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

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

Numerical instability of the Akhmediev breather and a finite-gap model of it

In this paper we study the numerical instabilities of the NLS Akhmediev breather, the simplest space periodic, one-mode perturbation of the unstable background, limiting our considerations to the simplest case of one unstable mode. In agreement with recent theoretical findings of the authors, in the situation in which the round-off errors are negligible with respect to the perturbations due to the discrete scheme used in the numerical experiments, the split-step Fourier method (SSFM), the numerical output is well-described by a suitable genus 2 finite-gap solution of NLS. This solution can be written in terms of different elementary functions in different time regions and, ultimately, it shows an exact recurrence of rogue waves described, at each appearance, by the Akhmediev breather. We discover a remarkable empirical formula connecting the recurrence time with the number of time steps used in the SSFM and, via our recent theoretical findings, we establish that the SSFM opens up a vertical unstable gap whose length can be computed with high accuracy, and is proportional to the inverse of the square of the number of time steps used in the SSFM. This neat picture essentially changes when the round-off error is sufficiently large. Indeed experiments in standard double precision show serious instabilities in both the periods and phases of the recurrence. In contrast with it, as predicted by the theory, replacing the exact Akhmediev Cauchy datum by its first harmonic approximation, we only slightly modify the numerical output. Let us also remark, that the first rogue wave appearance is completely stable in all experiments and is in perfect agreement with the Akhmediev formula and with the theoretical prediction in terms of the Cauchy data.Comment: 27 pages, 8 figures, Formula (30) at page 11 was corrected, arXiv admin note: text overlap with arXiv:1707.0565

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

Intraoperative Fluid Management a Modifiable Risk Factor for Surgical Quality - Improving Standardized Practice.

We aimed to determine a safe zone of intraoperative fluid management associated with the lowest postoperative complication rates without increased acute kidney injury (AKI) risk for elective colorectal surgery patients. Elective colorectal surgeries between 2018 and 2020 were included. Unadjusted odds ratios for postoperative ileus, prolonged length of stay (LOS), and AKI were plotted against the rate of intraoperative ringer's lactate (RL) infusion (mL/kg/h) and total intraoperative volume. Binary logistic regression analysis, including fluid volumes as a confounder, was used to identify risk factors for postoperative complications. A total of 2,900 patients were identified. Of them, 503 (17.3%) patients had ileus, 772 (26.6%) patients had prolonged LOS, and 240 (8.3%) patients had AKI. The intraoperative fluid resuscitation rate (mg/kg/h) was less impactful on postoperative ileus, LOS, and AKI than the total amount of intraoperative fluid. A total fluid administration range between 300 mL and 2.7 L was associated with the lowest complication rate. Total intraoperative RL ≥2.7 L was independently associated with a higher risk of ileus (adjusted OR 1.465;95% CI 1.154-1.858) and prolonged LOS (adjusted OR 1.300;95% CI 1.047-1.613), but not AKI. Intraoperative RL≤300 ml was not associated with an increased risk of AKI. Total intraoperative RL≥2.7L was independently associated with postoperative ileus and prolonged LOS in elective colorectal surgery patients. A new potential standard for intraoperative fluids will require anesthesia case planning (complexity and duration) to ensure total fluid volume meets this new opportunity to improve care

Modest agreement between magnetic resonance and pathological tumor regression after neoadjuvant therapy for rectal cancer in the real world.

Magnetic resonance imaging (MRI) is routinely used for preoperative tumor staging and to assess response to therapy in rectal cancer patients. The aim of our study was to evaluate the accuracy of MRI based restaging after neoadjuvant chemoradiotherapy (CRT) in predicting pathologic response. This multicenter cohort study included adult patients with histologically confirmed locally advanced rectal adenocarcinoma treated with neoadjuvant CRT followed by curative intent elective surgery between January 2014 and December 2019 at four academic high-volume institutions. Magnetic resonance tumor regression grade (mrTRG) and pathologic tumor regression grade (pTRG) were reviewed and compared for all the patients. The agreement between radiologist and pathologist was assessed with the weighted k test. Risk factors for poor agreement were investigated using logistic regression. A total of 309 patients were included. Modest agreement was found between mrTRG and pTRG when regression was classified according to standard five-tier systems (k = 0.386). When only two categories were considered for each regression system, (pTRG 0-3 vs pTRG 4; mrTRG 2-5 vs mrTRG 1) an accuracy of 78% (95% confidence interval [CI] 0.73-0.83) was found between radiologic and pathologic assessment with a k value of 0.185. The logistic regression model revealed that "T3 greater than 5 mm extent" was the only variable significantly impacting on disagreement (OR 0.33, 95% CI 0.15-0.68, P = .0034). Modest agreement exists between mrTRG and pTRG. The chances of appropriate assessment of the regression grade after neoadjuvant CRT appear to be higher in case of a T3 tumor with at least 5 mm extension in the mesorectal fat at the pretreatment MRI

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

Time course of risk factors associated with mortality of 1260 critically ill patients with COVID-19 admitted to 24 Italian intensive care units

