In this work,Langevin dynamics simulations were carried out to thoroughly investigate the swapping process of composite knots under tension in a cuboid nanochannel.From our analysis,the free energy profiles of knot sw...In this work,Langevin dynamics simulations were carried out to thoroughly investigate the swapping process of composite knots under tension in a cuboid nanochannel.From our analysis,the free energy profiles of knot swapping under different conditions were extracted from the overall probability distribution of the relative distance between the centers of composite knots.In addition,the impact of the stretching force,confinement size,and bending stiffness on the free energy profiles was directly identified.Especially,the influence of topology structure is for the first time reported.The increasing stretching force in a fixed confinement or the confinement size under a constant stretching force does not alter their respective equilibrium populations at the separate state and the entangled state.In contrast,a bending stiffness larger than 15 enhanced the formation of the entangled state.The topology structure of the 51knot,which was different from the 52knot,resulted in forming a metastable state in the free energy profiles.The increasing stretching forces yielded an enhancement of the following free energy barrier.展开更多
The boundary knot method(BKM)is a simple boundary-type meshless method.Due to the use of non-singular general solutions rather than singular fundamental solutions,BKM does not need to consider the artificial boundary....The boundary knot method(BKM)is a simple boundary-type meshless method.Due to the use of non-singular general solutions rather than singular fundamental solutions,BKM does not need to consider the artificial boundary.Therefore,this method has the merits of purely meshless,easy to program,high solution accuracy and so on.In this paper,we investigate the effectiveness of the BKM for solving Helmholtz-type problems under various conditions through a series of novel numerical experiments.The results demonstrate that the BKM is efficient and achieves high computational accuracy for problems with smooth or continuous boundary conditions.However,when applied to discontinuous boundary problems,the method exhibits significant numerical instability,potentially leading to substantial deviations in the computed results.Finally,three potential improvement strategies are proposed to mitigate this limitation.展开更多
The knots frequently occur in biopolymer and their diffusion plays an active role in the gene regulation.In this work,Langevin dynamics simulations were carried out to detect the diffusion behaviours of a knot along a...The knots frequently occur in biopolymer and their diffusion plays an active role in the gene regulation.In this work,Langevin dynamics simulations were carried out to detect the diffusion behaviours of a knot along a tensioned polymer in different spatial constraints.The polymer accommodating a knot was tethered to two macrospheres to block the unravelling of the knot.As a result,the curves for the diffusion coefficients of the knot with different bending stiffness as a function of the tension in different spatial constraints were obtained.In the space without constraints or with weak constraints,the corresponding curves for the knot with relatively large bending stiffness exhibited two turnover behaviours.On the contrary,for the knot with relatively small bending stiffness,the diffusion coefficients were monotonically reduced with increasing tension.However,in a space with strong constraints,all the curves showed one turnover behaviour regardless of the bending stiffness.The turnover behaviours divided the curves into different regimes,and the dominant diffusion mechanisms in the regimes,namely,knot-region breathing,self-reptation,and internal friction,were clearly identified.The effective friction coefficientsξof the knots with 3_(1),4_(1),5_(1) and 5_(2) types as a function of the knot size N at a fixed tension were well fitted by the relationξ∝N.The effective friction coefficients of the knots at relatively large tension f>3 sharply increased with the knot complexity,which is not dependent on the spatial constraints.By contrast,the values of these coefficients at relatively small tension f≤3 were remarkably dependent on the spatial constraints.Our work not only provides valuable simulation results to assist the understanding of the diffusion of DNA knot,but also highlights the single-molecule design for the manipulation of DNA knots in future.展开更多
Recent experimental observations of knotting in DNA and proteins have stimulated the simulation studies of polymer knots.Simulation studies usually identify knots in polymer conformations through the calculation of th...Recent experimental observations of knotting in DNA and proteins have stimulated the simulation studies of polymer knots.Simulation studies usually identify knots in polymer conformations through the calculation of the Alexander polynomial.However,the Alexander polynomial cannot directly discriminate knot chirality,while knot chirality plays important roles in many physical,chemical,and biological properties.In this work,we discover a new relationship for knot chirality and accordingly,develop a new algorithm to extend the applicability of the Alexander polynomial to the identification of knot chirality.Our algorithm adds an extra step in the ordinary calculation of the Alexander polynomial.This extra step only slightly increases the computational cost.The correctness of our algorithm has been proved mathematically by us.The implication of this algorithm in physical research has been demonstrated by our studies of the tube model for polymer knots.Without this algorithm,we would be unable to obtain the tubes for polymer knots.展开更多
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...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.展开更多
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 essentia...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.展开更多
