Unique method for removal of knotted lumbar epidural catheter: A case report

BACKGROUND Combined spinal-epidural(CSE)anesthesia is the preferred anesthesia method for cesarean delivery.The use of an epidural catheter is essential for administering additional drugs intraoperatively and managing postoperative pain.However,the insertion of epidural catheters is associated with various complications,such as total spinal anesthesia,symptoms indicative of spinal nerve root irritation,and challenges in epidural catheter removal.CASE SUMMARY We present a case report of a challenging epidural catheter removal due to knotting.The lumbar computed tomography scan results revealed that the catheter formed a tight knot in the epidural space.We used a novel extubation method and successfully removed the catheter.CONCLUSION The operator can use opposite forces to"spiral"apart the spinal joints by positioning the patient's body in a specific position.The findings indicate that,when combined with imaging examination results,this method is effective for the removal of epidural catheters.

Importance of Stewards and Other Protection Efforts for Conservation of Red Knots (Calidris canutus rufa) and Other Shorebirds on Delaware Bay, New Jersey

Understanding the factors that contribute to population stability in long-distance migrant birds is increasingly important, particularly given global climate change, sea level rise, and loss or disturbance at essential habitats. While the populations of most shorebirds are declining worldwide, those that migrate through Delaware Bay, New Jersey and Delaware, are declining at the most rapid rate despite conservation efforts. In this paper, we 1) provide background information on population declines of red knots (Calidris canutus rufa) using Delaware Bay, threats to their foraging, and efforts to reduce threats, 2) summarize briefly our studies of the effects of human activities on knots and other shorebirds, 3) present data on management efforts to protect knots and other shorebirds from the activities of people, and 4) discuss the efficacy of such efforts (usually referred to as “decreasing the effect of human disturbances”). The Shorebird Project on Delaware Bay is over 25 years old and provides long-term data to help assess the status of shorebird numbers, particularly for red knot, as well as the density of horseshoe crabs (Limulus polyphemus) and their eggs. Red knots have continued to decline even more precipitously in the last few years, presenting cause for concern. Protective efforts have been successful in reducing human disruption on the N.J. Delaware Bay beaches, but the lack of uniformity in implementation across the New Jersey side, and across the whole Bay have hampered further improvements. Implementation of signs, fencing, and stewards on some beaches significantly enhanced the use of these beaches by red knots, determined by examining the use of beaches pre- and post-implementation. Implementation of fencing and stewards had the greatest effect. From 1986 to 2018, there was a significant shift in the percent of Delaware Bay red knots using the NJ side, where protection efforts had been implemented on many of the beaches. Merely restricting access (without fencing or other efforts) did not result in more knots using the beaches post-restriction. This is the first paper that clearly shows the protective effects of having beach stewards. We discuss the long-term needs for continued management of Delaware Bay beaches, and other beaches coastwide, and of determining the causes of population declines of red knots.

Three-dimensional inversion of knot defects recognition in timber cutting

The comprehensive utilization of wood is the main goal of log cutting,but knot defects increase the diffi-culty of rationally optimizing cutting.Due to the lack of real shape data of knot defects in logs,it is diffi cult for detection methods to establish a correlation between signal and defect morphology.An image-processing method is proposed for knot inversion based on distance regularized level set segmentation(DRLSE)and spatial vertex clustering,and with the inversion of the defects existing relative board position in the log,an inversion model of the knot defect is established.First,the defect edges of the top and bottom images of the boards are extracted by DRLSE and ellipse fi tting,and the major axes of the ellipses made coplanar by angle correction;second,the coordinate points of the top and bottom ellipse edges are extracted to form a spatial straight line;third,to solve the intersection dispersion of spatial straight lines and the major axis plane,K-medoids clustering is used to locate the vertex.Finally,with the vertex and the large ellipse,a 3D cone model is constructed which can be used to invert the shape of knots in the board.The experiment was conducted on ten defective larch boards,and the experimental results showed that this method can accurately invert the shapes of defects in solid wood boards with the advantages of low cost and easy operation.

Incompressible Pairwise Incompressible Surfaces in Knot Exteriors

We discuss the properties of incompressible pairwise incompressible surfaces in a knot complement by using twist crossing number. Let K be a pretzel knot or rational knot that its twistindex is less than 6, and let F be an incompressible pairwise incompressible surface in S 3-K. Then F is a punctured sphere.

Using Parametric Mathematical Modeling to Develop a Geometric and Topological Intuition for Molecular Knots

Knot theory is a branch of topology in pure mathematics, however, it has been increasingly used in different sciences such as chemistry. Mathematically, a knot is a subset of three-dimensional space which is homeomorphic to a circle and it is only defined in a closed loop. In chemistry, knots have been applied to synthetic molecular design. Mathematics and chemistry together can work to determine, characterize and create knots which help to understand different molecular designs and then forecast their physical features. In this study, we provide an introduction to the knot theory and its topological concepts, and then we extend it to the context of chemistry. We present parametric representations for several synthetic knots. The main goal of this paper is to develop a geometric and topological intuition for molecular knots using parametric equations. Since parameterizations are non-unique;there is more than one set of parametric equations to specify the same molecular knots. This parametric representation can be used easily to express geometrically molecular knots and would be helpful to find out more complicated molecular models.

