Feedback in clinical education: untying the Gordian knot.
Weinstein, Debra F
2015-05-01
Feedback is essential to clinical education, especially in the era of competencies, milestones, and entrustable professional activities. It is, however, an area where medical educators often fall short. Although educational leaders and faculty supervisors provide feedback in a variety of clinical settings, surveys show important gaps in medical student and resident satisfaction with the feedback received, suggesting lost opportunities to identify performance problems as well as to help each learner reach his or her greatest potential.In this issue of Academic Medicine, Telio and colleagues extend the empirically validated concept of a "therapeutic alliance" to propose the "educational alliance" as a framework for enhancing feedback in medical education. They highlight the importance of source credibility, which depends on the teacher-learner relationship and alignment of values, the teacher's understanding of the learner's role and goals, the teacher's direct observation of the learner, and the learner's perception of the teacher's good intentions. The author of this Commentary suggests that the educational alliance framework should prompt medical educators to reconsider feedback and explore opportunities for optimizing it. Most medical schools and graduate medical education programs are not designed in a way that supports the education alliance model, but the Commentary author offers suggestions for cultivating educational alliances, including rethinking supervisor selection criteria. Such interventions should be combined with ongoing faculty development and efforts to improve coaching and mentoring for students, residents, and fellows. Untying the Gordian knot of effective feedback will require innovative approaches, exchange of successful strategies, and continued research. PMID:25406602
Hemoglobinopathies: slicing the Gordian knot of Plasmodium falciparum malaria pathogenesis.
Taylor, Steve M; Cerami, Carla; Fairhurst, Rick M
2013-01-01
Plasmodium falciparum malaria kills over 500,000 children every year and has been a scourge of humans for millennia. Owing to the co-evolution of humans and P. falciparum parasites, the human genome is imprinted with polymorphisms that not only confer innate resistance to falciparum malaria, but also cause hemoglobinopathies. These genetic traits--including hemoglobin S (HbS), hemoglobin C (HbC), and α-thalassemia--are the most common monogenic human disorders and can confer remarkable degrees of protection from severe, life-threatening falciparum malaria in African children: the risk is reduced 70% by homozygous HbC and 90% by heterozygous HbS (sickle-cell trait). Importantly, this protection is principally present for severe disease and largely absent for P. falciparum infection, suggesting that these hemoglobinopathies specifically neutralize the parasite's in vivo mechanisms of pathogenesis. These hemoglobin variants thus represent a "natural experiment" to identify the cellular and molecular mechanisms by which P. falciparum produces clinical morbidity, which remain partially obscured due to the complexity of interactions between this parasite and its human host. Multiple lines of evidence support a restriction of parasite growth by various hemoglobinopathies, and recent data suggest this phenomenon may result from host microRNA interference with parasite metabolism. Multiple hemoglobinopathies mitigate the pathogenic potential of parasites by interfering with the export of P. falciparum erythrocyte membrane protein 1 (PfEMP1) to the surface of the host red blood cell. Few studies have investigated their effects upon the activation of the innate and adaptive immune systems, although recent murine studies suggest a role for heme oxygenase-1 in protection. Ultimately, the identification of mechanisms of protection and pathogenesis can inform future therapeutics and preventive measures. Hemoglobinopathies slice the "Gordian knot" of host and parasite
Transcriptomics: a sword to cut the Gordian knot of traditional Chinese medicine.
Liu, Yufeng; Ai, Ni; Liao, Jie; Fan, Xiaohui
2015-01-01
The systemic effects of traditional Chinese medicine (TCM) seem to be a Gordian knot, impossible to untie for decades. With the advent of transcriptomics, a useful sword is provided to cut the knot and shed some light on complex bioprocesses and intrinsic connections among them. Here, we revisit studies on TCM ZHENGs using this approach, highlight its applications on elucidating the potential scientific basis of ZHENG and investigating mechanisms of action for the TCM formula, and demonstrating its unique role in novel TCM drug design and discovery through active ingredient detection from TCM and compatibility theory study of TCM. The limitations and future perspectives of transcriptomics approaches to TCM study are also discussed. PMID:26501686
Animal abolitionism meets moral abolitionism : cutting the Gordian knot of applied ethics.
Marks, Joel
2013-12-01
The use of other animals for human purposes is as contentious an issue as one is likely to find in ethics. And this is so not only because there are both passionate defenders and opponents of such use, but also because even among the latter there are adamant and diametric differences about the bases of their opposition. In both disputes, the approach taken tends to be that of applied ethics, by which a position on the issue is derived from a fundamental moral commitment. This commitment in turn depends on normative ethics, which investigates the various moral theories for the best fit to our moral intuitions. Thus it is that the use of animals in biomedical research is typically defended by appeal to a utilitarian theory, which legitimates harm to some for the greater good of others; while the opposition condemns that use either by appeal to the same theory, but disagreeing about the actual efficacy of animal experimentation, or by appeal to an alternative theory, such as the right of all sentient beings not to be exploited. Unfortunately, the normative issue seems likely never to be resolved, hence leaving the applied issue in limbo. The present essay seeks to circumvent this impasse by dispensing altogether with any moral claim or argument, thereby cutting the Gordian knot of animal ethics with a meta-ethical sword. The alternative schema defended is simply to advance relevant considerations, whereupon "there is nothing left but to feel." In a word, motivation replaces justification. PMID:24092403
NASA Astrophysics Data System (ADS)
Hufnagl, Marc; Peck, Myron A.; Nash, Richard D. M.; Dickey-Collas, Mark
2015-11-01
factors can form a Gordian knot of marine fish recruitment processes. We highlight gaps in process knowledge and recommend specific field, laboratory and modelling studies which, in our opinion, are most likely to unravel the dominant processes and advance predictive capacity of the environmental regulation of recruitment in autumn and winter-spawned fishes in temperate areas such as herring in the North Sea.
Nordhaus, B F
1991-01-01
This paper describes the applications of psychoanalytic and child development theory to the court-ordered visitation study of a 6-year-old child. In this case, the recommendation is for the sole custodial parent to be given the authority to regulate visitation with the noncustodial parent. This recommendation is consistent with the principle of the least detrimental alternative. PMID:1788387
Primary Care: Medicine's Gordian Knot.
Oddone, Eugene Z; Boulware, L Ebony
2016-01-01
Primary care is the cornerstone of effective and efficient healthcare systems. Patients prefer a trusted primary care provider to serve as the first contact for all of their healthcare questions, to help them make important health decisions, to help guide them through an expanding amount of medical information and to help coordinate their care with all other providers. Patients also prefer to establish an ongoing, continuous relationship with their primary care provider. However, fewer and fewer physicians are choosing primary care as a career, threatening the foundation of the health system. We explore the central challenges of primary care defined by work-force controversies about who can best deliver primary care. We also explore the current challenging reimbursement model for primary care that often results in fragmenting care for patients and providers. Finally, we explore new models of primary care health delivery that may serve as partial solutions to the current challenges. PMID:26802754
Chance and time: Cutting the Gordian knot
NASA Astrophysics Data System (ADS)
Hagar, Amit
One of the recurrent problems in the foundations of physics is to explain why we rarely observe certain phenomena that are allowed by our theories and laws. In thermodynamics, for example, the spontaneous approach towards equilibrium is ubiquitous yet the time-reversal-invariant laws that presumably govern thermal behaviour in the microscopic level equally allow spontaneous approach away from equilibrium to occur. Why are the former processes frequently observed while the latter are almost never reported? Another example comes from quantum mechanics where the formalism, if considered complete and universally applicable, predicts the existence of macroscopic superpositions---monstrous Schrodinger cats---and these are never observed: while electrons and atoms enjoy the cloudiness of waves, macroscopic objects are always localized to definite positions. A well-known explanatory framework due to Ludwig Boltzmann traces the rarity of "abnormal" thermodynamic phenomena to the scarcity of the initial conditions that lead to it. After all, physical laws are no more than algorithms and these are expected to generate different results according to different initial conditions, hence Boltzmann's insight that violations of thermodynamic laws are possible but highly improbable. Yet Boltzmann introduces probabilities into this explanatory scheme, and since the latter is couched in terms of classical mechanics, these probabilities must be interpreted as a result of ignorance of the exact state the system is in. Quantum mechanics has taught us otherwise. Here the attempts to explain why we never observe macroscopic superpositions have led to different interpretations of the formalism and to different solutions to the quantum measurement problem. These solutions introduce additional interpretations to the meaning of probability over and above ignorance of the definite state of the physical system: quantum probabilities may result from pure chance. Notwithstanding the success of the Boltzmannian framework in explaining the thermodynamic arrow in time it leaves us with a foundational puzzle: how can ignorance play a role in scientific explanation of objective reality? In turns out that two opposing solutions to the quantum measurement problem in which probabilities arise from the stochastic character of the underlying dynamics may scratch this explanatory itch. By offering a dynamical justification to the probabilities employed in classical statistical mechanics these two interpretations complete the Boltzmannian explanatory scheme and allow us to exorcize ignorance from scientific explanations of unobserved phenomena. In this thesis I argue that the puzzle of the thermodynamic arrow in time is closely related to the problem of interpreting quantum mechanics, i.e., to the measurement problem. We may solve one by fiat and thus solve the other, but it seems unwise to try solving them independently. I substantiate this claim by presenting two possible interpretations to non-relativistic quantum mechanics. Differing as they do on the meaning of the probabilities they introduce into the otherwise deterministic dynamics, these interpretations offer alternative explanatory schemes to the standard Boltzmannian statistical mechanical explanation of thermodynamic approach to equilibrium. I then show how notwithstanding their current empirical equivalence, the two approaches diverge at the continental divide between scientific realism and anti-realism.
The Substorm Gordian Knot: Onset Patterns and Frequencies
NASA Astrophysics Data System (ADS)
Sobel, E. I.; Kepko, L.
2014-12-01
For decades, scientists have struggled to understand what causes the aurora, and have developed two different theories to explain the phenomena. The magnetospheric and ground-based data necessary to test the two competing theories have only recently become available with the launch of NASA's THEMIS mission in 2007 and the Canadian Space Agency's (CSA) deployment of an all-sky imaging network. We present research testing the "Auroral Streamer" hypothesis given by Nishimura, Lyons, et al. in their various papers from 2010 to present. We compiled a list of all their published events (numbering 455, and covering a span from 2007 to 2011) and reviewed ground-based white- and red-light image files, THEMIS satellite bulk plasma velocity and magnetic field strength measurements, ground-based magnetometer observations, and 1-minute Auroral Electrojet (AL) index data. We visually categorized the events by auroral phenomenology, separating events with auroral streamers from those without, and analyzed the characteristics of the events with superposed epoch analyses. Although Nishimura, Lyons et al. argued that every event in their onset list constituted an "Auroral Streamer" onset, our results show that most events in the list are not poleward boundary intensifications (PBIs). In contrast to these previous studies, the results suggest that the "auroral streamer" model is not widely applicable. This is the first time these events have been analyzed with such detail, and call into question fundamental aspects of this model.
The real gordian knot: racemic mixtures versus pure enantiomers.
Szelenyi, I; Geisslinger, G; Polymeropoulos, E; Paul, W; Herbst, M; Brune, K
1998-04-01
Many drugs exist as asymmetric three-dimensional (chiral) molecules and will therefore have several stereoisomers. There are often pharmacodynamic, pharmacokinetic and/or toxicological differences between enantiomers. The choice between developing a racemate or single enantiomers depends on therapeutic advances and developmental costs involved. Regarding the target environment for drug intervention, even if natural physiological mediators are achiral, their receptors may demonstrate a preference for the (-)- or (+)-enantiomer of agonists or antagonists. It is also obvious that the majority of enzymes and channels are stereospecific, at least to a variable extent. From a pharmacokinetics point of view, chirality can have an influence on drug absorption, distribution, metabolism and elimination. With a few exceptions, toxicological differences between isomers of known drugs are less dramatic than thought to be and only seldom substantiate the necessity of a racemic switch. The pharmaceutical industry is currently very interested in the so-called "racemic switch." Before proceeding to a racemic switch it is necessary to determine if 1) it is chemically feasible to produce a single enantiomer; 2) a clinical advantage is obtainable through a racemic switch; and 3) a marketing advantage is obtainable. The real goal of a racemic switch should be the rational development of compounds that are profitable for the company and--first of all--beneficial for the patient. PMID:15616615
Metagenomics for studying unculturable microorganisms: cutting the Gordian knot
Schloss, Patrick D; Handelsman, Jo
2005-01-01
More than 99% of prokaryotes in the environment cannot be cultured in the laboratory, a phenomenon that limits our understanding of microbial physiology, genetics, and community ecology. One way around this problem is metagenomics, the culture-independent cloning and analysis of microbial DNA extracted directly from an environmental sample. Recent advances in shotgun sequencing and computational methods for genome assembly have advanced the field of metagenomics to provide glimpses into the life of uncultured microorganisms. PMID:16086859
Systematic Weighting and Ranking: Cutting the Gordian Knot.
ERIC Educational Resources Information Center
Davis, Charles H.; McKim, Geoffrey W.
1999-01-01
Describes SWEAR (Systematic Weighting and Ranking), a powers-of-two algorithm that can be used for searching the World Wide Web or any large database that automatically creates discrete, well-defined result sets and displays them in decreasing order of likely relevance. Also discusses fuzzy sets. (Author/LRW)
The Gordian Knot: Language, Literature, and Critical Thinking.
ERIC Educational Resources Information Center
Schultz, Jean Marie
This chapter contains a dialogue that challenges philosophical and practical divisions both inside and outside the academy regarding the development of literacy and literary competence in foreign language departments. It also describes curricular revisions that address those divisions. One author crafts an argument for reform based on the notion…
The Gordian Knot of dysbiosis, obesity and NAFLD.
Mehal, Wajahat Z
2013-11-01
The development of obesity and NAFLD is known to be determined by host genetics, diet and lack of exercise. In addition, the gut microbiota has been identified to influence the development of both obesity and NAFLD. Evidence for the role of the gut microbiota has been shown by preclinical studies of transfer of gut microbiota from lean and obese individuals, with the recipient developing the metabolic features of the donor. Many bidirectional interactions of the gut microbiota, including with food, bile and the intestinal epithelium, have been identified. These interactions might contribute to the distinct steps in the progression from lean to obese states, and to steatosis, steatohepatitis and eventually fibrosis. The predominant steps are efficient caloric extraction from the diet, intestinal epithelial damage and greater entry of bacterial components into the portal circulation. These steps result in activation of the innate immune system, liver inflammation and fibrosis. Fortunately, therapeutic interventions might not require a full understanding of these complex interactions. Although antibiotics are too unselective in their action, probiotics have shown efficacy in reversing obesity and NASH in experimental systems, and are under investigation in humans. PMID:23958600
Mallick, I H; Winslet, M C
2004-07-01
Intestinal obstruction is a common cause of emergency surgical admission. The most frequent causes are well known and may often be safely treated conservatively in the first instance. The rarer causes of intestinal obstruction require prompt diagnosis and surgery if they are not to progress rapidly to strangulation and gangrene. One such cause is the ileosigmoid knotting, which is associated with a high morbidity and mortality. With increasing travel activity and population migration this condition is now being seen outside its original geographical sites of origin. This article focuses on the aetiology, pathophysiology, clinical features, investigations and the various surgical options for the management of the ileosigmoid knotting. Studies and case reports in English literature were identified by PubMed, ISIS, Embase and CAS searches between the years 1966-2004 using the following free text keywords: ileo- sigmoid knotting, ileosigmoid knot(ting), intestinal knot(ting), compound volvulus and double volvulus. All the reference lists were reviewed to retrieve additional articles. Aggressive resuscitation, prompt surgical relief of obstruction, appropriate antibiotics, accurate intra-operative assessment of the viability of the involved loops of intestine and the use of modern postoperative intensive care will help reduce the mortality and morbidity associated with this life threatening condition. PMID:15206962
Subknots in ideal knots, random knots, and knotted proteins
Rawdon, Eric J.; Millett, Kenneth C.; Stasiak, Andrzej
2015-01-01
We introduce disk matrices which encode the knotting of all subchains in circular knot configurations. The disk matrices allow us to dissect circular knots into their subknots, i.e. knot types formed by subchains of the global knot. The identification of subknots is based on the study of linear chains in which a knot type is associated to the chain by means of a spatially robust closure protocol. We characterize the sets of observed subknot types in global knots taking energy-minimized shapes such as KnotPlot configurations and ideal geometric configurations. We compare the sets of observed subknots to knot types obtained by changing crossings in the classical prime knot diagrams. Building upon this analysis, we study the sets of subknots in random configurations of corresponding knot types. In many of the knot types we analyzed, the sets of subknots from the ideal geometric configurations are found in each of the hundreds of random configurations of the same global knot type. We also compare the sets of subknots observed in open protein knots with the subknots observed in the ideal configurations of the corresponding knot type. This comparison enables us to explain the specific dispositions of subknots in the analyzed protein knots. PMID:25753957
ERIC Educational Resources Information Center
Henrich, A.; MacNaughton, N.; Narayan, S.; Pechenik, O.; Silversmith, R.; Townsend, J.
2011-01-01
We introduce playing games on the shadows of knots and demonstrate two novel games, namely, "To Knot or Not to Knot" and "Much Ado about Knotting." We discuss winning strategies for these games on certain families of knot shadows and go on to suggest variations of these games for further study.
Haeckel or Hennig? The Gordian Knot of Characters, Development, and Procedures in Phylogeny.
ERIC Educational Resources Information Center
Dupuis, Claude
1984-01-01
Discusses the conditions for validating customary phylogenetic procedures. Concludes that the requisites of homogeneity and completeness for proved short lineages seem satisfied by the Hennigian but not the Haeckelian procedure. The epistemological antinomy of the two procedures is emphasized for the first time. (Author/RH)
Procedural vs. substantive in the NEPA law: Cutting the Gordian knot
Boggs, J.P. . Dept. of Anthropology)
1993-01-01
The debate whether the National Environmental Policy Act (NEPA) is procedural or substantive has become central both to agency implementation of the act and to court review of agency compliance. While NEPA mandates both procedural and substantive reform as a means to improve environmental quality, NEPA also focuses on cognitive reform--the improved utilization of knowledge in public affairs. Choices about what knowledge to base public decisions on, and how that knowledge will be used, build the social realities that shape lives. Thus, NEPA's mandates for the creation and use of public knowledge activate fundamentally conflicting values and visions of social order. However, debate about the procedural and substantive provisions of NEPA cannot resolve the conflict about values that actually motivates the debate, and this constrictive debate impoverishes public discussion about NEPA implementation and judicial review. This paper links the present debate with the values issues that underlie it, suggesting a more direct language for characterizing NEPA and a broader framework of legal theory for debating the issues it raises. This paper also finds that environmental and social science practitioners are strategically positioned to contribute materially to the issues raised by a NEPA properly understood as law that mandates knowledge utilization.
Untying the Gordian knot of creation: metaphors for the Human Genome Project in Greek newspapers.
Gogorosi, Eleni
2005-12-01
This article studies the metaphorical expressions used by newspapers to present the near completion of the Human Genome Project (HGP) to the Greek public in the year 2000. The analysis, based on cognitive metaphor theory, deals with the most frequent or captivating metaphors used to refer to the human genome, which give rise to both conventional and novel expressions. The majority of creative metaphorical expressions participate in the discourse of hope and promise propagated by the Greek media in an attempt to present the HGP and its outcome in a favorable light. Instances of the competing discourse of fear and danger are much rarer but can also be found in creative metaphorical expressions. Metaphors pertaining to the Greek culture or to ancient Greek mythology tend to carry a special rhetorical force. However, it will be shown that the Greek press strategically used most of the metaphors that circulated globally at the time, not only culture specific ones. PMID:16610131
Marriage, Depression, and Cognition: Unraveling the Gordian Knot-Reply to Ettinger et al.
ERIC Educational Resources Information Center
Snyder, Douglas K.; Heim, Susan Creekmore
1992-01-01
Heim and Snyder respond to Ettinger et al.'s comments in previous article concerning Heim and Snyder's 1991 study exploring interaction between marital discord and spouses' attributions in predicting depression. Discusses findings and reiterates complex and recursive relationships among marital difficulties, depression, cognitive processes, and…
Proliferation and Polarity in Breast Cancer: Untying the GordianKnot
Liu, Hong; Radisky, Derek C.; Bissell, Mina J.
2005-05-09
Epithelial cancers are associated with genomic instability and alterations in signaling pathways that affect proliferation, apoptosis, and integrity of tissue structure. Overexpression of a number of oncogenic protein kinases has been shown to malignantly transform cells in culture and to cause tumors in vivo, but the interconnected signaling events induced by transformation still awaits detailed dissection. We propose that the network of cellular signaling pathways can be classified into functionally distinct branches, and that these pathways are rewired in transformed cells and tissues after they lose tissue-specific architecture to favor tumor expansion and invasion. Using three-dimensional (3D) culture systems, we recently demonstrated that polarity and proliferation of human mammary epithelial cancer cells were separable consequences of signaling pathways downstream of PI3 kinase.These, and results from a number of other laboratories are beginning to provide insight into how different signaling pathways may become interconnected in normal tissues to allow homeostasis, and how they are disrupted during malignant progression.
Too Much Law...Too Much Structure: Together We Can Cut the Gordian Knot.
ERIC Educational Resources Information Center
Nussbaum, Thomas J.
Arguing that the multitude of federal, state and local laws governing the California Community Colleges (CCC) drains the system's capacity to serve students seeking educational opportunity, this paper examines how the state's colleges came to be micro-managed and offers possible solutions. Part I provides a history of laws and structures governing…
Disentangling Tfr cells from Treg cells and Tfh cells: How to untie the Gordian knot.
Amiezer, Mayan; Phan, Tri Giang
2016-05-01
T follicular regulatory (Tfr) cells are a subpopulation of Treg cells that have adopted the T follicular helper cell program to localize to the B-cell follicle. Because of the difficulties in generating mouse models in which Tfr cells are selectively affected, determining where and how Tfr cells regulate the germinal center response remains to be resolved. In this issue of the European Journal of Immunology, Dent and colleagues [Eur. J. Immunol. 2016. 46: 1152-1161] describe a simple, elegant mouse model to conditionally delete Tfr cells without impacting on the Treg- and Tfh-cell populations. Their initial studies suggest that Tfr cells have a more complex role than previously thought, particularly with respect to the regulation of immunoglobulin isotype switching to IgA. PMID:27109022
Manturov, Vassily O
2010-06-29
In this work we study knot theories with a parity property for crossings: every crossing is declared to be even or odd according to a certain preassigned rule. If this rule satisfies a set of simple axioms related to the Reidemeister moves, then certain simple invariants solving the minimality problem can be defined, and invariant maps on the set of knots can be constructed. The most important example of a knot theory with parity is the theory of virtual knots. Using the parity property arising from Gauss diagrams we show that even a gross simplification of the theory of virtual knots, namely, the theory of free knots, admits simple and highly nontrivial invariants. This gives a solution to a problem of Turaev, who conjectured that all free knots are trivial. In this work we show that free knots are generally not invertible, and provide invariants which detect the invertibility of free knots. The passage to ordinary virtual knots allows us to strengthen known invariants (such as the Kauffman bracket) using parity considerations. We also discuss other examples of knot theories with parity. Bibliography: 27 items.
[DNA knots and strong triviality].
Torisu, Ichiro
2009-06-01
A circle embedded in 3-space without self-intersection is called a knot. A knot is a mathematical object according to topology. Knot theory studies how complicated a given knot is, or whether it is trivial. Any knot can be represented by a diagram with above and below information at the crossings. Then a knot obtained by replacing the information at one crossing is generally another knot. This operation is called a crossing change. A crossing change is an important notion in knot theory. In this article, we survey the strong triviality of knots, which is one of the multi-crossing changes. PMID:19530562
Technology Transfer Automated Retrieval System (TEKTRAN)
Although root-knot nematodes (Meloidogyne species) can reduce crop yields worldwide, methods for their identification are often difficult to implement. This review summarizes the diagnostic morphological and molecular features for distinguishing the ten major previously described root-knot nematode ...
NASA Astrophysics Data System (ADS)
Hall, D. S.; Ray, M. W.; Tiurev, K.; Ruokokoski, E.; Gheorghe, A. H.; Möttönen, M.
2016-05-01
As topologically stable objects in field theories, knots have been put forward to explain various persistent phenomena in systems ranging from atoms and molecules to cosmic textures in the universe. Recent experiments have reported the observation of knots in different classical contexts. However, no experimental observation of knots has yet been reported in quantum matter. Here we demonstrate the experimental creation and detection of knot solitons in the order parameter of a spinor Bose-Einstein condensate. The observed texture corresponds to a topologically nontrivial element of the third homotopy group and exhibits the celebrated Hopf fibration, which unites many seemingly unrelated physical phenomena. Our work calls for future studies of the stability and dynamics knot solitons in the quantum regime.
Janse Van Rensburg, E.J.
1996-12-31
The geometry of polygonal knots in the cubic lattice may be used to define some knot invariants. One such invariant is the minimal edge number, which is the minimum number of edges necessary (and sufficient) to construct a lattice knot of given type. In addition, one may also define the minimal (unfolded) surface number, and the minimal (unfolded) boundary number; these are the minimum number of 2-cells necessary to construct an unfolded lattice Seifert surface of a given knot type in the lattice, and the minimum number of edges necessary in a lattice knot to guarantee the existence of an unfolded lattice Seifert surface. In addition, I derive some relations amongst these invariants. 8 refs., 5 figs., 2 tabs.
Sułkowska, Joanna I; Sułkowski, Piotr; Szymczak, Piotr; Cieplak, Marek
2010-10-13
A shoelace can be readily untied by pulling its ends rather than its loops. Attempting to untie a native knot in a protein can also succeed or fail depending on where one pulls. However, thermal fluctuations induced by the surrounding water affect conformations stochastically and may add to the uncertainty of the outcome. When the protein is pulled by the termini, the knot can only get tightened, and any attempt at untying results in failure. We show that, by pulling specific amino acids, one may easily retract a terminal segment of the backbone from the knotting loop and untangle the knot. At still other amino acids, the outcome of pulling can go either way. We study the dependence of the untying probability on the way the protein is grasped, the pulling speed, and the temperature. Elucidation of the mechanisms underlying this dependence is critical for a successful experimental realization of protein knot untying. PMID:20857930
Knot Theory with Young Children
ERIC Educational Resources Information Center
Handa, Yuichi; Mattman, Thomas
2008-01-01
There are many interesting explorations that can be done in knot theory, the study of mathematical knots. This article offers some knot theory activities that are appropriate for elementary grade children. These activities teach some basic concepts from knot theory as a natural extension of commonly-taught geometric ideas. (Contains 10 figures.)
NASA Astrophysics Data System (ADS)
Mironov, A.; Mkrtchyan, R.; Morozov, A.
2016-02-01
We present a universal knot polynomials for 2- and 3-strand torus knots in adjoint representation, by universalization of appropriate Rosso-Jones formula. According to universality, these polynomials coincide with adjoined colored HOMFLY and Kauffman polynomials at SL and SO/Sp lines on Vogel's plane, respectively and give their exceptional group's counterparts on exceptional line. We demonstrate that [m,n]=[n,m] topological invariance, when applicable, take place on the entire Vogel's plane. We also suggest the universal form of invariant of figure eight knot in adjoint representation, and suggest existence of such universalization for any knot in adjoint and its descendant representations. Properties of universal polynomials and applications of these results are discussed.
Knot theory in understanding proteins.
