Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations

We study the topology of quasiperiodic solutions of the vortex filament equation in a neighborhood of multiply covered circles. We construct these solutions by means of a sequence of isoperiodic deformations, at each step of which a real double point is "unpinched" to produce a new pair of branch points and therefore a solution of higher genus. We prove that every step in this process corresponds to a cabling operation on the previous curve, and we provide a labelling scheme that matches the deformation data with the knot type of the resulting filament.Comment: 33 pages, 5 figures; submitted to Journal of Nonlinear Scienc

Topological Aspect of Knotted Vortex Filaments in Excitable Media

Scroll waves exist ubiquitously in three-dimensional excitable media. It's rotation center can be regarded as a topological object called vortex filament. In three-dimensional space, the vortex filaments usually form closed loops, and even linked and knotted. In this letter, we give a rigorous topological description of knotted vortex filaments. By using the $\phi$-mapping topological current theory, we rewrite the topological current form of the charge density of vortex filaments and use this topological current we reveal that the Hopf invariant of vortex filaments is just the sum of the linking and self-linking numbers of the knotted vortex filaments. We think that the precise expression of the Hopf invariant may imply a new topological constraint on knotted vortex filaments.Comment: 4 pages, no figures, Accepted by Chin. Phys. Let

The branch processes of vortex filaments and Hopf Invariant Constraint on Scroll Wave

In this paper, by making use of Duan's topological current theory, the evolution of the vortex filaments in excitable media is discussed in detail. The vortex filaments are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of a complex function $Z(\vec{x},t)$. It is also shown that the Hopf invariant of knotted scroll wave filaments is preserved in the branch processes (splitting, merging, or encountering) during the evolution of these knotted scroll wave filaments. Furthermore, it also revealed that the "exclusion principle" in some chemical media is just the special case of the Hopf invariant constraint, and during the branch processes the "exclusion principle" is also protected by topology.Comment: 9 pages, 5 figure

Gross-Neveu Models, Nonlinear Dirac Equations, Surfaces and Strings

Recent studies of the thermodynamic phase diagrams of the Gross-Neveu model (GN2), and its chiral cousin, the NJL2 model, have shown that there are phases with inhomogeneous crystalline condensates. These (static) condensates can be found analytically because the relevant Hartree-Fock and gap equations can be reduced to the nonlinear Schr\"odinger equation, whose deformations are governed by the mKdV and AKNS integrable hierarchies, respectively. Recently, Thies et al have shown that time-dependent Hartree-Fock solutions describing baryon scattering in the massless GN2 model satisfy the Sinh-Gordon equation, and can be mapped directly to classical string solutions in AdS3. Here we propose a geometric perspective for this result, based on the generalized Weierstrass spinor representation for the embedding of 2d surfaces into 3d spaces, which explains why these well-known integrable systems underlie these various Gross-Neveu gap equations, and why there should be a connection to classical string theory solutions. This geometric viewpoint may be useful for higher dimensional models, where the relevant integrable hierarchies include the Davey-Stewartson and Novikov-Veselov systems.Comment: 27 pages, 1 figur

Symptomatic Uncomplicated Diverticular Disease (SUDD): Practical Guidance and Challenges for Clinical Management

Symptomatic Uncomplicated Diverticular Disease (SUDD) is a syndrome within the diverticular disease spectrum, characterized by local abdominal pain with bowel movement changes but without systemic inflammation. This narrative review reports current knowledge, delivers practical guidance, and reveals challenges for the clinical management of SUDD. A broad and common consensus on the definition of SUDD is still needed. However, it is mainly considered a chronic condition that impairs quality of life (QoL) and is characterized by persistent left lower quadrant abdominal pain with bowel movement changes (eg, diarrhea) and low-grade inflammation (eg, elevated calprotectin) but without systemic inflammation. Age, genetic predisposition, obesity, physical inactivity, low-fiber diet, and smoking are considered risk factors. The pathogenesis of SUDD is not entirely clarified. It seems to result from an interaction between fecal microbiota alterations, neuro-immune enteric interactions, and muscular system dysfunction associated with a low-grade and local inflammatory state. At diagnosis, it is essential to assess baseline clinical and Quality of Life (QoL) scores to evaluate treatment efficacy and, ideally, to enroll patients in cohort studies, clinical trials, or registries. SUDD treatments aim to improve symptoms and QoL, prevent recurrence, and avoid disease progression and complications. An overall healthy lifestyle – physical activity and a high-fiber diet, with a focus on whole grains, fruits, and vegetables – is encouraged. Probiotics could effectively reduce symptoms in patients with SUDD, but their utility is missing adequate evidence. Using Rifaximin plus fiber and Mesalazine offers potential in controlling symptoms in patients with SUDD and might prevent acute diverticulitis. Surgery could be considered in patients with medical treatment failure and persistently impaired QoL. Still, studies with well-defined diagnostic criteria for SUDD that evaluate the safety, QoL, effectiveness, and cost-effectiveness of these interventions using standard scores and comparable outcomes are needed

Exome-wide rare variant analysis identifies TUBA4A mutations associated with familial ALS

Exome sequencing is an effective strategy for identifying human disease genes. However, this methodology is difficult in late-onset diseases where limited availability of DNA from informative family members prohibits comprehensive segregation analysis. To overcome this limitation, we performed an exome-wide rare variant burden analysis of 363 index cases with familial ALS (FALS). The results revealed an excess of patient variants within TUBA4A, the gene encoding the Tubulin, Alpha 4A protein. Analysis of a further 272 FALS cases and 5,510 internal controls confirmed the overrepresentation as statistically significant and replicable. Functional analyses revealed that TUBA4A mutants destabilize the microtubule network, diminishing its repolymerization capability. These results further emphasize the role of cytoskeletal defects in ALS and demonstrate the power of gene-based rare variant analyses in situations where causal genes cannot be identified through traditional segregation analysis.</p

