Double Knot Research Articles

Semi-discrete Voronovskaya-type theorem for positive linear operators based on Hermite interpolation with two double knots

Since the classical asymptotic theorems of Voronovskaya-type for positive and linear operators are in fact based on the Taylor’s formula which is a very particular case of Lagrange-Hermite interpolation formula, in the recent paper Gal [3], I have obtained semi-discrete quantitative Voronovskaya-type theorems based on other Lagrange-Hermite interpolation formulas. These include Lagrange interpolation on two and three simple knots and Hermite interpolation on two knots, one simple and the other one double. In the present paper we obtain a semi-discrete quantitative Voronovskaya-type theorems based on Hermite interpolation on two double knots.

Crouching Woman

Crouching Woman Joan Larkin (bio) Camille Claudel, 1884 A double knot of flesh:nakedness as armor. Her taut arm grips her shoulder,shields her face. Ugly, beautiful––forget such words! A woman posing in a cold atelierplants her feet in stone dust,folds into herself, elbow pressed to knee, breasts drooping with gravity,thighs straining. Wills herselfto become stone. From a distance: a bouldertrembles on a rim of air . . . [End Page 64] Joan Larkin joan larkin has published five poetry collections, including Blue Hanuman and My Body: New and Selected Poems. She cotranslated Sor Juana’s Love Poems and coedited four anthologies, including Gay and Lesbian Poetry in Our Time. She has been a lifelong teacher. Her honors include the Lambda, nea, and Shelley Memorial awards. Copyright © 2023 Joan Larkin ...

PO-687-06 A CASE OF DIFFICULT LEADLESS PACEMAKER IMPLANTATION DUE TO PACEMAKER DELIVERY SYSTEM FAILURE

The Micra leadless pacing system (Medtronic) is an effective alternative to transvenous pacemaker in selected patients and can be safely implanted in > 99% cases. The tether in the delivery system serves as an important connection between the device and the delivery catheter, allowing multiple recaptures to be performed. Failure of the delivery system resulting in inability to deploy is extremely rare. We describe a case of difficult Micra implantation due to leadless pacemaker delivery system failure. N/A An 88-year-old male with complete heart block post transfemoral aortic valve replacement underwent placement of single chamber leadless pacemaker placement (Micra) using standard techniques. Under local anesthesia, access was obtained in the right femoral vein using ultrasound guidance and a 23 French long sheath was inserted and advanced into the right atrium under fluoroscopy. A Micra leadless pacing system was introduced and placed under fluoroscopic visualization into the right ventricular septum. Gentle manual tension on the tether demonstrated good contact with the myocardium. The tether was cut but significant resistance was felt when attempting to remove it. Despite multiple attempts the tether could not be safely removed, and it was decided to extract the Micra system. Unfortunately, despite multiple attempts by applying significant tension on the tether, the delivery catheter would not align with the pacing capsule for safe extraction. At this time it was decided to remove the delivery system leaving the pacing capsule with the tether in place. A 0 Vicryl suture was placed and using a double knot it was secured on a 035 wire and the suture was pulled through a large curve steerable Agilis sheath. Next, the Vicryl and the tether were knotted together and Agilis sheath was advanced to provide additional support and avoid trauma to any internal structure during extraction. Using Agilis as a rail, the Micra was extracted. Gross visual inspection revealed no clear knot on the tether. After the extraction, a new Micra system was placed using standard techniques. It is important to be aware of failure of the components of the leadless pacemaker delivery system and the techniques to safely extract it.

Flapless and transconjunctival double knot technique to repair iridodialysis.

Flapless and transconjunctival double knot technique to repair iridodialysis.

SP2.1.9Augmented terminal feedback influences cognitive ability of surgical trainees: a randomised controlled trial

Abstract Introduction Formative assessments in the form of Global assessment (GAS) and procedural based assessment (PBA) are the current methods used for feedback in British laparoscopic surgical training. Video error signature feedback (VESF) has been proposed as an alternative approach to enhance motor skills in laparoscopic training through influencing cognitive approach. Methods Twenty laparoscopic novice students were randomised into Current standard feedback (CSF) and VESF groups. Both groups tied laparoscopic double square knots in four sequential stages. Standard human reliability assessment method (HRA) was utilised to assess unedited video recordings for errors. A validated scoring system by expert trainers assessed proficiency gain. Similar assessment was performed for both groups. Unedited video recordings of the VESF group were annotated for errors at each stage and provided as feedback through video hosting website. CSF group received assessment sheet as their feedback, comparable to current practice. Error numbers, time execution and proficiency gain were the outcomes. Inter-rater reliability among trainers for error detection was established. Results A total of 6490 movements were studied with 1613 errors detected. VESF group committed significantly less errors as compared to the CSF group [1011/1613 (63%) vs 602/1613 (37%), p < 0.01]. VESF group gained proficiency earlier. Time execution was similar. Inter-rater reliability for error detection was high (p = 0.96). Discussion VESF effects cognitive framework of a laparoscopic task in trainee’s mind, ultimately reducing errors. This work demonstrated the practical application of video error signature feedback by demonstrating a simple laparoscopic task and analysing its learning process through novice brains.