Mishra, Rama; Bhushan, Shantha
2012-12-01
This paper aims to enthuse mathematicians, especially topologists, knot theorists and geometers to examine problems in the study of proteins. We have highlighted those advances and breakthroughs in knot theory that directly and indirectly help in understanding proteins. We have discussed the phenomena of knotting of protein backbone. This paper also provides a few open questions for knot theorists, the answers to which will help in further understanding of proteins. PMID:22105789
Shahal, Shir; Klein, Avi; Masri, Gilad; Fridman, Moti
2016-06-10
We present fusing of a fiber micro-knot by a CO_{2} laser beam. We demonstrate tuning of the coupling strength and tuning of the spectral resonance of the micro-knot by the fusing process. The experimental results reveal that fusing the fiber micro-knots increases the coupling efficiency and improves the robustness and the stability of the micro-knots. PMID:27409009
Hampel, Harald; Lista, Simone; Khachaturian, Zaven S
2012-07-01
The aim of this perspective article is to stimulate radical shifts in thinking and foster further discussion on the effective discovery, development, validation, and qualification process of biological markers derived from all available technical modalities that meet the complex conceptual and pathophysiological challenges across all stages of the complex, nonlinear, dynamic, and chronically progressive sporadic Alzheimer's disease (AD). This perspective evaluates the current state of the science regarding a broad spectrum of hypothesis-driven and exploratory technologies and "markers" as candidates for all required biomarker functions, in particular, surrogate indicators of adaptive to maladaptive and compensatory to decompensatory, reversible to irreversible brain "systems failure." We stress the future importance of the systems biology (SB) paradigm (next to the neural network paradigm) for substantial progress in AD research. SB represents an integrated and deeper investigation of interacting biomolecules within cells and organisms. This approach has only recently become feasible as high-throughput technologies and mass spectrometric analyses of proteins and lipids, together with rigorous bioinformatics, have evolved. Existing high-content data derived from clinically and experimentally derived neural tissues point to convergent pathophysiological pathways during the course of AD, transcending traditional descriptive studies to reach a more integrated and comprehensive understanding of AD pathophysiology, derived systems biomarkers, and "druggable" system nodes. The discussion is continued on the premise that the lack of integration of advanced biomarker technologies and transfertilization from more mature translational research fields (e.g., oncology, immunology, cardiovascular), which satisfy regulatory requirements for an accurate, sensitive, and well-validated surrogate marker of specific pathophysiological processes and/or clinical outcomes, is a major rate-limiting factor for the successful development and approval of effective treatments for AD prevention. We consider the conceptual, scientific, and technical challenges for the discovery-development-validation-qualification process of biomarker tools and analytical algorithms for detection of the earliest pathophysiological processes in asymptomatic individuals at elevated risk during preclinical stages of AD. The most critical need for rapid translation of putative markers into validated (performance) and standardized (harmonized standard operating procedures) biomarker tools that fulfill regulatory requirements (qualify for use in treatment trials: e.g., safety, target engagement, mechanism of action, enrichment, stratification, secondary and primary outcome, surrogate outcome) is the availability of a large-scale worldwide comprehensive longitudinal database that includes the following cohorts: (a) healthy aging, (b) people at elevated risks (genetic/epigenetic/lifestyle/comorbid conditions), and (c) asymptomatic-preclinical/prodromal-mild cognitive impairment/syndromal mild, moderate, or severe AD. Our proposal, as initial strategic steps for integrating markers into future development of diagnostic and therapy trial technologies, is to work toward: (a) creating the essential research and development infrastructure as an international shared resource, (b) building the organizational structure for managing such a multinational shared resource, and (c) establishing an integrated transsectoral multidisciplinary global network of collaborating investigators to help build and use the shared research resource. PMID:22748938
Kappelmann, Jannick; Wiechert, Wolfgang; Noack, Stephan
2016-03-01
Corynebacterium glutamicum is the major workhorse for the microbial production of several amino and organic acids. As long as these derive from tricarboxylic acid cycle intermediates, the activity of anaplerotic reactions is pivotal for a high biosynthetic yield. To determine single anaplerotic activities (13) C-Metabolic Flux Analysis ((13) C-MFA) has been extensively used for C. glutamicum, however with different network topologies, inconsistent or poorly determined anaplerotic reaction rates. Therefore, in this study we set out to investigate whether a focused isotopomer model of the anaplerotic node can at all admit a unique solution for all fluxes. By analyzing different scenarios of active anaplerotic reactions, we show in full generality that for C. glutamicum only certain anaplerotic deletion mutants allow to uniquely determine the anaplerotic fluxes from (13) C-isotopomer data. We stress that the result of this analysis for different assumptions on active enzymes is directly transferable to other compartment-free organisms. Our results demonstrate that there exist biologically relevant metabolic network topologies for which the flux distribution cannot be inferred by classical (13) C-MFA. PMID:26375179
Kosiewicz, S.T.; Triay, I.R.; Souza, L.A.; Michael, D.I.; Black, P.K.
1999-02-01
Through sampling and toxicity characteristic leaching procedure (TCLP) analyses, LANL and the DOE validated that a LANL transuranic (TRU) waste (TA-55-43, Lot No. 01) was not a Resource Recovery and Conservation Act (RCRA) hazardous waste. This paper describes the sampling and analysis project as well as the statistical assessment of the analytical results. The analyses were conducted according to the requirements and procedures in the sampling and analysis plan approved by the New Mexico Environmental Department. The plan used a statistical approach that was consistent with the stratified, random sampling requirements of SW-846. LANL adhered to the plan during sampling and chemical analysis of randomly selected items of the five major types of materials in this heterogeneous, radioactive, debris waste. To generate portions of the plan, LANL analyzed a number of non-radioactive items that were representative of the mix of items present in the waste stream. Data from these cold surrogates were used to generate means and variances needed to optimize the design. Based on statistical arguments alone, only two samples from the entire waste stream were deemed necessary, however a decision was made to analyze at least two samples of each of the five major waste types. To obtain these samples, nine TRU waste drums were opened. Sixty-six radioactively contaminated and four non-radioactive grab samples were collected. Portions of the samples were composited for chemical analyses. In addition, a radioactively contaminated sample of rust-colored powder of interest to the New Mexico Environment Department (NMED) was collected and qualitatively identified as rust.
Mutanen, Marko; Hausmann, Axel; Hebert, Paul D. N.; Landry, Jean-François; de Waard, Jeremy R.; Huemer, Peter
2012-01-01
Many cold adapted species occur in both montane settings and in the subarctic. Their disjunct distributions create taxonomic complexity because there is no standardized method to establish whether their allopatric populations represent single or different species. This study employs DNA barcoding to gain new perspectives on the levels and patterns of sequence divergence among populations of 122 arctic-alpine species of Lepidoptera from the Alps, Fennoscandia and North America. It reveals intraspecific variability in the barcode region ranging from 0.00–10.08%. Eleven supposedly different species pairs or groups show close genetic similarity, suggesting possible synonymy in many cases. However, a total of 33 species show evidence of cryptic diversity as evidenced by the presence of lineages with over 2% maximum barcode divergence in Europe, in North America or between the two continents. Our study also reveals cases where taxonomic names have been used inconsistently between regions and exposes misidentifications. Overall, DNA barcodes have great potential to both increase taxonomic resolution and to make decisions concerning the taxonomic status of allopatric populations more objective. PMID:23071761
Naro, Antonino; Bramanti, Placido; Leo, Antonino; Russo, Margherita; Calabrò, Rocco Salvatore
2016-07-01
Unresponsive wakefulness syndrome (UWS) is a chronic disorder of consciousness (DOC) characterized by a lack of awareness and purposeful motor behaviors, owing to an extensive brain connectivity impairment. Nevertheless, some UWS patients may retain residual brain connectivity patterns, which may sustain a covert awareness, namely functional locked-in syndrome (fLIS). We evaluated the possibility of bringing to light such residual neural networks using a non-invasive neurostimulation protocol. To this end, we enrolled 15 healthy individuals and 26 DOC patients (minimally conscious state-MCS- and UWS), who underwent a γ-band transcranial alternating current stimulation (tACS) over the right dorsolateral prefrontal cortex. We measured the effects of tACS on power and partial-directed coherence within local and long-range cortical networks, before and after the protocol application. tACS was able to specifically modulate large-scale cortical effective connectivity and excitability in all the MCS participants and some UWS patients, who could be, therefore, considered as suffering from fLIS. Hence, tACS could be a useful approach in supporting a DOC differential diagnosis, depending on the level of preservation of the cortical large-scale effective connectivity. PMID:27062669
pKNOT v.2: the protein KNOT web server.
Lai, Yan-Long; Chen, Chih-Chieh; Hwang, Jenn-Kang
2012-07-01
Knotted proteins have recently received lots of attention due to their interesting topological novelty as well as its puzzling folding mechanisms. We previously published a pKNOT server, which provides a structural database of knotted proteins, analysis tools for detecting and analyzing knotted regions from structures as well as a Java-based 3D graphics viewer for visualizing knotted structures. However, there lacks a convenient platform performing similar tasks directly from 'protein sequences'. In the current version of the web server, referred to as pKNOT v.2, we implement a homology modeling tool such that the server can now accept protein sequences in addition to 3D structures or Protein Data Bank (PDB) IDs and return knot analysis. In addition, we have updated the database of knotted proteins from the current PDB with a combination of automatic and manual procedure. We believe that the updated pKNOT server with its extended functionalities will provide better service to biologists interested in the research of knotted proteins. The pKNOT v.2 is available from http://pknot.life.nctu.edu.tw/. PMID:22693223
Holz, D.; Wheeler, J.A.; Kheyfets, A.; Miller, W.A.
1992-08-01
In this report the authors work out the relevant it-form-bit means to measure spacetime curvature. Also described are the essential new features of the knot description of gravity and the one index loop variable and the Einstein tensor. (LSP)
Holz, D.; Wheeler, J.A. . Dept. of Physics); Kheyfets, A. . Dept. of Mathematics); Miller, W.A. )
1992-01-01
In this report the authors work out the relevant it-form-bit means to measure spacetime curvature. Also described are the essential new features of the knot description of gravity and the one index loop variable and the Einstein tensor. (LSP)
Chowdhry, M
2000-01-01
SUMMARY This paper discusses the role of the personal experience in the writing process. Using a personal/journal writing style the author charts the journey of a recent play Skin into Rainbows from first draft to production. The author plays with the constructs of writing and juxtapositions these against a form of Knot Theory to measure their value, playing with math and language techniques in a search for truth. PMID:24802683
NASA Astrophysics Data System (ADS)
Dai, Liang; Renner, C. Benjamin; Doyle, Patrick
2015-03-01
Knotted structures can spontaneously occur in polymers such as DNA and proteins, and the formation of knots affects biological functions, mechanical strength and rheological properties. In this work, we calculate the equilibrium size distribution of trefoil knots in linear DNA using off-lattice simulations. We observe metastable knots on DNA, as predicted by Grosberg and Rabin. Furthermore, we extend their theory to incorporate the finite width of chains and show an agreement between our simulations and the modified theory for real chains. Our results suggest localized knots spontaneously occur in long DNA and the contour length in the knot ranges from 600 to 1800 nm. This research was supported by the National Research Foundation Singapore through the Singapore MIT Alliance for Research and Technology's research program in BioSystems and Micromechanics, the National Science Foundation (Grant No. 1335938).
Dynamic loading of surgical knots.
Brouwers, J E; Oosting, H; de Haas, D; Klopper, P J
1991-12-01
Lately, many suture materials have been introduced. Their physical characteristics in combination with knots are not well known. In this study, seven knots (square--1=1, 2=1, 2=1-S and 1=1=1--and sliding--SxSxS, S=S parallel S and 1-S parallel S parallel S) made in seven suture materials (plain catgut, Dexon [polyglycolic acid)] Maxon [polyglyconate], PDS [polydiaxone], Vicryl [polyglactine 910], Mersilene [polyester fiber], Prolene [polypropylene] were tested dynamically to ascertain tensile strength. The knots were classified as "predominantly breaking" (PB) and "predominantly slipping" (PS). A new method for statistical analysis, the Kaplan-Meier survival estimate, was introduced. Square knots provided good mechanical results but did not prevent slippage completely. Most sliding knots were weak. The 1=1=1 knot was superior. PS knots (1=1, 2=1, SxSxS and S=S parallel S) were unsuitable for surgical practice in monofilament or coated multifilament suture materials. The classification PB and PS knots gave an easy impression of the knot holding capacities. Application of the Kaplan-Meier estimate resulted in a more realistic analysis than classical methods. PMID:1948600
How superfluid vortex knots untie
NASA Astrophysics Data System (ADS)
Kleckner, Dustin; Kauffman, Louis H.; Irvine, William T. M.
2016-07-01
Knots and links often occur in physical systems, including shaken strands of rope and DNA (ref. ), as well as the more subtle structure of vortices in fluids and magnetic fields in plasmas. Theories of fluid flows without dissipation predict these tangled structures persist, constraining the evolution of the flow much like a knot tied in a shoelace. This constraint gives rise to a conserved quantity known as helicity, offering both fundamental insights and enticing possibilities for controlling complex flows. However, even small amounts of dissipation allow knots to untie by means of `cut-and-splice’ operations known as reconnections. Despite the potentially fundamental role of these reconnections in understanding helicity--and the stability of knotted fields more generally--their effect is known only for a handful of simple knots. Here we study the evolution of 322 elemental knots and links in the Gross-Pitaevskii model for a superfluid, and find that they universally untie. We observe that the centreline helicity is partially preserved even as the knots untie, a remnant of the perfect helicity conservation predicted for idealized fluids. Moreover, we find that the topological pathways of untying knots have simple descriptions in terms of minimal two-dimensional knot diagrams, and tend to concentrate in states which are twisted in only one direction. These results have direct analogies to previous studies of simple knots in several systems, including DNA recombination and classical fluids. This similarity in the geometric and topological evolution suggests there are universal aspects in the behaviour of knots in dissipative fields.
Pseudohaptic interaction with knot diagrams
NASA Astrophysics Data System (ADS)
Weng, Jianguang; Zhang, Hui
2012-07-01
To make progress in understanding knot theory, we need to interact with the projected representations of mathematical knots, which are continuous in three dimensions (3-D) but significantly interrupted in the projective images. One way to achieve such a goal is to design an interactive system that allows us to sketch two-dimensional (2-D) knot diagrams by taking advantage of a collision-sensing controller and explore their underlying smooth structures through a continuous motion. Recent advances of interaction techniques have been made that allow progress in this direction. Pseudohaptics that simulate haptic effects using pure visual feedback can be used to develop such an interactive system. We outline one such pseudohaptic knot diagram interface. Our interface derives from the familiar pencil-and-paper process of drawing 2-D knot diagrams and provides haptic-like sensations to facilitate the creation and exploration of knot diagrams. A centerpiece of the interaction model simulates a physically reactive mouse cursor, which is exploited to resolve the apparent conflict between the continuous structure of the actual smooth knot and the visual discontinuities in the knot diagram representation. Another value in exploiting pseudohaptics is that an acceleration (or deceleration) of the mouse cursor (or surface locator) can be used to indicate the slope of the curve (or surface) of which the projective image is being explored. By exploiting these additional visual cues, we proceed to a full-featured extension to a pseudohaptic four-dimensional (4-D) visualization system that simulates the continuous navigation on 4-D objects and allows us to sense the bumps and holes in the fourth dimension. Preliminary tests of the software show that main features of the interface overcome some expected perceptual limitations in our interaction with 2-D knot diagrams of 3-D knots and 3-D projective images of 4-D mathematical objects.
Periodic forces trigger knot untying during translocation of knotted proteins.
Szymczak, Piotr
2016-01-01
Proteins need to be unfolded when translocated through the pores in mitochondrial and other cellular membranes. Knotted proteins, however, might get stuck during this process, jamming the pore, since the diameter of the pore is smaller than the size of maximally tightened knot. The jamming probability dramatically increases as the magnitude of the driving force exceeds a critical value, Fc. In this numerical study, we show that for deep knots Fc lies below the force range over which molecular import motors operate, which suggest that in these cases the knots will tighten and block the pores. Next, we show how such topological traps might be prevented by using a pulling protocol of a repetitive, on-off character. Such a repetitive pulling is biologically relevant, since the mitochondrial import motor, like other molecular motors transforms chemical energy into directed motions via nucleotide-hydrolysis-mediated conformational changes, which are cyclic in character. PMID:26996878
Periodic forces trigger knot untying during translocation of knotted proteins
NASA Astrophysics Data System (ADS)
Szymczak, Piotr
2016-03-01
Proteins need to be unfolded when translocated through the pores in mitochondrial and other cellular membranes. Knotted proteins, however, might get stuck during this process, jamming the pore, since the diameter of the pore is smaller than the size of maximally tightened knot. The jamming probability dramatically increases as the magnitude of the driving force exceeds a critical value, Fc. In this numerical study, we show that for deep knots Fc lies below the force range over which molecular import motors operate, which suggest that in these cases the knots will tighten and block the pores. Next, we show how such topological traps might be prevented by using a pulling protocol of a repetitive, on-off character. Such a repetitive pulling is biologically relevant, since the mitochondrial import motor, like other molecular motors transforms chemical energy into directed motions via nucleotide-hydrolysis-mediated conformational changes, which are cyclic in character.
Periodic forces trigger knot untying during translocation of knotted proteins
Szymczak, Piotr
2016-01-01
Proteins need to be unfolded when translocated through the pores in mitochondrial and other cellular membranes. Knotted proteins, however, might get stuck during this process, jamming the pore, since the diameter of the pore is smaller than the size of maximally tightened knot. The jamming probability dramatically increases as the magnitude of the driving force exceeds a critical value, Fc. In this numerical study, we show that for deep knots Fc lies below the force range over which molecular import motors operate, which suggest that in these cases the knots will tighten and block the pores. Next, we show how such topological traps might be prevented by using a pulling protocol of a repetitive, on-off character. Such a repetitive pulling is biologically relevant, since the mitochondrial import motor, like other molecular motors transforms chemical energy into directed motions via nucleotide-hydrolysis-mediated conformational changes, which are cyclic in character. PMID:26996878
Knot invariants from Virasoro related representation and pretzel knots
NASA Astrophysics Data System (ADS)
Galakhov, D.; Melnikov, D.; Mironov, A.; Morozov, A.
2015-10-01
We remind the method to calculate colored Jones polynomials for the plat representations of knot diagrams from the knowledge of modular transformation (monodromies) of Virasoro conformal blocks with insertions of degenerate fields. As an illustration we use a rich family of pretzel knots, lying on a surface of arbitrary genus g, which was recently analyzed by the evolution method. Further generalizations can be to generic Virasoro modular transformations, provided by integral kernels, which can lead to the Hikami invariants.
Effects of Knots on Protein Folding Properties
Soler, Miguel A.; Faísca, Patrícia F. N.
2013-01-01
This work explores the impact of knots, knot depth and motif of the threading terminus in protein folding properties (kinetics, thermodynamics and mechanism) via extensive Monte Carlo simulations of lattice models. A knotted backbone has no effect on protein thermodynamic stability but it may affect key aspects of folding kinetics. In this regard, we found clear evidence for a functional advantage of knots: knots enhance kinetic stability because a knotted protein unfolds at a distinctively slower rate than its unknotted counterpart. However, an increase in knot deepness does not necessarily lead to more effective changes in folding properties. In this regard, a terminus with a non-trivial conformation (e.g. hairpin) can have a more dramatic effect in enhancing kinetic stability than knot depth. Nevertheless, our results suggest that the probability of the denatured ensemble to keep knotted is higher for proteins with deeper knots, indicating that knot depth plays a role in determining the topology of the denatured state. Refolding simulations starting from denatured knotted conformations show that not every knot is able to nucleate folding and further indicate that the formation of the knotting loop is a key event in the folding of knotted trefoils. They also show that there are specific native contacts within the knotted core that are crucial to keep a native knotting loop in denatured conformations which otherwise have no detectable structure. The study of the knotting mechanism reveals that the threading of the knotting loop generally occurs towards late folding in conformations that exhibit a significant degree of structural consolidation. PMID:24023962
Tightening of Knots in Proteins
NASA Astrophysics Data System (ADS)
Sułkowska, Joanna I.; Sułkowski, Piotr; Szymczak, P.; Cieplak, Marek
2008-02-01
We perform theoretical studies of stretching of 20 proteins with knots within a coarse-grained model. The knot’s ends are found to jump to well defined sequential locations that are associated with sharp turns, whereas in homopolymers they diffuse around and eventually slide off. The waiting times of the jumps are increasingly stochastic as the temperature is raised. Knots typically do not return to their native locations when a protein is released after stretching.
Knot theory and statistical mechanics
Jones, V.F.R. )
1990-11-01
Certain algebraic relations used to solve models in statistical mechanics were key to describing a mathematical property of knots known as a polynomial invariant. This connection, tenuous at first, has since developed into a significant flow of ideas. The appearance of such common ground is not atypical of recent developments in mathematics and physics--ideas from different fields interact and produce unexpected results. Indeed, the discovery of the connection between knots and statistical mechanics passed through a theory intimately related to the mathematical structure of quantum physics. This theory, called von Neumann algebras, is distinguished by the idea of continuous dimensionality. Spaces typically have dimensions that are natural numbers, such as 2, 3 or 11, but in von Neumann algebras dimensions such as 2 or {pi} are equally possible. This possibility for continuous dimension played a key role in joining knot theory and statistical mechanics. In another direction, the knot invariants were soon found to occur in quantum field theory. Indeed, Edward Witten of the Institute for Advanced Study in Princeton, N.J., has shown that topological quantum field theory provides a natural way of expressing the new ideas about knots. This advance, in turn, has allowed a beautiful generalization about the invariants of knots in more complicated three-dimensional spaces known as three-manifolds, in which space itself may contain holes and loops.
Stabilizing effect of knots on proteins
Sułkowska, Joanna I.; Sułkowski, Piotr; Szymczak, P.; Cieplak, Marek
2008-01-01
Molecular dynamics studies within a coarse-grained, structure-based model were used on two similar proteins belonging to the transcarbamylase family to probe the effects of the knot in the native structure of a protein. The first protein, N-acetylornithine transcarbamylase, contains no knot, whereas human ormithine transcarbamylase contains a trefoil knot located deep within the sequence. In addition, we also analyzed a modified transferase with the knot removed by the appropriate change of a knot-making crossing of the protein chain. The studies of thermally and mechanically induced unfolding processes suggest a larger intrinsic stability of the protein with the knot. PMID:19064918
Stabilizing effect of knots on proteins.
Sułkowska, Joanna I; Sulkowski, Piotr; Szymczak, P; Cieplak, Marek
2008-12-16
Molecular dynamics studies within a coarse-grained, structure-based model were used on two similar proteins belonging to the transcarbamylase family to probe the effects of the knot in the native structure of a protein. The first protein, N-acetylornithine transcarbamylase, contains no knot, whereas human ormithine transcarbamylase contains a trefoil knot located deep within the sequence. In addition, we also analyzed a modified transferase with the knot removed by the appropriate change of a knot-making crossing of the protein chain. The studies of thermally and mechanically induced unfolding processes suggest a larger intrinsic stability of the protein with the knot. PMID:19064918
Universal Racah matrices and adjoint knot polynomials: Arborescent knots
NASA Astrophysics Data System (ADS)
Mironov, A.; Morozov, A.
2016-04-01
By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in particular unifies the HOMFLY (SUN) and Kauffman (SON) polynomials. For E8 the adjoint representation is also fundamental. We suggest to extend the universality from the dimensions to the Racah matrices and this immediately produces a unified description of the adjoint knot polynomials for all arborescent (double-fat) knots, including twist, 2-bridge and pretzel. Technically we develop together the universality and the "eigenvalue conjecture", which expresses the Racah and mixing matrices through the eigenvalues of the quantum R-matrix, and for dealing with the adjoint polynomials one has to extend it to the previously unknown 6 × 6 case. The adjoint polynomials do not distinguish between mutants and therefore are not very efficient in knot theory, however, universal polynomials in higher representations can probably be better in this respect.
Spontaneous knotting of an agitated string.
Raymer, Dorian M; Smith, Douglas E
2007-10-16
It is well known that a jostled string tends to become knotted; yet the factors governing the "spontaneous" formation of various knots are unclear. We performed experiments in which a string was tumbled inside a box and found that complex knots often form within seconds. We used mathematical knot theory to analyze the knots. Above a critical string length, the probability P of knotting at first increased sharply with length but then saturated below 100%. This behavior differs from that of mathematical self-avoiding random walks, where P has been proven to approach 100%. Finite agitation time and jamming of the string due to its stiffness result in lower probability, but P approaches 100% with long, flexible strings. We analyzed the knots by calculating their Jones polynomials via computer analysis of digital photos of the string. Remarkably, almost all were identified as prime knots: 120 different types, having minimum crossing numbers up to 11, were observed in 3,415 trials. All prime knots with up to seven crossings were observed. The relative probability of forming a knot decreased exponentially with minimum crossing number and Möbius energy, mathematical measures of knot complexity. Based on the observation that long, stiff strings tend to form a coiled structure when confined, we propose a simple model to describe the knot formation based on random "braid moves" of the string end. Our model can qualitatively account for the observed distribution of knots and dependence on agitation time and string length. PMID:17911269
On ambiguity in knot polynomials for virtual knots
NASA Astrophysics Data System (ADS)
Morozov, A.; Morozov, And.; Popolitov, A.
2016-06-01
We claim that HOMFLY polynomials for virtual knots, defined with the help of the matrix-model recursion relations, contain more parameters, than just the usual q and A =qN. These parameters preserve topological invariance and do not show up in the case of ordinary (non-virtual) knots and links. They are most conveniently observed in the hypercube formalism: then they substitute q-dimensions of certain fat graphs, which are not constrained by recursion and can be chosen arbitrarily. The number of these new topological invariants seems to grow fast with the number of non-virtual crossings: 0, 1, 1, 5, 15, 91, 784, 9160, ... This number can be decreased by imposing the factorization requirement for composites, in addition to topological invariance - still freedom remains. None of these new parameters, however, appears in HOMFLY for Kishino unknot, which thus remains unseparated from the ordinary unknots even by this enriched set of knot invariants.
New Invariants in the Theory of Knots.
ERIC Educational Resources Information Center
Kauffman, Louis H.
1988-01-01
A diagrammatic approach to invariants of knots is the focus. Connections with graph theory, physics, and other topics are included, along with an explanation of how proofs of some old conjectures about alternating knots emerge from this work. (MNS)
Relation between strings and ribbon knots
Ahmed, E. Mansoura Univ. ); El-Rifai, E.A. ); Abdellatif, R.A. )
1991-02-01
A ribbon knot can be representation as the propagation of an open string in (Euclidean) space-time. By imposing physical conditions plus an ansatz on the string scattering amplitude. The authors get invariant polynomials of ribbon knots which correspond to Jones and Wadati et al. polynomials for ordinary knots. Motivated by the string scattering vertices, they derive an algebra which is a generalization of Hecke and Murakami-Birman-Wenzel (BMW) algebras of knots.
Relation between strings and ribbon knots
NASA Astrophysics Data System (ADS)
Ahmed, E.; El-Rifai, E. A.; Abdellatif, R. A.
1991-02-01
A ribbon knot can be represented as the propagation of an open string in (Euclidean) space-time. By imposing physical conditions plus an ansatz on the string scattering amplitude, we get invariant polynomials of ribbon knots which correspond to Jones and Wadati et al. polynomials for ordinary knots. Motivated by the string scattering vertices, we derive an algebra which is a generalization of Hecke and Murakami-Birman-Wenzel (BMW) algebras of knots.