Objective: To explore the clinical efficacy of shoulder arthroscopic one-knot-two-wire suture bridge technique in the treatment of small and medium-sized rotator cuff tears. Methods: The clinical data of 22 patients w...Objective: To explore the clinical efficacy of shoulder arthroscopic one-knot-two-wire suture bridge technique in the treatment of small and medium-sized rotator cuff tears. Methods: The clinical data of 22 patients with small and medium-sized rotator cuff injuries treated with the one-knot-two-wire suture bridge technique from February 2022 to June 2023 in the Department of Orthopaedics of Jingzhou Hospital Affiliated to Yangtze University were retrospectively analysed, among which 14 cases were male and 8 cases were female;the age ranged from 35 to 68 years old, with an average of (50.86 ± 10.80) years old. All cases underwent an MRI examination of the shoulder joint to understand the type and degree of injury. The duration of the disease ranged from 120 to 166 d, with a mean of (141.23 ± 13.46) d. The evaluation of the operation time, intraoperative bleeding, visual analogue scale (VAS) of pain, Constant-Murley score and Sugaya grading of shoulder MRI were performed at the last follow-up. Results: All 22 patients were followed up for 12 - 18 months, with a mean of (14.68 ± 1.89 d). The operation time was 38 - 58 min, mean (48.18 ± 5.92) min;intraoperative bleeding was 5 - 15 mL, mean (10.00 ± 3.45) mL. All patients achieved normal healing without re-tear, vascular and nerve injury, incision infection, anchor nail loosening and dislodgement and other complications. At the last follow-up, both shoulders were normal in shape and symmetrical on both sides. The VAS score was 0 - 1.2 points, with an average of 0.61 ± 0.42 points, and the Constant-Murley score was 70 - 98 points, with an average of 86.09 ± 8.56 points. The Sugaya classification of MRI examination was 17 cases of grade I, 4 cases of grade II, and 1 case of grade III. Conclusion: One-knot-two-wire suture bridge technique is used for the treatment of small and medium-sized rotator cuff tears with short operative time, low bleeding, and good clinical outcome.展开更多
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 l...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.展开更多
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 homeomorp...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.展开更多
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 availabilit...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.展开更多
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 ...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.展开更多
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 ...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.展开更多
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 ...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.展开更多
[ 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 ef...[ 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.展开更多
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.
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 betwe...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 .展开更多
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...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.展开更多
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 s...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.展开更多
Knots are discovered in biophysical systems,such as DNA and proteins.Knotted portions in knotted DNA are significantly bent and their corresponding bending angles are comparable with or larger than the sharp bending a...Knots are discovered in biophysical systems,such as DNA and proteins.Knotted portions in knotted DNA are significantly bent and their corresponding bending angles are comparable with or larger than the sharp bending angle resulting in flexible defects.The role of flexible defects in the interplay of supercoiling and knotting of circular DNA were predicted by a Monte Carlo simulation.In knotted DNA with a particular knot type,a flexible defect noticeably enhances the supercoiling of the knotted DNA and the decreasing excitation energy makes the knotted portion more compact.A reduction in twist rigidity and unwinding of flexible defects are incorporated into the numerical simulations,so that interplay of supercoiling and knotting of circular DNA is studied under torsional conditions.Increasing unwinding not only results in a wider linking number distribution,but also leads to a drift of the distribution to lower values.A flexible defect has obvious effects on knotting probability.The summation of equilibrium distribution probability for nontrivial knotted DNA with different contour length does not change with excitation energy monotonically and has a maximum at an intermediate value of excitation energy around 5 kBT.In the phase space of knot length and gyration radius of knotted DNA,knot length does not anticorrelate with its gyration radius,which is attributed to the flexible defect in the knotted portion,which leads to the release of bending energy and inhibited the competition between entropy and bending energy.展开更多
基金The National Natural Science Foundation of China under Grant Nos.11864006,11874309,12164007,and 12204118。
文摘In this work,Langevin dynamics simulations were carried out to thoroughly investigate the swapping process of composite knots under tension in a cuboid nanochannel.From our analysis,the free energy profiles of knot swapping under different conditions were extracted from the overall probability distribution of the relative distance between the centers of composite knots.In addition,the impact of the stretching force,confinement size,and bending stiffness on the free energy profiles was directly identified.Especially,the influence of topology structure is for the first time reported.The increasing stretching force in a fixed confinement or the confinement size under a constant stretching force does not alter their respective equilibrium populations at the separate state and the entangled state.In contrast,a bending stiffness larger than 15 enhanced the formation of the entangled state.The topology structure of the 51knot,which was different from the 52knot,resulted in forming a metastable state in the free energy profiles.The increasing stretching forces yielded an enhancement of the following free energy barrier.
