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An extended endoscopic endonasal approach (EEA) has become standard for parasellar and midline skull base lesions. However, postoperative leakage of cerebrospinal fluid (CSF) can result from dural defects after lesion removal. We present a simple and effective technique, the Osaka sliding knot, to prevent CSF leakage. Between November 2018 and March 2021, a total of 41 patients underwent reconstruction of skull base defects with intraoperative high-flow CSF leaks after extended EEA by using this closure technique, of whom only 1 patient experienced postoperative CSF leakage. This technically simple and efficient method seals the dural defect to prevent CSF leakage after surgeries using an extended EEA.

Background Intestinal knot formation, in which two segments of the intestine become knotted together, can result in intestinal obstruction. An ileo-ileal knot refers to knot formation between two ileal segments and is a very rare benign disease. We report a case of strangulated bowel obstruction caused by true ileo-ileal knot formation. Case presentation An 89-year-old woman was referred to our hospital with the diagnosis of intestinal obstruction. Contrast-enhanced computed tomography revealed the small bowel forming a closed loop, with poor contrast effect. Based on the findings, the patient was diagnosed as having strangulated bowel obstruction, and emergency surgery was performed. At laparotomy, two segments of the ileum were found to be tied together forming a knot, and both segments were necrotic. Although it was necessary to release the strangulated small bowel, we did not immediately release the knot, but first proceeded with ligation of the mesenteric vessels to the strangulated small bowel to prevent dissemination of toxic substances from the necrotic bowel into the systemic circulation. The surgery was completed with resection of the necrotic ileum and anastomosis of the small intestine. The postoperative course was uneventful, and the patient was discharged home. Conclusion We encountered a case of strangulated bowel obstruction caused by true ileo-ileal knot formation. Resection of the necrotic small intestine without releasing the knot could be performed safely, and might be considered as an option of surgical procedure.

Angin merupakan unsur cuaca yang sangat penting dalam keselamatan penerbangan. Penelitian ini bertujuan melakukan analisa profil angin bulanan dan potensi terjadinya Crosswind dalam pembangunan New Yogyakarta International Airport. Metode yang dipakai dengan memasang 4 (empat)buah AWS (Automatic Weather Station) di ujung landasan selama bulan Maret Huingga September 2017. Hasil pengamatan dan analisa menunjukan bahwa pola angin pada periode Maret – Mei memiliki arah yang bervariasi dengan kecepatan rata-rata 5 – 8 knot. Pada Juni – September, pola angin berhembus dari arah Timur – Tenggara dengan kecepatan rata-rata 6 – 9 knot. Selama periode pengamatan kecepatan angin maksimum yang terjadi antara 14 – 20 knot dan tidak ditemukan potensi terjadinya cross wind untuk panjang runway 3.600 meter.

In this paper, we study knot diagrams for which the underlying graph has treewidth two. We give a linear time algorithm for the following problem: given a knot diagram of treewidth two, does it represent the trivial knot? We also show that for a link diagram of treewidth two we can test in linear time if it represents the unlink. From the algorithm, it follows that a diagram of the trivial knot of treewidth 2 can always be reduced to the trivial diagram with at most n untwist and unpoke Reidemeister moves.

This paper describes a method for adding surface details to existing CAD models. Our approach is based on truncated powers, which allows us to align the added details with curved knot lines on the surface. Additionally, (truncated) powers give us precise control over the continuity of the perturbed surface across the (curved) knot lines. Our representation is compatible with current CAD/CAM practise and standards, and we showcase it on several examples.

We define a family of univariate many knot spline spaces of arbitrary degree defined on an initial partition that is refined by adding a point in each sub-interval. For an arbitrary smoothness r , splines of degrees 2 r and 2 r + 1 are considered by imposing additional regularity when necessary. For an arbitrary degree, a B-spline-like basis is constructed by using the Bernstein–Bezier representation. Blossoming is then used to establish a Marsden’s identity from which several quasi-interpolation operators having optimal approximation orders are defined.