Knotted stents: Case report and outcome analysis
Lee, Ha Na; Hwang, Hokyeong
2015-01-01
A knotted ureteral stent is an extremely rare condition, with fewer than 20 cases reported in the literature; however, it is difficult to treat. We report a case in which a folded Terumo guidewire was successfully used to remove a knotted stent percutaneously without anesthesia. We also review the current literature on predisposing factors and management strategies for knotted ureteral stents. PMID:25964843
Second IBEX Map Unties the Knot
One of the clear features visible in the IBEX maps is an apparent knot in the ribbon. The second map showed that the knot in the ribbon somehow spread out. It is as if the knot in the ribbon was li...
Oligothiophene catenanes and knots: a theoretical study.
Fomine, Serguei; Guadarrama, Patricia
2006-08-24
Oligothiophene [2]catenanes and knots containing up to 28 thiophene units have been studied at the BHandHLYP/3-21G level of theory. Small knots (less than 22 thiophene units) and [2]catenanes (less than 18 thiophene units) are strained molecules. Larger knots and [2]catenanes are almost strain-free. [2]Catenanes and knots having less than 18 and 24 units, respectively, show transversal electronic coupling destroying one-dimensionality of molecules reflecting in smaller band gaps compared to larger knots and catenanes. Ionization potentials of knots and catenanes are always higher compared to that of lineal oligomers due to less effective conjugation. Polaron formation in catenanes is delocalized only over one ring, leaving another intact. In the case of a knot containing 22 thiophene units, estimated polaron delocalization is 8 to 9 repeating units. PMID:16913684
The elusive quest for RNA knots
Burton, Aaron S.; Di Stefano, Marco; Lehman, Niles; Orland, Henri; Micheletti, Cristian
2016-01-01
ABSTRACT Physical entanglement, and particularly knots arise spontaneously in equilibrated polymers that are sufficiently long and densely packed. Biopolymers are no exceptions: knots have long been known to occur in proteins as well as in encapsidated viral DNA. The rapidly growing number of RNA structures has recently made it possible to investigate the incidence of physical knots in this type of biomolecule, too. Strikingly, no knots have been found to date in the known RNA structures. In this Point of View Article we discuss the absence of knots in currently available RNAs and consider the reasons why knots in RNA have not yet been found, despite the expectation that they should exist in Nature. We conclude by singling out a number of RNA sequences that, based on the properties of their predicted secondary structures, are good candidates for knotted RNAs. PMID:26828280
The elusive quest for RNA knots.
Burton, Aaron S; Di Stefano, Marco; Lehman, Niles; Orland, Henri; Micheletti, Cristian
2016-02-01
Physical entanglement, and particularly knots arise spontaneously in equilibrated polymers that are sufficiently long and densely packed. Biopolymers are no exceptions: knots have long been known to occur in proteins as well as in encapsidated viral DNA. The rapidly growing number of RNA structures has recently made it possible to investigate the incidence of physical knots in this type of biomolecule, too. Strikingly, no knots have been found to date in the known RNA structures. In this Point of View Article we discuss the absence of knots in currently available RNAs and consider the reasons why knots in RNA have not yet been found, despite the expectation that they should exist in Nature. We conclude by singling out a number of RNA sequences that, based on the properties of their predicted secondary structures, are good candidates for knotted RNAs. PMID:26828280
Biomechanical evaluation of the Nice knot
Hill, Shannon W.; Chapman, Christopher R.; Adeeb, Samer; Duke, Kajsa; Beaupre, Lauren; Bouliane, Martin J.
2016-01-01
Background: The Nice knot is a bulky double-stranded knot. Biomechanical data supporting its use as well as the number of half hitches required to ensure knot security is lacking. Materials and Methods: Nice knots with, one, two, or three half-hitches were compared with the surgeon's and Tennessee slider knots with three half hitches. Each knot was tied 10 times around a fixed diameter using four different sutures: FiberWire (Arthrex, Naples, FL), Ultrabraid (Smith and Nephew, Andover, MA), Hi-Fi (ConMed Linvatec, Largo, FL) and Force Fiber (Teleflex Medical OEM, Gurnee, IL). Cyclic testing was performed for 10 min between 10N and 45N, resulting in approximately 1000 cycles. Displacement from an initial 10N load was recorded. Knots surviving cyclic testing were subjected to a load to failure test at a rate of 60 mm/min. Load at clinical failure: 3 mm slippage or opening of the suture loop was recorded. Bulk, mode of ultimate failure, opening of the loop past clinical failure, was also recorded. Results: During cyclic testing, the Nice knots with one or more half-hitches performed the best, slipping significantly less than the surgeon's and Tennessee Slider (P < 0.002). After one half-hitch, the addition of half-hitches did not significantly improve Nice knot performance during cyclic testing (P > 0.06). The addition of half-hitches improved the strength of the Nice knot during the force to failure test, however after two half-hitches, increase of strength was not significant (P = 0.59). While FiberWire was the most bulky of the sutures tested, it also performed the best, slipping the least. Conclusion: The Nice knot, especially using FiberWire, is biomechanically superior to the surgeon's and Tennessee slider knots. Two half hitches are recommended to ensure adequate knot security. PMID:26980985
KnotPad: Visualizing and Exploring Knot Theory with Fluid Reidemeister Moves.
Zhang, Hui; Weng, Jianguang; Jing, Lin; Zhong, Yiwen
2012-12-01
We present KnotPad, an interactive paper-like system for visualizing and exploring mathematical knots; we exploit topological drawing and math-aware deformation methods in particular to enable and enrich our interactions with knot diagrams. Whereas most previous efforts typically employ physically based modeling to simulate the 3D dynamics of knots and ropes, our tool offers a Reidemeister move based interactive environment that is much closer to the topological problems being solved in knot theory, yet without interfering with the traditional advantages of paper-based analysis and manipulation of knot diagrams. Drawing knot diagrams with many crossings and producing their equivalent is quite challenging and error-prone. KnotPad can restrict user manipulations to the three types of Reidemeister moves, resulting in a more fluid yet mathematically correct user experience with knots. For our principal test case of mathematical knots, KnotPad permits us to draw and edit their diagrams empowered by a family of interactive techniques. Furthermore, we exploit supplementary interface elements to enrich the user experiences. For example, KnotPad allows one to pull and drag on knot diagrams to produce mathematically valid moves. Navigation enhancements in KnotPad provide still further improvement: by remembering and displaying the sequence of valid moves applied during the entire interaction, KnotPad allows a much cleaner exploratory interface for the user to analyze and study knot equivalence. All these methods combine to reveal the complex spatial relationships of knot diagrams with a mathematically true and rich user experience. PMID:26357111
KnotProt: a database of proteins with knots and slipknots
Jamroz, Michal; Niemyska, Wanda; Rawdon, Eric J.; Stasiak, Andrzej; Millett, Kenneth C.; Sułkowski, Piotr; Sulkowska, Joanna I.
2015-01-01
The protein topology database KnotProt, http://knotprot.cent.uw.edu.pl/, collects information about protein structures with open polypeptide chains forming knots or slipknots. The knotting complexity of the cataloged proteins is presented in the form of a matrix diagram that shows users the knot type of the entire polypeptide chain and of each of its subchains. The pattern visible in the matrix gives the knotting fingerprint of a given protein and permits users to determine, for example, the minimal length of the knotted regions (knot's core size) or the depth of a knot, i.e. how many amino acids can be removed from either end of the cataloged protein structure before converting it from a knot to a different type of knot. In addition, the database presents extensive information about the biological functions, families and fold types of proteins with non-trivial knotting. As an additional feature, the KnotProt database enables users to submit protein or polymer chains and generate their knotting fingerprints. PMID:25361973
DNA Knots: Theory and Experiments
NASA Astrophysics Data System (ADS)
Sumners, D. W.
Cellular DNA is a long, thread-like molecule with remarkably complex topology. Enzymes that manipulate the geometry and topology of cellular DNA perform many vital cellular processes (including segregation of daughter chromosomes, gene regulation, DNA repair, and generation of antibody diversity). Some enzymes pass DNA through itself via enzyme-bridged transient breaks in the DNA; other enzymes break the DNA apart and reconnect it to different ends. In the topological approach to enzymology, circular DNA is incubated with an enzyme, producing an enzyme signature in the form of DNA knots and links. By observing the changes in DNA geometry (supercoiling) and topology (knotting and linking) due to enzyme action, the enzyme binding and mechanism can often be characterized. This paper will discuss some personal research history, and the tangle model for the analysis of site-specific recombination experiments on circular DNA.
Vortex knots in tangled quantum eigenfunctions.
Taylor, Alexander J; Dennis, Mark R
2016-01-01
Tangles of string typically become knotted, from macroscopic twine down to long-chain macromolecules such as DNA. Here, we demonstrate that knotting also occurs in quantum wavefunctions, where the tangled filaments are vortices (nodal lines/phase singularities). The probability that a vortex loop is knotted is found to increase with its length, and a wide gamut of knots from standard tabulations occur. The results follow from computer simulations of random superpositions of degenerate eigenstates of three simple quantum systems: a cube with periodic boundaries, the isotropic three-dimensional harmonic oscillator and the 3-sphere. In the latter two cases, vortex knots occur frequently, even in random eigenfunctions at relatively low energy, and are constrained by the spatial symmetries of the modes. The results suggest that knotted vortex structures are generic in complex three-dimensional wave systems, establishing a topological commonality between wave chaos, polymers and turbulent Bose-Einstein condensates. PMID:27468801
Characteristic length of the knotting probability revisited
NASA Astrophysics Data System (ADS)
Uehara, Erica; Deguchi, Tetsuo
2015-09-01
We present a self-avoiding polygon (SAP) model for circular DNA in which the radius of impermeable cylindrical segments corresponds to the screening length of double-stranded DNA surrounded by counter ions. For the model we evaluate the probability for a generated SAP with N segments having a given knot K through simulation. We call it the knotting probability of a knot K with N segments for the SAP model. We show that when N is large the most significant factor in the knotting probability is given by the exponentially decaying part exp(-N/NK), where the estimates of parameter NK are consistent with the same value for all the different knots we investigated. We thus call it the characteristic length of the knotting probability. We give formulae expressing the characteristic length as a function of the cylindrical radius rex, i.e. the screening length of double-stranded DNA.
Vortex knots in tangled quantum eigenfunctions
Taylor, Alexander J.; Dennis, Mark R.
2016-01-01
Tangles of string typically become knotted, from macroscopic twine down to long-chain macromolecules such as DNA. Here, we demonstrate that knotting also occurs in quantum wavefunctions, where the tangled filaments are vortices (nodal lines/phase singularities). The probability that a vortex loop is knotted is found to increase with its length, and a wide gamut of knots from standard tabulations occur. The results follow from computer simulations of random superpositions of degenerate eigenstates of three simple quantum systems: a cube with periodic boundaries, the isotropic three-dimensional harmonic oscillator and the 3-sphere. In the latter two cases, vortex knots occur frequently, even in random eigenfunctions at relatively low energy, and are constrained by the spatial symmetries of the modes. The results suggest that knotted vortex structures are generic in complex three-dimensional wave systems, establishing a topological commonality between wave chaos, polymers and turbulent Bose–Einstein condensates. PMID:27468801
Vortex knots in tangled quantum eigenfunctions
NASA Astrophysics Data System (ADS)
Taylor, Alexander J.; Dennis, Mark R.
2016-07-01
Tangles of string typically become knotted, from macroscopic twine down to long-chain macromolecules such as DNA. Here, we demonstrate that knotting also occurs in quantum wavefunctions, where the tangled filaments are vortices (nodal lines/phase singularities). The probability that a vortex loop is knotted is found to increase with its length, and a wide gamut of knots from standard tabulations occur. The results follow from computer simulations of random superpositions of degenerate eigenstates of three simple quantum systems: a cube with periodic boundaries, the isotropic three-dimensional harmonic oscillator and the 3-sphere. In the latter two cases, vortex knots occur frequently, even in random eigenfunctions at relatively low energy, and are constrained by the spatial symmetries of the modes. The results suggest that knotted vortex structures are generic in complex three-dimensional wave systems, establishing a topological commonality between wave chaos, polymers and turbulent Bose-Einstein condensates.
The condensate from torus knots
NASA Astrophysics Data System (ADS)
Gorsky, A.; Milekhin, A.; Sopenko, N.
2015-09-01
We discuss recently formulated instanton-torus knot duality in Ω-deformed 5D SQED on {{R}}^4× {S}^1 focusing at the microscopic aspects of the condensate formation in the instanton ensemble. Using the chain of dualities and geometric transitions we embed the SQED with a surface defect into the SU(2) SQCD with N f = 4 and identify the numbers ( n, m) of the torus T n, m knot as instanton charge and electric charge. The HOMFLY torus knot invariants in the fundamental representation provide entropic factor in the condensate of the massless flavor counting the degeneracy of the instanton-W-boson web with instanton and electric numbers ( n, m) but different spin and flavor content. Using the inverse geometrical transition we explain how our approach is related to the evaluation of the HOMFLY invariants in terms of Wilson loop in 3d CS theory. The reduction to 4D theory is briefly considered and some analogy with baryon vertex is conjectured.
Knots and nonorientable surfaces in chiral nematics
Machon, Thomas; Alexander, Gareth P.
2013-01-01
Knots and knotted fields enrich physical phenomena ranging from DNA and molecular chemistry to the vortices of fluid flows and textures of ordered media. Liquid crystals provide an ideal setting for exploring such topological phenomena through control of their characteristic defects. The use of colloids in generating defects and knotted configurations in liquid crystals has been demonstrated for spherical and toroidal particles and shows promise for the development of novel photonic devices. Extending this existing work, we describe the full topological implications of colloids representing nonorientable surfaces and use it to construct torus knots and links of type (p,2) around multiply twisted Möbius strips. PMID:23940365
Lederman, Zohar
2014-06-01
In a recent article, Joel Marks presents the amoralist argument against vivisection, or animal laboratory experimentation. He argues that ethical theories that seek to uncover some universal morality are in fact useless and unnecessary for ethical deliberations meant to determine what constitutes an appropriate action in a specific circumstance. I agree with Marks' conclusion. I too believe that vivisection is indefensible, both from a scientific and philosophical perspective. I also believe that we should become vegan (unfortunately, like the two philosophers mentioned by Marks, I too am still struggling to reduce my meat and dairy consumption). However, I am in the dark as to Marks' vision of normative deliberations in the spirit of amoralism and desirism. PMID:24744177
Weber, Cédric; Carlen, Mathias; Dietler, Giovanni; Rawdon, Eric J; Stasiak, Andrzej
2013-01-01
We address the general question of the extent to which the hydrodynamic behaviour of microscopic freely fluctuating objects can be reproduced by macrosopic rigid objects. In particular, we compare the sedimentation speeds of knotted DNA molecules undergoing gel electrophoresis to the sedimentation speeds of rigid stereolithographic models of ideal knots in both water and silicon oil. We find that the sedimentation speeds grow roughly linearly with the average crossing number of the ideal knot configurations, and that the correlation is stronger within classes of knots. This is consistent with previous observations with DNA knots in gel electrophoresis. PMID:23346349
Weber, Cédric; Carlen, Mathias; Dietler, Giovanni; Rawdon, Eric J.; Stasiak, Andrzej
2013-01-01
We address the general question of the extent to which the hydrodynamic behaviour of microscopic freely fluctuating objects can be reproduced by macrosopic rigid objects. In particular, we compare the sedimentation speeds of knotted DNA molecules undergoing gel electrophoresis to the sedimentation speeds of rigid stereolithographic models of ideal knots in both water and silicon oil. We find that the sedimentation speeds grow roughly linearly with the average crossing number of the ideal knot configurations, and that the correlation is stronger within classes of knots. This is consistent with previous observations with DNA knots in gel electrophoresis. PMID:23346349
Knot theory and quantum gravity
Rovelli, C.; Smolin, L.
1988-09-05
A new represenatation for quantum general relativity is described, which is defined in terms of functionals of sets of loops in three-space. In this representation exact solutions of the quantum constraints may be obtained. This result is related to the simplification of the constraints in Ashtekar's new formalism. We give in closed form the general solution of the diffeomorphisms constraint and a large class of solutions of the full set of constraints. These are classified by the knot and link classes of the spatial three-manifold.
Knots, BPS States, and Algebraic Curves
NASA Astrophysics Data System (ADS)
Garoufalidis, Stavros; Kucharski, Piotr; Sułkowski, Piotr
2016-08-01
We analyze relations between BPS degeneracies related to Labastida-Mariño-Ooguri-Vafa (LMOV) invariants and algebraic curves associated to knots. We introduce a new class of such curves, which we call extremal A-polynomials, discuss their special properties, and determine exact and asymptotic formulas for the corresponding (extremal) BPS degeneracies. These formulas lead to nontrivial integrality statements in number theory, as well as to an improved integrality conjecture, which is stronger than the known M-theory integrality predictions. Furthermore, we determine the BPS degeneracies encoded in augmentation polynomials and show their consistency with known colored HOMFLY polynomials. Finally, we consider refined BPS degeneracies for knots, determine them from the knowledge of super-A-polynomials, and verify their integrality. We illustrate our results with twist knots, torus knots, and various other knots with up to 10 crossings.
Knots, BPS States, and Algebraic Curves
NASA Astrophysics Data System (ADS)
Garoufalidis, Stavros; Kucharski, Piotr; Sułkowski, Piotr
2016-07-01
We analyze relations between BPS degeneracies related to Labastida-Mariño-Ooguri-Vafa (LMOV) invariants and algebraic curves associated to knots. We introduce a new class of such curves, which we call extremal A-polynomials, discuss their special properties, and determine exact and asymptotic formulas for the corresponding (extremal) BPS degeneracies. These formulas lead to nontrivial integrality statements in number theory, as well as to an improved integrality conjecture, which is stronger than the known M-theory integrality predictions. Furthermore, we determine the BPS degeneracies encoded in augmentation polynomials and show their consistency with known colored HOMFLY polynomials. Finally, we consider refined BPS degeneracies for knots, determine them from the knowledge of super-A-polynomials, and verify their integrality. We illustrate our results with twist knots, torus knots, and various other knots with up to 10 crossings.
A pseudo-haptic knot diagram interface
NASA Astrophysics Data System (ADS)
Zhang, Hui; Weng, Jianguang; Hanson, Andrew J.
2011-01-01
To make progress in understanding knot theory, we will need to interact with the projected representations of mathematical knots which are of course continuous in 3D but significantly interrupted in the projective images. One way to achieve such a goal would be to design an interactive system that allows us to sketch 2D knot diagrams by taking advantage of a collision-sensing controller and explore their underlying smooth structures through a continuous motion. Recent advances of interaction techniques have been made that allow progress to be made in this direction. Pseudo-haptics that simulates haptic effects using pure visual feedback can be used to develop such an interactive system. This paper outlines one such pseudo-haptic knot diagram interface. Our interface derives from the familiar pencil-and-paper process of drawing 2D knot diagrams and provides haptic-like sensations to facilitate the creation and exploration of knot diagrams. A centerpiece of the interaction model simulates a "physically" reactive mouse cursor, which is exploited to resolve the apparent conflict between the continuous structure of the actual smooth knot and the visual discontinuities in the knot diagram representation. Another value in exploiting pseudo-haptics is that an acceleration (or deceleration) of the mouse cursor (or surface locator) can be used to indicate the slope of the curve (or surface) of whom the projective image is being explored. By exploiting these additional visual cues, we proceed to a full-featured extension to a pseudo-haptic 4D visualization system that simulates the continuous navigation on 4D objects and allows us to sense the bumps and holes in the fourth dimension. Preliminary tests of the software show that main features of the interface overcome some expected perceptual limitations in our interaction with 2D knot diagrams of 3D knots and 3D projective images of 4D mathematical objects.
Lou, Shih-Chi; Wetzel, Svava; Zhang, Hongyu; Crone, Elizabeth W; Lee, Yun-Tzai; Jackson, Sophie E; Hsu, Shang-Te Danny
2016-06-01
The human ubiquitin C-terminal hydrolase, UCH-L1, is an abundant neuronal deubiquitinase that is associated with Parkinson's disease. It contains a complex Gordian knot topology formed by the polypeptide chain alone. Using a combination of fluorescence-based kinetic measurements, we show that UCH-L1 has two distinct kinetic folding intermediates that are transiently populated on parallel pathways between the denatured and native states. NMR hydrogen-deuterium exchange (HDX) experiments indicate the presence of partially unfolded forms (PUFs) of UCH-L1 under native conditions. HDX measurements as a function of urea concentration were used to establish the structure of the PUFs and pulse-labelled HDX NMR was used to show that the PUFs and the folding intermediates are likely the same species. In both cases, a similar stable core encompassing most of the central β-sheet is highly structured and α-helix 3, which is partially formed, packs against it. In contrast to the stable β-sheet core, the peripheral α-helices display significant local fluctuations leading to rapid exchange. The results also suggest that the main difference between the two kinetic intermediates is structure and packing of α-helices 3 and 7 and the degree of structure in β-strand 5. Together, the fluorescence and NMR results establish that UCH-L1 neither folds through a continuum of pathways nor by a single discrete pathway. Its folding is complex, the β-sheet core forms early and is present in both intermediate states, and the rate-limiting step which is likely to involve the threading of the chain to form the 52-knot occurs late on the folding pathway. PMID:27067109
A knot or not a knot? SETting the record 'straight' on proteins.
Taylor, William R; Xiao, Bing; Gamblin, Steven J; Lin, Kuang
2003-02-01
A novel knot found in the SET domain is examined in the light of five recent crystal structures and their descriptions in the literature. Using the algorithm of Taylor it was established that the backbone chain does not form a true knot. However, only two crosslinks corresponding to hydrogen-bonds were needed to form a knotted structure. Such loosely knotted structures formed by hydrogen-bonded crosslinks were assessed as lying between covalent crosslinks (such as disulphide bonds) and threaded-loops which are formed by close (unbonded) contacts between different parts of the chain. The term pseudo-knot was introduced (from the RNA field) to distinguish hydrogen-bonded 'knots'. PMID:12798035
Molecular knots in biology and chemistry
NASA Astrophysics Data System (ADS)
Lim, Nicole C. H.; Jackson, Sophie E.
2015-09-01
Knots and entanglements are ubiquitous. Beyond their aesthetic appeal, these fascinating topological entities can be either useful or cumbersome. In recent decades, the importance and prevalence of molecular knots have been increasingly recognised by scientists from different disciplines. In this review, we provide an overview on the various molecular knots found in naturally occurring biological systems (DNA, RNA and proteins), and those created by synthetic chemists. We discuss the current knowledge in these fields, including recent developments in experimental and, in some cases, computational studies which are beginning to shed light into the complex interplay between the structure, formation and properties of these topologically intricate molecules.
Spontaneous knotting of self-trapped waves.
Desyatnikov, Anton S; Buccoliero, Daniel; Dennis, Mark R; Kivshar, Yuri S
2012-01-01
We describe theory and simulations of a spinning optical soliton whose propagation spontaneously excites knotted and linked optical vortices. The nonlinear phase of the self-trapped light beam breaks the wave front into a sequence of optical vortex loops around the soliton, which, through the soliton's orbital angular momentum and spatial twist, tangle on propagation to form links and knots. We anticipate similar spontaneous knot topology to be a universal feature of waves whose phase front is twisted and nonlinearly modulated, including superfluids and trapped matter waves. PMID:23105969
Spontaneous knotting of self-trapped waves
Desyatnikov, Anton S.; Buccoliero, Daniel; Dennis, Mark R.; Kivshar, Yuri S.
2012-01-01
We describe theory and simulations of a spinning optical soliton whose propagation spontaneously excites knotted and linked optical vortices. The nonlinear phase of the self-trapped light beam breaks the wave front into a sequence of optical vortex loops around the soliton, which, through the soliton's orbital angular momentum and spatial twist, tangle on propagation to form links and knots. We anticipate similar spontaneous knot topology to be a universal feature of waves whose phase front is twisted and nonlinearly modulated, including superfluids and trapped matter waves. PMID:23105969
Molecular knots in biology and chemistry.
Lim, Nicole C H; Jackson, Sophie E
2015-09-01
Knots and entanglements are ubiquitous. Beyond their aesthetic appeal, these fascinating topological entities can be either useful or cumbersome. In recent decades, the importance and prevalence of molecular knots have been increasingly recognised by scientists from different disciplines. In this review, we provide an overview on the various molecular knots found in naturally occurring biological systems (DNA, RNA and proteins), and those created by synthetic chemists. We discuss the current knowledge in these fields, including recent developments in experimental and, in some cases, computational studies which are beginning to shed light into the complex interplay between the structure, formation and properties of these topologically intricate molecules. PMID:26291690
Energy functions for knots: Beginning to predict physical behavior
Simon, J.
1996-12-31
Several definitions have been proposed for the {open_quotes}energy{close_quotes} of a knot. The intuitive goal is to define a number u(K) that somehow measures how {open_quotes}tangled{close_quotes} or {open_quotes}crumpled{close_quotes} a knot K is. Typically, one starts with the idea that a small piece of the knot somehow repels other pieces, and then adds up the contributions from all the pieces. From a purely mathematical standpoint, one may hope to define new knot-type invariants, e.g by considering the minimum of u(K) as K ranges over all the knots of a given knot-type. We also are motivated by the desire to understand and predict how knot-type affects the behavior of physically real knots, in particular DNA loops in gel electrophoresis or random knotting experiments. Despite the physical naivete of recently studied knot energies, there now is enough laboratory data on relative gel velocity, along with computer calculations of idealized knot energies, to justify the assertion that knot energies can predict relative knot behavior in physical systems. The relationships between random knot frequencies and either gel velocities or knot energies is less clear at this time. 50 refs., 8 figs., 2 tabs.
Knot theory realizations in nematic colloids.
Čopar, Simon; Tkalec, Uroš; Muševič, Igor; Žumer, Slobodan
2015-02-10
Nematic braids are reconfigurable knots and links formed by the disclination loops that entangle colloidal particles dispersed in a nematic liquid crystal. We focus on entangled nematic disclinations in thin twisted nematic layers stabilized by 2D arrays of colloidal particles that can be controlled with laser tweezers. We take the experimentally assembled structures and demonstrate the correspondence of the knot invariants, constructed graphs, and surfaces associated with the disclination loop to the physically observable features specific to the geometry at hand. The nematic nature of the medium adds additional topological parameters to the conventional results of knot theory, which couple with the knot topology and introduce order into the phase diagram of possible structures. The crystalline order allows the simplified construction of the Jones polynomial and medial graphs, and the steps in the construction algorithm are mirrored in the physics of liquid crystals. PMID:25624467
Cotranslational folding of deeply knotted proteins
NASA Astrophysics Data System (ADS)
Chwastyk, Mateusz; Cieplak, Marek
2015-09-01
Proper folding of deeply knotted proteins has a very low success rate even in structure-based models which favor formation of the native contacts but have no topological bias. By employing a structure-based model, we demonstrate that cotranslational folding on a model ribosome may enhance the odds to form trefoil knots for protein YibK without any need to introduce any non-native contacts. The ribosome is represented by a repulsive wall that keeps elongating the protein. On-ribosome folding proceeds through a a slipknot conformation. We elucidate the mechanics and energetics of its formation. We show that the knotting probability in on-ribosome folding is a function of temperature and that there is an optimal temperature for the process. Our model often leads to the establishment of the native contacts without formation of the knot.
Cotranslational folding of deeply knotted proteins.