30-day Morbidity and Mortality after Cholecystectomy for Benign Gallbladder Disease (AMBROSE): A Prospective, International Collaborative Cohort Study

Objective:This study aimed to assess 30-day morbidity and mortality rates following cholecystectomy for benign gallbladder disease and identify the factors associated with complications.Background:Although cholecystectomy is common for benign gallbladder disease, there is a gap in the knowledge of the current practice and variations on a global level.Methods:A prospective, international, observational collaborative cohort study of consecutive patients undergoing cholecystectomy for benign gallbladder disease from participating hospitals in 57 countries between January 1 and June 30, 2022, was performed. Univariate and multivariate logistic regression models were used to identify preoperative and operative variables associated with 30-day postoperative outcomes.Results:Data of 21,706 surgical patients from 57 countries were included in the analysis. A total of 10,821 (49.9%), 4263 (19.7%), and 6622 (30.5%) cholecystectomies were performed in the elective, emergency, and delayed settings, respectively. Thirty-day postoperative complications were observed in 1738 patients (8.0%), including mortality in 83 patients (0.4%). Bile leaks (Strasberg grade A) were reported in 278 (1.3%) patients, and severe bile duct injuries (Strasberg grades B-E) were reported in 48 (0.2%) patients. Patient age, American Society of Anesthesiologists physical status class, surgical setting, operative approach, and Nassar operative difficulty grade were identified as the 5 predictors demonstrating the highest relative importance in predicting postoperative complications.Conclusions:This multinational observational collaborative cohort study presents a comprehensive report of the current practices and outcomes of cholecystectomy for benign gallbladder disease. Ongoing global collaborative evaluations and initiatives are needed to promote quality assurance and improvement in cholecystectomy

Laparoscopic right hemicolectomy: a SICE (Società Italiana di Chirurgia Endoscopica e Nuove tecnologie) network prospective study on the approach to right colon lymphadenectomy in Italy: is there a standard?—CoDIG 2 (ColonDx Italian Group)

Background: Colon cancer is a disease with a worldwide spread. Surgery is the best option for the treatment of advanced colon cancer, but some aspects are still debated, such as the extent of lymphadenectomy. In Japanese guidelines, the gold standard was D3 dissection to remove the central lymph nodes (203, 213, and 223), but in 2009, Hoenberger et al. introduced the concept of complete mesocolic excision, in which surgical dissection follows the embryological planes to remove the mesentery entirely to prevent leakage of cancer cells and collect more lymph nodes. Our study describes how lymphadenectomy is currently performed in major Italian centers with an unclear indication on the type of lymphadenectomy that should be performed during right hemicolectomy (RH). Methods: CoDIG 2 is an observational multicenter national study that involves 76 Italian general surgery wards highly specialized in colorectal surgery. Each center was asked not to modify their usual surgical and clinical practices. The aim of the study was to assess the preference of Italian surgeons on the type of lymphadenectomy to perform during RH and the rise of any new trends or modifications in habits compared to the findings of the CoDIG 1 study conducted 4&nbsp;years ago. Results: A total of 788 patients were enrolled. The most commonly used surgical technique was laparoscopic (82.1%) with intracorporeal (73.4%), side-to-side (98.7%), or isoperistaltic (96.0%) anastomosis. The lymph nodes at the origin of the vessels were harvested in an inferior number of cases (203, 213, and 223: 42.4%, 31.1%, and 20.3%, respectively). A comparison between CoDIG 1 and CoDIG 2 showed a stable trend in surgical techniques and complications, with an increase in the robotic approach (7.7% vs. 12.3%). Conclusions: This analysis shows how lymphadenectomy is performed in Italy to achieve oncological outcomes in RH, although the technique to achieve a higher lymph node count has not yet been standardized. Trial registration (ClinicalTrials.gov) ID: NCT05943951

Deep learning neural network prediction of postoperative complications in patients undergoing laparoscopic right hemicolectomy with or without CME and CVL for colon cancer: insights from SICE (Società Italiana di Chirurgia Endoscopica) CoDIG data

BackgroundPostoperative complications in colorectal surgery can significantly impact patient outcomes and healthcare costs. Accurate prediction of these complications enables targeted perioperative management, improving patient safety and optimizing resource allocation. This study evaluates the application of machine learning (ML) models, particularly deep learning neural networks (DLNN), in predicting postoperative complications following laparoscopic right hemicolectomy for colon cancer.MethodsData were drawn from the CoDIG (ColonDx Italian Group) multicenter database, which includes information on patients undergoing laparoscopic right hemicolectomy with complete mesocolic excision (CME) and central vascular ligation (CVL). The dataset included demographic, clinical, and surgical factors as predictors. Models such as decision trees (DT), random forest (RF), and DLNN were trained, with DLNN evaluated using cross-validation metrics. To address class imbalance, the synthetic minority over-sampling technique (SMOTE) was employed. The primary outcome was the prediction of postoperative complications within 1 month of surgery.ResultsThe DLNN model outperformed other models, achieving an accuracy of 0.86, precision of 0.84, recall of 0.90, and an F1 score of 0.87. Relevant predictors identified included intraoperative minimal bleeding, blood transfusion, and adherence to the fast-track recovery protocol. The absence of intraoperative bleeding, intracorporeal anastomosis, and fast-track protocol adherence were associated with a reduced risk of complications.ConclusionThe DLNN model demonstrated superior predictive performance for postoperative complications compared to other ML models. The findings highlight the potential of integrating ML models into clinical practice to identify high-risk patients and enable tailored perioperative care. Future research should focus on external validation and implementation of these models in diverse clinical settings to further optimize surgical outcomes