The knot is one of the most remarkable topological features identified in an increasing number of proteins with important functions. However, little is known about how the knot is formed during protein folding, and untied or maintained in protein unfolding. By means of all-atom molecular dynamics simulation, here we employ methyltransferase YbeA as the knotted protein model to analyze changes of the knotted conformation coupled with protein unfolding under thermal and mechanical denaturing conditions. Our results show that the trefoil knot in YbeA is occasionally untied via knot loosening rather than sliding under enhanced thermal fluctuations. Through correlating protein unfolding with changes in the knot position and size, several aspects of barriers that jointly suppress knot untying are revealed. In particular, protein unfolding is always prior to knot untying and starts preferentially from separation of two α-helices (α1 and α5), which protect the hydrophobic core consisting of β-sheets (β1–β4) from exposure to water. These β-sheets form a loop through which α5 is threaded to form the knot. Hydrophobic and hydrogen bonding interactions inside the core stabilize the loop against loosening. In addition, residues at N-terminal of α5 define a rigid turning to impede α5 from sliding out of the loop. Site mutations are designed to specifically eliminate these barriers, and easier knot untying is achieved under the same denaturing conditions. These results provide new molecular level insights into the folding/unfolding of knotted proteins.

Growing of vegetable crops under protected conditions are relatively, an innovative technology and most popular among farmers throughout the country. In last few decades protected cultivation has shown potential enhancement in horticultural production. The southern root-knot nematode, Meloidogyne incognita, is an emerging nematode under protected conditions. This nematode can cause chlorosis, stunting and reduce yields associated with the induction of many root galls on host plants. Root-knot nematode severely affect the plant root system by inducing specialized feeding cells i.e., giant cells in the vascular tissues. Recently, this nematode has been considered as a worldwide menace for combat root-knot nematodes, integrated nematode management strategies such as soil solarization, biological control, organic amendment, crop rotation, field sanitation, and fumigants have been developed and successfully used in the past. Here, in this book chapter discussed on biology and life cycle, control measures and proposed future strategies to improve Megalaima incognita management under protected conditions.

Content Translation has been used since 2015 by more than 78,000 editors to create over 800,000 Wikipedia articles. Section Translation aims to bring the option of translation to mobile editors, and can be used to expand existing articles. The session will present a brief history of the research and design process that led to Section Translation, as well as recent research done on the experiences of early adopters. It will conclude with a short demo of Section Translation.

We propose a definition of persistent Stiefel-Whitney classes of vector bundle filtrations. It relies on seeing vector bundles as subsets of some Euclidean spaces. The usual \v{C}ech filtration of such a subset can be endowed with a vector bundle structure, that we call a \v{C}ech bundle filtration. We show that this construction is stable and consistent. When the dataset is a finite sample of a line bundle, we implement an effective algorithm to compute its persistent Stiefel-Whitney classes. In order to use simplicial approximation techniques in practice, we develop a notion of weak simplicial approximation. As a theoretical example, we give an in-depth study of the normal bundle of the circle, which reduces to understanding the persistent cohomology of the torus knot (1,2). We illustrate our method on several datasets inspired by image analysis., Comment: To appear in Journal of Applied and Computational Topology

Approximately 1 decade ago, Brew and Cysique1 in their compelling editorial addressed the need for conducting further studies of amyloid metabolism in aged people living with HIV. They also noted the need for future research to provide tools capable of identifying the causes of HIV-associated neurocognitive disorder (HAND) within the context of successful highly active antiretroviral therapy (HAART). Alisky in 20072 had accurately predicted that successful treatment with HAART in the HIV population means more long-term survivors and an aging HIV population vulnerable to develop Alzheimer disease (AD).