基金Supported by the Key Scientific Research Plan of Colleges and Universities in Henan Province(23B140006)。
文摘The boundary knot method(BKM)is a simple boundary-type meshless method.Due to the use of non-singular general solutions rather than singular fundamental solutions,BKM does not need to consider the artificial boundary.Therefore,this method has the merits of purely meshless,easy to program,high solution accuracy and so on.In this paper,we investigate the effectiveness of the BKM for solving Helmholtz-type problems under various conditions through a series of novel numerical experiments.The results demonstrate that the BKM is efficient and achieves high computational accuracy for problems with smooth or continuous boundary conditions.However,when applied to discontinuous boundary problems,the method exhibits significant numerical instability,potentially leading to substantial deviations in the computed results.Finally,three potential improvement strategies are proposed to mitigate this limitation.
基金The National Natural Science Foundation of China under Grant Nos.11864006, 11874309, 12164007, and 12204118
文摘The knots frequently occur in biopolymer and their diffusion plays an active role in the gene regulation.In this work,Langevin dynamics simulations were carried out to detect the diffusion behaviours of a knot along a tensioned polymer in different spatial constraints.The polymer accommodating a knot was tethered to two macrospheres to block the unravelling of the knot.As a result,the curves for the diffusion coefficients of the knot with different bending stiffness as a function of the tension in different spatial constraints were obtained.In the space without constraints or with weak constraints,the corresponding curves for the knot with relatively large bending stiffness exhibited two turnover behaviours.On the contrary,for the knot with relatively small bending stiffness,the diffusion coefficients were monotonically reduced with increasing tension.However,in a space with strong constraints,all the curves showed one turnover behaviour regardless of the bending stiffness.The turnover behaviours divided the curves into different regimes,and the dominant diffusion mechanisms in the regimes,namely,knot-region breathing,self-reptation,and internal friction,were clearly identified.The effective friction coefficientsξof the knots with 3_(1),4_(1),5_(1) and 5_(2) types as a function of the knot size N at a fixed tension were well fitted by the relationξ∝N.The effective friction coefficients of the knots at relatively large tension f>3 sharply increased with the knot complexity,which is not dependent on the spatial constraints.By contrast,the values of these coefficients at relatively small tension f≤3 were remarkably dependent on the spatial constraints.Our work not only provides valuable simulation results to assist the understanding of the diffusion of DNA knot,but also highlights the single-molecule design for the manipulation of DNA knots in future.
基金This work was financially supported by the National Natural Science Foundation of China(No.21973080)Research Grants Council of Hong Kong(Nos.21302520,11313322 and 14301819)Guangdong Basic and Applied Basic Research Fund(No.2022A1515010484).
文摘Recent experimental observations of knotting in DNA and proteins have stimulated the simulation studies of polymer knots.Simulation studies usually identify knots in polymer conformations through the calculation of the Alexander polynomial.However,the Alexander polynomial cannot directly discriminate knot chirality,while knot chirality plays important roles in many physical,chemical,and biological properties.In this work,we discover a new relationship for knot chirality and accordingly,develop a new algorithm to extend the applicability of the Alexander polynomial to the identification of knot chirality.Our algorithm adds an extra step in the ordinary calculation of the Alexander polynomial.This extra step only slightly increases the computational cost.The correctness of our algorithm has been proved mathematically by us.The implication of this algorithm in physical research has been demonstrated by our studies of the tube model for polymer knots.Without this algorithm,we would be unable to obtain the tubes for polymer knots.
文摘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.
文摘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.