Chwastyk, Mateusz; Cieplak, Marek
2015-09-01
Proper folding of deeply knotted proteins has a very low success rate even in structure-based models which favor formation of the native contacts but have no topological bias. By employing a structure-based model, we demonstrate that cotranslational folding on a model ribosome may enhance the odds to form trefoil knots for protein YibK without any need to introduce any non-native contacts. The ribosome is represented by a repulsive wall that keeps elongating the protein. On-ribosome folding proceeds through a a slipknot conformation. We elucidate the mechanics and energetics of its formation. We show that the knotting probability in on-ribosome folding is a function of temperature and that there is an optimal temperature for the process. Our model often leads to the establishment of the native contacts without formation of the knot. PMID:26292194
Knot theory realizations in nematic colloids
Čopar, Simon; Tkalec, Uroš; Muševič, Igor; Žumer, Slobodan
2015-01-01
Nematic braids are reconfigurable knots and links formed by the disclination loops that entangle colloidal particles dispersed in a nematic liquid crystal. We focus on entangled nematic disclinations in thin twisted nematic layers stabilized by 2D arrays of colloidal particles that can be controlled with laser tweezers. We take the experimentally assembled structures and demonstrate the correspondence of the knot invariants, constructed graphs, and surfaces associated with the disclination loop to the physically observable features specific to the geometry at hand. The nematic nature of the medium adds additional topological parameters to the conventional results of knot theory, which couple with the knot topology and introduce order into the phase diagram of possible structures. The crystalline order allows the simplified construction of the Jones polynomial and medial graphs, and the steps in the construction algorithm are mirrored in the physics of liquid crystals. PMID:25624467
Vortex knot cascade in polynomial skein relations
NASA Astrophysics Data System (ADS)
Ricca, Renzo L.
2016-06-01
The process of vortex cascade through continuous reduction of topological complexity by stepwise unlinking, that has been observed experimentally in the production of vortex knots (Kleckner & Irvine, 2013), is shown to be reproduced in the branching of the skein relations of knot polynomials (Liu & Ricca, 2015) used to identify topological complexity of vortex systems. This observation can be usefully exploited for predictions of energy-complexity estimates for fluid flows.
Absence of knots in known RNA structures.
Micheletti, Cristian; Di Stefano, Marco; Orland, Henri
2015-02-17
The ongoing effort to detect and characterize physical entanglement in biopolymers has so far established that knots are present in many globular proteins and also, abound in viral DNA packaged inside bacteriophages. RNA molecules, however, have not yet been systematically screened for the occurrence of physical knots. We have accordingly undertaken the systematic profiling of the several thousand RNA structures present in the Protein Data Bank (PDB). The search identified no more than three deeply knotted RNA molecules. These entries are rRNAs of about 3,000 nt solved by cryo-EM. Their genuine knotted state is, however, doubtful based on the detailed structural comparison with homologs of higher resolution, which are all unknotted. Compared with the case of proteins and viral DNA, the observed incidence of knots in available RNA structures is, therefore, practically negligible. This fact suggests that either evolutionary selection or thermodynamic and kinetic folding mechanisms act toward minimizing the entanglement of RNA to an extent that is unparalleled by other types of biomolecules. A possible general strategy for designing synthetic RNA sequences capable of self-tying in a twist-knot fold is finally proposed. PMID:25646433
Torus Knots and the Topological Vertex
NASA Astrophysics Data System (ADS)
Jockers, Hans; Klemm, Albrecht; Soroush, Masoud
2014-08-01
We propose a class of toric Lagrangian A-branes on the resolved conifold that is suitable to describe torus knots on S 3. The key role is played by the transformation, which generates a general torus knot from the unknot. Applying the topological vertex to the proposed A-branes, we rederive the colored HOMFLY polynomials for torus knots, in agreement with the Rosso and Jones formula. We show that our A-model construction is mirror symmetric to the B-model analysis of Brini, Eynard and Mariño. Compared to the recent proposal by Aganagic and Vafa for knots on S 3, we demonstrate that the disk amplitude of the A-brane associated with any knot is sufficient to reconstruct the entire B-model spectral curve. Finally, the construction of toric Lagrangian A-branes is generalized to other local toric Calabi-Yau geometries, which paves the road to study knots in other three-manifolds such as lens spaces.
Origin of metastable knots in single flexible chains.
Dai, Liang; Renner, C Benjamin; Doyle, Patrick S
2015-01-23
Recent theoretical progress has explained the physics of knotting of semiflexible polymers, yet knotting of flexible polymers is relatively unexplored. We herein develop a new theory for the size distribution of knots on a flexible polymer and the existence of metastable knots. We show the free energy of a flexible molecule in a tube can be mapped to quantitatively reproduce the free energy distribution of a knot on a flexible chain. The size distribution of knots on flexible chains is expected to be universal and might be observed at a macroscopic scale, such as a string of hard balls. PMID:25659023
Comparing models of Red Knot population dynamics
McGowan, Conor
2015-01-01
Predictive population modeling contributes to our basic scientific understanding of population dynamics, but can also inform management decisions by evaluating alternative actions in virtual environments. Quantitative models mathematically reflect scientific hypotheses about how a system functions. In Delaware Bay, mid-Atlantic Coast, USA, to more effectively manage horseshoe crab (Limulus polyphemus) harvests and protect Red Knot (Calidris canutus rufa) populations, models are used to compare harvest actions and predict the impacts on crab and knot populations. Management has been chiefly driven by the core hypothesis that horseshoe crab egg abundance governs the survival and reproduction of migrating Red Knots that stopover in the Bay during spring migration. However, recently, hypotheses proposing that knot dynamics are governed by cyclical lemming dynamics garnered some support in data analyses. In this paper, I present alternative models of Red Knot population dynamics to reflect alternative hypotheses. Using 2 models with different lemming population cycle lengths and 2 models with different horseshoe crab effects, I project the knot population into the future under environmental stochasticity and parametric uncertainty with each model. I then compare each model's predictions to 10 yr of population monitoring from Delaware Bay. Using Bayes' theorem and model weight updating, models can accrue weight or support for one or another hypothesis of population dynamics. With 4 models of Red Knot population dynamics and only 10 yr of data, no hypothesis clearly predicted population count data better than another. The collapsed lemming cycle model performed best, accruing ~35% of the model weight, followed closely by the horseshoe crab egg abundance model, which accrued ~30% of the weight. The models that predicted no decline or stable populations (i.e. the 4-yr lemming cycle model and the weak horseshoe crab effect model) were the most weakly supported.
Optimal tissue tension for secure laparoscopic knots.
Raut, Vikram N; Takaori, Kyoichi; Uemoto, Shinji
2011-02-01
Security and strength of a knot are main concerns of the surgeon since last 4000 years. The advancement of endoscopic and minimally invasive surgery in last few decades had a significant influence on a knot tying. The most difficult methods of a knot tying are performed during endoscopic procedures, in which the surgeon execute instrumentation from outside the body without palpation of organs and three-dimensional vision. In addition, laparoscopic instruments due to friction in transmission mechanism have very poor force feedback. This results into difficulty in applying the appropriate grasping force to the tissue, resulting in slippage or damage to the tissue. Our hypothesis highlights the need of tissue approximation at the 'optimum tissue tension' sufficient to resist the slippage of suture/clip without strangulation. The purpose of suture is to maintain an approximation of the tissue until healing progresses to the point where artificial support is no longer necessary for the wound to resist normal stress. When the approximation is too tight, tension in tissue leads to diminished blood supply resulting into the necrosis. Various tissues need different blood supply and different tissue pressure for optimum healings. Proposed hypothesis helps to improve the feedback of current knot pushers or clip applicators used in laparoscopic surgery using optimum tissue tension. Tissue approximation at an optimal tissue tension translates into the secure laparoscopic knot/clip application resulting in prevention of wound dehiscence, anastomosis leak, and secondary haemorrhages. PMID:21071154
The inner knot of the Crab nebula
NASA Astrophysics Data System (ADS)
Lyutikov, Maxim; Komissarov, Serguei S.; Porth, Oliver
2016-02-01
We model the inner knot of the Crab nebula as a synchrotron emission coming from the non-spherical MHD termination shock of relativistic pulsar wind. The post-shock flow is mildly relativistic; as a result the Doppler beaming has a strong impact on the shock appearance. The model can reproduce the knot location, size, elongation, brightness distribution, luminosity and polarization provided the effective magnetization of the section of the pulsar wind producing the knot is low, σ ≤ 1. In the striped wind model, this implies that the striped zone is rather wide, with the magnetic inclination angle of the Crab pulsar ≥45°; this agrees with the previous model-dependent estimate based on the gamma-ray emission of the pulsar. We conclude that the tiny knot is indeed a bright spot on the surface of a quasi-stationary magnetic relativistic shock and that this shock is a site of efficient particle acceleration. On the other hand, the deduced low magnetization of the knot plasma implies that this is an unlikely site for the Crab's gamma-ray flares, if they are related to the fast relativistic magnetic reconnection events.
Simulations of electrophoretic collisions of DNA knots with gel obstacles
NASA Astrophysics Data System (ADS)
Weber, C.; DeLos Rios, P.; Dietler, G.; Stasiak, A.
2006-04-01
Gel electrophoresis can be used to separate nicked circular DNA molecules of equal length but forming different knot types. At low electric fields, complex knots drift faster than simpler knots. However, at high electric field the opposite is the case and simpler knots migrate faster than more complex knots. Using Monte Carlo simulations we investigate the reasons of this reversal of relative order of electrophoretic mobility of DNA molecules forming different knot types. We observe that at high electric fields the simulated knotted molecules tend to hang over the gel fibres and require passing over a substantial energy barrier to slip over the impeding gel fibre. At low electric field the interactions of drifting molecules with the gel fibres are weak and there are no significant energy barriers that oppose the detachment of knotted molecules from transverse gel fibres.
Polymer theta-point as a knot delocalization transition.
Orlandini, E; Stella, A L; Vanderzande, C
2003-09-01
We study numerically the tightness of prime flat knots in a model of self-attracting polymers with excluded volume. We find that these knots are localized in the high temperature swollen regime, but become delocalized in the low temperature globular phase. Precisely at the collapse transition, the knots are weakly localized. Some of our results can be interpreted in terms of the theory of polymer networks, which allows one to conjecture exact exponents for the knot length probability distributions. PMID:14524795
Nonlinear electrodynamics is skilled with knots
NASA Astrophysics Data System (ADS)
Goulart, E.
2016-07-01
The aim of this letter is threefold: First is to show that nonlinear generalizations of electrodynamics support various types of knotted solutions in vacuum. The solutions are universal in the sense that they do not depend on the specific Lagrangian density, at least if the latter gives rise to a well-posed theory. Second, is to describe the interaction between probe waves and knotted background configurations. We show that the qualitative behaviour of this interaction may be described in terms of Robinson congruences, which appear explicitly in the causal structure of the theory. Finally, we argue that optical arrangements endowed with intense background fields could be the natural place to look for the knots experimentally.
Are there p-adic knot invariants?
NASA Astrophysics Data System (ADS)
Morozov, A. Yu.
2016-04-01
We suggest using the Hall-Littlewood version of the Rosso-Jones formula to define the germs of p-adic HOMFLY-PT polynomials for torus knots [ m, n] as coefficients of superpolynomials in a q-expansion. In this form, they have at least the [ m, n] ↔ [ n, m] topological invariance. This opens a new possibility to interpret superpolynomials as p-adic deformations of HOMFLY polynomials and poses a question of generalizing to other knot families, which is a substantial problem for several branches of modern theory.
On the geometry of stiff knots
NASA Astrophysics Data System (ADS)
Pierre-Louis, O.
2009-09-01
We analyse the geometry of a thin knotted string with bending rigidity. Two types of geometric properties are investigated. First, following the approach of von der Mosel [H. von der Mosel, Asymptotic Anal. 18, 49 (1998)], we derive upper bounds for the multiplicity of crossings and braids. Then, using a general inequality for the length of 3D curves derived by Chakerian [G.D. Chakerian, Proc. of the American Math. Soc. 15, 886 (1964)], we analyze the size and confinement of a knot
Ortillés, A; Rodríguez, J; Calvo, B
2014-10-01
Several types of materials and surgical suture patterns are used in conventional surgery. Their combination with an appropriate knot is the basis for correct tissue apposition and healing. Knot security is essential to prevent loosening or slipping before the suture line is completely closed. Nevertheless, the knot itself is the weakest link in any surgical handling. The aim of this study is to determine and compare the mechanical behavior of four surgical knot types (square knot, surgeon׳s knot, square slipknot and Miller׳s knot) performed with three different suture materials (absorbable monofilament glyconate, non-absorbable monofilament polyamide and absorbable braided polyglycolic acid) in a non-biological experimental in vitro model (a tube of synthetic material with non-linear mechanical behavior). The mechanical properties of each suture material are also compared. Ten samples were mechanically tested for each suture and knot using a uniaxial tensile test until complete sample rupture. The failure Cauchy stress and stretch were calculated. The Cauchy stress at 5%, 10% and 15% strain and standard deviation were compared for each suture and knot type. The results demonstrated that all the suture materials had statistically significant differences in their non-linear mechanical behavior. Absorbable monofilament glyconate was the most compliant suture with the greatest tensile strength, while absorbable braided polyglycolic acid was the stiffest. Regardless of the suture type used, the Miller׳s knot had the greatest failure Cauchy stress and stretch, while the square, surgeon׳s and square slipknot had the lowest. In all cases, the Miller׳s knot was more compliant and had greater tensile strength than the other knots. The square knot, surgeon׳s knot, and square slipknot had statistically significant similarities in their mechanical behavior. Therefore, the Miller׳s knot could be classified as the gold standard and an alternative to the surgical knotting
A trefoil knotted polymer produced through ring expansion.
Cao, Peng-Fei; Mangadlao, Joey; Advincula, Rigoberto
2015-04-20
A synthetic strategy is reported for the production of a trefoil knotted polymer from a copper(I)-templated helical knot precursor through ring expansion. The expected changes in the properties of the knotted polymer compared to a linear analogue, for example, reduced hydrodynamic radius and lower intrinsic viscosity, together with an atomic force microscopy (AFM) image of individual molecular knots, confirmed the formation of the resulting trefoil knotted polymer. The strategies employed here could be utilized to enrich the variety of available polymers with new architectures. PMID:25728998
Knotted proteins: A tangled tale of Structural Biology
Faísca, Patrícia F.N.
2015-01-01
Knotted proteins have their native structures arranged in the form of an open knot. In the last ten years researchers have been making significant efforts to reveal their folding mechanism and understand which functional advantage(s) knots convey to their carriers. Molecular simulations have been playing a fundamental role in this endeavor, and early computational predictions about the knotting mechanism have just been confirmed in wet lab experiments. Here we review a collection of simulation results that allow outlining the current status of the field of knotted proteins, and discuss directions for future research. PMID:26380658
Untying vortex knots in fluids and superfluids
NASA Astrophysics Data System (ADS)
Kleckner, Dustin; Scheeler, Martin; Kedia, Hridesh; Irvine, William T. M.
Recent work has demonstrated that vortex knots appear to always untie in fluids and superfluids. Should we expect the same behavior from these two very different systems? I will discuss this unknotting behavior, both quantitatively - through helicity - and qualitatively through the geometry and topology of the vortex lines as they evolve.
High velocity knot in the Helix nebula
Meaburn, J.; Walsh, J.R.
1980-01-01
A high velocity (about 66 km/s) split feature about 15 arcseconds in extent has been detected in forbidden O II emission over a dark knot in the loop of the Helix nebula. This velocity splitting is much greater than the 20 km/s large scale splitting observed previously, and several mechanisms are proposed to account for this feature.
A preliminary design of a knot undulator.
Xi, Fuchun; Shi, Tan; Fan, Qingyan; Prestemon, Soren; Wan, Weishi; An, Zhenghua; Qiao, S
2013-01-01
The magnetic field configuration of the previously proposed knot undulator [Qiao et al. (2009). Rev. Sci. Instrum. 80, 085108] is realised in the design of a hybridized elliptically polarized undulator, which is presented. Although the details of the field distribution are not the same as those in the theoretical proposal, it is demonstrated that the practical knot undulator could work perfectly. In order to understand the minor discrepancies of the two, mathematical formulae of the synchrotron radiation are derived based on the Fourier transform of the magnetic field. From the results of calculations by simulation program, the discrepancies could be well interpreted by the corresponding formulae. The results show the importance of optimization of the end sections of the knot undulator to suppress the on-axis heat load. Furthermore, a study of the impact of the undulator on beam dynamics of the storage ring was conducted using the Shanghai Synchrotron Radiation Facility as an example and the results show that the knot undulator has little effect on the beam. PMID:23254667
Black hole physics: More similar than knot
NASA Astrophysics Data System (ADS)
Gómez, José L.
2016-08-01
The detection of a discrete knot of particle emission from the active galaxy M81* reveals that black hole accretion is self-similar with regard to mass, producing the same knotty jets irrespective of black hole mass and accretion rate.
Spontaneous Intravesical Knotting of Urethral Catheter
2011-01-01
Infant feeding tubes (IFT) have been universally used as urethral catheters in neonates and children for several decades. Though generally a safe procedure, it may cause significant morbidity if the catheter spontaneously knots inside the bladder. We report this complication in three children including a neonate. PMID:22953288
Towards effective topological field theory for knots
NASA Astrophysics Data System (ADS)
Mironov, A.; Morozov, A.
2015-10-01
Construction of (colored) knot polynomials for double-fat graphs is further generalized to the case when "fingers" and "propagators" are substituting R-matrices in arbitrary closed braids with m-strands. Original version of [25] corresponds to the case m = 2, and our generalization sheds additional light on the structure of those mysterious formulas. Explicit expressions are now combined from Racah matrices of the type R ⊗ R ⊗ R bar ⟶ R bar and mixing matrices in the sectors R⊗3 ⟶ Q. Further extension is provided by composition rules, allowing to glue two blocks, connected by an m-strand braid (they generalize the product formula for ordinary composite knots with m = 1).
Parity and cobordism of free knots
Manturov, Vassily O
2012-02-28
A simple invariant is constructed which obstructs a free knot to be truncated. In particular, this invariant provides an obstruction to the truncatedness of curves immersed in two-dimensional surfaces. A curve on an oriented two-dimensional surface S{sub g} is referred to as truncated (null-cobordant) if there exists a three-dimensional manifold M with boundary S{sub g} and a smooth proper map of a two-disc to M such that the image of the boundary of the disc coincides with the curve. The problem of truncatedness for free knots is solved in this paper using the notion of parity recently introduced by the author. Bibliography: 12 titles.
Cometary Knots Around A Dying Star
NASA Technical Reports Server (NTRS)
1994-01-01
These gigantic, tadpole-shaped objects are probably the result of a dying star's last gasps. Dubbed 'cometary knots' because their glowing heads and gossamer tails resemble comets, the gaseous objects probably were formed during a star's final stages of life. Hubble astronomer C. Robert O'Dell and graduate student Kerry P. Handron of Rice University in Houston, Texas discovered thousands of these knots with the Hubble Space Telescope while exploring the Helix nebula, the closest planetary nebula to Earth at 450 light-years away in the constellation Aquarius. Although ground-based telescopes have revealed such objects, astronomers have never seen so many of them. The most visible knots all lie along the inner edge of the doomed star's ring, trillions of miles away from the star's nucleus. Although these gaseous knots appear small, they're actually huge. Each gaseous head is at least twice the size of our solar system; each tail stretches for 100 billion miles, about 1,000 times the distance between the Earth and the Sun. Astronomers theorize that the doomed star spews hot, lower-density gas from its surface, which collides with cooler, higher-density gas that had been ejected 10,000 years before. The crash fragments the smooth cloud surrounding the star into smaller, denser finger-like droplets, like dripping paint. This image was taken in August, 1994 with Hubble's Wide Field Planetary Camera 2. The red light depicts nitrogen emission ([NII] 6584A); green, hydrogen (H-alpha, 6563A); and blue, oxygen (5007A).
Monopoles and knots in skyrme theory.
Cho, Y M
2001-12-17
We show that the Skyrme theory is actually a theory of monopoles which allows a new type of soliton, the topological knot made of the monopole-antimonopole pair, which is different from the well-known skyrmion. Furthermore, we derive a generalized Skyrme action from the Yang-Mills action of QCD, which we propose to be an effective action of QCD in the infrared limit. We discuss the physical implications of our results. PMID:11736568
Magnetohydrodynamic solitons and radio knots in jets
NASA Technical Reports Server (NTRS)
Fiedler, R.
1986-01-01
Weakly nonlinear surface waves are examined in the context of the beam model for jetlike radio sources. By introducing a finite scale length, viz. the beam radius, geometrical dispersion can act to balance nonlinear wave growth and thereby produce solitons, localized wave packets of stable waveform. A method for obtaining a soliton equation from the MHD equations is presented and then applied to radio knots in jets.
Stretching Response of Knotted and Unknotted Polymer Chains
NASA Astrophysics Data System (ADS)
Caraglio, Michele; Micheletti, Cristian; Orlandini, Enzo
2015-10-01
Recent theoretical and experimental advances have clarified the major effects of knotting on the properties of stretched chains. Yet, how knotted chains respond to weak mechanical stretching and how this behavior differs from the unknotted case are still open questions and we address them here by profiling the complete stretching response of chains of hundreds of monomers and different topology. We find that the ratio of the knotted and unknotted chain extensions varies nonmonotonically with the applied force. This surprising feature is shown to be a signature of the crossover between the well-known high-force stretching regime and the previously uncharacterized low-force one. The observed differences of knotted and unknotted chain response increases with knot complexity and are sufficiently marked that they could be harnessed in single-molecule contexts to infer the presence and complexity of physical knots in micron-long biomolecules.
Allosteric initiation and regulation of catalysis with a molecular knot.
Marcos, Vanesa; Stephens, Alexander J; Jaramillo-Garcia, Javier; Nussbaumer, Alina L; Woltering, Steffen L; Valero, Alberto; Lemonnier, Jean-François; Vitorica-Yrezabal, Iñigo J; Leigh, David A
2016-06-24
Molecular knots occur in DNA, proteins, and other macromolecules. However, the benefits that can potentially arise from tying molecules in knots are, for the most part, unclear. Here, we report on a synthetic molecular pentafoil knot that allosterically initiates or regulates catalyzed chemical reactions by controlling the in situ generation of a carbocation formed through the knot-promoted cleavage of a carbon-halogen bond. The knot architecture is crucial to this function because it restricts the conformations that the molecular chain can adopt and prevents the formation of catalytically inactive species upon metal ion binding. Unknotted analogs are not catalytically active. Our results suggest that knotting molecules may be a useful strategy for reducing the degrees of freedom of flexible chains, enabling them to adopt what are otherwise thermodynamically inaccessible functional conformations. PMID:27339983
Knotting and unknotting of a protein in single molecule experiments.
Ziegler, Fabian; Lim, Nicole C H; Mandal, Soumit Sankar; Pelz, Benjamin; Ng, Wei-Ping; Schlierf, Michael; Jackson, Sophie E; Rief, Matthias
2016-07-01
Spontaneous folding of a polypeptide chain into a knotted structure remains one of the most puzzling and fascinating features of protein folding. The folding of knotted proteins is on the timescale of minutes and thus hard to reproduce with atomistic simulations that have been able to reproduce features of ultrafast folding in great detail. Furthermore, it is generally not possible to control the topology of the unfolded state. Single-molecule force spectroscopy is an ideal tool for overcoming this problem: by variation of pulling directions, we controlled the knotting topology of the unfolded state of the 52-knotted protein ubiquitin C-terminal hydrolase isoenzyme L1 (UCH-L1) and have therefore been able to quantify the influence of knotting on its folding rate. Here, we provide direct evidence that a threading event associated with formation of either a 31 or 52 knot, or a step closely associated with it, significantly slows down the folding of UCH-L1. The results of the optical tweezers experiments highlight the complex nature of the folding pathway, many additional intermediate structures being detected that cannot be resolved by intrinsic fluorescence. Mechanical stretching of knotted proteins is also of importance for understanding the possible implications of knots in proteins for cellular degradation. Compared with a simple 31 knot, we measure a significantly larger size for the 52 knot in the unfolded state that can be further tightened with higher forces. Our results highlight the potential difficulties in degrading a 52 knot compared with a 31 knot. PMID:27339135
A comparison of ultrasonic suture welding and traditional knot tying.
Richmond, J C
2001-01-01
The slippage of knots and the technical challenge of tying them securely are potential impediments to certain arthroscopic procedures. Ultrasonic energy delivered at 70 kHz can be used to weld No. 2 polypropylene suture. This method was compared with a traditional knot (surgeon's knot with four alternating half hitches) tied with an open technique to determine whether welding of sutures is comparable, in mechanical properties, to hand-tied knots. Both loops were fashioned around a 0.25-inch mandrel and then tested. The load to reach 3-mm elongation (point of likely biologic failure of a repair) was significantly greater for welded sutures than for knots. The elongation at ultimate failure was significantly less for welded sutures than for knots. The number of cycles to failure and the creep after initial displacement were similar for both welded and knotted suture loops. The ultimate load to failure was significantly greater for the knotted than for the welded suture. The welding of suture for the repair of musculoskeletal soft tissue presents an attractive alternative to traditional knot tying, particularly for arthroscopic applications. PMID:11394598
Escape of a knot from a DNA molecule in flow
NASA Astrophysics Data System (ADS)
Renner, Benjamin; Doyle, Patrick
2014-03-01
Macroscale knots are an everyday occurrence when trying to unravel an unorganized flexible string (e.g. an iPhone cord taken out of your pocket). In nature, knots are found in proteins and viral capsid DNA, and the properties imbued by their topologies are thought to have biological significance. Unlike their macroscale counterparts, thermal fluctuations greatly influence the dynamics of polymer knots. Here, we use Brownian Dynamics simulations to study knot diffusion along a linear polymer chain. The model is parameterized to dsDNA, a model polymer used in previous simulation and experimental studies of knot dynamics. We have used this model to study the process of knot escape and transport along a dsDNA strand extended by an elongational flow. For a range of knot topologies and flow strengths, we show scalings that result in collapse of the data onto a master curve. We show a topologically mediated mode of transport coincides with observed differences in rates of knot transport, and we provide a simple mechanistic explanation for its effect. We anticipate these results will build on the growing body of fundamental studies of knotted polymers and inform future experimental study. This work is supported by the Singapore-MIT Alliance for Research and Technology (SMART) and National Science Foundation (NSF) grant CBET-0852235.
Fractions of Particular Knots in Gaussian Random Polygons
NASA Astrophysics Data System (ADS)
Tsurusaki, Kyoichi; Deguchi, Tetsuo
1995-05-01
Fractions of knotted polygons in Gaussian random polygonare numerically studied. Three dimensional random polygons with N stepsare prepared by closed N-step Gaussian random walks. LetPK(N) denote the probability that an N-step Gaussian polygon has aknot type K. For prime knots (31, 41, 51, 52) andcomposite knots (31 #31, 31 #41, 31 #31 #31),PK(N)'s are evaluated in the range 30≤N≤2400. We confirm thata scaling formula gives nice fitting curves for the numerical dataplots of PK(N) versus N for the different knot types.
