Searching edges in the overlap of two plane graphs

Consider a pair of plane straight-line graphs, whose edges are colored red and blue, respectively, and let n be the total complexity of both graphs. We present a O(n log n)-time O(n)-space technique to preprocess such pair of graphs, that enables efficient searches among the red-blue intersections along edges of one of the graphs. Our technique has a number of applications to geometric problems. This includes: (1) a solution to the batched red-blue search problem [Dehne et al. 2006] in O(n log n) queries to the oracle; (2) an algorithm to compute the maximum vertical distance between a pair of 3D polyhedral terrains one of which is convex in O(n log n) time, where n is the total complexity of both terrains; (3) an algorithm to construct the Hausdorff Voronoi diagram of a family of point clusters in the plane in O((n+m) log^3 n) time and O(n+m) space, where n is the total number of points in all clusters and m is the number of crossings between all clusters; (4) an algorithm to construct the farthest-color Voronoi diagram of the corners of n axis-aligned rectangles in O(n log^2 n) time; (5) an algorithm to solve the stabbing circle problem for n parallel line segments in the plane in optimal O(n log n) time. All these results are new or improve on the best known algorithms.Comment: 22 pages, 6 figure

Superconductivity and spin-glass like behavior in system with Pd sheet sandwiched between graphene sheets

Pd-metal graphite (Pd-MG) has a layered structure, where each Pd sheet is sandwiched between adjacent graphene sheets. DC magnetization and AC magnetic susceptibility of Pd-MG have been measured using a SQUID magnetometer. Pd-MG undergoes a superconducting transition at $T_{c}$ ($= 3.63 \pm 0.04$ K). The superconductivity occurs in Pd sheets. The relaxation of $M_{ZFC}$ (aging), which is common to spin glass systems, is also observed below $T_{c}$. The relaxation rate $S(t)$ shows a peak at a characteristic time $t_{cr}$, which is longer than a wait time $t_{w}$. The irreversibility between $\chi_{ZFC}$ and $\chi_{FC}$ occurs well above $T_{c}$. The susceptibility $\chi_{FC}$ obeys a Curie-Weiss behavior with a negative Curie-Weiss temperature ($-13.1 \leq \Theta \leq -5.4$ K). The growth of antiferromagnetic order is limited by the disordered nature of nanographites, forming spin glass-like behavior at low temperatures in graphene sheets.Comment: 21 pages, 15 figures; submitted to J. Phys.: Condensed Matte

Illumination diagnosis for retrieval of reflections from ambient-noise seismic data in the Siilinjärvi mining site, Finland

Reflection seismic methods are becoming popular in mineral exploration, because they allow high-resolution delineation of the exploration targets, even at great depths. Seismic interferometry can be used to retrieve reflections from passive seismic data, removing the need for active seismic sources and, therefore, reducing the cost and environmental impact of exploration. The retrieval of reflections can be challenging, since passive seismic records are typically dominated by surface waves. Therefore, illumination diagnosis, a method which allows the isolation of the portions of the passive data where body-wave signals are stronger, can be a valuable step that improves the quality of the reflections retrieved from seismic interferometry and reduces the overall computational cost of the processing stage. Here, we validate the performance of the method to effectively isolate the portions of the passive data dominated by body waves and apply it on an ambient-noise seismic dataset acquired in the Siilinjärvi mining site in Finland

Nonlinear AC resistivity in s-wave and d-wave disordered granular superconductors

We model s-wave and d-wave disordered granular superconductors with a three-dimensional lattice of randomly distributed Josephson junctions with finite self-inductance. The nonlinear ac resistivity of these systems was calculated using Langevin dynamical equations. The current amplitude dependence of the nonlinear resistivity at the peak position is found to be a power law characterized by exponent $\alpha$. The later is not universal but depends on the self-inductance and current regimes. In the weak current regime $\alpha$ is independent of the self-inductance and equal to 0.5 or both of s- and d-wave materials. In the strong current regime this exponent depends on the screening. We find $\alpha \approx 1$ for some interval of inductance which agrees with the experimental finding for d-wave ceramic superconductors.Comment: 4 pages, 5 figures, to appear in Phys. Rev. Let

Application of surface-wave tomography to mineral exploration : a case study from Siilinjarvi, Finland

In order to assess the feasibility and validity of surface-wave tomography as a tool for mineral exploration, we present an active seismic three-dimensional case study from the Siilinjarvi mine in Eastern Finland. The aim of the survey is to identify the formation carrying the mineralization in an area south of the main pit, which will be mined in the future. Before acquiring the data, we performed an accurate survey design to maximize data coverage and minimize the time for deployment and recollection of the equipment. We extract path-averaged Rayleigh-wave phase-velocity dispersion curves by means of a two-station method. We invert them using a computationally efficient tomographic code which does not require the computation of phase-velocity maps and inverts directly for one-dimensional S-wave velocity models. The retrieved velocities are in good agreement with the data from a borehole in the vicinity, and the pseudo three-dimensional S-wave velocity volume allows us to identify the geological contact between the formation hosting most of the mineralization and the surrounding rock. We conclude that the proposed method is a valid tool, given the small amount of equipment used and the acceptable amount of time required to process the data.Peer reviewe

Involved margins after lumpectomy for breast cancer: Always to be re-excised?

Background: The oncologic benefit of upfront re-excision of involved margins after breast-conserving surgery in the context of current multimodal clinical management of breast cancer is unclear. The aim of the present study was to assess the 5-years locoregional recurrence (LRR)-free and distant metastases (DM)-free survival probabilities in patients not undergoing re-excision of positive margins after lumpectomy for breast cancer. Methods: A cohort of 104 patients with positive margins not undergoing re-excision was matched by propensity score with a cohort of 2006 control patients with clear margins after breast-conserving surgery, treated between 2008 and 2018. A multivariate survival analysis was performed accounting for all variables related to LRR and DM, including adjuvant treatments. Results: After adjusting for potential confounders, avoiding to re-excise a positive margin after lumpectomy had no effect on 5-years LRR-free survival probability (HR 0.98, 95%CI 0.36-2.67, p = 0.96) or 5-years DM-free survival probability (HR 0.37, 95%CI 0.08-1.61, p = 0.18). No correlation was found between occurrence of LRR and number of involved margins (HR 1.28, 95%CI 0.10-12.4, Log-rank p = 0.83), or extension of infiltrating disease (HR 1.21, 95%CI 0.20-7.40, Log-rank p = 0.83), but a trend toward higher LRR probability was found for invasive ductal (HR 6.92, 95%CI 0.7-68.8, Log-rank p = 0.10) and invasive lobular cancer (HR 12.95, 95%CI 0.79-213.6, Log-rank p = 0.07) on positive margins. Conclusions: In the era of multimodal treatment of breast cancer and accurate strategies to reduce the probability of residual disease in the post-lumpectomy cavity, re-excision of positive margins might be omitted in selected patients with low-risk breast cancers