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.

BACKGROUND Educational mobility at the macro-level is a common measure of social inequality. Nonetheless, the correlates of mobility of education at the individual level are less well studied. We evaluated whether educational mobility of the second generation (compared to the first generation level) predicts differences in parenting practices of the second generation and school achievement and intelligence in the third generation. METHODS Data from a population-based cohort of children in the Netherlands (N = 3547; 49.4% boys) were analyzed. Maternal, grandparental education and family routines, a parenting practice, were reported by the mother. Child school achievement at the end of primary school (∼12 years, with the national Dutch academic test score) and child intelligence (∼6 and 13 years) were measured in a standardized manner. Also, a child genome-wide polygenic score of academic attainment was calculated. To estimate the effect of educational mobility, inverse probability-weighted linear models and Diagonal Reference Models (DRM) were used. RESULTS Upward maternal educational mobility was associated with better offspring school achievement, higher intelligence, and more family routines if compared to offspring of mothers with no upward mobility. However, mothers did not implement the same level of family routines as similarly educated mothers and grandfathers who already had achieved this educational level. Likewise, children of mothers with upward educational mobility had lower school achievement and intelligence than children of similarly educated mothers with no mobility. Child's genetic potential for education followed a similar association pattern with higher potential in children of upward mobile mothers. CONCLUSION Policymakers might overlook social inequalities when focused on parental socioeconomic status. Grandparental socioeconomic status, which independently predicts child school achievement, intelligence, and parental family routines, should also be assessed. The child's genetic endowment reflects the propensity for education across generations that partly underlies mobility and some of its effect on the offspring.

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.

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 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.

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.

Aim To analyse the correlation between different surgical methodologies employed in valve diseases treatment and their subsequent impact on the duration of hospitalization. Methods This retrospective study conducted at the Clinical Centre of the University of Sarajevo analysed medical records of 163 valve disease patients treated between January 2019 and November 2022. The patients were divided into two groups: 77 had openheart valve surgery and 86 underwent minimally invasive cardiac surgery (MICS). Results The mean duration of the surgical procedures was 3.9±1.3 hours, with conventional open-heart surgery requiring an average of 3.6±1.1 hours and minimally invasive cardiac surgery (MICS) procedure 4.2±1.5 hours. No substantial disparities were found in the total length of hospitalization between the two groups, as both conventional (8.2±4.5 days) and MICS (8.7±7.0 days) demonstrated similar duration. Similarly, the total duration of intensive care unit (ICU) stay displayed similarity, with conventional surgery patients staying an average of 3.9±2.8 days and MICS patients of 4.2±4.1 days. The pattern of blood transfusion and fresh-frozen plasma usage revealed higher rates in the conventional valve surgery group comparing to the MICS group. Conclusion Minimally invasive valve surgery, despite slightly longer operative times, resulted in lower blood transfusion requirements and comparable hospitalization and ICU stay.