Applied Sciences

This review surveys the mathematical theory and methods of state estimation for stochastic dynamical systems when the Gaussian-linear-least-squares paradigm fails, focusing on the role of sparsity-promoting and constraint-encoding regularization. The exposition is organized around a single regularized estimation functional in which the weighted least-squares terms of classical filtering and smoothing are augmented by nonsmooth penalty functions and indicator functions of constraint sets. Bayesian recursion, Gaussian approximation, sequential Monte Carlo, and moving-horizon optimization emerge as different structural assumptions on this common objective. Recent work is reviewed through five relaxations of the classical assumptions: heavy-tailed and non-Gaussian noise, unknown or misspecified models, distributed and networked architectures, unused structural prior information such as sparsity and safety constraints, and switching or unknown external inputs. Emphasis is placed on variable-splitting and augmented-Lagrangian techniques that interface Gaussian recursions with nonsmooth optimization, on convergence and stability guarantees, and on the mathematical challenges that remain open, including convergence rates for alternating minimization, statistical efficiency relative to least-squares baselines, and provable guarantees for learning-enhanced filters.

Federated black-box prompt tuning enables organizations to adapt a proprietary frozen language model without centralizing their labeled data, but local search-state aggregation does not directly define a shared pooled-data objective, and client-specific feedback can expose private signals. We propose FedSTIP-Tuning, which composes a three-party permutation-based protected forward propagation with a common-candidate population and pairwise-masked loss aggregation in a cross-silo setting. All participating clients evaluate the same prompt candidates, and the coordinator ranks their sample-weighted aggregate losses, thereby optimizing the empirical objective over the fixed union of client shards under full participation. Under the stated semi-honest and non-collusion assumptions, the aggregation layer hides each released loss vector’s client-level decomposition, while the aggregate values and execution metadata remain observable to their authorized parties. On RoBERTa-large, FedSTIP-Tuning exceeds the strongest evaluated FedBPT configuration by 6.40, 2.66, and 7.60 percentage points on AG News, SST-2, and DBpedia, respectively, under matched forward budgets. Its protected forward preserves all candidate rankings across 600 paired generations and is 861× and 957× faster than a generic interactive two-party computation reference on the RoBERTa-base warm and cold paths, and 694× and 578× on RoBERTa-large.

The monitoring of agroclimatic variables is one of the fundamental pillars for anticipating and mitigating frost phenomena in potato crops, especially in the rural mountain area located in the municipality of La Calera (Colombia). Low-power, long-range communication technologies such as LoRa and LoRaWAN allow the creation of low-cost solutions for the acquisition and remote transmission of environmental data in agricultural production. This work presents the design and validation of a wireless sensor node and a LoRaWAN network oriented towards climate monitoring in a real agricultural production environment. This study aimed to design and validate a low-cost environmental monitoring system based on LoRa and LoRaWAN technology for measuring temperature and relative humidity as the most relevant variables for the early detection of frost in potato crops in the municipality of La Calera. A sensor node was developed using the Heltec LoRa 32 V3 microcontroller and the AM2305B sensor. The node was configured to transmit data through LoRaWAN technology in the US-915 MHz band, using an SX1302 Gateway integrated into The Things Network, where the devices and data reception were managed. A total of 70 measurements were carried out over three days in a controlled environment, covering a temperature range from 20 °C to 50 °C and from 70% to 20% RH, and the measurements were compared with a PeakTech-5035 reference instrument through statistical analysis. The statistical analysis confirmed that the developed node presents an accuracy of ±0.7 °C in temperature and ±5% RH in relative humidity, with a Pearson correlation coefficient of r = 0.99 for temperature and r = 0.96 for relative humidity compared with the reference sensors. Additionally, the root mean square error (RMSE) was 0.82 °C for temperature and 4.6% RH for relative humidity, supporting the quality of the generated data. Furthermore, urban and rural propagation tests were conducted to evaluate the communication performance of the LoRaWAN infrastructure through RSSI and SNR measurements under real deployment conditions. The communication analysis demonstrated stable connectivity in both dense urban and rural agricultural environments, maintaining operational wireless communication at distances approaching 1 km under low power conditions. The results demonstrate that the prototype offers performance comparable to commercial sensors at an approximately 50% lower cost, establishing it as a viable alternative for building wireless sensor networks (WSN) based on LPWAN technology. In this way, the proposed solution facilitates access to climate monitoring technologies in rural areas and strengthens farmers’ ability to anticipate frost events in potato crops.