Diet of Great Knots (Calidris tenuirostris) during spring stopover at Chongming Dongtan,China

Variable and unpredictable food resources at stopover sites bring severe challenges to migrating shorebirds. Opportunistic foraging strategies, referring to shorebirds consuming prey in proportion to their availability, allow shorebirds to replenish fuel and nutrient reserves efficiently for continuing their migration. Chongming Dongtan, located in the Yangtze River estuary of eastern China, is the first major stopover site of shorebirds on the Chinese mainland during their northward migration. We investigated the diet of Great Knots (Calidris tenuirostris) at Chongming Dongtan during the spring stopovers of 2009 and 2010 through benthos sampling and dropping analysis. The benthos samples were categorized into gastropods, bivalves, polychaetes, crustaceans and insect larvae. Dropping analysis indicated that gastropods and bivalves constituted more than 70% of the diet of the Great Knot, with Assiminea violacea and Corbicula fluminea being the most frequently consumed. Chi-square tests indicated that for each prey category, there was no significant difference between the frequency of its occurrence in the benthos samples and dropping samples during the early stopover periods of 2009 and 2010 and during the late stopover periods of 2010. Although there was a statistically significant difference between the frequency of occurrence of prey in the total macrobenthos and in the droppings of the Great Knots during the late stopover period in 2009, the more abundant prey were more frequently consumed by the Great Knots. This suggests that Great Knots adopted an opportunistic foraging strategy during their stopover at Chongming Dongtan.

Zeros of the Jones Polynomial for Torus Knots and 2-bridge Knots

We study zeros of the Jones polynomial and their distributions for torus knots and 2-bridge knots. We prove that e(2m+1)πi/2and e(2m+1)πi/4(m is a positive integer)can not be the zeros of Jones polynomial for torus knots T p,q by the knowledge of the trigonometric function. We elicit the normal form of Jones polynomials of the 2-bridge knot C(-2, 2, ···,(-1)r2) by the recursive form and discuss the distribution of their zeros.

Predicting Financial Contagion and Crisis by Using Jones, Alexander Polynomial and Knot Theory

Topological methods are rapidly developing and are becoming more used in physics, biology and chemistry. One area of topology has showed its immense potential in explaining potential financial contagion and financial crisis in financial markets. The aforementioned method is knot theory. The movement of stock price has been marked and braids and knots have been noted. By analysing the knots and braids using Jones polynomial, it is tried to find if there exists an untrivial knot equal to unknot? After thorough analysis, possible financial contagion and financial crisis prediction are analysed by using instruments of knot theory pertaining in that sense to Jones, Laurent and Alexander polynomial. It is proved that it is possible to predict financial disruptions by observing possible knots in the graphs and finding appropriate polynomials. In order to analyse knot formation, the following approach is used: “Knot formation in three-dimensional space is considered and the equations about knot forming and its disentangling are considered”. After having defined the equations in three-dimensional space, the definition of Brownian bridge concerning formation of knots in three-dimensional space is defined. Using analogy method, the notion of Brownian bridge is translated into 2-dimensional space and the foundations for the application of knot theory in 2-dimensional space have been set up. At the same time, the aforementioned approach is innovative and it could be used in accordance with stochastic analysis and quantum finance.

KNOT STRENGTH OF INDUSTRIAL TEXTILE FIBRES

In this paper, the knot strengths of the seven strands which were made of polyethleneterephthalate(PET), nylon 6, polyvinyl formal fibre, polypropylene and polyethylene with differentspecification used for industrial purposes were tested and discussed. The results of experimentshow: the knot strength loss does not only depend on the breaking elongation and the diameter ofsample, but also on the shape of the load-extension curve and twist factor of sample and other fac-tors; the range of the knot strength loss and the breaking energy loss vary in a wide range, in thepresent case. the former is from 2.7% to 58.14% and the latter from 16.36% to 78.76%. Thestrength loss of the polypropylene filament is the least among the samples investigated.

