latitude

Global biodiversity gradients are generally expected to reflect greater species replacement closer to the equator. However, empirical validation of global biodiversity gradients largely relies on vertebrates, plants, and other less diverse taxa. Here we assess the temporal and spatial dynamics of global arthropod biodiversity dynamics using a beta-diversity framework. Sampling includes 129 sampling sites whereby malaise traps are deployed to monitor temporal changes in arthropod communities. Overall, we encountered more than 150,000 unique barcode index numbers (BINs) (i.e. species proxies). We assess between site differences in community diversity using beta-diversity and the partitioned components of species replacement and richness difference. Global total beta-diversity (dissimilarity) increases with decreasing latitude, greater spatial distance and greater temporal distance. Species replacement and richness difference patterns vary across biogeographic regions. Our findings support long-standing, general expectations of global biodiversity patterns. However, we also show that the underlying processes driving patterns may be regionally linked.

Co-simulation of cool down process from 300 to 80 K for ITER Tokamak

Dynamic simulation of Tokamak superconducting magnet system has been conducted to investigate the cool-down process from 300 to 80 K. The simulation focuses on the cool-down speed variations with respect to the global temperature gradients in the different coils; Toroidal Field (TF) coil, TF STructure (TF-ST), Central Solenoid (CS) and Poloidal Field (PF)/Correction Coil (CC) systems. As imposing the maximum temperature gradients dT max ≤ 50K, the speed should be adjusted, ensuring the limited mechanical stresses due to thermal contractions. So far, the process simulation of Tokamak cryogenic system has been concentrated on the Deuterium Tritium (DT) operation phase; therefore, it is necessary to revise the model to extend its capability for the cool-down; for example, the thermo-hydraulic properties of Cable-in-Conduit Conductor (CICC) for each coil, mechanical properties of materials for the magnet system. The cool-down process is implemented at the helium refrigerator by utilizing LN2 heat exchanger up to 80 K. Its speed is set at -0.8 K/hr as a baseline, which can be controlled by the global temperature gradients in the magnet system. The process will be on hold as dT max ≥ 50K, and resumed once dT max < 50K. The paper discusses the cool-down processes of the Tokamak and identifies the impact on the speed, dT i/dt, of each component.

Global patterns of nuclear and mitochondrial genetic diversity in marine fishes.

Genetic diversity is a fundamental component of biodiversity. Examination of global patterns of genetic diversity can help highlight mechanisms underlying species diversity, though a recurring challenge has been that patterns may vary by molecular marker. Here, we compiled 6862 observations of genetic diversity from 492 species of marine fish and tested among hypotheses for diversity gradients: the founder effect hypothesis, the kinetic energy hypothesis, and the productivity-diversity hypothesis. We fit generalized linear mixed effect models (GLMMs) and explored the extent to which various macroecological drivers (latitude, longitude, temperature (SST), and chlorophyll-a concentration) explained variation in genetic diversity. We found that mitochondrial genetic diversity followed geographic gradients similar to those of species diversity, being highest near the Equator, particularly in the Coral Triangle, while nuclear genetic diversity did not follow clear geographic patterns. Despite these differences, all genetic diversity metrics were correlated with chlorophyll-a concentration, while mitochondrial diversity was also positively associated with SST. Our results provide support for the kinetic energy hypothesis, which predicts that elevated mutation rates at higher temperatures increase mitochondrial but not necessarily nuclear diversity, and the productivity-diversity hypothesis, which posits that resource-rich regions support larger populations with greater genetic diversity. Overall, these findings reveal how environmental variables can influence mutation rates and genetic drift in the ocean, caution against using mitochondrial macrogenetic patterns as proxies for whole-genome diversity, and aid in defining global gradients of genetic diversity.

Global latitudinal gradients and the evolution of body size in dinosaurs and mammals

Global climate patterns fundamentally shape the distribution of species and ecosystems. For example, Bergmann’s rule predicts that homeothermic animals, including birds and mammals, inhabiting cooler climates are generally larger than close relatives from warmer climates. The modern world, however, lacks the comparative data needed to evaluate such macroecological rules rigorously. Here, we test for Bergmann’s rule in Mesozoic dinosaurs and mammaliaforms that radiated within relatively temperate global climate regimes. We develop a phylogenetic model that accounts for biases in the fossil record and allows for variable evolutionary dispersal rates. Our analysis also includes new fossil data from the extreme high-latitude Late Cretaceous Arctic Prince Creek Formation. We find no evidence for Bergmann’s rule in Mesozoic dinosaurs or mammaliaforms, the ancestors of extant homeothermic birds and mammals. When our model is applied to thousands of extant dinosaur (bird) and mammal species, we find that body size evolution remains independent of latitude. A modest temperature effect is found in extant, but not in Mesozoic, birds, suggesting that body size evolution in modern birds was influenced by Bergmann’s rule during Cenozoic climatic change. Our study provides a general approach for studying macroecological rules, highlighting the fossil record’s power to address longstanding ecological principles.

SDGMNet: Statistic-Based Dynamic Gradient Modulation for Local Descriptor Learning

Rescaling the backpropagated gradient of contrastive loss has made significant progress in descriptor learning. However, current gradient modulation strategies have no regard for the varying distribution of global gradients, so they would suffer from changes in training phases or datasets. In this paper, we propose a dynamic gradient modulation, named SDGMNet, for contrastive local descriptor learning. The core of our method is formulating modulation functions with dynamically estimated statistical characteristics. Firstly, we introduce angle for distance measure after deep analysis on backpropagation of pair-wise loss. On this basis, auto-focus modulation is employed to moderate the impact of statistically uncommon individual pairs in stochastic gradient descent optimization; probabilistic margin cuts off the gradients of proportional triplets that have achieved enough optimization; power adjustment balances the total weights of negative pairs and positive pairs. Extensive experiments demonstrate that our novel descriptor surpasses previous state-of-the-art methods in several tasks including patch verification, retrieval, pose estimation, and 3D reconstruction.

Optimal Output Consensus of Heterogeneous Linear Multiagent Systems Over Weight-Unbalanced Directed Networks.

This article investigates the distributed optimal output consensus problem of heterogeneous linear multiagent systems over weight-unbalanced directed networks. A novel distributed continuous-time state feedback controller is proposed to steer the outputs of all the agents to converge to the optimal solution of the global cost function. Under the standard condition that the unbalanced digraph is strongly connected and the local cost functions are strongly convex with global Lipschitz gradients, the exponential convergence of the closed-loop multiagent system is established. Then, the proposed state feedback control law is extended to an observer-based output feedback setting. Two examples are finally provided to illustrate the effectiveness of the proposed control schemes.