Biomechanical study of a newly developed continuous double knots technique compared with the 4-strand double-modified Kessler technique for flexor tendon repair

PurposeIn this study we compare the biomechanical properties of a novel suture technique that we developed called the continuous double knots technique for repairing flexor tendon injuries with the standard 4-strand double-modified Kessler technique.MethodsThis was an experimental study. Eighty porcine flexor digitorum profundus tendons were harvested and divided randomly into two groups of 40. The first group (N = 40) was repaired using the 4-strand double modified Kessler technique and the second group (N = 40) was repaired using our new continuous double knots technique. The two groups were randomly divided and the ultimate failure load (n = 20) and cyclic testing to failure (n = 20) were compared.ResultsThe mean ultimate failure load was 25.90 ± 7.11 (N) and cyclic testing to failure 88 ± 47.87 (cycles) for the 4-strand double modified Kessler technique and 34.56 ± 6.60 (N) and 189 ± 66.36 (cycles) for our new continuous double knots technique. The T-test revealed a significant difference between the 2 techniques (p < 0.05). In terms of biomechanical properties in tendon repair, the continuous double knots technique group had a higher tensile strength than the 4-strand double-modified Kessler technique group. There were also significant differences between the ultimate failure load and cyclic testing to failure for the flexor tendon sutures.ConclusionsThe continuous double knots technique suture technique had significantly higher maximum tensile strength and cyclic testing than the 4-strand double modified Kessler technique in an in vitro study, and in thus an optional technique for flexor tendon repair.

The reduced Dijkgraaf–Witten invariant of double twist knots in the Bloch group of 𝔽p

In 2004, Neumann showed that the complex hyperbolic volume of a hyperbolic 3-manifold [Formula: see text] can be obtained as the image of the Dijkgraaf–Witten invariant of [Formula: see text] by a certain 3-cocycle. After that, Zickert gave an analogue of Neumann’s work for free fields containing finite fields. The author formulated a geometric method to calculate a weaker version of Zickert’s analogue, called the reduced Dijkgraaf–Witten invariant, for finite fields and gave a formula for twist knot complements and [Formula: see text] in his previous work. In this paper, we show concretely how to calculate the reduced Dijkgraaf–Witten invariants of double twist knot complements and [Formula: see text], and give a formula of them for [Formula: see text].

Modified Technique for Scleral-Sutured Fixation with the Double Knots Technique for Posterior Chamber Intraocular Lens: Short-Term Observation

Purpose To evaluate the short-term safety and efficacy of a novel approach of utilizing the 9-0 looped polypropylene suture with double knots buried into the scleral groove and the scleral tunnel to minimize the risk of the suture erosion and suture knot exposure. Design Clinical-based retrospective study. Methods Records of consecutive patients who had anterior vitrectomy and scleral-fixated posterior chamber intraocular lens (IOL) implantation between July 2018 and April 2020 with a minimum follow-up of 3 months were reviewed. Results This study enrolled a total of 21 eyes from 20 patients (15 male). These patients had a mean age of 58.52 ± 8.55 years and were followed for an average of 1.08 ± 0.58 years postoperatively. Best-corrected visual acuity (BCVA) improved from a preoperative mean of 0.43 ± 0.41 logMAR to a significantly higher mean 3-month postoperative value of 0.09 ± 0.21 logMAR (Z = -3.35, p < 0.01). There were no statistical differences between the preoperative and postoperative corneal endothelial cell density (p=0.71). The postoperative complications included transient increased intraocular pressure in 5 eyes (24%). No other complications were detected during the follow-up. Conclusions The modified technique proposed is a safe, effective, and reliable approach resulting in good visual outcomes. Our procedure might have the potential benefit to avoid suture-related complications in scleral-fixated IOL implantation. Trial registration. Retrospective case series study, not applicable.

