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Broadcast protocols enable a set of n parties to agree on the input of a designated sender, even in the face of malicious parties who collude to attack the protocol. In the honest-majority setting, a fruitful line of work harnessed randomization and cryptography to achieve low-communication broadcast protocols with sub-quadratic total communication and with "balanced" sub-linear communication cost per party. However, comparatively little is known in the dishonest-majority setting. Here, the most communication-efficient constructions are based on the protocol of Dolev and Strong (SICOMP '83), and sub-quadratic broadcast has not been achieved even using randomization and cryptography. On the other hand, the only nontrivial ω(n) communication lower bounds are restricted to deterministic protocols, or against strong adaptive adversaries that can perform "after the fact" removal of messages. We provide communication lower bounds in this space, which hold against arbitrary cryptography and setup assumptions, as well as a simple protocol showing near tightness of our first bound. - Static adversary. We demonstrate a tradeoff between resiliency and communication for randomized protocols secure against n-o(n) static corruptions. For example, Ω(n⋅ polylog(n)) messages are needed when the number of honest parties is n/polylog(n); Ω(n√n) messages are needed for O(√n) honest parties; and Ω(n²) messages are needed for O(1) honest parties. Complementarily, we demonstrate broadcast with O(n⋅polylog(n)) total communication and balanced polylog(n) per-party cost, facing any constant fraction of static corruptions. - Weakly adaptive adversary. Our second bound considers n/2 + k corruptions and a weakly adaptive adversary that cannot remove messages "after the fact." We show that any broadcast protocol within this setting can be attacked to force an arbitrary party to send messages to k other parties. Our bound implies limitations on the feasibility of balanced low-communication protocols: For example, ruling out broadcast facing 51% corruptions, in which all non-sender parties have sublinear communication locality. 

Given the increasing prevalence of droughts, unpredictable rainfall patterns, and limited access to dependable water sources in the United States and worldwide, it has become crucial to implement effective irrigation scheduling strategies. Irrigation is triggered when some variables, such as soil moisture or accumulated water deficit, exceed a given threshold in the most common approaches applied in irrigation scheduling. A High-Resolution Land Data Assimilation System (HRLDAS) was used in this study to generate timely and accurate soil moisture and evapotranspiration (ET) data for irrigation management. By integrating HRLDAS products and the crop growth model (AquaCrop), an automated data-driven irrigation scheduling approach was developed and evaluated. For HRLDAS ET and soil moisture, the ET-water balance (ET-WB)-based method and soil-moisture-based method were applied accordingly. The ET-WB-based method showed a 10.6~33.5% water-saving result in dry and set seasons, whereas the soil moisture-based method saved 7.2~37.4% of irrigation water in different weather conditions. Both of these methods demonstrated good results in saving water (with a varying range of 10~40%) without harming crop yield. The optimized thresholds in the two approaches were partially consistent with the default values from the Food and Agriculture Organization and showed a similar trend in the growing season. Furthermore, the forecasted rainfall was integrated into this model to see its water-saving effect. The results showed that an additional 10% of irrigation water, which is 20~50%, can be saved without harming the crop yield. This study automated the data-driven approach for irrigation scheduling by taking advantage of HRLDAS products, which can be generated in a near-real-time manner. The results indicated the great potential of this automated approach for saving water and irrigation decision making.