The topological framework of circuit topology has recently been introduced to complement knot theory and to help in understanding the physics of molecular folding. Naturally evolved linear molecular chains, such as proteins and nucleic acids, often fold into 3D conformations with critical chain entanglements and local or global structural symmetries stabilised by formation contacts between different parts of the chain. Circuit topology captures the arrangements of intra-chain contacts within a given folded linear chain and allows for the classification and comparison of chains. Contacts keep chain segments in physical proximity and can be either mechanically hard attachments or soft entanglements that constrain a physical chain. Contrary to knot theory, which offers many established knot invariants, circuit invariants are just being developed. Here, we present polynomial invariants that are both efficient and sufficiently powerful to deal with any combination of soft and hard contacts. A computer implementation and table of chains with up to three contacts is also provided.

The debate on religious minority rights has long been stranded in the shallows of a sterile juxtaposition between the politics of sameness and the politics of difference [...]

A highly enantioselective protocol has been recently described as allowing the synthesis of five-membered cyclic imines harnessing the selective generation of a β-Csp3-centered radical of acyl heterocyclic derivatives and its subsequent interaction with diverse NH-ketimines. The overall transformation represents a novel cascade process strategy crafted by individual well-known steps, however, the construction of the new C-C bond highlights a crucial knot from a mechanistically perspective. We believe that the full understanding of this enigmatic step may enrich the current literature and expand latent future ideas. Therefore, a detailed mechanistic study of the protocol has been conducted. Here, we provide theoretical insight into the mechanism using quantum chemistry calculations. Two possible pathways have been investigated: (a) imine reduction followed by radical–radical coupling and (b) radical addition followed by product reduction. In addition, investigations to unveil the origin behind the enantioselectivity of the 1-pyrroline derivatives have been conducted as well.

Cor‐Knot fastener use in sternotomy‐based aortic arch procedures has not been reported. We present Cor‐Knot fastener use over a Hegar dilator in an anatomically challenging total aortic arch replacement with no short‐term and/or long‐term complications.

Background Although most epidural catheter knot formation has been reported in lumbar epidural catheter placement, knot formation in a thoracic epidural catheter has been experienced. Case presentation A 72-year-old woman was scheduled for laparoscopic cholecystectomy under general anesthesia combined with epidural anesthesia. The epidural catheter was inserted through the Th10–Th11 intervertebral space and was placed 7 cm into the epidural space. Two days after the surgery, the anesthesiologist was called because of difficulty in removing the epidural catheter. The catheter was eventually removed when the anesthesiologist carefully pulled it while strongly bending the patient’s body to the right, although resistance was still noted. The removed catheter was observed to have a hard single knot formed at about 3 mm from the tip. Conclusions A knot formation of an epidural catheter placed at the thoracic level was experienced. Limiting the length of catheter placement may prevent knot formation.

The topological classification of nodal links and knot has enamored physicists and mathematicians alike, both for its mathematical elegance and implications on optical and transport phenomena. Central to this pursuit is the Seifert surface bounding the link/knot, which has for long remained a mathematical abstraction. Here we propose an experimentally realistic setup where Seifert surfaces emerge as boundary states of 4D topological systems constructed by stacking 3D nodal line systems along a 4th quasimomentum. We provide an explicit realization with 4D circuit lattices, which are freed from symmetry constraints and are readily tunable due to the dimension and distance agnostic nature of circuit connections. Importantly, their Seifert surfaces can be imaged in 3D via their pronounced impedance peaks, and are directly related to knot invariants like the Alexander polynomial and knot Signature. This work thus unleashes the great potential of Seifert surfaces as sophisticated yet accessible tools in exotic bandstructure studies. Although characterizing the Seifert surface is central to the realization of novel phases in topological materials, this has been a purely mathematical construction so far. This paper proposes an experimentally realistic scheme for the realization and imaging of 4D-embedded Seifert surfaces, opening up a way for experimental topological characterization

For centuries, Kurds have been carrying out activities aimed at obtaining their own state. Due to the cooperation of Turkey, Iraq, Iran and Syria, it was impossible in the twentieth century. As a result of Operation Desert Storm, a Kurdish enclave was created in the north of Iraq, which over the years developed and allowed for real dreams of recognized independence, at least for some of the Kurds living in the Middle East. A&er the overthrow of Saddam Hussein and the withdrawal of US troops from Iraq in 2011, there was a political vacuum in which we observe the weakening of the Iraqi state, the outbreak of the Arab Spring and the emergence of the Islamic State, which also had direct consequences for the Kurds. The weakness of the central government in Baghdad, the need to fight the Kurdish army against IS fighters raised the importance of arguments for the proclamation of an independent Kurdish state in the Middle East, or maybe even two, including the possible division of Syria.

