This scientific paper investigates the application of the Voltaire-Gurset-Riemann method in solving partial differential equations, using a flickering wire as an example. The method proves to be a powerful tool in the analysis of dynamic systems, providing a deeper understanding of flicker behavior in a wire. The developed numerical solutions enable precise modeling and prediction of the behavior of the flickering structure. This study highlights the key steps in applying the method to a concrete example, providing a useful basis for further research in the field of partial differential equations

Let $M$ be a finite volume hyperbolic Riemann surface with arbitrary signature, and let $\chi$ be an arbitrary $m$-dimensional multiplier system of weight $k$. Let $R(s,\chi)$ be the associated Ruelle zeta function, and $\varphi(s,\chi)$ the determinant of the scattering matrix. We prove the functional equation that $R(s,\chi)\varphi(s,\chi) = R(-s,\chi)\varphi(s,\chi)H(s,\chi)$ where $H(s,\chi)$ is a meromorphic function of order one explicitly determined using the topological data of $M$ and of $\chi$, and the trigonometric function $\sin(s)$. From this, we determine the order of the divisor of $R(s,\chi)$ at $s=0$ and compute the lead coefficient in its Laurent expansion at $s=0$. When combined with results by Kitano and by Yamaguchi, we prove further instances of the Fried conjecture, which states that the R-torsion of the above data is simply expressed in terms of $R(0,\chi)$.

Background : Mammographic (or breast) density is an established risk factor for breast cancer. There are a variety of approaches to measurement including quantitative, semi-automated and automated approaches. We present a new automated measure, AutoCumulus, learnt from applying deep learning to semi-automated measures. Methods: We used mammograms of 9,057 population-screened women in the BRAIx study for which semi-automated measurements of mammographic density had been made by experienced readers using the CUMULUS software. The dataset was split into training, testing, and validation sets (80%, 10%, 10%, respectively). We applied a deep learning regression model (fine-tuned ConvNeXtSmall) to estimate percentage density and assessed performance by the correlation between estimated and measured percent density and a Bland-Altman plot. The automated measure was tested on an independent CSAW-CC dataset in which density had been measured using the LIBRA software, comparing measures for left and right breasts, sensitivity for high sensitivity, and areas under the receiver operating characteristic curve (AUCs). Results: Based on the testing dataset, the correlation in percent density between the automated and human measures was 0.95, and the differences were only slightly larger for women with higher density. Based on the CSAW-CC dataset, AltoCumulus outperformed LIBRA in correlation between left and right breast (0.95 versus 0.79; P<0.001), specificity for 95% sensitivity (13% versus 10% (P<0.001)), and AUC (0.638 cf. 0.597; P<0.001). Conclusion: We have created an automated measure of mammographic density that is accurate and gives superior performance on repeatability within a woman, and for prediction of interval cancers, than another well-established automated measure.

Aim To determine a correlation between the localization of the parathyroid gland (PTG), based on ultrasound (US) examination and the operative findings, as well as the correlation between the size of the parathyroid glands measured by ultrasonography (USG) with pathological findings+, and prevalence of enlarged parathyroid glands in various forms of hyperparathyroidism. Methods A total of 83 patients with hyperparathyroidism who had undergone parathyroidectomy over a period of seven years were included in the study. US examinations of the neck and scintigraphy were performed before surgery in 83 and 42 patients, respectively. In the pathohistological analysis, in addition to diagnosis, the size and weight of the parathyroid gland were measured. Results US examination revealed 125 enlarged parathyroid glands and two normal-sized glands. Scintigraphy revealed 52 enlarged and three normal-sized parathyroid glands. Enlarged parathyroid glands were more frequently found in the projection of the lower pole thyroid glands. A significantly higher number of enlarged upper parathyroid glands were found by the operative findings than by US. There was no statistically significant difference in the diagnosis of enlarged parathyroid glands in all three forms of hyperparathyroidism. There was a positive correlation between the size of the parathyroid glands obtained by US and the size of the operative finding (κ=0.51; p=0.00 and p<0.0005, respectively). The relationship between parathyroid gland size measured by ultrasound and pathological analysis showed a positive correlation. Conclusion Ultrasound was useful in evaluating enlarged parathyroid glands, especially in combination with scintigraphy.

Efficiently mapping quantum circuits onto hardware is an integral part of the quantum compilation process, wherein a quantum circuit is modified in accordance with the stringent architectural demands of a quantum processor. Many techniques exist for solving the quantum circuit mapping problem, many of which relate quantum circuit mapping to classical computer science. This work considers a novel perspective on quantum circuit mapping, in which the routing process of a simplified circuit is viewed as a composition of quantum operations acting on density matrices representing the quantum circuit and processor. Drawing on insight from recent advances in quantum information theory and information geometry, we show that a minimal SWAP gate count for executing a quantum circuit on a device emerges via the minimization of the distance between quantum states using the quantum Jensen-Shannon divergence. Additionally, we develop a novel initial placement algorithm based on a graph similarity search that selects the partition nearest to a graph isomorphism between interaction and coupling graphs. From these two ingredients, we then construct a polynomial-time algorithm for calculating the SWAP gate lower bound, which is directly compared alongside the IBM Qiskit compiler for over 600 realistic benchmark experiments, as well as against a brute-force method for smaller benchmarks. In our simulations, we unambiguously find that neither the brute-force method nor the Qiskit compiler surpass our bound, implying utility as a precise estimation of minimal overhead when realizing quantum algorithms on constrained quantum hardware. This work constitutes the first use of quantum circuit uncomplexity to practically-relevant quantum computing. We anticipate that this method may have diverse applicability outside of the scope of quantum information science, and we discuss several of these possibilities.

This research paper delves into the two-dimensional discrete plant-herbivore model. In this model, herbivores are food-limited and affect the plants' density in their environment. Our analysis reveals that this system has equilibrium points of extinction, exclusion, and coexistence. We analyze the behavior of solutions near these points and prove that the extinction and exclusion equilibrium points are globally asymptotically stable in certain parameter regions. At the boundary equilibrium, we prove the existence of transcritical and period-doubling bifurcations with stable two-cycle. Transcritical bifurcation occurs when the plant's maximum growth rate or food-limited parameter reaches a specific boundary. This boundary serves as an invasion boundary for populations of plants or herbivores. At the interior equilibrium, we prove the occurrence of transcritical, Neimark-Sacker, and period-doubling bifurcations with an unstable two-cycle. Our research also establishes that the system is persistent in certain regions of the first quadrant. We demonstrate that the local asymptotic stability of the interior equilibrium does not guarantee the system's persistence. Bistability exists between boundary attractors (logistic dynamics) and interior equilibrium for specific parameters' regions. We conclude that changes to the food-limitation parameter can significantly alter the system's dynamic behavior. To validate our theoretical findings, we conduct numerical simulations.