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.

Aim To analyse the impact of the length of antiviral therapy with tenofovir disoproxil fumarate (TDF) on the renal function in patients with chronic hepatitis B (CHB). Methods A cross-sectional study included 75 patients with CHB treated with tenofovir, who had a normal renal function at the beginning of the treatment. Renal function was determined based on glomerular filtration rate (eGFR) value using the Modification of Diet in Renal Disease formula (MDRD). Measurement of serum creatinine concentration and urinary protein excretion were performed using standard laboratory analyses. Viral load quantification (HBV-DNA) was determined by polymerase chain reaction (PCR). The degree of liver fibrosis was determined using fibrosis4 (FIB-4) and aspartate transaminase to platelet ratio index (APRI) fibrosis score. Results Out of 75 CHB patients, 37 were on antiviral treatment for up to 2 years (group 1) and 38 patients on antiviral treatment longer than two years (group 2). Mean age of patients was not significantly different between the groups (p=0.076), nor was the gender distribution. There was no statistically significant difference between the mean values of the eGFR in the two groups (91.89±9.24 vs. 88.42±7.84 mL/min/1.73m2; p=0.42), as well as between the mean values of serum creatinine (p=0.360) and 24-hour urine protein excretion (p=0.380). There was no statistically significant correlation between renal parameters and viral load, APRI and FIB-4 fibrosis score. Conclusion Results of our study did not show significant changes in the measured parameters of renal function in group 1 and group 2 of patients, regardless of the length of antiviral treatment, indicating a good renal safety profile of TDF.

Aim To examine safety and efficiency of electrocardioversion (EC) in elective treatment of atrial fibrillation and atrial flutter in the setting of Day Hospital by determining success rate, frequency of adverse events and possible cost benefit compared to admitting a patient into hospital. Methods This prospective observational cohort study was performed in Day Hospital and in Intensive Care Department of Internal Medicine Clinic, University Clinical Centre Tuzla from January 2019 to December 2022 and included 98 patients with a persistent form of atrial fibrillation (AF) or atrial flutter. The patients who were divided in two groups, 56 hospitalized and 42 patients accessed in Day Hospital. In all patients, medical history, physical examination, electrocardiogram (ECG) and transthoracic echocardiogram (TTE) evaluation was performed in addition to laboratory findings. Electrocardioversion was performed with a monophasic General Electric defibrillator in anterolateral electrode position with up to three repetitive shocks. Results In hospital setting group overall succes rate of electrocardioversion was 85%, with average 2.1 EC attemps, there was with one fatal outcome due to stroke, one case of ventricular fibrillation (VF) due to human error, and 6 minor adverse events; with average cost of was 1408.70 KM (720.23 €) per patient. In Day Hospital setting succes rate was 88%, with average 2 EC attempts, no major adverse events, 8 minor adverse events; and average cost was of 127.23 KM (65.05 €) per patient. Conclusion Performing elective electrocardioversion in Day Hospital setting is as safe as admitting patients into hospital but substantially more cost effective.

Aim To determine the success of endovenous laser ablation (EVLA) treatment and long-term occlusion of small saphenous vein (SSV), as well as factors and conditions that influence the effectiveness of EVLA treatment. Methods A total of 250 patients treated with EVLA method over a period of seven years were followed one year after treatment. The main factors monitored and recorded during EVLA treatment were laser power (W), amount of delivered energy (J), duration of treatment (sec), veins length (cm), diameter (mm) and reflux (sec). Results Within the first six months, the recanalization or insufficiently occluded SSV was noticed in ten, and after one year in one patient. The overall assessment of occlusion and satisfactory findings after one year of SSV was 95.6%. Conclusion It is important to choose adequate power and the amount of delivered energy. The physician's assessment and selection of an adequate patient greatly improves the outcome of the treatment. It is important to treat larger branches and double SSV between two fascias. Successful and effective EVLA treatment greatly reduces the possibility of recanalization of the treated vein.