文摘Objective: To explore the clinical efficacy of shoulder arthroscopic one-knot-two-wire suture bridge technique in the treatment of small and medium-sized rotator cuff tears. Methods: The clinical data of 22 patients with small and medium-sized rotator cuff injuries treated with the one-knot-two-wire suture bridge technique from February 2022 to June 2023 in the Department of Orthopaedics of Jingzhou Hospital Affiliated to Yangtze University were retrospectively analysed, among which 14 cases were male and 8 cases were female;the age ranged from 35 to 68 years old, with an average of (50.86 ± 10.80) years old. All cases underwent an MRI examination of the shoulder joint to understand the type and degree of injury. The duration of the disease ranged from 120 to 166 d, with a mean of (141.23 ± 13.46) d. The evaluation of the operation time, intraoperative bleeding, visual analogue scale (VAS) of pain, Constant-Murley score and Sugaya grading of shoulder MRI were performed at the last follow-up. Results: All 22 patients were followed up for 12 - 18 months, with a mean of (14.68 ± 1.89 d). The operation time was 38 - 58 min, mean (48.18 ± 5.92) min;intraoperative bleeding was 5 - 15 mL, mean (10.00 ± 3.45) mL. All patients achieved normal healing without re-tear, vascular and nerve injury, incision infection, anchor nail loosening and dislodgement and other complications. At the last follow-up, both shoulders were normal in shape and symmetrical on both sides. The VAS score was 0 - 1.2 points, with an average of 0.61 ± 0.42 points, and the Constant-Murley score was 70 - 98 points, with an average of 86.09 ± 8.56 points. The Sugaya classification of MRI examination was 17 cases of grade I, 4 cases of grade II, and 1 case of grade III. Conclusion: One-knot-two-wire suture bridge technique is used for the treatment of small and medium-sized rotator cuff tears with short operative time, low bleeding, and good clinical outcome.
文摘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.
文摘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.
基金supported by the National Natural Science Foundation of China(Grant No.30670269,31071939)
文摘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.
基金Supported by the National Science Foundation of China（11471151） Supported by Program for Liaoning Excellent Talents in University（LR2011031）
Acknowledgment The authors would like to thank the referees for kind suggestions and many useful comments
文摘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.
文摘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.
文摘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.
基金Supported by Transformation and Promotion Projects of Agriculture Science and Technology Achievements of Tianjin City"Integration and Demonstration of Integrated Control Technology of Greenhouse Vegetable Fields with Continuous Cropping Obstacles"(0804140)Basic Application and Cutting-edge Technology Research Projects of Tianjin City"Risk Assessment and Regulation Research of Nitrogen and Phosphorus Non-point Source Pollution in Facility Agriculture"(09JCYBJC08600)~~
文摘[ 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.
文摘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.
文摘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 .
文摘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.
文摘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.
基金The National Natural Science Foundation of China under Grant Nos.11464004,11864006 and 11564015Guizhou Scientific and Technological Program(20185781 and 20185781-15)the Foundation of Key Laboratory of Animal Genetics,Breeding and Reproduction in The Plateau Mountainous Region,Ministry of Education(Guizhou University),KY2020243。
文摘Knots are discovered in biophysical systems,such as DNA and proteins.Knotted portions in knotted DNA are significantly bent and their corresponding bending angles are comparable with or larger than the sharp bending angle resulting in flexible defects.The role of flexible defects in the interplay of supercoiling and knotting of circular DNA were predicted by a Monte Carlo simulation.In knotted DNA with a particular knot type,a flexible defect noticeably enhances the supercoiling of the knotted DNA and the decreasing excitation energy makes the knotted portion more compact.A reduction in twist rigidity and unwinding of flexible defects are incorporated into the numerical simulations,so that interplay of supercoiling and knotting of circular DNA is studied under torsional conditions.Increasing unwinding not only results in a wider linking number distribution,but also leads to a drift of the distribution to lower values.A flexible defect has obvious effects on knotting probability.The summation of equilibrium distribution probability for nontrivial knotted DNA with different contour length does not change with excitation energy monotonically and has a maximum at an intermediate value of excitation energy around 5 kBT.In the phase space of knot length and gyration radius of knotted DNA,knot length does not anticorrelate with its gyration radius,which is attributed to the flexible defect in the knotted portion,which leads to the release of bending energy and inhibited the competition between entropy and bending energy.
