Abstract
The staggered model is a recent, very general variant of discrete-time quantum walks which, avoiding the use of a coin to direct the walker evolution, explores the underlying graph structure to build an evolution operator based on local unitaries induced by adjacent vertices. Optimising their implementation to increase resilience to decoherence phenomena motivates their analysis with the ZX-calculus. The whole optimisation can be seen as a graph reconfiguration process along which the original circuit is rewrote, significantly reducing the number of (expensive) gates used. The exercise identified an underlying pattern leading to an alternative, potentially more efficient evolution operator.

Abstract
This paper introduces Paraconsistent Reactive Graphs, as an extension of Reactive graphs that incorporates paraconsistency into the ground edges to address vagueness and inconsistency within dynamic systems. By assigning pairs of truth values to ground edges, this framework captures the uncertainty and contradictions stemming from incomplete or conflicting information. We explore the semantics of these graphs and provide a practical example to illustrate the proposed approach.

Abstract
In previous work, we introduced an 'invisible' ECG system with electrodes integrated into a toilet seat, capturing signals from the thighs. Here, we present the tOLIet dataset with single-lead thigh ECGs to advance cardiovascular assessment using this novel approach. The dataset includes 149 records from 86 individuals (50 females, 36 males; mean age 31.73 +/- 13.11 years; weight 66.89 +/- 10.70 kg; height 166.82 +/- 6.07 cm). Participants were recruited via the Centro Hospitalar Universit & aacute;rio de Lisboa Central (CHULC). Each recording features four differential signals from toilet-seat electrodes alongside reference data from a hospital-grade 12-lead ECG. Beyond signal collection and quality evaluation, we conducted a gender-specific analysis comparing valid signal percentages relative to Body Mass Index (BMI). This analysis explores anatomical or physiological factors affecting thigh-based ECG acquisition, guiding system design and customization to enhance signal reliability across populations.

Abstract
Cardiovascular diseases remain the leading cause of morbidity and mortality worldwide. Continuous electrocardiographic (ECG) monitoring is essential for prevention and treatment, but conventional approaches based on the need for some voluntary action often limit comfort and adherence in long-term use. This study investigates the feasibility of acquiring ECG signals from a toilet seat interface embedding dry electrodes in the posterior thighs. A total of 30 hospitalised patients with diverse cardiovascular conditions-including arrhythmias, ischemic heart disease, heart failure, structural abnormalities, and aneurysms-were enrolled. Thigh-acquired ECGs were recorded simultaneously with conventional limb-lead signals and analysed for morphology, heart rate variability (HRV), and disease-related clustering. Thigh-based ECGs demonstrated clear P-QRS-T complexes with preserved morphology, allowing reliable extraction of mean templates and HRV metrics. The comparison between pathological and normal groups showed that post-surgical aortic repair patients had ECG profiles closest to the normal cluster; in contrast, aortic stenosis (AS) appeared most distant. HRV analysis revealed disease-specific autonomic patterns: patients with tricuspid or mitral involvement exhibited higher variability (SDNN up to 140 ms), whereas those with aortic valve disease presented markedly reduced parasympathetic indices (RMSSD and pNN50). Principal component analysis of multi-feature ECG data identified overlapping groups of Acute Coronary Syndrome, Unstable Angina and Ascending Aortic Aneurysm. At the same time, hierarchical clustering confirmed the distinct separation of conditions with severe hemodynamic disruption, such as PS and AS. These findings support the feasibility of unobtrusive thigh-based ECG monitoring via a toilet-seat interface, enabling reliable signal acquisition, HRV analysis, and preliminary patient stratification. This approach may lay the groundwork for future home-based cardiovascular screening and telemedicine applications.

Abstract
This special issue showcases state-of-the-art research at the intersection of analytics and retail operations. As the retail landscape becomes increasingly complex - driven by omnichannel strategies, evolving customer expectations, and a surge in data availability - analytics has emerged as a critical enabler of operational efficiency, customer experience, responsiveness, and sustainability and ethics. Collectively, these contributions demonstrate how advanced analytics can support retailers in navigating uncertainty, personalizing services, and scaling up innovation across formats and channels. The articles featured in this issue address a diverse set of decision domains, including warehousing, inventory and assortment planning, and distribution and last-mile delivery. Methodologically, they span descriptive, prescriptive, and hybrid approaches, leveraging tools such as machine learning, stochastic modeling, and dynamic optimization. By grounding models in real-world data and focusing on practical implementation, the issue provides actionable insights for both scholars and practitioners. It also highlights emerging opportunities for future research on behavioral integration, human-machine collaboration, and the ethical dimensions of retail analytics.

Abstract
In this paper, we introduce a novel approach for rigorously verifying safety properties of state machine specifications. Our method leverages an auto-active verifier and centers around the use of action functions annotated with contracts. These contracts facilitate inductive invariant checking, ensuring correctness during system execution. Our approach is further supported by the Why3-do library, which extends the Why3 tool's capabilities to verify concurrent and distributed algorithms using state machines. Two distinctive features of Why3-do are: (i) it supports specification refinement through refinement mappings, enabling hierarchical reasoning about distributed algorithms; and (ii) it can be easily extended to make verifying specific classes of systems more convenient. In particular, the library contains models allowing for message-passing algorithms to be described with programmed handlers, assuming different network semantics. A gallery of examples, all verified with Why3 using SMT solvers as proof tools, is also described in the paper. It contains several auto-actively verified concurrent and distributed algorithms, including the Paxos consensus algorithm.