Xu, An An; Zhu, Jiang Fan; Su, Yuantao
2015-01-01
INTRODUCTION: Knot tying is difficult but important for laparo-endoscopic single-site surgery (LESS). There are several techniques for LESS knot-tying. However, objective assessment of these skills has not yet been established. The aim of this study was to assess three different knot-tying techniques in LESS using mechanical methods. MATERIALS AND METHODS: The subject tied 24 knots, eight knots with each of the three techniques in an inanimate box laparoscopic trainer while the movements of their instruments were evaluated using a LESS mechanical evaluation platform. The operations were assessed on the basis of the time, average load of the dominant hand. Then, forces caused the knots to rupture were measured using a material testing system and used to compare the knots's strength. RESULTS: The intracorporeal one-hand knot-tying technique presented significantly better time and average load scores than the extracorporeal knot-tying technique (P < 0.01), and the intracorporeal side winding technique was more time and average load consuming in comparison to other techniques during the performance of knot-tying (P < 0.01). The intracorporeal one-handed knot-tying knots can tolerate better distraction forces compared with the intracorporeal side winding knot-tying knots and the extracorporeal knot-tying knots (P < 0.05). CONCLUSIONS: The intracorporeal one-hand knot-tying technique and knots showed better results than the intracorporeal “side winding” technique and the extracorporeal knot-tying technique in terms of the time, average load taken and the force caused the knot to rupture. PMID:26622113
Optical knots and contact geometry II. From Ranada dyons to transverse and cosmetic knots
NASA Astrophysics Data System (ADS)
Kholodenko, Arkady L.
2016-08-01
Some time ago Ranada (1989) obtained new nontrivial solutions of the Maxwellian gauge fields without sources. These were reinterpreted in Kholodenko (2015) [10] (part I) as particle-like (monopoles, dyons, etc.). They were obtained by the method of Abelian reduction of the non-Abelian Yang-Mills functional. The developed method uses instanton-type calculations normally employed for the non-Abelian gauge fields. By invoking the electric-magnetic duality it then becomes possible to replace all known charges/masses by the particle-like solutions of the source-free Abelian gauge fields. To employ these results in high energy physics, it is essential to extend Ranada's results by carefully analyzing and classifying all dynamically generated knotted/linked structures in gauge fields, including those discovered by Ranada. This task is completed in this work. The study is facilitated by the recent progress made in solving the Moffatt conjecture. Its essence is stated as follows: in steady incompressible Euler-type fluids the streamlines could have knots/links of all types. By employing the correspondence between the ideal hydrodynamics and electrodynamics discussed in part I and by superimposing it with the already mentioned method of Abelian reduction, it is demonstrated that in the absence of boundaries only the iterated torus knots and links could be dynamically generated. Obtained results allow to develop further particle-knot/link correspondence studied in Kholodenko (2015) [13].
Knot security: how many throws does it really take?
Tidwell, John E; Kish, Vincent L; Samora, Julie B; Prud'homme, Joseph
2012-04-01
The purpose of this study was to determine the minimum number of throws needed for knot security for square knots using 5 common suture materials and 3 common sizes by in vitro single load to failure biomechanical testing. The hypothesis was that each suture combination studied would share a common minimum of at least 5 throws to guarantee security. Five suture materials (FiberWire [Arthrex, Inc, Naples, Florida], Monosof, Surgipro, Maxon, and Polysorb [Covidien, Mansfield, Massachusetts]) with varying suture sizes (#5, #2, 0, 2-0, and 4-0) were tied in vitro, varying the number of square knot throws (3, 4, 5, and 6). Twenty knots for each combination were statically loaded to failure in tension; whether the knot failed by fracture or slippage and the tensile strength at knot failure was determined. For the tested materials, at least 5 flat square throws should be used to confer knot security based on a binomial proportion score 95% confidence interval (CI) 0.84 to 1.0 or at least 4 throws for a 95% CI of 0.76 to 0.99. FiberWire requires 6 flat square throws per knot for security at either 95% CI level. Unless a surgeon has specific knowledge of experimental evidence that fewer throws are necessary for a specific application, the default should be a minimum of 4 throws, with 5 conferring additional security in most situations, and FiberWire requiring 6 throws. PMID:22495855
Structural recognition and nomenclature standardization in forensic knot analysis.
Chisnall, Robert Charles
2016-07-01
The analysis of knots during civil and criminal investigations is characterized by two fundamental challenges: the precise recognition of all structural nuances and the application of accurate, universally recognized terms. These challenges are exacerbated by inconsistencies, contradictions and regional terminology, which occur in common practice and in mainstream books as well as within forensic science. Some knots bear multiple or value-laden names, even misnomers, and some terms have manifold applications. This can lead to ambiguity and confusion. Additionally, many topological concepts and terms are applicable to practical knot-tying, despite the differences between real-world and theoretical knots, but the esoterica of topology are inaccessible to anyone unfamiliar with that branch of mathematics. To highlight these challenges some examples of knots encountered in case work are presented. Significantly, an overview of a few previously ignored issues is examined and several new concepts are introduced. An emphasis is placed on identifying structural variations, standardized nomenclature is outlined, and recommended terminology is derived from fields such as forensic science, chemistry, archaeology, topology and the textile industry. Greater precision in knot identifications, characterizations and descriptions can assist investigators in linking specific tying practises to potential suspects, analysing the manner in which knotted evidence was tied, and understanding how knots and ligatures perform in given scenarios. PMID:27320402
Root-knot nematode resistant rootstocks for grafted watermelon
Technology Transfer Automated Retrieval System (TEKTRAN)
Rootstock lines of wild watermelon (Citrullus lanatus var. citroides) with resistance to root-knot nematodes (RKN) were developed by our team at the U.S. Vegetable Laboratory. Rootstock lines RKVL 301, RKVL 316, and RKVL 318 (RKVL = Root Knot Vegetable Laboratory) were compared to wild tinda (Praec...
The Verbal Facilitation Effect in Learning to Tie Nautical Knots
ERIC Educational Resources Information Center
Huff, Markus; Schwan, Stephan
2012-01-01
Motor skills are often demonstrated with a combination of verbal information and video demonstration. In this study, participants learned to tie nautical knots with a video clip demonstrating the motor task preceded by a descriptive or a metaphorical, picture-like verbalization. In a control condition participants learned the knots with a video…
Ventriculoperitoneal Shunt Peritoneal Catheter Knot Formation
Ul-Haq, Anwar; Al-Otaibi, Faisal; Alshanafey, Saud; Sabbagh, Mohamed Diya; Al Shail, Essam
2013-01-01
The ventriculoperitoneal (VP) shunt is a common procedure in pediatric neurosurgery that carries a risk of complications at cranial and abdominal sites. We report on the case of a child with shunt infection and malfunction. The peritoneal catheter was tethered within the abdominal cavity, precluding its removal. Subsequently, laparoscopic exploration identified a knot at the distal end of the peritoneal catheter around the omentum. A new VP shunt was inserted after the infection was healed. This type of complication occurs rarely, so there are a limited number of case reports in the literature. This report is complemented by a literature review. PMID:24109528
Knot invariants as nondegenerate quantum geometries
Bruegmann, B.; Gambini, R.; Pullin, J. Instituto de Fisica, Facultad de Ciencias, Tristan Narvaja 1674, Montevideo Department of Physics, University of Utah, Salt Lake City, Utah 84112 )
1992-01-27
The loop-space representation based on Ashtekar's new variables has allowed for the first time the construction of quantum states of the gravitational field. However, all states known up to the present were associated with spacetime metrics that were everywhere degenerate. In this Letter we present a new exact solution of the constraint equations of quantum gravity that is the first quantum state of the gravitational field known to be associated with a not-everywhere-degenerate metric. The state is associated with the second coefficient of the Alexander-Conway polynomial of knot theory.
Influence of a knot on the strength of a polymer strand.
Saitta, A M; Soper, P D; Wasserman, E; Klein, M L
1999-05-01
Many experiments have been done to determine the relative strengths of different knots, and these show that the break in a knotted rope almost invariably occurs at the point just outside the 'entrance' to the knot. The influence of knots on the properties of polymers has become of great interest, in part because of their effect on mechanical properties. Knot theory applied to the topology of macromolecules indicates that the simple trefoil or 'overhand' knot is likely to be present in any long polymer strand. Fragments of DNA have been observed to contain such knots in experiments and computer simulations. Here we use ab initio computational methods to investigate the effect of a trefoil knot on the breaking strength of a polymer strand. We find that the knot weakens the strand significantly, and that, like a knotted rope, it breaks under tension at the entrance to the knot. PMID:10331387
Knot Solitons in Spinor Bose-Einstein Condensates
NASA Astrophysics Data System (ADS)
Hall, David; Ray, Michael; Tiurev, Konstantin; Ruokokoski, Emmi; Gheorghe, Andrei Horia; Möttönen, Mikko
2016-05-01
Knots are familiar entities that appear at a captivating nexus of art, technology, mathematics and science. Following a lengthy period of theoretical investigation and development, they have recently attracted great experimental interest in classical contexts ranging from knotted DNA and nanostructures to vortex knots in fluids. We demonstrate here the controlled creation and detection of knot solitons in the quantum-mechanical order parameter of a spinor Bose-Einstein condensate. Images of the superfluid reveal the circular shape of the soliton core and its associated linked rings. Our observations of the knot soliton establish an experimental foundation for future studies of their stability, dynamics and applications within quantum systems. Supported in part by NSF Grant PHY-1205822.
UNEXPECTED IONIZATION STRUCTURE IN ETA CARINAE'S ''WEIGELT KNOTS''
Remmen, Grant N.; Davidson, Kris; Mehner, Andrea
2013-08-10
The Weigelt knots, dense slow-moving ejecta near {eta} Carinae, are mysterious in structure as well as in origin. Using spatially dithered spectrograms obtained with the Hubble Space Telescope/Space Telescope Imaging Spectrograph (HST/STIS), we have partially resolved the ionization zones of one knot. Contrary to simple models, higher ionization levels occur on the outer side, i.e., farther from the star. They cannot represent a bow shock, and no satisfying explanation is yet available-though we sketch one qualitative possibility. STIS spectrograms provide far more reliable spatial measurements of the Weigelt knots than HST images do, and this technique can also be applied to the knots' proper motion problem. Our spatial measurement accuracy is about 10 mas, corresponding to a projected linear scale of the order of 30 AU, which is appreciably smaller than the size of each Weigelt knot.
Design principles for rapid folding of knotted DNA nanostructures.
Kočar, Vid; Schreck, John S; Čeru, Slavko; Gradišar, Helena; Bašić, Nino; Pisanski, Tomaž; Doye, Jonathan P K; Jerala, Roman
2016-01-01
Knots are some of the most remarkable topological features in nature. Self-assembly of knotted polymers without breaking or forming covalent bonds is challenging, as the chain needs to be threaded through previously formed loops in an exactly defined order. Here we describe principles to guide the folding of highly knotted single-chain DNA nanostructures as demonstrated on a nano-sized square pyramid. Folding of knots is encoded by the arrangement of modules of different stability based on derived topological and kinetic rules. Among DNA designs composed of the same modules and encoding the same topology, only the one with the folding pathway designed according to the 'free-end' rule folds efficiently into the target structure. Besides high folding yield on slow annealing, this design also folds rapidly on temperature quenching and dilution from chemical denaturant. This strategy could be used to design folding of other knotted programmable polymers such as RNA or proteins. PMID:26887681
Design principles for rapid folding of knotted DNA nanostructures
Kočar, Vid; Schreck, John S.; Čeru, Slavko; Gradišar, Helena; Bašić, Nino; Pisanski, Tomaž; Doye, Jonathan P. K.; Jerala, Roman
2016-01-01
Knots are some of the most remarkable topological features in nature. Self-assembly of knotted polymers without breaking or forming covalent bonds is challenging, as the chain needs to be threaded through previously formed loops in an exactly defined order. Here we describe principles to guide the folding of highly knotted single-chain DNA nanostructures as demonstrated on a nano-sized square pyramid. Folding of knots is encoded by the arrangement of modules of different stability based on derived topological and kinetic rules. Among DNA designs composed of the same modules and encoding the same topology, only the one with the folding pathway designed according to the ‘free-end' rule folds efficiently into the target structure. Besides high folding yield on slow annealing, this design also folds rapidly on temperature quenching and dilution from chemical denaturant. This strategy could be used to design folding of other knotted programmable polymers such as RNA or proteins. PMID:26887681
The genomes of root-knot nematodes.
Bird, David McK; Williamson, Valerie M; Abad, Pierre; McCarter, James; Danchin, Etienne G J; Castagnone-Sereno, Philippe; Opperman, Charles H
2009-01-01
Plant-parasitic nematodes are the most destructive group of plant pathogens worldwide and are extremely challenging to control. The recent completion of two root-knot nematode genomes opens the way for a comparative genomics approach to elucidate the success of these parasites. Sequencing revealed that Meloidogyne hapla, a diploid that reproduces by facultative, meiotic parthenogenesis, encodes approximately 14,200 genes in a compact, 54 Mpb genome. Indeed, this is the smallest metazoan genome completed to date. By contrast, the 86 Mbp Meloidogyne incognita genome encodes approximately 19,200 genes. This species reproduces by obligate mitotic parthenogenesis and exhibits a complex pattern of aneuploidy. The genome includes triplicated regions and contains allelic pairs with exceptionally high degrees of sequence divergence, presumably reflecting adaptations to the strictly asexual reproductive mode. Both root-knot nematode genomes have compacted gene families compared with the free-living nematode Caenorhabditis elegans, and both encode large suites of enzymes that uniquely target the host plant. Acquisition of these genes, apparently via horizontal gene transfer, and their subsequent expansion and diversification point to the evolutionary history of these parasites. It also suggests new routes to their control. PMID:19400640
On the groundstate energy spectrum of magnetic knots and links
NASA Astrophysics Data System (ADS)
Ricca, Renzo L.; Maggioni, Francesca
2014-05-01
By using analytical results for the constrained minimum energy of magnetic knots we determine the influence of internal twist on the minimum magnetic energy levels of knots and links, and by using ropelength data from the RIDGERUNNER tightening algorithm (Ashton et al 2011 Exp. Math. 20 57-90) we obtain the groundstate energy spectra of the first 250 prime knots and 130 prime links. The two spectra are found to follow an almost identical logarithmic law. By assuming that the number of knot types grows exponentially with the topological crossing number, we show that this generic behavior can be justified by a general relationship between ropelength and crossing number, which is in good agreement with former analytical estimates (Buck and Simon 1999 Topol. Appl. 91 245-57, Diao 2003 J. Knot Theory Ramifications 12 1-16). Moreover, by considering the ropelength averaged over a given knot family, we establish a new connection between the averaged ropelength and the topological crossing number of magnetic knots.
Controlling the Motion of Knotted Polymers through Nanopores
NASA Astrophysics Data System (ADS)
Narsimhan, Vivek; Renner, C. Benjamin; Doyle, Patrick
Nanopore sequencing is a technique where DNA moves through a pore and base-pair information is read along the chain as an electric signal. One hurdle facing this technique is that DNA passes too quickly through the pore, rendering the signal to be too noisy. In this talk, we discuss one strategy to control the speed by which polymers move through pores. By tying a knot on a polymer chain, we find that we can jam the polymer at the pore's entrance and halt translocation completely. This idea by itself may not seem useful, but by cycling the field on and off at the relaxation time scale of the knot, we can control the swelling dynamics of the knot at the pore's entrance, and hence ratchet the polymer through the pore. This talk focuses on two parts. First, we will discuss the dynamics of a knot jamming at the pore entrance and determine what sets the critical tension to halt translocation. We will determine how knot topology affects these results and discuss what regimes lead to large fluctuations in the translocation speed. We will then discuss the dynamics of a knot under a time-dependent, periodic force. Lastly, we develop a model to describe the knot's swelling dynamics during relaxation, and use this to explain some of the trends observed in our simulations. Now at Liquiglide.
Development of knotting during the collapse transition of polymers.
Mansfield, Marc L
2007-12-28
A dynamic Monte Carlo simulation of the collapse transition of polymer chains is presented. The chains are represented as self-avoiding walks on the simple cubic lattice with a nearest-neighbor contact potential to model the effect of solvent quality. The knot state of the chains is determined using the knot group procedure presented in the accompanying paper. The equilibrium knot spectrum and the equilibrium rms radius of gyration as functions of the chain length and the contact potential are reported. The collapse transition was studied following quenches from good-to poor-solvent conditions. Our results confirm the prediction that the newly formed globule is not yet at equilibrium, since it has not yet achieved its equilibrium knot spectrum. For our model system, the relaxation of the knot spectrum is about an order of magnitude slower than that of the radius of gyration. The collapse transition is also studied for a model in which both ends of the chain remain in good-solvent conditions. Over the time scale of these simulations, knot formation is frustrated in this inhomogeneous model, verifying that the mechanism of knotting is the tunneling of chain ends in and out of the globule. PMID:18163701
Multimedia article. The keys to the new laparoscopic world Thumbs up! knot and Tornado knot.
Uchida, K; Haruta, N; Okajima, M; Matsuda, M; Yamamoto, M
2005-06-01
Most laparoscopic surgeons feel some anxiety when performing intracorporeal knotting with conventional techniques [1, 2]. Two factors contribute to this anxiety. The first is the necessity of recognizing three dimensions on a two-dimensional monitor. The conventional intracorporeal knotting techniques make loops by twisting the thread with a second pair of forceps. This necessitates cooperative movement of both hands, with the added difficulties of depth perception. Regular touch confirmations reduce problems with depth perception. However, touch confirmation is more complicated in laparoscopic surgery than in laparotomy. The second problem is that tied loops can come loose and escape the instruments, especially with hard thread. This is not only stressful but also increases operation time. PMID:15868264
EJECTA KNOT FLICKERING, MASS ABLATION, AND FRAGMENTATION IN CASSIOPEIA A
Fesen, Robert A.; Zastrow, Jordan A.; Hammell, Molly C.; Shull, J. Michael; Silvia, Devin W.
2011-08-01
Ejecta knot flickering, ablation tails, and fragmentation are expected signatures associated with the gradual dissolution of high-velocity supernova (SN) ejecta caused by their passage through an inhomogeneous circumstellar medium or interstellar medium (ISM). Such phenomena mark the initial stages of the gradual merger of SN ejecta with and the enrichment of the surrounding ISM. Here we report on an investigation of this process through changes in the optical flux and morphology of several high-velocity ejecta knots located in the outskirts of the young core-collapse SN remnant Cassiopeia A using Hubble Space Telescope images. Examination of WFPC2 F675W and combined ACS F625W + F775W images taken between 1999 June and 2004 December of several dozen debris fragments in the remnant's northeast ejecta stream and along the remnant's eastern limb reveal substantial emission variations ('flickering') over timescales as short as nine months. Such widespread and rapid variability indicates knot scale lengths {approx_equal} 10{sup 15} cm and a highly inhomogeneous surrounding medium. We also identify a small percentage of ejecta knots located all around the remnant's outer periphery which show trailing emissions typically 0.''2-0.''7 in length aligned along the knot's direction of motion suggestive of knot ablation tails. We discuss the nature of these trailing emissions as they pertain to ablation cooling, knot disruption, and fragmentation, and draw comparisons to the emission 'strings' seen in {eta} Car. Finally, we identify several tight clusters of small ejecta knots which resemble models of shock-induced fragmentation of larger SN ejecta knots caused by a high-velocity interaction with a lower density ambient medium.
Pore translocation of polymer chains with physical knots
NASA Astrophysics Data System (ADS)
Suma, Antonio; Rosa, Angelo; Micheletti, Cristian
The driven traslocation of knotted chains through narrow pores has important implications for single-molecule manipulation contexts. Its complex phenomenology is, however, still largely unexplored, both as a function of knot complexity and the magnitude of the driving, translocating force. We accordingly report on a systematic theoretical and computational investigation of both aspects. In particular we consider the case of flexible chains accommodating a large repertoire of knots that are driven through pores too narrow to allow for their passage. We show that the observed rich translocation phenomenology can be rationalised in a transparent mechanical framework that can further be used for predictive purposes.
Ileosigmoid knotting in early pregnancy: A case report
Maunganidze, Aspect Jacob Vengani; Mungazi, Simbarashe Gift; Siamuchembu, Maphios; Mlotshwa, Makhosini
2016-01-01
Ileosigmoid knotting refers to the wrapping of the ileum around the base of the sigmoid colon, or vice versa thus forming a knot. It is a rare cause of intestinal obstruction, more so in pregnancy. We herein report a case of a primigravid woman who presented with an acute abdomen at 13weeks of gestation. The patient underwent emergency surgery. Laparotomy showed ileosigmoid knotting with gangrenous loops of both small bowel and sigmoid colon. The gangrenous bowel was resected. Primary anastomosis of small bowel and a Hartman’s procedure was performed. PMID:27082994
Two Adhesive Sites Can Enhance the Knotting Probability of DNA
2015-01-01
Self-entanglement, or knotting, is entropically favored in long polymers. Relatively short polymers such as proteins can knot as well, but in this case the entanglement is mainly driven by fine-tuned, sequence-specific interactions. The relation between the sequence of a long polymer and its topological state is here investigated by means of a coarse-grained model of DNA. We demonstrate that the introduction of two adhesive regions along the sequence of a self-avoiding chain substantially increases the probability of forming a knot. PMID:26136125
Particle on a Torus Knot: A Hamiltonian Analysis
NASA Astrophysics Data System (ADS)
Das, Praloy; Ghosh, Subir
2016-08-01
We have studied the dynamics and symmetries of a particle constrained to move in a torus knot. The Hamiltonian system turns out to be Second Class in Dirac's formulation and the Dirac brackets yield novel noncommutative structures. The equations of motion are obtained for a path in general where the knot is present in the particle orbit but it is not restricted to a particular torus. We also study the motion when it is restricted to a specific torus. The rotational symmetries are studied as well. We have also considered the behavior of small fluctuations of the particle motion about a fixed torus knot.
Knots in the cath lab, an embarrassing complication of radial angiography
Gupta, Prabha Nini; Praveen, G K; Ahmed, Sajan Z; Kumar, B Krishna; V S, Sajith
2013-01-01
Most case reports or series describe knots in the venous system such as knots of Swan-Ganz catheters, pacing wires or thermodilution catheters. Knots during radial angiography are relatively rare. Here we describe a simple method of unravelling a radial knot via the femoral route, together with a review of the literature on knots in the catherisation laboratory and the techniques to deal with them.
Knotted Strings and Leptonic Flavor Structure
NASA Astrophysics Data System (ADS)
Kephart, T. W.; Leser, P.; Päs, H.
2012-12-01
We propose a third idea for the explanation of the leptonic flavor structure in addition to the prominent approaches based on flavor symmetry and anarchy. Typical flavor patterns can be modeled by using mass spectra obtained from the discrete lengths spectrum of tight knots and links. We assume that a string theory model exists in which this idea can be incorporated via the Majorana mass structure of a type I seesaw model. It is shown by a scan over the parameter space that such a model is able to provide an excellent fit to current neutrino data and that it predicts a normal neutrino mass hierarchy as well as a small mixing angle θ13. Startlingly, such scenarios could be related to the dimensionality of spacetime via an anthropic argument.
Torus Knot Polynomials and Susy Wilson Loops
NASA Astrophysics Data System (ADS)
Giasemidis, Georgios; Tierz, Miguel
2014-12-01
We give, using an explicit expression obtained in (Jones V, Ann Math 126:335, 1987), a basic hypergeometric representation of the HOMFLY polynomial of ( n, m) torus knots, and present a number of equivalent expressions, all related by Heine's transformations. Using this result, the symmetry and the leading polynomial at large N are explicit. We show the latter to be the Wilson loop of 2d Yang-Mills theory on the plane. In addition, after taking one winding to infinity, it becomes the Wilson loop in the zero instanton sector of the 2d Yang-Mills theory, which is known to give averages of Wilson loops in = 4 SYM theory. We also give, using matrix models, an interpretation of the HOMFLY polynomial and the corresponding Jones-Rosso representation in terms of q-harmonic oscillators.
New knotted solutions of Maxwell's equations
NASA Astrophysics Data System (ADS)
Hoyos, Carlos; Sircar, Nilanjan; Sonnenschein, Jacob
2015-06-01
In this paper we have further developed the study of topologically non-trivial solutions of vacuum electrodynamics. We have discovered a novel method of generating such solutions by applying conformal transformations with complex parameters on known solutions expressed in terms of Bateman's variables. This has enabled us to obtain a wide class of solutions from the basic configuration, such as constant electromagnetic fields and plane-waves. We have introduced a covariant formulation of Bateman's construction and discussed the conserved charges associated with the conformal group as well as a set of four types of conserved helicities. We have also given a formulation in terms of quaternions. This led to a simple map between the electromagnetic knotted and linked solutions into flat connections of SU(2) gauge theory. We have computed the corresponding Chern-Simons charge in a class of solutions and the charge takes integer values.
Ejecta Knot Evolution in Cas A
NASA Astrophysics Data System (ADS)
Rutherford, John; Figueroa-Feliciano, E.; Dewey, D.; Trowbridge, S.; Bastien, F.; Sato, K.
2011-01-01
Supernova remnants are remarkable laboratories for studying, among other phenomena, explosive nucleosynthesis and plasma dynamics. Time-dependent signatures of such processes can further inform our understanding, and may be found in widely spaced epochs of observation from high spatial and spectral resolution instruments. We investigated the spectral evolution in the X-ray band of the bright ejecta knots in Cassiopeia A over the last decade. Both dispersed and non-dispersed spectra from the Chandra HETG and ACIS instruments were used for this study, helping to better constrain signs of evolution. We present our findings of how such physical properties as the temperature, elemental abundances, velocity, and non-equilibrium ionization age changed over ten years of the several hundred year old remnant's lifetime, along with a careful analysis of the confounding background contamination and model parameter correlations.
Linked and knotted chimera filaments in oscillatory systems
NASA Astrophysics Data System (ADS)
Lau, Hon Wai; Davidsen, Jörn
2016-07-01
While the existence of stable knotted and linked vortex lines has been established in many experimental and theoretical systems, their existence in oscillatory systems and systems with nonlocal coupling has remained elusive. Here, we present strong numerical evidence that stable knots and links such as trefoils and Hopf links do exist in simple, complex, and chaotic oscillatory systems if the coupling between the oscillators is neither too short ranged nor too long ranged. In this case, effective repulsive forces between vortex lines in knotted and linked structures stabilize curvature-driven shrinkage observed for single vortex rings. In contrast to real fluids and excitable media, the vortex lines correspond to scroll wave chimeras [synchronized scroll waves with spatially extended (tubelike) unsynchronized filaments], a prime example of spontaneous synchrony breaking in systems of identical oscillators. In the case of complex oscillatory systems, this leads to a topological superstructure combining knotted filaments and synchronization defect sheets.
Knots cascade detected by a monotonically decreasing sequence of values
NASA Astrophysics Data System (ADS)
Liu, Xin; Ricca, Renzo L.
2016-04-01
Due to reconnection or recombination of neighboring strands superfluid vortex knots and DNA plasmid torus knots and links are found to undergo an almost identical cascade process, that tend to reduce topological complexity by stepwise unlinking. Here, by using the HOMFLYPT polynomial recently introduced for fluid knots, we prove that under the assumption that topological complexity decreases by stepwise unlinking this cascade process follows a path detected by a unique, monotonically decreasing sequence of numerical values. This result holds true for any sequence of standardly embedded torus knots T(2, 2n + 1) and torus links T(2, 2n). By this result we demonstrate that the computation of this adapted HOMFLYPT polynomial provides a powerful tool to measure topological complexity of various physical systems.
