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We consider a general non-stochastic online pricing bandit setting in a procurement scenario where a buyer with a budget wants to procure items from a fixed set of sellers to maximize the buyer's reward by dynamically offering purchasing prices to the sellers, where the sellers' costs and values at each time period can change arbitrarily and the sellers determine whether to accept the offered prices to sell the items. This setting models online pricing scenarios of procuring resources or services in multi-agent systems. We first consider the offline setting when sellers' costs and values are known in advance and investigate the best fixed-price policy in hindsight. We show that it has a tight approximation guarantee with respect to the offline optimal solutions. In the general online setting, we propose an online pricing policy, Granularity-based Pricing (GAP), which exploits underlying side-information from the feedback graph when the budget is given as the input. We show that GAP achieves an upper bound of O(n{v_{max}}{c_{min}}sqrt{B/c_{min}}ln B) on the alpha-regret where n, v_{max}, c_{min}, and B are the number, the maximum value, the minimum cost of sellers, and the budget, respectively. We then extend it to the unknown budget case by developing a variant of GAP, namely Doubling-GAP, and show its alpha-regret is at most O(n{v_{max}}{c_{min}}sqrt{B/c_{min}}ln2 B). We also provide an alpha-regret lower bound Omega(v_{max}sqrt{Bn/c_{min}}) of any online policy that is tight up to sub-linear terms. We conduct simulation experiments to show that the proposed policy outperforms the baseline algorithms. 

Abstract While the positive relationship between plant diversity and ecosystem functioning is frequently observed and often attributed to direct plant–plant interactions, it remains unclear whether and how the effects of plant diversity endure through soil legacy effects, particularly at the level of genotypic diversity. We manipulated the genotypic diversity ofScirpus mariqueterand tested its soil legacy effects on a conspecific phytometer under low‐ and high‐water availability conditions. We found that genotypic diversity enhanced phytometer productivity through soil legacies, with stronger effects under low‐water availability conditions, improving its resistance to water stress. Moreover, this effect was attributed to the association between asexual and sexual reproductive strategies by increasing ramet number to ensure plant survival under low‐water availability and promoting sexual reproduction to escape stress. The observed diversity effects were primarily associated with increased levels of microbial biomass in soils trained by populations with diverse genotypes. Our findings highlight the importance of plant genotypic diversity in modulating ecosystem functioning through soil legacies and call for management measures that promote genetic diversity to make ecosystems sustainable in the face of climate change. 

In recent decades, the design of budget feasible mechanisms for a wide range of procurement auction settings has received significant attention in the Artificial Intelligence (AI) community. These procurement auction settings have practical applications in various domains such as federated learning, crowdsensing, edge computing, and resource allocation. In a basic procurement auction setting of these domains, a buyer with a limited budget is tasked with procuring items (\eg, goods or services) from strategic sellers, who have private information on the true costs of their items and incentives to misrepresent their items' true costs. The primary goal of budget feasible mechanisms is to elicit the true costs from sellers and determine items to procure from sellers to maximize the buyer valuation function for the items and ensure that the total payment to the sellers is no more than the budget. In this survey, we provide a comprehensive overview of key procurement auction settings and results of budget feasible mechanisms. We provide several promising future research directions. 

A<sc>bstract</sc> We analyze a general class of locally supersymmetric, CP and modular invariant models of lepton masses depending on two complex moduli taking values in the vicinity of a fixed point, where the theory enjoys a residual symmetry under a finite group. Like in models that depend on a single modulus, we find that all physical quantities exhibit a universal scaling with the distance from the fixed point. There is no dependence on the level of the construction, the weights of matter multiplets and their representations, with the only restriction that electroweak lepton doublets transform as irreducible triplets of the finite modular group. Also the form of the kinetic terms, which here are assumed to be neither minimal nor flavor blind, is irrelevant to the outcome. The result is remarkably simple and the whole class of examined theories gives rise to five independent patterns of neutrino mass matrices. Only in one of them, the predicted scaling agrees with the observed neutrino mass ratios and lepton mixing angles, exactly as in single modulus theories living close toτ=i. 

A<sc>bstract</sc> Inspired by the structure of top-down derived models endowed with modular flavor symmetries, we investigate the yet phenomenologically unexplored binary dihedral group 2D₃. After building the vector-valued modular forms in the representations of 2D₃with small modular weights, we systematically classify all (Dirac and Majorana) mass textures of fermions with fractional modular weights and all possible 2 + 1-family structures. This allows us to explore the parameter space of fermion models based on 2D₃, aiming at a description of both quarks and leptons with a minimal number of parameters and best compatibility with observed data. We consider the separate possibilities of neutrino masses generated by either a type-I seesaw mechanism or the Weinberg operator. We identify a model that, besides fitting all known flavor observables, delivers predictions for six not-yet measured parameters and favors normal-ordered neutrino masses generated by the Weinberg operator. It would be interesting to figure out whether it is possible to embed our model within a top-down scheme, such as$${\mathbb{T}}^{2}/{\mathbb{Z}}_{4}$$heterotic orbifold compactifications. 

Interactions among the underlying agents of a complex system are not only limited to dyads but can also occur in larger groups. Currently, no generic model has been developed to capture high-order interactions (HOI), which, along with pairwise interactions, portray a detailed landscape of complex systems. Here, we integrate evolutionary game theory and behavioral ecology into a unified statistical mechanics framework, allowing all agents (modeled as nodes) and their bidirectional, signed, and weighted interactions at various orders (modeled as links or hyperlinks) to be coded into hypernetworks. Such hypernetworks can distinguish between how pairwise interactions modulate a third agent (active HOI) and how the altered state of each agent in turn governs interactions between other agents (passive HOI). The simultaneous occurrence of active and passive HOI can drive complex systems to evolve at multiple time and space scales. We apply the model to reconstruct a hypernetwork of hexa-species microbial communities, and by dissecting the topological architecture of the hypernetwork using GLMY homology theory, we find distinct roles of pairwise interactions and HOI in shaping community behavior and dynamics. The statistical relevance of the hypernetwork model is validated using a series of in vitro mono-, co-, and tricultural experiments based on three bacterial species.