Background The closure of high-tension incisions without any assistance can be difficult and challenging for surgeons. A common practice is to fix the first knot with a clamp and then tie a reverse locking knot; however, this practice has certain disadvantages. The aim of this study was to introduce a novel and efficient surgical knotting technique with various advantages. Methods The two knotting methods used in this study were the absorbable braided suture where the first suture was fixed with a clamp (with assistance) and the SH-9Hospital knotting technique (without assistance) applied on the smooth surface of a cylinder. Mechanical testing was performed using a universal material testing machine. The load-elongation curve and ultimate tensile load (UTL) were recorded. Results The mean knotting time was 36.40±1.50 s (range, 32-41 s) and 24.80±1.16 s (range, 21-28 s) in the clamp and SH-9Hosptial groups, respectively. The mean UTL was 120.8±10.14 N (range, 81.11-136.55 N)and 126.5±6.29 N (range, 104.88-139.56 N) in the clamp and SH-9Hospital groups, respectively. The knot strength of the SH-9Hospital technique was not inferior to traditional clinical practice. Conclusions The SH-9Hospital knotting technique was a secure, convenient, and efficient method for high-tension closure.

We present ALMA $^{12}$CO (2-1), $^{13}$CO (2-1), C$^{18}$O (2-1) molecular line observations of a very young proto-brown dwarf system, ISO-OPH 200. We have conducted physical+chemical modelling of the complex internal structure for this system using the core collapse simulations for brown dwarf formation. The model at an age of $\sim$6000 yr can provide a good fit to the observed kinematics, spectra, and reproduce the complex structures seen in the moment maps. Results from modelling indicate that $^{12}$CO emission is tracing an extended ($\sim$1000 au) molecular outflow and a bright shock knot, $^{13}$CO is tracing the outer ($\sim$1000 au) envelope/pseudo-disc, and C$^{18}$O is tracing the inner ($\sim$500 au) pseudo-disc. The source size of $\sim$8.6 au measured in the 873$\mu$m image is comparable to the inner Keplerian disc size predicted by the model. A 3D model structure of ISO-OPH 200 suggests that this system is viewed partially through a wide outflow cavity resulting in a direct view of the outflow and a partial view of the envelope/pseudo-disc. We have argued that ISO-OPH 200 has been mis-classified as a Class Flat object due to the unusual orientation. The various signatures of this system, notably, the young $\sim$616 yr outflow dynamical age and high outflow rate ($\sim$1$\times$10$^{-7}$ M$_{\odot}$ yr$^{-1}$), silicate absorption in the 10$\mu$m mid-infrared spectrum, pristine ISM-like dust in the envelope/disc, comparable sizes of the extended envelope and outflow, indicate that ISO-OPH 200 is an early Class 0 stage system formed in a star-like mechanism via gravitational collapse of a very low-mass core., Comment: Accepted in MNRAS

Aim: Loosing of cerclage wire is a common problem in the fixation of fractures and alternative techniques are required to provide more strength cable systems. The aim of this study was to evaluate the benefit of an additional knot to the cable system to increase durability and strength of wire

A Kakeya set $\mathcal{K}$ in an affine plane of order $q$ is the point set covered by a set $\mathcal{L}$ of $q+1$ pairwise non-parallel lines. Large Kakeya sets were studied by Dover and Mellinger; in [6] they showed that Kakeya sets with size at least $q^2-3q+9$ contain a large knot (a point of $\mathcal{K}$ lying on many lines of $\mathcal{L}$). In this paper, we improve on this result by showing that Kakeya set of size at least $\approx q^2-q\sqrt{q}+\frac{3}{2}q$ contain a large knot. Furthermore, we obtain a sharp result for planes of square order containing a Baer subplane., To appear in Advances in Geometry

