Connectivity of 33-distance graphs

For a simple graph $G$, the $3$-distance graph, $D_3(G)$, is a graph with the vertex set $V(G)$ and two vertices are adjacent if and only if their distance is $3$ in the graph $G$. For a connected graph $G$, we provide some conditions for the connectedness of $D_3(G)$. Also, we characterize all trees and unicyclic graphs with connected $3$-distance graph.Comment: 10 pages, 7 figure

Connectivity of 2-distance graphs

For a simple graph $G$, the $2$-distance graph, $D_2(G)$, is a graph with the vertex set $V(G)$ and two vertices are adjacent if and only if their distance is $2$ in the graph $G$. In this paper, we characterize all graphs with connected 2-distance graph. For graphs with diameter 2, we prove that $D_2(G)$ is connected if and only if $G$ has no spanning complete bipartite subgraphs. For graphs with a diameter greater than 2, we define a maximal Fine set and by contracting $G$ on these subsets, we get a new graph $\hat G$ such that $D_2(G)$ is connected if and only if $D_2(\hat G)$ is connected. Especially, $D_2(G)$ is disconnected if and only if $\hat G$ is bipartite.Comment: 7 pages, 6 figure

Diameter of 2-distance graphs

For a simple graph $G$, the $2$-distance graph, $D_2(G)$, is a graph with the vertex set $V(G)$ and two vertices are adjacent if and only if their distance is $2$ in the graph $G$. In this paper, for graphs $G$ with diameter 2, we show that $diam(D_2(G))$ can be any integer $t\geqslant2$. For graphs $G$ with $diam(G)\geqslant3$, we prove that $\frac{1}{2}diam(G)\leqslant diam(D_2(G))$ and this inequality is sharp. Also, for $diam(G)=3$, we prove that $diam(D_2(G))\leqslant5$ and this inequality is sharp.Comment: 10 pages, 15 figures. arXiv admin note: text overlap with arXiv:2306.15301, arXiv:2403.0613

Insight into mechanics of AFM tip-based nanomachining: bending of cantilevers and machined grooves

Atomic force microscope (AFM) tip-based nanomachining is currently the object of intense research investigations. Values of the load applied to the tip at the free end of the AFM cantilever probe used for nanomachining are always large enough to induce plastic deformation on the specimen surface contrary to the small load values used for the conventional contact mode AFM imaging. This study describes an important phenomenon specific for AFM nanomachining in the forward direction: under certain processing conditions, the deformed shape of the cantilever probe may change from a convex to a concave orientation. The phenomenon can principally change the depth and width of grooves machined, e.g. the grooves machined on a single crystal copper specimen may increase by 50% on average following such a change in the deformed shape of the cantilever. It is argued that this phenomenon can take place even when the AFM-based tool is operated in the so-called force-controlled mode. The study involves the refined theoretical analysis of cantilever probe bending, the analysis of experimental signals monitored during the backward and forward AFM tip-based machining and the inspection of the topography of produced grooves

Pathological Complete Response in Patients With Resected Pancreatic Adenocarcinoma After Preoperative Chemotherapy

Importance: Preoperative chemo(radio)therapy is increasingly used in patients with localized pancreatic adenocarcinoma, leading to pathological complete response (pCR) in a small subset of patients. However, multicenter studies with in-depth data about pCR are lacking. Objective: To investigate the incidence, outcome, and risk factors of pCR after preoperative chemo(radio)therapy. Design, Setting, and Participants: This observational, international, multicenter cohort study assessed all consecutive patients with pathology-proven localized pancreatic adenocarcinoma who underwent resection after 2 or more cycles of chemotherapy (with or without radiotherapy) in 19 centers from 8 countries (January 1, 2010, to December 31, 2018). Data collection was performed from February 1, 2020, to April 30, 2022, and analyses from January 1, 2022, to December 31, 2023. Median follow-up was 19 months. Exposures: Preoperative chemotherapy (with or without radiotherapy) followed by resection. Main Outcomes and Measures: The incidence of pCR (defined as absence of vital tumor cells in the sampled pancreas specimen after resection), its association with OS from surgery, and factors associated with pCR. Factors associated with overall survival (OS) and pCR were investigated with Cox proportional hazards and logistic regression models, respectively. Results: Overall, 1758 patients (mean [SD] age, 64 [9] years; 879 [50.0%] male) were studied. The rate of pCR was 4.8% (n = 85), and pCR was associated with OS (hazard ratio, 0.46; 95% CI, 0.26-0.83). The 1-, 3-, and 5-year OS rates were 95%, 82%, and 63% in patients with pCR vs 80%, 46%, and 30% in patients without pCR, respectively (P < .001). Factors associated with pCR included preoperative multiagent chemotherapy other than (m)FOLFIRINOX ([modified] leucovorin calcium [folinic acid], fluorouracil, irinotecan hydrochloride, and oxaliplatin) (odds ratio [OR], 0.48; 95% CI, 0.26-0.87), preoperative conventional radiotherapy (OR, 2.03; 95% CI, 1.00-4.10), preoperative stereotactic body radiotherapy (OR, 8.91; 95% CI, 4.17-19.05), radiologic response (OR, 13.00; 95% CI, 7.02-24.08), and normal(ized) serum carbohydrate antigen 19-9 after preoperative therapy (OR, 3.76; 95% CI, 1.79-7.89). Conclusions and Relevance: This international, retrospective cohort study found that pCR occurred in 4.8% of patients with resected localized pancreatic adenocarcinoma after preoperative chemo(radio)therapy. Although pCR does not reflect cure, it is associated with improved OS, with a doubled 5-year OS of 63% compared with 30% in patients without pCR. Factors associated with pCR related to preoperative chemo(radio)therapy regimens and anatomical and biological disease response features may have implications for treatment strategies that require validation in prospective studies because they may not universally apply to all patients with pancreatic adenocarcinoma