Magnetic knot cascade via the stepwise reconnection of helical flux tubes

Abstract

A Modified Flexor Tendon Suture Technique Combining Kessler and Loop Lock Flexor Tendon Sutures

OBJECTIVES:In the present study, a novel single knot tenorrhaphy was developed by combining the modified Kessler flexor tendon suture (MK) with the loop lock technique.METHODS:A total of 48 porcine flexor digitorum profundus tendons were collected and randomly divided into six groups. The tendons were transversely cut and then repaired using six different techniques, the MK method, double knot Kessler-loop lock flexor tendon suture (DK), and single knot Kessler-loop lock flexor tendon suture (SK), each in combination with the epitendinous suture (P), and the same three techniques without P. Furthermore, by performing the load-to-failure tests, the biomechanical properties and the time taken to complete a repair, for each tenorrhaphy, were assessed.RESULTS:Compared to the MK+P method, DK+P was more improved, thereby enhancing the ultimate tensile strength. The SK+P method, which required fewer knots than DK+P, was easier to perform. Moreover, the SK+P repair increased the force at a 2-mm gap formation, while requiring lesser knots than DK+P.CONCLUSION:As opposed to the traditional MK+P method, the SK+P method was improved and exhibited better biomechanical properties, which may facilitate early mobilization after the repair.

Water knot: Case report of a rare complication during a urodynamic test

Intravesical catheter knotting is a rarely reported event that could lead to serious complications. We present a case that occurred during urodynamic test with two K30 tubes: a 56-year-old female with a double knot of two K30 (8.4 Fr) tubes. This case was resolved by removing the catheters with sustained traction. Because catheter knotting can be a serious complication, we recommend the use of a double-lumen catheter when possible and assessment of a safe insertion length.

2758 Easy-to-Master Slipknot

Video Objective In laparoscopic intracorporal knot tying, we have to ligate securely in the limited space. The slip knot technique is useful in these situations. I will show the key and logic of slip knot using a two-color suture, and some techniques. Setting The procedures to perform slip knot are as following: Firstly, you make a square knot by two opposite half knots consisted of one clockwise and the other counter-clockwise. Then, you can push and slide the “unlocked” square knot toward the ligation point and secure the tissues. “Unlocked” means the state of which the square knot is slidable, and keeping this state is the secret of slip knot. A two-color suture is helpful to understand this state. Various slip knot techniques are below: 1) Standard slip knot. This is the basic way, an unlocked square knot is slid to the ligation point. 2) Loose one-hand slip knot. As a square knot is unlocked and loose, you can tie the knot by pulling the long tail one-handed. 3) In case of the locked knot. You should pull the long tail and release the knot before you slide it. 4) Pulling the short tail. You can also tie the knot by pulling short tail in theory. 5) Knot tying combined with surgeon's knot. You can alter the first opposite half knot to double half knot. To get your slip knot more smoothly and quickly, you should manage the suture near the knot, omit the time and effort for catching the suture of second opposite half knot. And training never cheats on you. Interventions N/A Conclusion These techniques can help your operation get better definitely.

Ejection of Double Knots from the Radio Core of PKS 1510–089 during the Strong Gamma-Ray Flares in 2015

Abstract PKS 1510–089 is a bright and active γ-ray source that showed strong and complex γ-ray flares in mid-2015 during which the Major Atmospheric Gamma Imaging Cerenkov telescopes detected variable very high energy (photon energies &gt;100 GeV) emission. We present long-term multifrequency radio, optical, and γ-ray light curves of PKS 1510–089 from 2013 to 2018, and results of an analysis of the jet kinematics and linear polarization using 43 GHz Very Long Baseline Array data observed between late 2015 and mid-2017. We find that a strong radio flare trails the γ-ray flares in 2015, showing an optically thick spectrum at the beginning and becoming optically thin over time. Two laterally separated knots of emission are observed to emerge from the radio core nearly simultaneously during the γ-ray flares. We detect an edge-brightened linear polarization near the core in the active jet state in 2016, similar to the quiescent jet state in 2008–2013. These observations indicate that the γ-ray flares may originate from compression of the knots by a standing shock in the core and the jet might consist of multiple complex layers showing time-dependent behavior, rather than of a simple structure of a fast jet spine and a slow jet sheath.

