Monotonicity Principle in Tomography of Nonlinear Conducting Materials

We treat an inverse electrical conductivity problem which deals with the reconstruction of nonlinear electrical conductivity starting from boundary measurements in steady currents operations. In this framework, a key role is played by the Monotonicity Principle, which establishes a monotonic relation connecting the unknown material property to the (measured) Dirichlet-to-Neumann operator (DtN). Monotonicity Principles are the foundation for a class of non-iterative and real-time imaging methods and algorithms. In this article, we prove that the Monotonicity Principle for the Dirichlet Energy in nonlinear problems holds under mild assumptions. Then, we show that apart from linear and $p$-Laplacian cases, it is impossible to transfer this Monotonicity result from the Dirichlet Energy to the DtN operator. To overcome this issue, we introduce a new boundary operator, identified as an Average DtN operator.Comment: 28 pages, 6 figure

Identification of spatially-resolved markers of malignant transformation in Intraductal Papillary Mucinous Neoplasms

The existing Intraductal Papillary Mucinous Neoplasm (IPMN) risk stratification relies on clinical and histological factors, resulting in inaccuracies and leading to suboptimal treatment. This is due to the lack of appropriate molecular markers that can guide patients toward the best therapeutic options. Here, we assess and confirm subtype-specific markers for IPMN across two independent cohorts of patients using two Spatial Transcriptomics (ST) technologies. Specifically, we identify HOXB3 and ZNF117 as markers for Low-Grade Dysplasia, SPDEF and gastric neck cell markers in borderline cases, and NKX6-2 and gastric isthmus cell markers in High-Grade-Dysplasia Gastric IPMN, highlighting the role of TNFα and MYC activation in IPMN progression and the role of NKX6-2 in the specific Gastric IPMN progression. In conclusion, our work provides a step forward in understanding the gene expression landscapes of IPMN and the critical transcriptional networks related to PDAC progression