Untangling the mechanics versus topology of overhand knots
NASA Astrophysics Data System (ADS)
Reis, Pedro; Jawed, Mohammad; Dieleman, Peter; Audoly, Basile
2015-03-01
We study the interplay between mechanics and topology of overhand knots in slender elastic rods. We perform precision desktop experiments of overhand knots with increasing values for the crossing number (our measure of topology) and characterize their mechanical response through tension-displacement tests. The tensile force required to tighten the knot is governed by an intricate balance between topology, bending, friction, and contact forces. Digital imaging is employed to characterize the configuration of the contact braid as a function of crossing number. A robust scaling law is found for the pulling force in terms of the geometric and topological parameters of the knot. A reduced theory is developed, which predictively rationalizes the process.
Knots cascade detected by a monotonically decreasing sequence of values.
Liu, Xin; Ricca, Renzo L
2016-01-01
Due to reconnection or recombination of neighboring strands superfluid vortex knots and DNA plasmid torus knots and links are found to undergo an almost identical cascade process, that tend to reduce topological complexity by stepwise unlinking. Here, by using the HOMFLYPT polynomial recently introduced for fluid knots, we prove that under the assumption that topological complexity decreases by stepwise unlinking this cascade process follows a path detected by a unique, monotonically decreasing sequence of numerical values. This result holds true for any sequence of standardly embedded torus knots T(2, 2n + 1) and torus links T(2, 2n). By this result we demonstrate that the computation of this adapted HOMFLYPT polynomial provides a powerful tool to measure topological complexity of various physical systems. PMID:27052386
Knots cascade detected by a monotonically decreasing sequence of values
Liu, Xin; Ricca, Renzo L.
2016-01-01
Due to reconnection or recombination of neighboring strands superfluid vortex knots and DNA plasmid torus knots and links are found to undergo an almost identical cascade process, that tend to reduce topological complexity by stepwise unlinking. Here, by using the HOMFLYPT polynomial recently introduced for fluid knots, we prove that under the assumption that topological complexity decreases by stepwise unlinking this cascade process follows a path detected by a unique, monotonically decreasing sequence of numerical values. This result holds true for any sequence of standardly embedded torus knots T(2, 2n + 1) and torus links T(2, 2n). By this result we demonstrate that the computation of this adapted HOMFLYPT polynomial provides a powerful tool to measure topological complexity of various physical systems. PMID:27052386
Linked and knotted chimera filaments in oscillatory systems.
Lau, Hon Wai; Davidsen, Jörn
2016-07-01
While the existence of stable knotted and linked vortex lines has been established in many experimental and theoretical systems, their existence in oscillatory systems and systems with nonlocal coupling has remained elusive. Here, we present strong numerical evidence that stable knots and links such as trefoils and Hopf links do exist in simple, complex, and chaotic oscillatory systems if the coupling between the oscillators is neither too short ranged nor too long ranged. In this case, effective repulsive forces between vortex lines in knotted and linked structures stabilize curvature-driven shrinkage observed for single vortex rings. In contrast to real fluids and excitable media, the vortex lines correspond to scroll wave chimeras [synchronized scroll waves with spatially extended (tubelike) unsynchronized filaments], a prime example of spontaneous synchrony breaking in systems of identical oscillators. In the case of complex oscillatory systems, this leads to a topological superstructure combining knotted filaments and synchronization defect sheets. PMID:27575065
The folding of knotted proteins: insights from lattice simulations.
Faísca, Patrícia F N; Travasso, Rui D M; Charters, Tiago; Nunes, Ana; Cieplak, Marek
2010-01-01
We carry out systematic Monte Carlo simulations of Gō lattice proteins to investigate and compare the folding processes of two model proteins whose native structures differ from each other due to the presence of a trefoil knot located near the terminus of one of the protein chains. We show that the folding time of the knotted fold is larger than that of the unknotted protein and that this difference in folding time is particularly striking in the temperature region below the optimal folding temperature. Both proteins display similar folding transition temperatures, which is indicative of similar thermal stabilities. By using the folding probability reaction coordinate as an estimator of folding progression we have found out that the formation of the knot is mainly a late folding event in our shallow knot system. PMID:20130340
The folding of knotted proteins: insights from lattice simulations
NASA Astrophysics Data System (ADS)
Faísca, Patrícia F. N.; Travasso, Rui D. M.; Charters, Tiago; Nunes, Ana; Cieplak, Marek
2010-03-01
We carry out systematic Monte Carlo simulations of Gō lattice proteins to investigate and compare the folding processes of two model proteins whose native structures differ from each other due to the presence of a trefoil knot located near the terminus of one of the protein chains. We show that the folding time of the knotted fold is larger than that of the unknotted protein and that this difference in folding time is particularly striking in the temperature region below the optimal folding temperature. Both proteins display similar folding transition temperatures, which is indicative of similar thermal stabilities. By using the folding probability reaction coordinate as an estimator of folding progression we have found out that the formation of the knot is mainly a late folding event in our shallow knot system.
Probe knots and Hopf insulators with ultracold atoms
NASA Astrophysics Data System (ADS)
Deng, Dong-Ling; Wang, Sheng-Tao; Sun, Kai; Duan, Lu-Ming
2015-05-01
Knots and links are fascinating and intricate topological objects that have played a prominent role in physical and life sciences. Their influence spans from DNA and molecular chemistry to vortices in superfluid helium, defects in liquid crystals and cosmic strings in the early universe. Here, we show that knotted structures also exist in a peculiar class of three dimensional topological insulators--the Hopf insulators. In particular, we demonstrate that the spin textures of Hopf insulators in momentum space are twisted in a nontrivial way, which implies various knot and link structures. We further illustrate that the knots and nontrivial spin textures can be probed via standard time-of-flight images in cold atoms as preimage contours of spin orientations in stereographic coordinates. The extracted Hopf invariants, knots, and links are validated to be robust to typical experimental imperfections. Our work establishes the existence of knotted structures in cold atoms and may have potential applications in spintronics and quantum information processings. We thank X.-J. Liu and G. Ortiz for helpful discussions. S.T.W., D.L.D., and L.M.D. are supported by the NBRPC 2011CBA00300, the IARPA MUSIQC program, the ARO and the AFOSR MURI program. K.S. acknowledges support from NSF under Grant No. PHY1402971.
Colored HOMFLY polynomials of knots presented as double fat diagrams
NASA Astrophysics Data System (ADS)
Mironov, A.; Morozov, A.; Morozov, An.; Ramadevi, P.; Singh, Vivek Kumar
2015-07-01
Many knots and links in S 3 can be drawn as gluing of three manifolds with one or more four-punctured S 2 boundaries. We call these knot diagrams as double fat graphs whose invariants involve only the knowledge of the fusion and the braiding matrices of four -strand braids. Incorporating the properties of four-point conformal blocks in WZNW models, we conjecture colored HOMFLY polynomials for these double fat graphs where the color can be rectangular or non-rectangular representation. With the recent work of Gu-Jockers, the fusion matrices for the non-rectangular [21] representation, the first which involves multiplicity is known. We verify our conjecture by comparing with the [21] colored HOMFLY of many knots, obtained as closure of three braids. The conjectured form is computationally very effective leading to writing [21]-colored HOMFLY polynomials for many pretzel type knots and non-pretzel type knots. In particular, we find class of pretzel mutants which are distinguished and another class of mutants which cannot be distinguished by [21] representation. The difference between the [21]-colored HOMFLY of two mutants seems to have a general form, with A-dependence completely defined by the old conjecture due to Morton and Cromwell. In particular, we check it for an entire multi-parametric family of mutant knots evaluated using evolution method.
Tensile strength of a surgeon’s or a square knot
Muffly, Tyler M.; Boyce, Jamie; Kieweg, Sarah L.; Bonham, Aaron J.
2014-01-01
Objective To test the integrity of surgeon’s knots and flat square knots using four different suture materials. Study Design Chromic catgut, polyglactin 910, silk, and polydioxanone sutures were tied in the two types of knot configurations. For all sutures, a 0-gauge United States Pharmacopeia suture was used. Knots were tied by a single investigator (JB). Suture was soaked in 0.9 % sodium chloride for 60 seconds and subsequently transferred to a tensiometer where the tails were cut to 3 mm length. We compared the knots, measuring knot strength using a tensiometer until the sutures broke or untied. Results A total of 119 knots were tied. We found no difference in mean tension at failure between a surgeon’s knot (79.7 Newtons) and a flat square knot (82.9 Newtons). Using a Chi-square test, we did not find a statistically significant difference in the likelihood of knots coming untied between surgeon’s knots (29%) and flat square knots (38%). Conclusions Under laboratory conditions, surgeon’s knots and flat square knots did not differ in tension at failure or likelihood of untying. PMID:20816357
Soliton stability in some knot soliton models
Adam, C.; Sanchez-Guillen, J.; Wereszczynski, A.
2007-02-15
We study the issue of stability of static solitonlike solutions in some nonlinear field theories which allow for knotted field configurations. Concretely, we investigate the Aratyn-Ferreira-Zimerman model [Phys. Lett. B 456, 162 (1999); Phys. Rev. Lett. 83, 1723 (1999)], based on a Lagrangian quartic in first derivatives with infinitely many conserved currents, for which infinitely many soliton solutions are known analytically. For this model we find that sectors with different (integer) topological charges (Hopf index) are not separated by an infinite energy barrier. Further, if variations which change the topological charge are allowed, then the static solutions are not even critical points of the energy functional. We also explain why soliton solutions can exist at all, in spite of these facts. In addition, we briefly discuss the Nicole model [J. Phys. G 4, 1363 (1978)], which is based on a sigma-model-type Lagrangian. For the Nicole model we find that different topological sectors are separated by an infinite energy barrier.
Evolutionary origin of inhibitor cystine knot peptides.
Zhu, Shunyi; Darbon, Herve; Dyason, Karin; Verdonck, Fons; Tytgat, Jan
2003-09-01
The inhibitor cystine knot (ICK) fold is an evolutionarily conserved structural motif shared by a large group of polypeptides with diverse sequences and bioactivities. Although found in different phyla (animal, plant, and fungus), ICK peptides appear to be most prominent in venoms of cone snail and spider. Recently, two scorpion toxins activating a calcium release channel have been found to adopt an ICK fold. We have isolated and identified both cDNA and genomic clones for this family of ICK peptides from the scorpion Opistophthalmus carinatus. The gene characterized by three well-delineated exons respectively coding for three structural and functional domains in the toxin precursors illustrates the correlation between exon and module as suggested by the "exon theory of genes." Based on the analysis of precursor organization and gene structure combined with the 3-D fold and functional data, our results highlight a common evolutionary origin for ICK peptides from animals. In contrast, ICK peptides from plant and fungus might be independently evolved from another ancestor. PMID:12958203
Knots and Gamma Classes in Open Topological String Theory
NASA Astrophysics Data System (ADS)
Mahowald, Matthew
This thesis explores some mathematical applications of string dualities in open topological string theory and presents some new techniques for studying and computing open Gromov-Witten invariants. First, we prove a mild generalization of the gamma class formula of [BCR13], and show that it applies in two novel examples: the quintic threefold Q with Lagrangian given by the real quintic QR Q, and for Lagrangians LK ? X = O P1 (--1, --1) obtained from the conormal bundles of (r, s) torus knots K ? S3 via the conifold transition. Disk enumeration on (Q, Q R ) was first considered in [PSW08], and disk enumeration for (X, LK) was studied in winding-1 in [DSV13]. The gamma class formula agrees with the results of [DSV13] and [PSW08], and we generalize the formula of [DSV13] to arbitrary winding. Next we study a relationship between mirror symmetry and knot contact homology described in [AENV14, AV12]. For knots K ? S 3 , large-N duality relates open Gromov-Witten theory on (X, L_K ) to SU (N) Chern-Simons theory on (S3, K). We use the conjecture of [AV12] to compute open Gromov-Witten invariants of (X, L K) through mirror symmetry in many examples, including several non-toric knots. We also find further evidence for this conjecture: for ( r, s) torus knots, we find a formula for the genus-0, 1-boundary-component, degree-d, winding-w open Gromov-Witten invariants of (X, LK ) using localization. This formula agrees with the results of the mirror symmetry calculation. Moreover, using this formula, we describe a method for obtaining the augmentation polynomial of a knot K from the open Gromov-Witten invariants of ( X, LK ). This method is shown to correctly recover the augmentation polynomial for the unknot and (3, 2) torus knot.
NASA Astrophysics Data System (ADS)
Amin, Susan; Khorshid, Ahmed; Zeng, Lili; Zimny, Philip; Reisner, Walter
Knots can form during DNA packaging in chromosome and obstruct mapping of DNA in nanochannels. Studies have focused on theoretical and numerical studies of knots, but an efficient and fully controlled means of knotting has not yet been explored. Here, we introduce a knot factory on chip based on pneumatic compression of single T4 DNA against a slit barrier in a nanochannel. The DNA are compressed to a well-defined fraction of their initial equilibrium extension. The pressure is then released and the DNA molecules relax back to their equilibrium extension; knots are present along the relaxed DNA, visualized as sharply localized regions of high intensity. Via repeated compression and relaxation, we can measure the probabilities of forming single and multiple knot states and the distribution of knot sizes as a function of fractional compression and waiting time in the compressed state. We show that the total probability of knot formation increases with greater compression and waiting time.These findings are well described via a knot formation free energy derived from scaling arguments, suggesting that the enhanced knotting probability at high compression arises from avoiding the free energy cost due to self-exclusion interactions that would arise from contour stored in the knot.
Equations on knot polynomials and 3d/5d duality
Mironov, A.; Morozov, A.
2012-09-24
We briefly review the current situation with various relations between knot/braid polynomials (Chern-Simons correlation functions), ordinary and extended, considered as functions of the representation and of the knot topology. These include linear skein relations, quadratic Plucker relations, as well as 'differential' and (quantum) A-polynomial structures. We pay a special attention to identity between the A-polynomial equations for knots and Baxter equations for quantum relativistic integrable systems, related through Seiberg-Witten theory to 5d super-Yang-Mills models and through the AGT relation to the q-Virasoro algebra. This identity is an important ingredient of emerging a 3d- 5d generalization of the AGT relation. The shape of the Baxter equation (including the values of coefficients) depend on the choice of the knot/braid. Thus, like the case of KP integrability, where (some, so far torus) knots parameterize particular points of the Universal Grassmannian, in this relation they parameterize particular points in the moduli space of many-body integrable systems of relativistic type.
Characterization of the red knot (Calidris canutus) mitochondrial control region.
Buehler, Deborah M; Baker, Allan J
2003-08-01
We sequenced the complete mitochondrial control regions of 11 red knots (Calidris canutus). The control region is 1168 bp in length and is flanked by tRNA glutamate (glu) and the gene ND6 at its 5' end and tRNA phenylalanine (phe) and the gene 12S on its 3' end. The sequence possesses conserved sequence blocks F, E, D, C, CSB-1, and the bird similarity box (BSB), as expected for a mitochondrial copy. Flanking tRNA regions show correct secondary structure, and a relative rate test indicated no significant difference between substitution rates in the sequence we obtained versus the known mitochondrial sequence of turnstones (Charadriiformes: Scolopacidae). These characteristics indicate that the sequence is mitochondrial in origin. To confirm this, we sequenced the control region of a single individual using both purified mitochondrial DNA and genomic DNA. The sequences were identical using both methods. The sequence and methods presented in this paper may now serve as a reference for future studies using knot and other avian control regions. Furthermore, the discovery of five variable sites in 11 knots towards the 3' end of the control region, and the variability of this region in contrast to the more conserved central domain in the alignment between knots and other Charadriiformes, highlights the importance of this area as a source of variation for future studies in knots and other birds. PMID:12897864
Topological zoo of free-standing knots in confined chiral nematic fluids.
Seč, David; Copar, Simon; Zumer, Slobodan
2014-01-01
Knotted fields are an emerging research topic relevant to different areas of physics where topology plays a crucial role. Recent realization of knotted nematic disclinations stabilized by colloidal particles raised a challenge of free-standing knots. Here we demonstrate the creation of free-standing knotted and linked disclination loops in the cholesteric ordering fields, which are confined to spherical droplets with homeotropic surface anchoring. Our approach, using free energy minimization and topological theory, leads to the stabilization of knots via the interplay of the geometric frustration and intrinsic chirality. Selected configurations of the lowest complexity are characterized by knot or link types, disclination lengths and self-linking numbers. When cholesteric pitch becomes short on the confinement scale, the knotted structures change to practically unperturbed cholesteric structures with disclinations expelled close to the surface. The drops with knots could be controlled by optical beams and may be used for photonic elements. PMID:24419153
Topological zoo of free-standing knots in confined chiral nematic fluids
NASA Astrophysics Data System (ADS)
Seč, David; Čopar, Simon; Žumer, Slobodan
2014-01-01
Knotted fields are an emerging research topic relevant to different areas of physics where topology plays a crucial role. Recent realization of knotted nematic disclinations stabilized by colloidal particles raised a challenge of free-standing knots. Here we demonstrate the creation of free-standing knotted and linked disclination loops in the cholesteric ordering fields, which are confined to spherical droplets with homeotropic surface anchoring. Our approach, using free energy minimization and topological theory, leads to the stabilization of knots via the interplay of the geometric frustration and intrinsic chirality. Selected configurations of the lowest complexity are characterized by knot or link types, disclination lengths and self-linking numbers. When cholesteric pitch becomes short on the confinement scale, the knotted structures change to practically unperturbed cholesteric structures with disclinations expelled close to the surface. The drops with knots could be controlled by optical beams and may be used for photonic elements.
Novel application of an established technique for removing a knotted ureteric stent.
Tempest, Heidi; Turney, Ben; Kumar, Sunil
2011-01-01
This report describes a case whereby a ureteric stent became knotted during removal and lodged within the upper ureter. The authors describe a novel minimally invasive technique to remove the knotted ureteric stent using the holmium laser. PMID:22701009
One-handed knot tying technique in single-incision laparoscopic surgery
Thanakumar, John; John, Pravin Hector
2011-01-01
In an open surgery, two-handed as well as one-handed knot tying is commonplace. Knot tying in laparoscopic surgery traditionally involves the use of two instruments (for fashioning an intracorporeal knot) or passing of a ligature around a tubular structure, exteriorising it, fashioning a knot, and sliding it down with a knot-pusher (external slip knot). With increasing interest in expanding applications of single-incision laparoscopic surgery (SILS), surgeons are faced with new challenges. In SILS it is not usually possible to utilise two instruments for knot tying as they lie almost parallel. We describe a novel one-handed knot tying technique devised specifically for use in SILS. PMID:21197256
One-handed knot tying technique in single-incision laparoscopic surgery.
Thanakumar, John; John, Pravin Hector
2011-01-01
In an open surgery, two-handed as well as one-handed knot tying is commonplace. Knot tying in laparoscopic surgery traditionally involves the use of two instruments (for fashioning an intracorporeal knot) or passing of a ligature around a tubular structure, exteriorising it, fashioning a knot, and sliding it down with a knot-pusher (external slip knot). With increasing interest in expanding applications of single-incision laparoscopic surgery (SILS), surgeons are faced with new challenges. In SILS it is not usually possible to utilise two instruments for knot tying as they lie almost parallel. We describe a novel one-handed knot tying technique devised specifically for use in SILS. PMID:21197256
Knots, Braids and Hedgehogs from the Eikonal Equation
NASA Astrophysics Data System (ADS)
Wereszczyński, A.
The complex eikonal equation in the three space dimensions is considered. We show that apart from the recently found torus knots, this equation can also generate other topological configurations with a nontrivial value of the π2(S2) index: braided open strings as well as hedgehogs. In particular, cylindric strings, i.e. string solutions located on a cylinder with a constant radius are found. Moreover, solutions describing strings lying on an arbitrary surface topologically equivalent to cylinder are presented. We discuss them in the context of the eikonal knots. The physical importance of the results originates in the fact that the eikonal knots have been recently used to approximate the Faddeev-Niemi hopfions.
Sequence Controlled Self-Knotting Colloidal Patchy Polymers
NASA Astrophysics Data System (ADS)
Coluzza, Ivan; van Oostrum, Peter D. J.; Capone, Barbara; Reimhult, Erik; Dellago, Christoph
2013-02-01
Knotted chains are a promising class of polymers with many applications for materials science and drug delivery. Here we introduce an experimentally realizable model for the design of chains with controllable topological properties. Recently, we have developed a systematic methodology to construct self-assembling chains of simple particles, with final structures fully controlled by the sequence of particles along the chain. The individual particles forming the chain are colloids decorated with mutually interacting patches, which can be manufactured in the laboratory with current technology. Our methodology is applied to the design of sequences folding into self-knotting chains, in which the end monomers are by construction always close together in space. The knotted structure can then be externally locked simply by controlling the interaction between the end monomers, paving the way to applications in the design and synthesis of active materials and novel carriers for drugs delivery.
Extraordinary line-emitting knots in the Crab Nebula
NASA Technical Reports Server (NTRS)
Macalpine, Gordon M.; Lawrence, Stephen S.; Brown, Beth A.; Uomoto, Alan; Woodgate, Bruce E.; Brown, Larry W.; Oliversen, Ronald J.; Lowenthal, James D.; Liu, Charles
1994-01-01
Extraordinary, semistellar, line-emitting knots are apparent in images of the Crab Nebula which were obtained with the Goddard Fabry-Perot imager at the Michigan-Dartmouth-MIT Observatory. The knots are most prominent for (O III) lambda 5007 emission through a 5.3 A (Full Width at Half Maximum (FWHM)) bandpass centered at 5015.3 A, with representative fluxes of roughly 10(exp -14) ergs/sq cm. They are aligned in arcs, seven to the north and four to the south, from the pulsar. The northern group appears to be in a bounded corridor through the filamentary structure. Measurements over a 2 year baseline yield proper motions of order 0.1 sec/yr, corresponding to transverse velocities of order 900 km/s for a distance of 1830 pc. The knots are characterized by remarkably strong (Ar III) emission, possibly indicating high argon abundances, high gas temperatures, or anomalous physical processes.
Ferromagnetic Switching of Knotted Vector Fields in Liquid Crystal Colloids.
Zhang, Qiaoxuan; Ackerman, Paul J; Liu, Qingkun; Smalyukh, Ivan I
2015-08-28
We experimentally realize polydomain and monodomain chiral ferromagnetic liquid crystal colloids that exhibit solitonic and knotted vector field configurations. Formed by dispersions of ferromagnetic nanoplatelets in chiral nematic liquid crystals, these colloidal ferromagnets exhibit spontaneous long-range alignment of magnetic dipole moments of individual platelets, giving rise to a continuum of the magnetization field M(r). Competing effects of surface confinement and chirality prompt spontaneous formation and enable the optical generation of localized twisted solitonic structures with double-twist tubes and torus knots of M(r), which exhibit a strong sensitivity to the direction of weak magnetic fields ∼1 mT. Numerical modeling, implemented through free energy minimization to arrive at a field-dependent three-dimensional M(r), shows a good agreement with experiments and provides insights into the torus knot topology of observed field configurations and the corresponding physical underpinnings. PMID:26371682
Classification of knotted tori in 2-metastable dimension
Cencelj, Matija; Repovs, Dusan; Skopenkov, Mihail B
2012-11-30
This paper is devoted to the classical Knotting Problem: for a given manifold N and number m describe the set of isotopy classes of embeddings N{yields}S{sup m}. We study the specific case of knotted tori, that is, the embeddings S{sup p} Multiplication-Sign S{sup q}{yields}S{sup m}. The classification of knotted tori up to isotopy in the metastable dimension range m {>=} p + 3/2q + 2, p{<=}q, was given by Haefliger, Zeeman and A. Skopenkov. We consider the dimensions below the metastable range and give an explicit criterion for the finiteness of this set of isotopy classes in the 2-metastable dimension. Bibliography: 35 titles.
Untangling Knots Via Reaction-Diffusion Dynamics of Vortex Strings.
Maucher, Fabian; Sutcliffe, Paul
2016-04-29
We introduce and illustrate a new approach to the unknotting problem via the dynamics of vortex strings in a nonlinear partial differential equation of reaction-diffusion type. To untangle a given knot, a Biot-Savart construction is used to initialize the knot as a vortex string in the FitzHugh-Nagumo equation. Remarkably, we find that the subsequent evolution preserves the topology of the knot and can untangle an unknot into a circle. Illustrative test case examples are presented, including the untangling of a hard unknot known as the culprit. Our approach to the unknotting problem has two novel features, in that it applies field theory rather than particle mechanics and uses reaction-diffusion dynamics in place of energy minimization. PMID:27176541
Untangling Knots Via Reaction-Diffusion Dynamics of Vortex Strings
NASA Astrophysics Data System (ADS)
Maucher, Fabian; Sutcliffe, Paul
2016-04-01
We introduce and illustrate a new approach to the unknotting problem via the dynamics of vortex strings in a nonlinear partial differential equation of reaction-diffusion type. To untangle a given knot, a Biot-Savart construction is used to initialize the knot as a vortex string in the FitzHugh-Nagumo equation. Remarkably, we find that the subsequent evolution preserves the topology of the knot and can untangle an unknot into a circle. Illustrative test case examples are presented, including the untangling of a hard unknot known as the culprit. Our approach to the unknotting problem has two novel features, in that it applies field theory rather than particle mechanics and uses reaction-diffusion dynamics in place of energy minimization.
Characterization of Root-Knot Nematode Resistance in Medicago truncatula
Dhandaydham, Murali; Charles, Lauren; Zhu, Hongyan; Starr, James L.; Huguet, Thierry; Cook, Douglas R.; Prosperi, Jean-Marie; Opperman, Charles
2008-01-01
Root knot (Meloidogyne spp.) and cyst (Heterodera and Globodera spp.) nematodes infect all important crop species, and the annual economic loss due to these pathogens exceeds $90 billion. We screened the worldwide accession collection with the root-knot nematodes Meloidogyne incognita, M. arenaria and M. hapla, soybean cyst nematode (SCN-Heterodera glycines), sugar beet cyst nematode (SBCN-Heterodera schachtii) and clover cyst nematode (CLCN-Heterodera trifolii), revealing resistant and susceptible accessions. In the over 100 accessions evaluated, we observed a range of responses to the root-knot nematode species, and a non-host response was observed for SCN and SBCN infection. However, variation was observed with respect to infection by CLCN. While many cultivars including Jemalong A17 were resistant to H. trifolii, cultivar Paraggio was highly susceptible. Identification of M. truncatula as a host for root-knot nematodes and H. trifolii and the differential host response to both RKN and CLCN provide the opportunity to genetically and molecularly characterize genes involved in plant-nematode interaction. Accession DZA045, obtained from an Algerian population, was resistant to all three root-knot nematode species and was used for further studies. The mechanism of resistance in DZA045 appears different from Mi-mediated root-knot nematode resistance in tomato. Temporal analysis of nematode infection showed that there is no difference in nematode penetration between the resistant and susceptible accessions, and no hypersensitive response was observed in the resistant accession even several days after infection. However, less than 5% of the nematode population completed the life cycle as females in the resistant accession. The remainder emigrated from the roots, developed as males, or died inside the roots as undeveloped larvae. Genetic analyses carried out by crossing DZA045 with a susceptible French accession, F83005, suggest that one gene controls resistance in DZA
A Comparative Study in Learning Curves of Two Different Intracorporeal Knot Tying Techniques
Thiyagarajan, Manuneethimaran; Ravindrakumar, Chandru
2016-01-01
Objectives. In our study we are aiming to analyse the learning curves in our surgical trainees by using two standard methods of intracorporeal knot tying. Material and Method. Two randomized groups of trainees are trained with two different intracorporeal knot tying techniques (loop and winding) by single surgeon for eight sessions. In each session participants were allowed to make as many numbers of knots in thirty minutes. The duration for each set of knots and the number of knots for each session were calculated. At the end each session, participants were asked about their frustration level, difficulty in making knot, and dexterity. Results. In winding method the number of knots tied was increasing significantly in each session with less frustration and less difficulty level. Discussion. The suturing and knotting skill improved in every session in both groups. But group B (winding method) trainees made significantly higher number of knots and they took less time for each set of knots than group A (loop method). Although both knotting methods are standard methods, the learning curve is better in loop method. Conclusion. The winding method of knotting is simpler and easier to perform, especially for the surgeons who have limited laparoscopic experience. PMID:27022482
The life of vortex knots and the flow of helicity
NASA Astrophysics Data System (ADS)
Irvine, William
What happens if you take a vortex loop - akin to a smoke ring in air - and tie it into a knot or a link? The knottiness (Helicity) of a fluid is a conserved quantity in many idealized situations (such as Euler fluids) offering the potential for fundamental insights into fluid flow. In real fluids, progress has been hindered by lack of accessible experimental systems. I will tell of how to make a vortex knot and link in water, in the wave function of a superfluid (on a computer) and of what happens thence, with an emphasis on universal aspects of the dynamics and the flow of helicity.