We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids. We focus on capsules and vesicles, whose discretization is particularly challenging due to the higher-order derivatives that appear in their formulations. In two-dimensional settings, we employ cubic B-splines with periodic knot vectors to obtain discretizations of closed curves with C^2 inter-element continuity. In three-dimensional settings, we use analysis-suitable bi-cubic T-splines to obtain discretizations of closed surfaces with at least C^1 inter-element continuity. Large spurious changes of the fluid volume inside closed co-dimension one solids is a well-known issue for IB methods. The DCIB method results in volume changes orders of magnitude lower than conventional IB methods. This is a byproduct of discretizing the velocity-pressure pair with divergence-conforming B-splines, which lead to negligible incompressibility errors at the Eulerian level. The higher inter-element continuity of divergence-conforming B-splines is also crucial to avoid the quadrature/interpolation errors of IB methods becoming the dominant discretization error. Benchmark and application problems of vesicle and capsule dynamics are solved, including mesh-independence studies and comparisons with other numerical methods., For supplementary movies go to https://www.andrew.cmu.edu/user/hugocp/research.html

We give simple homological conditions for a rational homology 3-sphere Y to have infinite order in the rational homology cobordism group, and for a collection of rational homology spheres to be linearly independent. These translate immediately to statements about knot concordance when Y is the branched double cover of a knot, recovering some results of Livingston and Naik. The statements depend only on the homology groups of the 3-manifolds, but are proven through an analysis of correction terms and their behavior under connected sums., 12 pages. To appear in J. Inst. Math. Jussieu

The trace of the -framed surgery on a knot in is a 4-manifold homotopy equivalent to the 2-sphere. We characterise when a generator of the second homotopy group of such a manifold can be realised by a locally flat embedded -sphere whose complement has abelian fundamental group. Our characterisation is in terms of classical and computable -dimensional knot invariants. For each, this provides conditions that imply a knot is topologically -shake slice, directly analogous to the result of Freedman and Quinn that a knot with trivial Alexander polynomial is topologically slice., Compositio Mathematica, 157 (10), ISSN:0010-437X, ISSN:1570-5846

Background Amyotrophic lateral sclerosis (ALS) is a universally fatal neurodegenerative disease. ALS is determined by gene-environment interactions and improved understanding of these interactions may lead to effective personalised medicine. The role of physical exercise in the development of ALS is currently controversial. Methods First, we dissected the exercise-ALS relationship in a series of two-sample Mendelian randomisation (MR) experiments. Next we tested for enrichment of ALS genetic risk within exercise-associated transcriptome changes. Finally, we applied a validated physical activity questionnaire in a small cohort of genetically selected ALS patients. Findings We present MR evidence supporting a causal relationship between genetic liability to frequent and strenuous leisure-time exercise and ALS using a liberal instrument (multiplicative random effects IVW, p=0.01). Transcriptomic analysis revealed that genes with altered expression in response to acute exercise are enriched with known ALS risk genes (permutation test, p=0.013) including C9ORF72, and with ALS-associated rare variants of uncertain significance. Questionnaire evidence revealed that age of onset is inversely proportional to historical physical activity for C9ORF72-ALS (Cox proportional hazards model, Wald test p=0.007, likelihood ratio test p=0.01, concordance=74%) but not for non-C9ORF72-ALS. Variability in average physical activity was lower in C9ORF72-ALS compared to both non-C9ORF72-ALS (F-test, p=0.002) and neurologically normal controls (F-test, p=0.049) which is consistent with a homogeneous effect of physical activity in all C9ORF72-ALS patients. Interpretation Our MR approach suggests a positive causal relationship between ALS and physical exercise. Exercise is likely to cause motor neuron injury only in patients with a risk-genotype. Consistent with this we have shown that ALS risk genes are activated in response to exercise. In particular, we propose that G4C2-repeat expansion of C9ORF72 predisposes to exercise-induced ALS. Funding We acknowledge support from the Wellcome Trust (JCK, 216596/Z/19/Z), NIHR (PJS, NF-SI-0617-10077; IS-BRC-1215-20017) and NIH (MPS, CEGS 5P50HG00773504, 1P50HL083800, 1R01HL101388, 1R01-HL122939, S10OD025212, P30DK116074, and UM1HG009442).