Protein-Lipid Interfaces Drive DkTx-Mediated TRPV1 Channel Activation

A recent cryo-EM structure and a molecular model of the TRPV1 ion channel in complex with its potent agonist, the double knot toxin (DkTx), have provided valuable information on the membrane lipid-binding sites of this complex.To interrogate the functional significance of these protein-lipid interfaces and to compare them with that of lipid-devoid DkTx-TRPV1 interfaces, we generated a series of DkTx variants and characterized their TRPV1-activating properties electrophysiologically. The results of these experiments together with those from our membrane partitioning experiments demonstrate that these structurally extremely similar toxin-lipid interfaces play dominant yet non-overlapping roles in channel activation. The lipid interfaces formed by one of the knots of toxin were observed to confer the toxin with its strong membrane partitioning ability resulting in its slow dissociation from the complex. In contrast, the lipid interfaces formed by the other knot was found to contribute minimally to toxin dissociation rates yet profoundly to the toxin's TRPV1-activating potency. These studies demonstrate that protein-lipid interfaces can play key roles in the function of membrane embedded protein-protein complexes.

Concordance invariants of doubled knots and blowing up

Let $\nu$ be either the Ozsvath-Szabo $\tau$-invariant or the Rasmussen $s$-invariant, suitably normalized. For a knot $K$, Livingston and Naik defined the invariant $t_\nu(K)$ to be the minimum of $k$ for which $\nu$ of the $k$-twisted positive Whitehead double of $K$ vanishes. They proved that $t_\nu(K)$ is bounded above by $-TB(-K)$, where $TB$ is the maximal Thurston-Bennequin number. We use a blowing up process to find a crossing change formula and a new upper bound for $t_\nu$ in terms of the unknotting number. As an application, we present infinitely many knots $K$ such that the difference between Livingston-Naik's upper bound $-TB(-K)$ and $t_\nu(K)$ can be arbitrarily large.

Histological study on the safety of the controllable ileostomy with pipe

To investigate the safety of the controllable ileostomy with pipe in view of histology. Twenty-eight Beagle dogs undergoing controllable ileostomy with pipe were studied. The special fistula tube with balloon was placed into the hole locating at the cecal root opposing the mesenteric side, and fixed by double knot compression method. The fistula tube was removed 14 days after surgery, then the safety of the procedure was preliminarily evaluated by gastrointestinal radiography and anatomical observation. The small intestine tissue at the compression suture was used as the experimental segment, and the small intestine tissue at the proximal non-compression suture was used as the control segment. The histological staining and the immunohistochemical staining of S-100 protein, c-kit protein and α-smooth muscle actin(α-SMA) protein between two segment were compared, while quantitative comparison of myenteric plexus, intestinal Cajal cell(ICC) and smooth muscle cells in intestinal wall was carried out. After removal of fistula tube at 14 days postoperative, the dogs were normal in feeding and defecation. The digestive tract radiography showed that the intestine was patent without obvious stenosis and obstruction. The dogs were dissected 21 days after operation. The abdominal sinus ostium was well healed and the internal sinus was well formed. Under gross inspection, blood supply, morphology and motor function of experimental intestine segment were similar from the proximal and distal segments of control intestine. S-100 immunohistochemical staining showed that the morphology and distribution of S-100 protein positive cells and "blank area" cells in the experimental and control segments were consistent. Myenteric plexus counting showed that the experimental segment was 3.62±1.82/field and the control segment was 3.27±1.62/field, whose difference was not statistically significant(t=1.30, P=0.20). Immunohistochemical staining of c-kit showed that the distribution of c-kit positive cells in both segments was consistent. Counting of the number of ICCs in myenteric plexus revealed that experimental segment was 2.96±2.57/plexus, and control segment was 2.49±1.80/plexus without significant difference(t=1.81, P=0.07). Immunohistochemical staining of α-SMA showed that the morphology and distribution of smooth muscle cells in whole intestinal wall(muscle layer, longitudinal muscle, ring muscle) in experimental and control segments were consistent. The average absorbance(A) value of α-SMA staining in ring muscle layer was detected and quantified. The experimental segment was 0.15±0.03 and control segment was 0.14±0.04 without significant difference(t=1.16, P=0.25). The technique of controllable ileostomy with pipe is safe in view of histology, which may replace the traditional protective ileostomy.

Do the stump knotting technique and specimen retrieval method effect morbidity in laparoscopic appendectomy?