KNOTS AND RANDOM WALKS IN VIBRATED GRANULAR CHAINS
E. BEN-NAIM; ET AL
2000-08-01
The authors study experimentally statistical properties of the opening times of knots in vertically vibrated granular chains. Our measurements are in good qualitative and quantitative agreement with a theoretical model involving three random walks interacting via hard core exclusion in one spatial dimension. In particular, the knot survival probability follows a universal scaling function which is independent of the chain length, with a corresponding diffusive characteristic time scale. Both the large-exit-time and the small-exit-time tails of the distribution are suppressed exponentially, and the corresponding decay coefficients are in excellent agreement with the theoretical values.
Excitation of knotted vortex lines in matter waves
NASA Astrophysics Data System (ADS)
Maucher, F.; Gardiner, S. A.; Hughes, I. G.
2016-06-01
We study the creation of knotted ultracold matter waves in Bose–Einstein condensates via coherent two-photon Raman transitions with a Λ level configuration. The Raman transition allows an indirect transfer of atoms from the internal state | a> to the target state | b> via an excited state | e> , that would be otherwise dipole-forbidden. This setup enables us to imprint three-dimensional knotted vortex lines embedded in the probe field to the density in the target state. We elaborate on experimental feasibility as well as on subsequent dynamics of the matter wave.
Material Properties of Hagfish Skin, with Insights into Knotting Behaviors.
Clark, Andrew J; Crawford, Callie H; King, Brooke D; Demas, Andrew M; Uyeno, Theodore A
2016-06-01
Hagfishes (Myxinidae) often integrate whole-body knotting movements with jawless biting motions when reducing large marine carcasses to ingestible items. Adaptations for these behaviors include complex arrangements of axial muscles and flexible, elongate bodies without vertebrae. Between the axial muscles and the hagfish skin is a large, blood-filled subcutaneous sinus devoid of the intricate, myoseptal tendon networks characteristic of the taut skins of other fishes. We propose that the loose-fitting skin of the hagfish facilitates the formation and manipulation of body knots, even if it is of little functional significance to steady swimming. Hagfish skin is a relatively thick, anisotropic, multilayered composite material comprising a superficial, thin, and slimy epidermis, a middle dermal layer densely packed with fibrous tissues, and a deep subdermal layer comprised of adipose tissue. Hagfish skin is stiffer when pulled longitudinally than circumferentially. Stress-strain data from uniaxial tensile tests show that hagfish skins are comparable in tensile strength and stiffness to the taut skins of elongate fishes that do not engage in knotting behaviors (e.g., sea lamprey and penpoint gunnel). Sheath-core-constructed ropes, which serve as more accurate models for hagfish bodies, demonstrate that loose skin (extra sheathing) enhances flexibility of the body (rope). Along with a loose-fitting skin, the morphologies of hagfish skin parallel those of moray eels, which are also known for generating and manipulating figure-eight-style body knots when struggling with prey. PMID:27365419
WEEDS AS HOSTS FOR THE SOUTHERN ROOT-KNOT NEMATODE
Technology Transfer Automated Retrieval System (TEKTRAN)
The southern root-knot nematode, Meloidogyne incognita, can reproduce on many different plants, including many weeds, but the amount of reproduction that occurs on weeds is not well documented. This study was conducted to document the relative host status of weeds common in Georgia. Seeds of cotton,...
Utilization of biological control for managing root-knot nematodes
Technology Transfer Automated Retrieval System (TEKTRAN)
Our research goal is to enhance and conserve introduced and naturally occurring antagonists of root-knot nematodes (Meloidogyne spp.) to improve biological control. Towards that end, we have evaluated the effect of crop production practices such as rotation, nematicide application, and cover crops,...
Knot invariants and the thermodynamics of lattice gas automata
Meyer, D.A.
1992-01-01
The goal of this project is to build on the understanding of the connections between knot invariants, exactly solvable statistical mechanics models and discrete dynamical systems that we have gained in earlier work, toward an answer to the question of how early and robust thermodynamic behavior appears in lattice gas automata.
Untangling Some Knots in K-8 Writing Instruction.
ERIC Educational Resources Information Center
Peterson, Shelley, Ed.
This book brings together the perspectives of teachers, administrators, consultants, and researchers on teaching writing to create a bridge between theory and practice. The book's 11 chapters are organized into three sections that tackle some persistent knots of writing instruction and assessment. Under Section I-Students' and Teachers' Learning…
The New Polynomial Invariants of Knots and Links.
ERIC Educational Resources Information Center
Lickorish, W. B. R.; Millett, K. C.
1988-01-01
Knot theory has been inspirational to algebraic and geometric topology. The principal problem has been to ascertain whether two links are equivalent. New methods have been discovered which are effective and simple. Considered are background information; the oriented polynomial; the Jones polynomial; the semioriented polynomial; and calculations,…
The multivariable Alexander polynomial and modern knot theory
Saleur, H. . Dept. of Physics)
1992-06-01
This paper is a summary of several recent works (by the author and collaborators) that study the Conway-Alexander link invariant in the light of quantum groups and topological quantum field theories. Their purpose is to understand connections between modern knot theory and more classical topological concepts.
Coaxial rings and H2 knots in Hubble 12
NASA Astrophysics Data System (ADS)
Hsia, Chih-Hao; Kwok, Sun; Chau, Wayne; Zhang, Yong
2016-07-01
Hubble 12 (Hb 12) is a young planetary nebula (PN) exhibiting nested shells. We present new near-infrared narrow-band imaging observations of Hb 12 using the Canada-France- Hawaii Telescope (CFHT). A number of co-axial rings aligned with the bipolar lobes and two pairs of separate H2 knots with different orientations are detected.
Factorization of colored knot polynomials at roots of unity
NASA Astrophysics Data System (ADS)
Kononov, Ya.; Morozov, A.
2015-07-01
HOMFLY polynomials are the Wilson-loop averages in Chern-Simons theory and depend on four variables: the closed line (knot) in 3d space-time, representation R of the gauge group SU (N) and exponentiated coupling constant q. From analysis of a big variety of different knots we conclude that at q, which is a 2m-th root of unity, q2m = 1, HOMFLY polynomials in symmetric representations [ r ] satisfy recursion identity: Hr+m =Hr ṡHm for any A =qN, which is a generalization of the property Hr = H1r for special polynomials at m = 1. We conjecture a further generalization to arbitrary representation R, which, however, is checked only for torus knots. Next, Kashaev polynomial, which arises from HR at q2 = e 2 πi / | R |, turns equal to the special polynomial with A substituted by A| R |, provided R is a single-hook representations (including arbitrary symmetric) - what provides a q - A dual to the similar property of Alexander polynomial. All this implies non-trivial relations for the coefficients of the differential expansions, which are believed to provide reasonable coordinates in the space of knots - existence of such universal relations means that these variables are still not unconstrained.
Wall-crossing invariants: from quantum mechanics to knots
Galakhov, D. E-mail: galakhov@physics.rutgers.edu; Mironov, A. Morozov, A.
2015-03-15
We offer a pedestrian-level review of the wall-crossing invariants. The story begins from the scattering theory in quantum mechanics where the spectrum reshuffling can be related to permutations of S-matrices. In nontrivial situations, starting from spin chains and matrix models, the S-matrices are operatorvalued and their algebra is described in terms of R- and mixing (Racah) U-matrices. Then the Kontsevich-Soibelman (KS) invariants are nothing but the standard knot invariants made out of these data within the Reshetikhin-Turaev-Witten approach. The R and Racah matrices acquire a relatively universal form in the semiclassical limit, where the basic reshufflings with the change of moduli are those of the Stokes line. Natural from this standpoint are matrices provided by the modular transformations of conformal blocks (with the usual identification R = T and U = S), and in the simplest case of the first degenerate field (2, 1), when the conformal blocks satisfy a second-order Shrödinger-like equation, the invariants coincide with the Jones (N = 2) invariants of the associated knots. Another possibility to construct knot invariants is to realize the cluster coordinates associated with reshufflings of the Stokes lines immediately in terms of check-operators acting on solutions of the Knizhnik-Zamolodchikov equations. Then the R-matrices are realized as products of successive mutations in the cluster algebra and are manifestly described in terms of quantum dilogarithms, ultimately leading to the Hikami construction of knot invariants.
Resistance of Watermelon Germplasm to Root-Knot Nematodes
Technology Transfer Automated Retrieval System (TEKTRAN)
Root-knot nematodes (Meloidogyne spp.) seriously impact yields of watermelon throughout the southern U.S. Pre-plant fumigation of soil with methyl bromide is the primary method for controlling these pests in watermelon. Although host resistance would be one of the most economical and environmental...
Wall-crossing invariants: from quantum mechanics to knots
NASA Astrophysics Data System (ADS)
Galakhov, D.; Mironov, A.; Morozov, A.
2015-03-01
We offer a pedestrian-level review of the wall-crossing invariants. The story begins from the scattering theory in quantum mechanics where the spectrum reshuffling can be related to permutations of S-matrices. In nontrivial situations, starting from spin chains and matrix models, the S-matrices are operatorvalued and their algebra is described in terms of R- and mixing (Racah) U-matrices. Then the Kontsevich-Soibelman (KS) invariants are nothing but the standard knot invariants made out of these data within the Reshetikhin-Turaev-Witten approach. The R and Racah matrices acquire a relatively universal form in the semiclassical limit, where the basic reshufflings with the change of moduli are those of the Stokes line. Natural from this standpoint are matrices provided by the modular transformations of conformal blocks (with the usual identification R = T and U = S), and in the simplest case of the first degenerate field (2, 1), when the conformal blocks satisfy a second-order Shrödinger-like equation, the invariants coincide with the Jones ( N = 2) invariants of the associated knots. Another possibility to construct knot invariants is to realize the cluster coordinates associated with reshufflings of the Stokes lines immediately in terms of check-operators acting on solutions of the Knizhnik-Zamolodchikov equations. Then the R-matrices are realized as products of successive mutations in the cluster algebra and are manifestly described in terms of quantum dilogarithms, ultimately leading to the Hikami construction of knot invariants.
Homochiral and meso figure eight knots and a Solomon link.
Ponnuswamy, Nandhini; Cougnon, Fabien B L; Pantoş, G Dan; Sanders, Jeremy K M
2014-06-11
A homochiral naphthalenediimide-based building block forms in water a disulfide library of macrocycles containing topological isomers. We attempted to identify each of these isomers, and explored the mechanisms leading to their formation. The two most abundant species of the library were assigned as a topologically chiral Solomon link (60% of the library, as measured by high-performance liquid chromatography (HPLC)) and a topologically achiral figure eight knot (18% by HPLC), competing products with formally different geometries but remarkably similar 4-fold symmetries. In contrast, a racemic mixture of building blocks gives the near-quantitative formation of another new and more stable structure, assigned as a meso figure eight knot. Taken together, these results seem to uncover a correlation between the point chirality of the building block used and the topological chirality of the major structure formed. These and the earlier discovery of a trefoil knot also suggest that the number of rigid components in the building block may translate into corresponding knot symmetry and could set the basis of a new strategy for constructing complex topologies. PMID:24831779
Minimum lattice length and ropelength of 2-bridge knots and links
NASA Astrophysics Data System (ADS)
Huh, Youngsik; Hong, Kyungpyo; Kim, Hyoungjun; No, Sungjong; Oh, Seungsang
2014-11-01
Knots are commonly found in molecular chains such as DNA and proteins, and they have been considered to be useful models for structural analysis of these molecules. One interested quantity is the minimum number of monomers necessary to realize a molecular knot. The minimum lattice length Len(K) of a knot K indicates the minimum length necessary to construct K in the cubic lattice. Another important quantity in physical knot theory is the ropelength which is one of the knot energies measuring the complexity of knot conformation. The minimum ropelength Rop(K) is the minimum length of an ideally flexible rope necessary to tie a given knot K. Much effort has been invested in the research project for finding upper bounds on both quantities in terms of the minimum crossing number c(K) of the knot. It is known that Len(K) and Rop(K) lie between O(c(K)^{3/4}) and O(c(K)[ln (c(K))]5), but unknown yet whether any family of knots has superlinear growth. In this paper, we focus on 2-bridge knots and links. Linear growth upper bounds on the minimum lattice length and minimum ropelength for nontrivial 2-bridge knots or links are presented as Len(K) ⩽ 8c(K) + 2 and Rop(K) ⩽ 11.39c(K) + 12.37.
Technology Transfer Automated Retrieval System (TEKTRAN)
Nematodes are a worldwide problem in agriculture, with losses estimated to $100 billion per year in the US. Damage caused by root-knot nematodes (Meloidogyne spp.) (RKN) disrupts the flow of water and nutrients to the plant and increases the plant’s vulnerability to other pathogens. While studies ...
The life of a vortex knot (in experiment)
NASA Astrophysics Data System (ADS)
Kleckner, Dustin; Scheeler, Martin; Proment, Davide; Irvine, William T. M.
2013-11-01
In recent experiments on linked and knotted vortices in classical fluids, we have found that they undergo a spontaneous change in topology: they untie themselves through a series of local reconnections. This outcome is at odds with the notion that fluid helicity (knottedness) should be conserved, as it should be for a dissipation-less fluid. Remarkably similar behavior is found for simulations of superfluid knots using the Gross-Pitaevskii equation. We will discuss our search for the missing helicity and the possibility of a universal driving mechanism for reconnections in topological vortices. This work was supported by the National Science Foundation Materials Research and Engineering Centers (MRSEC) Program at the University of Chicago (DMR-0820054) and the Packard Foundation through a Packard fellowship.
Unexpected connections between Burnside groups and knot theory.
Dabkowski, Mieczyslaw K; Przytycki, Józef H
2004-12-14
In classical knot theory and the theory of quantum invariants substantial effort was directed toward the search for unknotting moves on links. We solve, in this article, several classical problems concerning unknotting moves. Our approach uses a concept, Burnside groups of links, that establishes an unexpected relationship between knot theory and group theory. Our method has the potential to be used in computational biology in the analysis of DNA via tangle embedding theory, as developed by D. W. Sumners [Sumners, D. W., ed. (1992) New Scientific Applications of Geometry and Topology (Am Math. Soc., Washington, DC) and Ernst, C. & Sumners, D. W. (1999) Math. Proc. Cambridge Philos. Soc. 126, 23-36]. PMID:15576510
Self-Organizing Knotted Magnetic Structures in Plasma.
Smiet, C B; Candelaresi, S; Thompson, A; Swearngin, J; Dalhuisen, J W; Bouwmeester, D
2015-08-28
We perform full-magnetohydrodynamics simulations on various initially helical configurations and show that they reconfigure into a state where the magnetic field lines span nested toroidal surfaces. This relaxed configuration is not a Taylor state, as is often assumed for relaxing plasma, but a state where the Lorentz force is balanced by the hydrostatic pressure, which is lowest on the central ring of the nested tori. Furthermore, the structure is characterized by a spatially slowly varying rotational transform, which leads to the formation of a few magnetic islands at rational surfaces. We then obtain analytic expressions that approximate the global structure of the quasistable linked and knotted plasma configurations that emerge, using maps from S^{3} to S^{2} of which the Hopf fibration is a special case. The knotted plasma configurations have a highly localized magnetic energy density and retain their structure on time scales much longer than the Alfvénic time scale. PMID:26371659
Knots as a Topological Order Parameter for Semiflexible Polymers
NASA Astrophysics Data System (ADS)
Marenz, Martin; Janke, Wolfhard
2016-03-01
Using a combination of the multicanonical Monte Carlo algorithm and the replica-exchange method, we investigate the influence of bending stiffness on the conformational phases of a bead-stick homopolymer model and present the pseudophase diagram for the complete range of semiflexible polymers, from flexible to stiff. Although it is a simple model, we observe a rich variety of conformational phases, reminiscent of conformations observed for synthetic polymers or biopolymers. Depending on the bending stiffness, the model exhibits different pseudophases like bent, hairpin, or toroidal. In particular, we find thermodynamically stable knots and unusual transitions into these knotted phases with a clear phase coexistence, but almost constant mean total energy, and hence almost no latent heat.
Knots as a Topological Order Parameter for Semiflexible Polymers.
Marenz, Martin; Janke, Wolfhard
2016-03-25
Using a combination of the multicanonical Monte Carlo algorithm and the replica-exchange method, we investigate the influence of bending stiffness on the conformational phases of a bead-stick homopolymer model and present the pseudophase diagram for the complete range of semiflexible polymers, from flexible to stiff. Although it is a simple model, we observe a rich variety of conformational phases, reminiscent of conformations observed for synthetic polymers or biopolymers. Depending on the bending stiffness, the model exhibits different pseudophases like bent, hairpin, or toroidal. In particular, we find thermodynamically stable knots and unusual transitions into these knotted phases with a clear phase coexistence, but almost constant mean total energy, and hence almost no latent heat. PMID:27058105
Shepherd model for knot-limited polymer ejection from a capsid.
Antal, Tibor; Krapivsky, P L; Redner, S
2009-12-01
We construct a tractable model to describe the rate at which a knotted polymer is ejected from a spherical capsid via a small pore. Knots are too large to fit through the pore and must reptate to the end of the polymer for ejection to occur. The reptation of knots is described by symmetric exclusion on the line, with the internal capsid pressure represented by an additional biased particle that drives knots to the end of the chain. We compute the exact ejection speed for a finite number of knots L and find that it scales as 1/L. We establish a mapping to the solvable zero-range process. We also construct a continuum theory for many knots that matches the exact discrete theory for large L. PMID:19703473
In-vitro comparison of 3 knotting techniques for lateral fabellotibial suture stabilization
Dycus, David L.; Wardlaw, Jennifer L.; Rowe, Dennis; Elder, Steve
2013-01-01
This study evaluated the biomechanical characteristics of a single self-locking knot (sSLK) and a double self-locking knot (dSLK) compared with the square knot (SQ) for stabilization of cranial cruciate ligament rupture. Each knot underwent monotonic tensile and cyclical loading. Starting tension, elongation, stiffness, and load to failure were all evaluated. A value of P < 0.05 was considered significant. Starting tension, overall stiffness, and load to failure were all significantly greater in both the sSLK and dSLK compared with the SQ. There was no difference in elongation among the knots. There were no significant differences in starting tension, elongation, stiffness, and load to failure between the sSLK and the dSLK. The self-locking knots were stronger and stiffer than the SQ; there is no biomechanical advantage in using the dSLK compared with the sSLK. PMID:24082161
Probability of DNA knotting and the effective diameter of the DNA double helix.
Rybenkov, V V; Cozzarelli, N R; Vologodskii, A V
1993-01-01
During the random cyclization of long polymer chains, knots of different types are formed. We investigated experimentally the distribution of knot types produced by random cyclization of phage P4 DNA via its long cohesive ends. The simplest knots (trefoils) predominated, but more complex knots were also detected. The fraction of knots greatly diminished with decreasing solution Na+ concentration. By comparing these experimental results with computer simulations of knotting probability, we calculated the effective diameter of the DNA double helix. This important excluded-volume parameter is a measure of the electrostatic repulsion between segments of DNA molecules. The calculated effective DNA diameter is a sensitive function of electrolyte concentration and is several times larger than the geometric diameter in solutions of low monovalent cation concentration. Images Fig. 1 PMID:8506378
"Security loop" tie: a new technique to overcome loosening of surgical knots.
Alzacko, Saadallah Mohammad; Majid, Omer Waleed
2007-11-01
Sutures require knots so as to ensure optimal tissue closure strength. Loosening of surgical knots during or after tying can lead to an ineffective suture and compromise the final result. Loosening is affected mainly by the type of suture material and nature of surgical field. In palatal surgery, tying secure knots is a major consideration and may present a technical challenge. In this article, and after a review of the literature, we present a new modification of the usual knot-tying technique to maximize knot security and prevent knot loosening after the first throw is done. This technique was found to be effective, simple, fast, easy to learn, and saves time and material. PMID:17964468
Insecticidal plant cyclotides and related cystine knot toxins.
Gruber, Christian W; Cemazar, Masa; Anderson, Marilyn A; Craik, David J
2007-03-15
Cyclotides are small disulphide-rich peptides found in plants from the violet (Violaceae), coffee (Rubiaceae) and cucurbit (Cucurbitaceae) families. They have the distinguishing structural features of a macrocyclic peptide backbone and a cystine knot made up of six conserved cysteine residues, which makes cyclotides exceptionally stable. Individual plants express a suite of cyclotides in a wide range of tissue types, including leaves, flowers, stems and roots and it is thought that their natural function in plants is as defence agents. This proposal is supported by their high expression levels in plants and their toxic and growth retardant activity in feeding trials against Helicoverpa spp. insect pests. This review describes the structures and activities of cyclotides with specific reference to their insecticidal activity and compares them with structurally similar cystine knot proteins from peas (Pisum sativum) and an amaranthus crop plant (Amaranthus hypocondriancus). More broadly, cystine knot proteins are common in a wide range of organisms from fungi to mammals, and it appears that this interesting structural motif has evolved independently in different organisms as a stable protein framework that has a variety of biological functions. PMID:17224167
High energy mechanism from the knot of OJ 287
NASA Astrophysics Data System (ADS)
Kushwaha, Pankaj; Sahayanathan, Sunder; Singh, K. P.
The detection of gamma-ray flare from the BL Lac object, OJ 287 during October 2009 is associated with the ejection of a superluminal radio knot as suggested by discrete cross-correlation analysis of gamma-ray and 1 mm radio light curve. We study plausible mechanisms responsible for the high energy emission from this knot. We reproduce the quasi-simultaneous broadband spectral energy distribution from the knot considering synchrotron and inverse Compton emission from a broken power-law particle distribution. Explanation of X-ray and gamma-ray by either synchrotron-self Compton (SSC) or external Compton (EC) alone cannot reproduce the broadband spectrum and/or require unphysical set of parameters. Hence we model the high energy emission as an outcome of both SSC and EC models. The temperature of external photon field inferred from this model suggests that the gamma-ray emission must be resulting from the inverse Compton scattering of infra-red photon from the warm region surrounding the super massive black hole in OJ 287.
Folding analysis of the most complex Stevedore's protein knot.
Wang, Iren; Chen, Szu-Yu; Hsu, Shang-Te Danny
2016-01-01
DehI is a homodimeric haloacid dehalogenase from Pseudomonas putida that contains the most complex 61 Stevedore's protein knot within its folding topology. To examine how DehI attains such an intricate knotted topology we combined far-UV circular dichroism (CD), intrinsic fluorescence spectroscopy and small angle X-ray scattering (SAXS) to investigate its folding mechanism. Equilibrium unfolding of DehI by chemical denaturation indicated the presence of two highly populated folding intermediates, I and I'. While the two intermediates vary in secondary structure contents and tertiary packing according to CD and intrinsic fluorescence, respectively, their overall dimension and compactness are similar according to SAXS. Three single-tryptophan variants (W34, W53, and W196) were generated to probe non-cooperative unfolding events localized around the three fluorophores. Kinetic fluorescence measurements indicated that the transition from the intermediate I' to the unfolded state is rate limiting. Our multiparametric folding analyses suggest that DehI unfolds through a linear folding pathway with two distinct folding intermediates by initial hydrophobic collapse followed by nucleation condensation, and that knotting precedes the formation of secondary structures. PMID:27527519
Elastic knots of Space-Time may improve QED, QCD
NASA Astrophysics Data System (ADS)
Kriske, Richard
2016-03-01
This author had previously suggested that the time dimension of Electric fields and Magnetic fields are different. This matter was apparently settled with the Special Theory, in which each Observer, has his own Dimension of Time, that is ``elastic'' with one Dimension of Space. The independence of E and M, when they are not varying with time, leads one wonder if they are the same time. For a moving Observer, the two fields are joined through Faraday and Ampere's law. Particle Physics has made the simple Special Relativity interpretation murky. A photon does not simply become either an Electric field or a Magnetic field when viewed in its ''rest frame''. Because of this all kinds of extra sub theories are used, such as the Photon is quantized, and is massless in its rest frame, and always moves at the velocity of light. As for the Photon of the magnetic, or just the electric field, it is ``off the mass shell''. Perhaps a better theory is that the elasticity of time and the fact the ``Two'' observers show up in the theory, is that there has to be two dimensions of time, tied in a knot, in order for a field to become a Particle. The knot tying in EM is simple, when the E field varies it produces M, and vice-versa. For massive particles the knots are more complicated, more dimensions.
Endopathogenic lifestyle of Pseudomonas savastanoi pv. savastanoi in olive knots
Rodríguez‐Moreno, Luis; Jiménez, Antonio J.; Ramos, Cayo
2009-01-01
Summary The endophytic phase of Pseudomonas savastanoi pv. savastanoi in olive stems and the structural and ultrastructural histogenesis of olive knots have been studied. Construction of a stable plasmid vector expressing the green fluorescent protein, in combination with the use of in vitro olive plants, allowed real‐time monitoring of P. savastanoi pv. savastanoi infection. The infection process was also examined by bright field and epifluorescence microscopy as well as by scanning and transmission electron microscopy. Hypertrophy of the stem tissue was concomitant with the formation of bacterial aggregates, microcolonies and multilayer biofilms, over the cell surfaces and the interior of plasmolysed cells facing the air‐tissue interface of internal opened fissures, and was followed by invasion of the outer layers of the hypertrophied tissue. Pathogenic invasion of the internal lumen of newly formed xylem vessels, which were connected with the stem vascular system, was also observed in late stages of infection. Ultrastructural analysis of knot sections showed the release of outer membrane vesicles from the pathogen surface, a phenomenon not described before for bacterial phytopathogens during host infection. This is the first real‐time monitoring of P. savastanoi disease development and the first illustrated description of the ultrastructure of P. savastanoi‐induced knots. PMID:21255279
Fine-structure infrared lines from the Cassiopeia A knots
NASA Astrophysics Data System (ADS)
Docenko, D.; Sunyaev, R. A.