Effect of Anti-nematode Preparations on Physiological Traits of Tomato Leaves Affected by Root-knot Nematode

[ Objective ] The paper was to study the effects of anti-nematode preparations with different mechanisms on changes of enzyme systems and membrane permeability of tomato leaves, so as to provide reference basis for effective control of soil root-knot nematode in greenhouse. [ Method] With tomato seedlings af- fected by root-knot nematode as material, changes of superoxide dismutase（SOD）, peroxidase（ POD）, relative conductivity and malondialdehyde （MDA） in toma- toes were tested after the seedling soil was treated by preparations of Wuxianmei, Hailvsu, Duxiandna and Avermectin. [ Result] After treated by different prepara- tions, SOD and POD activity of tomato leaves were higher than control, and that treated by Wuxianmei was the highest. In addition to Duxiandna, the relative con- ductivity and MDA content of other treatments were significantly lower than control. When tomatoes were planted for 70 d, the effect of Avermectin against reot-knot nematode Was the best of 66.3%. [ Conclusion] After tomatoes were infected by root-knot nematode, different preparation treatments all had certain control effect, which made the physical indicators of tomato have obvious change. Integrated control of multiple preparations in greenhouse was beneficial to control soil root-knot nematode.

Knotted pictures of the Bell bases on the surface of a trivial torus

By means of the method of torus knot theory, this paper gives the complete processes of obtaining the knotted pictures of four Bell b^es from the knotted pictures of four basic two qubit states.

SOME APPLICATIONS OF PLANAR GRAPH IN KNOT THEORY

The relationship between a link diagram and its corresponding planar graph is briefly reviewed. A necessary and sufficient condition is given to detect when a planar graph corresponds to a knot. The relationship between planar graph and almost planar Seifert surface is discussed. Using planar graph, we construct an alternating amphicheiral prime knot with crossing number n for any even number n 〉 4. This gives an affirmative answer to problem 1.66（B） on Kirby＇s problem list .

Knotted pictures of the GHZ states on the surface of a trivial torus

By means of the torus knot theory method, this paper presents the complete process of obtaining the knotted pictures of eight GHZ states on the surface of a trivial torus from the knotted pictures of eight basic three-qubit states on the surface of a trivial torus. Thus, we obtain eight knotted pictures 121 linkage on the ordinary plane.

Rational-slice Knots via Strongly Negative-amphicheiral Knots

We show that certain satellite knots of every strongly negative-amphicheiral rational knot are rational-slice knots. This proof also shows that the O-surgery manifold of a certain strongly negative amphicheiral knot such as the figure-eight knot bounds a compact oriented smooth 4-manifold homotopy equivalent to the 2-sphere such that a second homology class of the 4-manifold is represented by a smoothly embedded 2-sphere if and only if the modulo two reduction of it is zero.

两类特殊的Unknotting数为1的纽结

就纽结不变量中的Unknotting数进行一些研究,将Unknotting数为1的纽结必为素纽结这一结论推广得出:当u(k_1)+u(k_2)=2时,有u(k_1#k_2)=u(k1)+u(k2),利用Unknotting数为1的2- Bridge结的等价定理,得出Unknotting数为1的特殊的2-Bridge结,再根据纽结的性质,给出了两种Un- knotting数为1的特殊的排叉结。

Knotted Picture of Single Qubit Quantum Logic Gate

This paper briefly introduces the five types of the surgical operations in knot theory and obtains the expression of single qubit quantum logic gate in terms of these surgical operations.

H(2)-unknotting Number of a Knot

An H（2）-move is a local move of a knot which is performed by adding a half-twisted band. It is known an H（2）-move is an unknotting operation. We define the H（2）-unknotting number of a knot K to be the minimum number of H（2）-moves needed to transform K into a trivial knot. We give several methods to estimate the H（2）-unknotting number of a knot. Then we give tables of H（2）-unknotting numbers of knots with up to 9 crossings.

Knotted Pictures of Hadamard Gate and CNOT Gate

This paper obtains the knotted pictures of Hadamard gate and CNOT gate in terms of surgical operations described in knot theory.

KNOT认证加密算法的零和区分器分析

KNOT认证加密算法是国际轻量级密码算法征集竞赛活动第2轮入围的候选算法之一。该算法具有软硬件实现快、资源消耗低等特点,其安全性受到了全球广泛的关注。基于标志位技术,提出了密码S盒的新可分性模型构建方法。同时,利用KNOT-256的算法结构,构建了KNOT-256密码算法新的可分性的混合整数线性规划模型,并由此设计了该算法零和区分器的自动化新搜索方法。研究结果表明:KNOT-256置换存在30轮的零和区分器,尽管该区分器对KNOT认证加密算法(分组长度为256的版本的初始化轮数是52轮)的安全性没有造成实际的威胁,但得到的结果证实了新的零和区分器构造方法是有效的。

FREE VIBRATION ANALYSIS OF ARBITRARY SHAPED PLATES BY BOUNDARY KNOT METHOD

The boundary knot method （BKM） is a truly meshless boundary-type radial basis function （RBF） collocation scheme, where the general solution is employed instead of the fundamental solution to avoid the fictitious outside boundary of the physical domain of interest. In this study, the BKM is first used to calculate the free vibration of free and simply-upported thin plates. Compared with the analytical solution and ANSYS （a commercial FEM code） results, the present BKM is highly accurate and fast convergent.