Stump closure is the most important part of a laparoscopic appendectomy (LA). Closing the appendix base with knot tying is the most cost-effective method. The defined risk factor for surgical site infection (SSI) after LA is the contamination of trocar entry area by inflamed appendicitis. This study aims to compare the single and double knot technique for stump control and specimen removal methods in LA. The data of patients who underwent LA between January 2015 and January 2017 were obtained from prospectively collected database. Single and double knot technique, specimen removal method, operation duration, hospital stay, and perioperative-postoperative complications were compared. Extracorporeal double knot was used in 134 patients (63%), and single knot was used in 79 patients (37%). There was no difference between operation duration in the two groups (p=0.97). No stump leakage was observed in any patient. Intraabdominal abscess developed in three patients (1.4%). Appendix was removed from the abdomen directly in 101 patients (47%) and using specimen retrieval bag in 112 (53%). SSI developed in five patients (2.3%), and appendices of all of these five patients were removed from abdomen without using specimen retrieval bag. No SSI was detected in the group that used the specimen retrieval bag (p=0.02). Single or double knot(s) tying can be defined as safe and cost-effective stump closure method. The risk of developing SSI can be reduced using specimen retrieval bag.

Volumes of hyperbolic double twist knot cone-manifolds

We give explicit formulas for the volumes of hyperbolic cone-manifolds of double twist knots, a class of two-bridge knots which includes twist knots and two-bridge knots with Conway notation [Formula: see text]. We also study the Riley polynomial of a class of one-relator groups which includes two-bridge knot groups.

Analysis of the tractive force pattern on a knot by force measurement during laparoscopic knot tying

BackgroundQuantifying surgical skills assists novice surgeons when learning operative techniques. We measured the interaction force at a ligation point and clarified the features of the force pattern among surgeons with different skill levels during laparoscopic knot tying. MethodsForty-four surgeons were divided into three groups based on experience: 13 novice (0–5 years), 16 intermediate (6–15 years), and 15 expert (16–30 years). To assess the tractive force direction and volume during knot tying, we used a sensor that measures six force-torque values (x-axis: Fx, y-axis: Fy, z-axis: Fz, and xy-axis: Fxy) attached to a slit Penrose drain. All participants completed one double knot and five single knot sequences. We recorded completion time, force volume (FV), maximum force (MF), time over 1.5 N, duration of non-zero force, and percentage time when vertical force exceeded horizontal force (PTz). ResultsThere was a significant difference between groups for completion time (p = 0.007); FV (total: p = 0.002; Fx: p = 0.004, Fy: p = 0.007, Fxy: p = 0.004, Fz: p < 0.001, Fxy/Fz: p = 0.003), MF (total: p = 0.004; Fx: p = 0.015, Fy: p = 0.035, Fxy: p = 0.009, Fz: p = 0.001, Fxy/Fz: p = 0.041); time over 1.5 N (p = 0.002); duration of non-zero force (p = 0.029); and PTz (p < 0.001). PTz showed the only significant difference comparing intermediates with experts (intermediates: 13.7 ± 9.0, experts: 4.9 ± 3.2; p < 0.001). ConclusionsWe clarified the characteristics of the force pattern at the ligation point during suturing by surgeons with three levels of experience using a force measurement system. We revealed that both force volume and force direction differed depending on surgeons' skill level during knot tying.

Early range of motion exercise in pediatric patients with olecranon fractures treated with tension band suture with double loops and double knots

Pediatric patients with olecranon fractures are uncommon. The tension band suture technique was introduced to reduce the burden of implant removal and other complications. However, to our knowledge, early range of motion (ROM) exercise has not been introduced in this population of patients. Double Vicryl loops and knots with 2 cross-pins are used to maintain the benefits of the tension band suture technique and to enhance fixation tensile strength. We believe that early ROM exercises could be achieved without nonunion or fixation failure. Twelve pediatric patients with olecranon fractures were treated with tension band suture with double loops and knots between 2004 and 2015. Vicryl No. 1 was used for wiring. ROM exercises were initiated 1 week postoperatively with a customized functional brace. Early functional outcomes were evaluated by the Mayo Elbow Performance Score at every visit after 8 weeks postoperatively. Nine boys and 3 girls (average age, 10.6 years; range, 5 years 7 months-16 years 2 months) were included in the study. Initial displacement and angulation of the fractures were 5 mm (2-7 mm) and 12° (4°-25°), respectively. Two cases had radial neck fractures of the ipsilateral elbow. All patients had a perfect Mayo Elbow Performance Score after 8 weeks postoperatively. Pin removals were performed at 13.1 weeks. No complications, including growth arrest, were observed. Tension band suture with double loops and knots, combined with early ROM exercise, may be a complete alternative to tension band wiring.