2010-01-01
Aims: Archival observations of infrared fine-structure lines of the young Galactic supernova remnant Cassiopeia A allow us to test existing models and determine the physical parameters of various regions of the fast-moving knots, which are metal-dominated clouds of material ejected by the supernova explosion. Methods: The fluxes of far-infrared [O i] and [O iii] lines are extracted from previously unpublished archival ISO data. The archival Spitzer data are used to determine the fluxes of the O, Ne, Si, S, Ar, and Fe ion fine-structure lines originating in the fast-moving knots. The ratios of these line fluxes are used as plasma diagnostics. We also determine the infrared line flux ratios with respect to the optical [O iii] 5007 Å line in the knots with previously measured reddening. Additionally, we analyze several optical and near-infrared observations of the fast-moving knots to obtain clearer insight into the post-shock photoionized region structure. Results: We show that the infrared oxygen line flux predictions of all existing theoretical models are correct only to within a factor of a several. Comparison of the model predictions shows that to reproduce the observations it is essential to include the effects of the electron conductivity and dust. Detailed analysis of the diagnostic line flux ratios of various ions allows us to qualitatively confirm the general model of fast-moving knot emission and determine observationally for the first time the physical conditions in the photoionized region after the shock. We infer from the [O iii] line flux ratios that the pre-shock cloud densities are higher than assumed in existing theoretical models and most probably correspond to several hundred particles per cm3. We also determine the Cas A luminosity in the infrared continuum and lines. We show that accounting for the charge exchange processes in the post-shock photoionized region allows us to reproduce most of the relevant spectral line ratios even in the frame of
Kauffman knot polynomials in classical abelian Chern-Simons field theory
Liu Xin
2010-12-15
Kauffman knot polynomial invariants are discovered in classical abelian Chern-Simons field theory. A topological invariant t{sup I(L)} is constructed for a link L, where I is the abelian Chern-Simons action and t a formal constant. For oriented knotted vortex lines, t{sup I} satisfies the skein relations of the Kauffman R-polynomial; for un-oriented knotted lines, t{sup I} satisfies the skein relations of the Kauffman bracket polynomial. As an example the bracket polynomials of trefoil knots are computed, and the Jones polynomial is constructed from the bracket polynomial.
NASA Astrophysics Data System (ADS)
Tubiana, Luca
2014-05-01
Using Monte Carlo simulations and advanced knot localization methods, we analyze the length and distribution of prime components in composite knots tied on freely jointed rings. For increasing contour length, we observe the progressive factorization of composite knots into separated prime components. However, we observe that a complete factorization, equivalent to the "decorated ring" picture, is not obtained even for rings of contour lengths N ≃3N0, about tens of times the most probable length of the prime knots tied on the rings. The decorated ring hypothesis has been used in the literature to justify the factorization of composite knot probabilities into the knotting probabilities of their prime components. Following our results, we suggest that such a hypothesis may not be necessary to explain the factorization of the knotting probabilities, at least when polymers excluding volume is not relevant. We rationalize the behavior of the system through a simple one-dimensional model in which prime knots are replaced by slip links randomly placed on a circle, with the only constraint being that the length of the loops has the same distribution as that of the length of the corresponding prime knots.
Rojas, David; Cristancho, Sayra; Rueda, Claudia; Grierson, Lawrence; Monclou, Alex; Dubrowski, Adam
2011-01-01
The construct validity of a surgical bench-top simulator with built-in computer acquired assessments was examined. It features two parallel elastic tubes instrumented with flexion sensors that simulate the walls of a wound. Participants from three groups (9 novices, 7 intermediates, 9 experts) performed 10 two-handed, double square knots. The peak tensions at the initiation of the first knot, the completion of the first knot and the completion of the second knot, as well as measures of movement economy indicated technical performance. Product quality was indicated by knot stability defined as the amount of slippage of the knot under the tension. There were significant differences between experts and novices for peak tension on first knot (p=.03), movement economy (p=.02), and knot stability (p=.002). The results support the construct validity of these objective measures. PMID:21335849
High finesse microfiber knot resonators made from double-ended tapered fibers.
Xiao, Limin; Birks, T A
2011-04-01
We fabricated optical microfiber knot resonators from thin tapered fibers (diameter down to 1 μm) linked to untapered fiber at both ends. We demonstrated a finesse of about 100, over twice as high as previously reported for microfiber resonators. Low-loss encapsulation of microfiber knot resonators in hydrophobic silica aerogel was also investigated. PMID:21478995
Ethnomathematics in Arfak (West Papua-Indonesia): Hidden Mathematics on Knot of Rumah Kaki Seribu
ERIC Educational Resources Information Center
Haryanto; Nusantara, Toto; Subanji; Abadyo
2016-01-01
This ethnomathematics article focused on the models of knot which is used in the frame of "Rumah Kaki Seribu." The knot model itself was studied mathematically. The results of this study revealed the way Arfak tribal communities think mathematically. This article uses exploration, documentation, interview, experiments and literature…
Cotton Cultivar Response to Root-Knot Nematodes in Two Tillage Regimes, 2008
Technology Transfer Automated Retrieval System (TEKTRAN)
Six cotton cultivars were evaluated for yield response to the root-knot nematode in a naturally infested field at E. V. Smith Research and Extension Center, near Shorter, Alabama. The field had a long history of root-knot nematode infestation, and the soil type was classified as a sandy loam. Plots ...
PA-560, A Southern Root-knot Nematode Resistant, Yellow-fruited, Habanero-type Pepper
Technology Transfer Automated Retrieval System (TEKTRAN)
The USDA has developed a yellow-fruited, Habanero-type pepper (Capsicum chinense Jacq.) that is highly resistant to root-knot nematodes. The new breeding line, designated PA-560, is the product of a backcross/pedigree breeding procedure to incorporate a root-knot nematode resistance gene from the S...
Response of Watermelon Germplasm to Southern Root-Knot Nematode in Field Tests
Technology Transfer Automated Retrieval System (TEKTRAN)
Southern root-knot nematode (Meloidogyne incognita) is a serious pest of cultivated watermelon (Citrullus lanatus var. lanatus) in southern regions of the US. While there is no known resistance to southern root-knot nematode in watermelon cultivars to date, wild watermelon relatives (C. lanatus var...
Percutaneous Retrieval of a Pulmonary Artery Catheter Knot in Pacing Electrodes
Valenzuela-Garcia, Luis Felipe Almendro-Delia, Manuel; Gonzalez-Valdayo, Miguel; Munoz-Campos, Juan; Dorado-Garcia, Jose C.; Gomez-Rosa, Francisco; Vazquez-Garcia, Rafael; Calderon-Leal, Jose M.
2007-09-15
To illustrate a successful approach to resolving a pulmonary artery catheter knot in the pacing leads of a cardiac resynchronization device. When planning invasive monitoring for patients having right chamber electrodes, fluoroscopic-guided catheter insertion and extraction is advisable. In the event of coiling or knotting, an interventional radiologist should be contacted as soon as possible to avoid serious complications.
Translocation dynamics of knotted polymers under a constant or periodic external field.
Narsimhan, Vivek; Renner, C Benjamin; Doyle, Patrick S
2016-06-14
We perform Brownian dynamics simulations to examine how knots alter the dynamics of polymers moving through nanopores under an external field. In the first part of this paper, we study the situation when the field is constant. Here, knots halt translocation above a critical force with jamming occurring at smaller forces for twist topologies compared to non-twist topologies. Slightly below the jamming transition, the polymer's transit times exhibit large fluctuations. This phenomenon is an example of the knot's molecular individualism since the conformation of the knot plays a large role in the chain's subsequent dynamics. In the second part of the paper, we study the motion of the chain when one cycles the field on and off. If the off time is comparable to the knot's relaxation time, one can adjust the swelling of the knot at the pore and hence design strategies to ratchet the polymer in a controllable fashion. We examine how the off time affects the ratcheting dynamics. We also examine how this strategy alters the fluctuations in the polymer's transit time. We find that cycling the force field can reduce fluctuations near the knot's jamming transition, but can enhance the fluctuations at very high forces since knots get trapped in metastable states during the relaxation process. The latter effect appears to be more prominent for non-torus topologies than torus ones. We conclude by discussing the feasibility of this approach to control polymer motion in biotechnology applications such as sequencing. PMID:27181288
Macromolecular knot in good and poor solvents: a Monte Carlo simulation.
Sun, Huan-Quan; Zhang, Lu; Liao, Qi
2010-09-30
The probability and dimension of the simple macromolecular knots over a wide range of temperatures corresponding from good to poor solvents are investigated by Monte Carlo simulation. Macromolecular knots are modeled as rings of self-avoiding walks on a simple cubic lattice with the nearest neighbor attractions. We found that there is a minimum probability for the unknotted ring at a certain temperature. The size dependence of trivial, trefoil, and figure-eight knots on chain lengths and temperatures is presented. The simulation results for the size dependence on the knot's complication in different solvents are in good qualitative agreement with prediction of the scaling model proposed by Grosberg et al. The critical exponent for long chain is independent of the knot types based on the simulation results, although the mean square radius of gyration is influenced significantly by the knot types for a shorter length macromolecular ring. We calculated the ratio of the topological invariant p of trefoil knot and figure-eight knot and found that the ratio is approaching to 1.3 with the increasing of the chain length. PMID:20825151
Expression of almond KNOTTED1 homologue (PdKn1) anticipates adventitious shoot initiation
Technology Transfer Automated Retrieval System (TEKTRAN)
Background and Aims: The transcription factor encoded by the gene Knotted1 is a nuclear homeodomain protein, regulating meristematic cells at the shoot apical meristem. It has been proven that Knotted1 (KN1) has a role in the switch from an indeterminate to determinate cell fate and as such this gen...
Technology Transfer Automated Retrieval System (TEKTRAN)
The peanut root-knot nematode [Meloidogyne arenaria (Neal) Chitwood race 1] and tomato spotted wilt virus Tospovirus (TSWV) are economically significant pathogens of peanut in the southeastern United States. Peanut cultivars are available that have resistance to either the peanut root-knot nematode...
Design and performance of the APPLE-Knot undulator
Ji, Fuhao; Chang, Rui; Zhou, Qiaogen; Zhang, Wei; Ye, Mao; Sasaki, Shigemi; Qiao, Shan
2015-01-01
Along with the development of accelerator technology, synchrotron emittance has continuously decreased. This results in increased brightness, but also causes a heavy heat load on beamline optics. Recently, optical surfaces with 0.1 nm micro-roughness and 0.05 µrad slope error (r.m.s.) have become commercially available and surface distortions due to heat load have become a key factor in determining beamline performance, and heat load has become a serious problem at modern synchrotron radiation facilities. Here, APPLE-Knot undulators which can generate photons with arbitrary polarization, with low on-axis heat load, are reported. PMID:26134793
Writhe-induced knotting in a lattice polymer
NASA Astrophysics Data System (ADS)
Dagrosa, E.; Owczarek, A. L.; Prellberg, T.
2015-02-01
We consider a simple lattice model of a topological phase transition in open polymers. To be precise, we study a model of self-avoiding walks on the simple cubic lattice tethered to a surface and weighted by an appropriately defined writhe. We also consider the effect of pulling the untethered end of the polymer from the surface. Regardless of the force we find a first-order phase transition which we argue is a consequence of increased knotting in the lattice polymer, rather than due to other effects such as the formation of plectonemes.
Racah matrices and hidden integrability in evolution of knots
NASA Astrophysics Data System (ADS)
Mironov, A.; Morozov, A.; Morozov, An.; Sleptsov, A.
2016-09-01
We construct a general procedure to extract the exclusive Racah matrices S and S bar from the inclusive 3-strand mixing matrices by the evolution method and apply it to the first simple representations R = [ 1 ], [2], [3] and [ 2 , 2 ]. The matrices S and S bar relate respectively the maps (R ⊗ R) ⊗ R bar ⟶ R with R ⊗ (R ⊗ R bar) ⟶ R and (R ⊗ R bar) ⊗ R ⟶ R with R ⊗ (R bar ⊗ R) ⟶ R. They are building blocks for the colored HOMFLY polynomials of arbitrary arborescent (double fat) knots. Remarkably, the calculation realizes an unexpected integrability property underlying the evolution matrices.
Unraveling the Helix Nebula: Its Structure and Knots
NASA Astrophysics Data System (ADS)
O'Dell, C. R.; McCullough, Peter R.; Meixner, Margaret
2004-11-01
Through Hubble Space Telescope (HST) imaging of the inner part of the main ring of the Helix Nebula, together with CTIO 4 m images of the fainter outer parts, we have a view of unprecedented quality of the nearest bright planetary nebula. These images have allowed us to determine that the main ring of the nebula is composed of an inner disk of about 499" diameter (0.52 pc) surrounded by an outer ring (in reality a torus) of 742" diameter (0.77 pc) whose plane is highly inclined to the plane of the disk. This outer ring is surrounded by an outermost ring of 1500" (1.76 pc) diameter, which is flattened on the side colliding with the ambient interstellar medium. The inner disk has an extended distribution of low-density gas along its rotational axis of symmetry, and the disk is optically thick to ionizing radiation, as is the outer ring. Published radial velocities of the knots provide support for the two-component structure of the main ring of the nebula and for the idea that the knots found there are expanding along with the nebular material from which they recently originated. These velocities indicate a spatial expansion velocity of the inner disk of 40 and 32 km s-1 for the outer ring, which yields expansion ages of 6560 and 12,100 yr, respectively. The outermost ring may be partially ionized through scattered recombination continuum from the inner parts of the nebula, but shocks certainly are occurring in it. This outermost ring probably represents a third period of mass loss by the central star. There is one compact, outer object that is unexplained, showing shock structures indicating a different orientation of the gas flow from that of the nebula. There is a change in the morphology of the knots as a function of the distance from the local ionization front. This supports a scenario in which the knots are formed in or near the ionization front and are then sculpted by the stellar radiation from the central star as the ionization front advances beyond them
Papazian, Nazareth J; Chahine, Fadl; Atiyeh, Bishara; Deeba, Samer; Zgheib, Elias; Abu-Sittah, Ghassan
2015-09-01
Tying sutures is an integral aspect of any surgery and reliable instruments are essential for hassle-free procedures including craniofacial surgeries. Knot pushers have been widely known for their application in various laparoscopic, arthroscopic, and anal surgeries. The literature reveals numerous articles pertaining to knot pushers, as well as improvements on existing designs. Nevertheless, no application of knot pushers in the surgical repair of cleft palates has been described. We describe a new knot pusher "Papazian Pusher" (PP) finely designed for application in oral surgeries in general and repair of cleft palates in particular. The instrument was used satisfactorily in repair of cleft palate surgeries and no complications were encountered. The PP was found, overall, to be easy to use, and helps in performing faster, stronger, smooth, and secure knots. PMID:26355980
Untangling the mechanics and topology in the frictional response of long overhand elastic knots.
Jawed, M K; Dieleman, P; Audoly, B; Reis, P M
2015-09-11
We combine experiments and theory to study the mechanics of overhand knots in slender elastic rods under tension. The equilibrium shape of the knot is governed by an interplay between topology, friction, and bending. We use precision model experiments to quantify the dependence of the mechanical response of the knot as a function of the geometry of the self-contacting region, and for different topologies as measured by their crossing number. An analytical model based on the nonlinear theory of thin elastic rods is then developed to describe how the physical and topological parameters of the knot set the tensile force required for equilibrium. Excellent agreement is found between theory and experiments for overhand knots over a wide range of crossing numbers. PMID:26406861
Complexity of knotting in chaotic 3D eigenfunctions
NASA Astrophysics Data System (ADS)
Taylor, Alexander; Dennis, Mark
Quantised vortices occur generically in disordered 3D complex scalar fields, forming a geometrically complex and statistically random large scale tangle even in systems with very different origins of complexity such as turbulent superfluids, optical volume speckle, the quantum eigenfunctions of chaotic 3D cavities, and liquid crystal phases. Although all such systems are random and fractal on large scales, it has previously been established that topological measures such as the probability of vortices knotting or linking with one another are sensitive to the local physics. We use the wave chaos as a universal model system with just one physical lengthscale, the wavelength, beyond which its vortices are Brownian. To access finite-volume realisations of wavefields, vortices are traced numerically in three different random degenerate eigenfunction systems, each approximating the random isotropic limit but with different constraints and symmetries that significantly impact topological statistics even at high energies. By a simple mode counting argument, we observe that the probability of a generic eigenfunction containing a knotted vortex line reaches 50% by around its 1000-3000th mode.
High Proteolytic Resistance of Spider-Derived Inhibitor Cystine Knots
Kikuchi, Kyoko; Sugiura, Mika; Kimura, Tadashi
2015-01-01
Proteolytic stability in gastrointestinal tract and blood plasma is the major obstacle for oral peptide drug development. Inhibitor cystine knots (ICKs) are linear cystine knot peptides which have multifunctional properties and could become promising drug scaffolds. ProTx-I, ProTx-II, GTx1-15, and GsMTx-4 were spider-derived ICKs and incubated with pepsin, trypsin, chymotrypsin, and elastase in physiological conditions to find that all tested peptides were resistant to pepsin, and ProTx-II, GsMTx-4, and GTx1-15 showed resistance to all tested proteases. Also, no ProTx-II degradation was observed in rat blood plasma for 24 hours in vitro and ProTx-II concentration in circulation decreased to half in 40 min, indicating absolute stability in plasma and fast clearance from the system. So far, linear peptides are generally thought to be unsuitable in vivo, but all tested ICKs were not degraded by pepsin and stomach could be selected for the alternative site of drug absorption for fast onset of the drug action. Since spider ICKs are selective inhibitors of various ion channels which are related to the pathology of many diseases, engineered ICKs will make a novel class of peptide medicines which can treat variety of bothering symptoms. PMID:26843868
Warmerdam, E. G.; Toorop, R. J.; Abrahams, A. C.; Berger, P.
2011-01-01
Urethral catheterization is a common procedure with a relatively low complication rate. Knotting of an indwelling urethral catheter is a very rare complication, and there are only a few case reports on knotted catheters, most of them concerning children. We report an especially rare case where a urethral catheter formed a knot around a double-J ureteral stent after a kidney transplantation. We will discuss the various risk factors for knotting of a catheter and the methods to untangle a knot. PMID:24533194
Armstrong, Lucas C; Chong, Alexander; Livermore, Ryan W; Prohaska, Daniel J; Doyon, Amanda N; Wooley, Paul H
2015-04-01
We conducted a study to evaluate biomechanical performance during destructive testing of several different suture materials in various arthroscopic knot configurations under both in vitro and in situ conditions. Surgeons of different levels of experience tied the knots. Three different arthroscopic knots (static surgeon's, Weston, Tennessee slider) with 3 reverse half-hitches on alternating posts were tested using Fiberwire, ForceFiber, Orthocord, and Ultrabraid suture materials under both in vitro and in situ (blood plasma at 37°C) conditions. Three surgeons of different experience levels tied the knots on a post 30 mm in circumference. A single load-to-failure test was performed. There were no significant in vitro-in situ differences for Ultrabraid in the different knot configurations or with the different experience levels. Surgeon B (intermediate experience) showed no significant differences between test conditions for any knot configuration or suture material. With Tennessee slider knots, surgeon C (least experience) showed significantly lower clinical failure load under both test conditions and had a higher percentage of complete knot slippage. Surgeon B had no knot slippage with use of Fiberwire. Both the aqueous environment and the surgeon's familiarity with certain knots have an effect on knot security. PMID:25844588
Li, Wenfei; Terakawa, Tsuyoshi; Wang, Wei; Takada, Shoji
2012-10-30
While fast folding of small proteins has been relatively well characterized by experiments and theories, much less is known for slow folding of larger proteins, for which recent experiments suggested quite complex and rich folding behaviors. Here, we address how the energy landscape theory can be applied to these slow folding reactions. Combining the perfect-funnel approximation with a multiscale method, we first extended our previous atomic-interaction based coarse grained (AICG) model to take into account local flexibility of protein molecules. Using this model, we then investigated the energy landscapes and folding routes of two proteins with complex topologies: a multidomain protein adenylate kinase (AKE) and a knotted protein 2ouf-knot. In the AKE folding, consistent with experimental results, the kinetic free energy surface showed several substates between the fully unfolded and native states. We characterized the structural features of these substates and transitions among them, finding temperature-dependent multiroute folding. For protein 2ouf-knot, we found that the improved atomic-interaction based coarse-grained model can spontaneously tie a knot and fold the protein with a probability up to 96%. The computed folding rate of the knotted protein was much slower than that of its unknotted counterpart, in agreement with experimental findings. Similar to the AKE case, the 2ouf-knot folding exhibited several substates and transitions among them. Interestingly, we found a dead-end substate that lacks the knot, thus suggesting backtracking mechanisms. PMID:22753508
Effects of horseshoe crab harvest in delaware bay on red knots: Are harvest restrictions working?
Niles, L.J.; Bart, J.; Sitters, H.P.; Dey, A.D.; Clark, K.E.; Atkinson, P.W.; Baker, A.J.; Bennett, K.A.; Kalasz, K.S.; Clark, N.A.; Clark, J.; Gillings, S.; Gates, A.S.; Gonzalez, P.M.; Hernandez, D.E.; Minton, C.D.T.; Morrison, R.I.G.; Porter, R.R.; Ross, R.K.; Veitch, C.R.
2009-01-01
Each May, red knots (Calidris canutus rufa) congregate in Delaware Bay during their northward migration to feed on horseshoe crab eggs (Limulus polyphemus) and refuel for breeding in the Arctic. During the 1990s, the Delaware Bay harvest of horseshoe crabs for bait increased 10-fold, leading to a more than 90% decline in the availability of their eggs for knots. The proportion of knots achieving weights of more than 180 grams by 26-28 May, their main departure period, dropped from 0.6-0.8 to 0.14-0.4 over 1997-2007. During the same period, the red knot population stopping in Delaware Bay declined by more than 75%, in part because the annual survival rate of adult knots wintering in Tierra del Fuego declined. Despite restrictions, the 2007 horseshoe crab harvest was still greater than the 1990 harvest, and no recovery of knots was detectable. We propose an adaptive management strategy with recovery goals and annual monitoring that, if adopted, will both allow red knot and horseshoe crab populations to recover and permit a sustainable harvest of horseshoe crabs.
Slipknotting upon native-like loop formation in a trefoil knot protein.
Noel, Jeffrey K; Sułkowska, Joanna I; Onuchic, José N
2010-08-31
Protein knots and slipknots, mostly regarded as intriguing oddities, are gradually being recognized as significant structural motifs. Recent experimental results show that knotting, starting from a fully extended polypeptide, has not yet been observed. Understanding the nucleation process of folding knots is thus a natural challenge for both experimental and theoretical investigation. In this study, we employ energy landscape theory and molecular dynamics to elucidate the entire folding mechanism. The full free energy landscape of a knotted protein is mapped using an all-atom structure-based protein model. Results show that, due to the topological constraint, the protein folds through a three-state mechanism that contains (i) a precise nucleation site that creates a correctly twisted native loop (first barrier) and (ii) a rate-limiting free energy barrier that is traversed by two parallel knot-forming routes. The main route corresponds to a slipknot conformation, a collapsed configuration where the C-terminal helix adopts a hairpin-like configuration while threading, and the minor route to an entropically limited plug motion, where the extended terminus is threaded as through a needle. Knot formation is a late transition state process and results show that random (nonspecific) knots are a very rare and unstable set of configurations both at and below folding temperature. Our study shows that a native-biased landscape is sufficient to fold complex topologies and presents a folding mechanism generalizable to all known knotted protein topologies: knotting via threading a native-like loop in a preordered intermediate. PMID:20702769
Multiple folding pathways of proteins with shallow knots and co-translational folding
NASA Astrophysics Data System (ADS)
Chwastyk, Mateusz; Cieplak, Marek
2015-07-01
We study the folding process in the shallowly knotted protein MJ0366 within two variants of a structure-based model. We observe that the resulting topological pathways are much richer than identified in previous studies. In addition to the single knot-loop events, we find novel, and dominant, two-loop mechanisms. We demonstrate that folding takes place in a range of temperatures and the conditions of most successful folding are at temperatures which are higher than those required for the fastest folding. We also demonstrate that nascent conditions are more favorable to knotting than off-ribosome folding.
Multiple folding pathways of proteins with shallow knots and co-translational folding.
Chwastyk, Mateusz; Cieplak, Marek
2015-07-28
We study the folding process in the shallowly knotted protein MJ0366 within two variants of a structure-based model. We observe that the resulting topological pathways are much richer than identified in previous studies. In addition to the single knot-loop events, we find novel, and dominant, two-loop mechanisms. We demonstrate that folding takes place in a range of temperatures and the conditions of most successful folding are at temperatures which are higher than those required for the fastest folding. We also demonstrate that nascent conditions are more favorable to knotting than off-ribosome folding. PMID:26233164
Ball lightning as a force-free magnetic knot
Ranada; Soler; Trueba
2000-11-01
The stability of fireballs in a recent model of ball lightning is studied. It is shown that the balls shine while relaxing in an almost quiescent expansion, and that three effects contribute to their stability: (i) the formation in each one during a process of Taylor relaxation of a force-free magnetic field, a concept introduced in 1954 in order to explain the existence of large magnetic fields and currents in stable configurations of astrophysical plasmas; (ii) the so called Alfven conditions in magnetohydrodynamics; and (iii) the approximate conservation of the helicity integral. The force-free fields that appear are termed "knots" because their magnetic lines are closed and linked. PMID:11102074
Syncytial knots and intervillous bridges in the human placenta: an ultrastructural study.
Jones, C J; Fox, H
1977-11-01
An electron microscopic study has shown that the syncytial knots of the villi of the human placenta contain aggregated nuclei which exhibit marked degenerative changes; within the cytoplasm there is an abundance of cytoplasmic filaments and many stacks of annulate lamellae. It is suggested that syncytial knots are a sequestration phenomenon in which senescent nuclear material is aggregated and removed from metabolically active areas of the syncytiotrophoblast. Intervillous bridges appear to be formed chiefly by fusion of syncytial knots from adjacent villi, and it seems reasonable that the effete material in a syncytial knot should be used for this purpose. The intervillous bridges hava a fine structure which suggests that they have a mechanical function, and this lends support to the theory that they form an internal strut system within the placenta. PMID:591426
New conformational search method using genetic algorithm and knot theory for proteins.
Sakae, Y; Hiroyasu, T; Miki, M; Okamoto, Y
2011-01-01
We have proposed a parallel simulated annealing using genetic crossover as one of powerful conformational search methods, in order to find the global minimum energy structures for protein systems. The simulated annealing using genetic crossover method, which incorporates the attractive features of the simulated annealing and the genetic algorithm, is useful for finding a minimum potential energy conformation of protein systems. However, when we perform simulations by using this method, we often find obviously unnatural stable conformations, which have "knots" of a string of an amino-acid sequence. Therefore, we combined knot theory with our simulated annealing using genetic crossover method in order to avoid the knot conformations from the conformational search space. We applied this improved method to protein G, which has 56 amino acids. As the result, we could perform the simulations, which avoid knot conformations. PMID:21121049
Ileoileal Knot as a Content of Obstructed Hernia: What Are the Odds?
Gopivallabh, Madhusudhan Madihalli; Jaganmaya, Kajekar; Hanumanthaiah, Kunthurdoddi Sanjeevaiah; Babannavar, Prashantha; Crithic, Vilas
2016-01-01
An obstructed inguinal hernia is a common surgical emergency, which presents with a variety of contents like the small intestine, omentum, and colon. Intestinal knotting is a rare entity encountered in surgical practice; it occurs when one coil of intestine wraps around the other and eventually leads to complications such as intestinal obstruction, ischemia, and gangrene. Both conditions are considered surgical emergencies and should be dealt with through appropriate surgical measures forthwith. We report the case of an obstructed inguinal hernia, which, on exploration, showed an ileoileal knot as its content. Ileoileal knotting is a very rare phenomenon and, to the best of our knowledge, such an ileoileal knot as a content of obstructed inguinal hernia has not been reported in the surgical literature so far. PMID:27175047