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Structuralism in Differential Equations
No full textStructuralism in philosophy of mathematics has largely focused on arithmetic, algebra, and basic analysis. Some have doubted whether distinctively structural working methods have any impact in other fields such as differential equations. We show narrowly construed structuralism as offered by Benacerraf has no practical role in differential equations. But Dedekind’s approach to the continuum already did not fit that narrow sense, and little of mathematics today does. We draw on one calculus textbook, one celebrated analysis textbook, and a monograph on the Navier–Stokes equation to show structural methods like Dedekind’s have long been central to differential equations, and have philosophically respectable ontology and epistemology
Hybrid Energy Systems: Synergy Margin and Control Co-Design
No full textExtraordinary properties emerge from subsystems\u27 interactions. Hybrid energy systems (HESs) are a promising concept that could change the renewable energy landscape. By co-designing generation, storage, and conversion technologies, HESs can provide new electrical power services, increase grid stability and control authority, and generate energy and/or nonenergy products such as electricity, hydrogen, ammonia, heat, digital data, or fresh water. This article discusses some conditions the co-design of HESs should follow to optimize the combined system (synergy), avoiding deterioration (dysfunction). It introduces some technoeconomic synergy conditions, develops a synergy margin, and analyses several case studies, exploring also the control co-design methodology to optimize synergistically the hybrid system
Nodes for Modes: Nodal Honeycomb Metamaterial Enables a Soft Robot with Multimodal Locomotion
No full textSoft-bodied animals, such as worms and snakes, use many muscles in different ways to traverse unstructured environments and inspire tools for accessing confined spaces. They demonstrate versatility of locomotion which is essential for adaptation to changing terrain conditions. However, replicating such versatility in untethered soft-bodied robots with multimodal locomotion capabilities have been challenging due to complex fabrication processes and limitations of soft body structures to accommodate hardware such as actuators, batteries and circuit boards. Here, we present MetaCrawler, a 3D printed metamaterial soft robot designed for multimodal and omnidirectional locomotion. Our design approach facilitated an easy fabrication process through a discrete assembly of a modular nodal honeycomb lattice with soft and hard components. A crucial benefit of the nodal honeycomb architecture is the ability of its hard components, nodes, to accommodate a distributed actuation system, comprising servomotors, control circuits, and batteries. Enabled by this distributed actuation, MetaCrawler achieves five locomotion modes: peristalsis, sidewinding, sideways translation, turn-in-place, and anguilliform. Demonstrations showcase MetaCrawler’s adaptability in confined channel navigation, vertical traversing, and maze exploration. This soft robotic system holds the potential to offer easy-to-fabricate and accessible solutions for multimodal locomotion in applications such as search and rescue, pipeline inspection, and space missions
To Revise or Not Revise? Isolated Margin Positivity in Localized Pancreatic Ductal Adenocarcinoma
Get PDFBackground: The study determined the proportion of patients with pancreatic adenocarcinoma (PDAC) who had margin-positive disease and no other adverse pathologic findings (APF) using institutional and administrative datasets. Methods: Patients with clinical stage I or II PDAC in the National Cancer Database (NCDB 2010–2020) and those who underwent pancreatectomy at the authors’ institution (2010–2021) were identified. Isolated margin positivity (IMP) was defined as a positive surgical margin with no APF (negative nodes, no lymphovascular/perineural invasion). Results: The study included 225 patients from the authors’ institution and 23,598 patients from the NCDB. The margin-positive rates were 21.8% and 20.3%, and the IMP rates were 0.4% and 0.5%, respectively. In the institutional cohort, 68.4% of the patients had recurrence, and most of the patients (65.6%) had distant recurrences. The median recurrence-free survival (RFS) was 63.3 months for no APF, not reached for IMP, 14.8 months for negative margins & 1 APF, 20.3 months for positive margins & 2 APFs, and 12.9 months with all APF positive. The patients in the NCDB with IMP had a lower median OS than the patients with no APF (20.5 vs 390 months), but a higher median OS than those with margin positivity plus 1 APF (20.5 vs 18.0 months) or all those with APF positivity (20.5 vs 15.4 months). Based on institutional rates of IMP, any margin positivity, neck margin positivity (NMP), and no APF, the fraction of patients who might benefit from neck margin revision was 1 in 100,000, and those likely to benefit from any margin revision was 1 in 18,500. In the NCDB, those estimated to derive potential benefit from margin revision was 1 in 25,000. Conclusions: Isolated margin positivity in resected PDAC is rare, and most patients experience distant recurrence. Revision of IMP appears unlikely to confer benefit to most patients
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