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This paper presents a sandbox study proposal focused on the distributed processing of personal health data within the Vinnova-funded SARDIN project. The project aims to develop the Health Data Bank (H\"alsodatabanken in Swedish), a secure platform for research and innovation that complies with the European Health Data Space (EHDS) legislation. By minimizing the sharing and storage of personal data, the platform sends analysis tasks directly to the original data locations, avoiding centralization. This approach raises questions about data controller responsibilities in distributed environments and the anonymization status of aggregated statistical results. The study explores federated analysis, secure multi-party aggregation, and differential privacy techniques, informed by real-world examples from clinical research on Parkinson's disease, stroke rehabilitation, and wound analysis. To validate the proposed study, numerical experiments were conducted using four open-source datasets to assess the feasibility and effectiveness of the proposed methods. The results support the methods for the proposed sandbox study by demonstrating that differential privacy in combination with secure aggregation techniques significantly improves the privacy-utility trade-off., Comment: 20 pages, 5 figures, 4 tables

In multiwinner approval voting, forming a committee that proportionally represents voters' approval ballots is an essential task. The notion of justified representation (JR) demands that any large "cohesive" group of voters should be proportionally "represented". The "cohesiveness" is defined in different ways; two common ways are the following: (C1) demands that the group unanimously approves a set of candidates proportional to its size, while (C2) requires each member to approve at least a fixed fraction of such a set. Similarly, "representation" have been considered in different ways: (R1) the coalition's collective utility from the winning set exceeds that of any proportionally sized alternative, and (R2) for any proportionally sized alternative, at least one member of the coalition derives less utility from it than from the winning set. Three of the four possible combinations have been extensively studied: (C1)-(R1) defines Proportional Justified Representation (PJR), (C1)-(R2) defines Extended Justified Representation (EJR), (C2)-(R2) defines Full Justified Representation (FJR). All three have merits, but also drawbacks. PJR is the weakest notion, and perhaps not sufficiently demanding; EJR may not be compatible with perfect representation; and it is open whether a committee satisfying FJR can be found efficiently. We study the combination (C2)-(R1), which we call Full Proportional Justified Representation (FPJR). We investigate FPJR's properties and find that it shares PJR's advantages over EJR: several proportionality axioms (e.g. priceability, perfect representation) imply FPJR and PJR but not EJR. We also find that efficient rules like the greedy Monroe rule and the method of equal shares satisfy FPJR, matching a key advantage of EJR over FJR. However, the Proportional Approval Voting (PAV) rule may violate FPJR, so neither of EJR and FPJR implies the other., Comment: 18 pages, Accepted to AAMAS 25

Large Language Models (LLMs) hold promise for advancing legal practice by automating complex tasks and improving access to justice. However, their adoption is limited by concerns over client confidentiality, especially when lawyers include sensitive Personally Identifiable Information (PII) in prompts, risking unauthorized data exposure. To mitigate this, we introduce LegalGuardian, a lightweight, privacy-preserving framework tailored for lawyers using LLM-based tools. LegalGuardian employs Named Entity Recognition (NER) techniques and local LLMs to mask and unmask confidential PII within prompts, safeguarding sensitive data before any external interaction. We detail its development and assess its effectiveness using a synthetic prompt library in immigration law scenarios. Comparing traditional NER models with one-shot prompted local LLM, we find that LegalGuardian achieves a F1-score of 93% with GLiNER and 97% with Qwen2.5-14B in PII detection. Semantic similarity analysis confirms that the framework maintains high fidelity in outputs, ensuring robust utility of LLM-based tools. Our findings indicate that legal professionals can harness advanced AI technologies without compromising client confidentiality or the quality of legal documents., Comment: 10 pages, 3 figures

As one of the mainstream approaches in system identification, subspace identification methods (SIMs) are known for their simple parameterization for MIMO systems and robust numerical properties. However, a comprehensive statistical analysis of SIMs remains an open problem. Amid renewed focus on identifying state-space models in the non-asymptotic regime, this work presents a finite sample analysis for a large class of open-loop SIMs. It establishes high-probability upper bounds for system matrices obtained via SIMs, and reveals that convergence rates for estimating Markov parameters and system matrices are $\mathcal{O}(1/\sqrt{N})$ up to logarithmic terms, in line with classical asymptotic results. Following the key steps of SIMs, we arrive at the above results by a three-step procedure. In Step 1, we begin with a parsimonious SIM (PARSIM) that uses least-squares regression to estimate multiple high-order ARX models in parallel. Leveraging a recent analysis of an individual ARX model, we obtain a union error bound for a bank of ARX models. Step 2 involves model reduction via weighted singular value decomposition (SVD), where we consider different data-dependent weighting matrices and use robustness results for SVD to obtain error bounds on extended controllability and observability matrices, respectively. The final Step 3 focuses on deriving error bounds for system matrices, where two different realization algorithms, the MOESP type and the Larimore type, are considered. Although our study initially focuses on PARSIM, the methodologies apply broadly across many variants of SIMs.