94noopenPurpose: To evaluate the daily values and trends over time of relevant clinical, ventilatory and laboratory parameters during the intensive care unit (ICU) stay and their association with outcome in critically ill patients with coronavirus disease 19 (COVID-19). Methods: In this retrospective–prospective multicentric study, we enrolled COVID-19 patients admitted to Italian ICUs from February 22 to May 31, 2020. Clinical data were daily recorded. The time course of 18 clinical parameters was evaluated by a polynomial maximum likelihood multilevel linear regression model, while a full joint modeling was fit to study the association with ICU outcome. Results: 1260 consecutive critically ill patients with COVID-19 admitted in 24 ICUs were enrolled. 78% were male with a median age of 63 [55–69] years. At ICU admission, the median ratio of arterial oxygen partial pressure to fractional inspired oxygen (PaO2/FiO2) was 122 [89–175] mmHg. 79% of patients underwent invasive mechanical ventilation. The overall mortality was 34%. Both the daily values and trends of respiratory system compliance, PaO2/FiO2, driving pressure, arterial carbon dioxide partial pressure, creatinine, C-reactive protein, ferritin, neutrophil, neutrophil–lymphocyte ratio, and platelets were associated with survival, while for lactate, pH, bilirubin, lymphocyte, and urea only the daily values were associated with survival. The trends of PaO2/FiO2, respiratory system compliance, driving pressure, creatinine, ferritin, and C-reactive protein showed a higher association with survival compared to the daily values. Conclusion: Daily values or trends over time of parameters associated with acute organ dysfunction, acid–base derangement, coagulation impairment, or systemic inflammation were associated with patient survival.openZanella A.; Florio G.; Antonelli M.; Bellani G.; Berselli A.; Bove T.; Cabrini L.; Carlesso E.; Castelli G.P.; Cecconi M.; Citerio G.; Coloretti I.; Corti D.; Dalla Corte F.; De Robertis E.; Foti G.; Fumagalli R.; Girardis M.; Giudici R.; Guiotto L.; Langer T.; Mirabella L.; Pasero D.; Protti A.; Ranieri M.V.; Rona R.; Scudeller L.; Severgnini P.; Spadaro S.; Stocchetti N.; Vigano M.; Pesenti A.; Grasselli G.; Aspesi M.; Baccanelli F.; Bassi F.; Bet A.; Biagioni E.; Biondo A.; Bonenti C.; Bottino N.; Brazzi L.; Buquicchio I.; Busani S.; Calini A.; Calligaro P.; Cantatore L.P.; Carelli S.; Carsetti A.; Cavallini S.; Cimicchi G.; Coppadoro A.; Dall'Ara L.; Di Gravio V.; Erba M.; Evasi G.; Facchini A.; Fanelli V.; Feliciotti G.; Fusarini C.F.; Ferraro G.; Gagliardi G.; Garberi R.; Gay H.; Giacche L.; Grieco D.; Guzzardella A.; Longhini F.; Manzan A.; Maraggia D.; Milani A.; Mischi A.; Montalto C.; Mormina S.; Noseda V.; Paleari C.; Pedeferri M.; Pezzi A.; Pizzilli G.; Pozzi M.; Properzi P.; Rauseo M.; Russotto V.; Saccarelli L.; Servillo G.; Spano S.; Tagliabue P.; Tonetti T.; Tullo L.; Vetrugno L.; Vivona L.; Volta C.A.; Zambelli V.; Zanoni A.Zanella, A.; Florio, G.; Antonelli, M.; Bellani, G.; Berselli, A.; Bove, T.; Cabrini, L.; Carlesso, E.; Castelli, G. P.; Cecconi, M.; Citerio, G.; Coloretti, I.; Corti, D.; Dalla Corte, F.; De Robertis, E.; Foti, G.; Fumagalli, R.; Girardis, M.; Giudici, R.; Guiotto, L.; Langer, T.; Mirabella, L.; Pasero, D.; Protti, A.; Ranieri, M. V.; Rona, R.; Scudeller, L.; Severgnini, P.; Spadaro, S.; Stocchetti, N.; Vigano, M.; Pesenti, A.; Grasselli, G.; Aspesi, M.; Baccanelli, F.; Bassi, F.; Bet, A.; Biagioni, E.; Biondo, A.; Bonenti, C.; Bottino, N.; Brazzi, L.; Buquicchio, I.; Busani, S.; Calini, A.; Calligaro, P.; Cantatore, L. P.; Carelli, S.; Carsetti, A.; Cavallini, S.; Cimicchi, G.; Coppadoro, A.; Dall'Ara, L.; Di Gravio, V.; Erba, M.; Evasi, G.; Facchini, A.; Fanelli, V.; Feliciotti, G.; Fusarini, C. F.; Ferraro, G.; Gagliardi, G.; Garberi, R.; Gay, H.; Giacche, L.; Grieco, D.; Guzzardella, A.; Longhini, F.; Manzan, A.; Maraggia, D.; Milani, A.; Mischi, A.; Montalto, C.; Mormina, S.; Noseda, V.; Paleari, C.; Pedeferri, M.; Pezzi, A.; Pizzilli, G.; Pozzi, M.; Properzi, P.; Rauseo, M.; Russotto, V.; Saccarelli, L.; Servillo, G.; Spano, S.; Tagliabue, P.; Tonetti, T.; Tullo, L.; Vetrugno, L.; Vivona, L.; Volta, C. A.; Zambelli, V.; Zanoni, A