We show that any two bridge positions of a handlebody-knot are stably equivalent., 14 pages, 18 figures

We consider 32 homotopy classifications of knot projections (images of generic immersions from a circle into a 2-sphere). These 32 equivalence relations are obtained based on which moves are forbidden among the five type of Reidemeister moves. We show that 32 cases contain 20 non-trivial cases that are mutually different. To complete the proof, we obtain new tools, i.e., new invariants., 11 pages, 13 figures

The Gukov-Manolescu series, denoted by $F_K$, is a conjectural invariant of knot complements that, in a sense, analytically continues the colored Jones polynomials. In this paper we use the large color $R$-matrix to study $F_K$ for some simple links. Specifically, we give a definition of $F_K$ for positive braid knots, and compute $F_K$ for various knots and links. As a corollary, we present a class of `strange identities' for positive braid knots., 27 pages, 13 figures. v2 minor corrections

In 2001, \"Ostlund formulated the question: are Reidemeister moves of types 1 and 3 sufficient to describe a homotopy from any generic immersion of a circle in a two-dimensional plane to an embedding of the circle? The positive answer to this question was treated as a conjecture (\"Ostlund conjecture). In 2014, Hagge and Yazinski disproved the conjecture by showing the first counterexample with a minimal crossing number of 16. This example is naturally extended to counterexamples with given even minimal crossing numbers more than 14. This paper obtains the first counterexample with a minimal crossing number of 15. This example is naturally extended to counterexamples with given odd minimal crossing numbers more than 13., Comment: 8 pages, 14 figures

Link/knot invariants are series with integer coefficients, and it is a long-standing problem to get them positive and possessing cohomological interpretation. Constructing positive "superpolynomials" is not straightforward, especially for colored invariants. A simpler alternative is a multi-parametric generalization of the character expansion, which leads to colored "hyperpolynomials". The third construction involves branes on resolved conifolds, which gives rise to still another family of invariants associated with composite representations. We revisit this triality issue in the simple case of the Hopf link and discover a previously overlooked way to produce positive colored superpolynomials from the DIM-governed four-point functions, thus paving a way to a new relation between super- and hyperpolynomials., Comment: 12 pages

We define the affinization of an arbitrary monoidal category $\mathcal{C}$, corresponding to the category of $\mathcal{C}$-diagrams on the cylinder. We also give an alternative characterization in terms of adjoining dot generators to $\mathcal{C}$. The affinization formalizes and unifies many constructions appearing in the literature. In particular, we describe a large number of examples coming from Hecke-type algebras, braids, tangles, and knot invariants. When $\mathcal{C}$ is rigid, its affinization is isomorphic to its horizontal trace, although the two definitions look quite different. In general, the affinization and the horizontal trace are not isomorphic., 32 pages; v2: minor corrections, published version

Monte Carlo simulations are used to study the conformational behavior of a semiflexible polymer confined to cylindrical and conical channels. The channels are sufficiently narrow that the conditions for the Odijk regime are marginally satisfied. For cylindrical confinement, we examine polymers with a single knot of topology $3_1$, $4_1$, or $5_1$, as well as unknotted polymers that are capable of forming S-loops. We measure the variation of the free energy $F$ with the end-to-end polymer extension length $X$ and examine the effect of varying the polymer topology, persistence length $P$ and cylinder diameter $D$ on the free energy functions. Similarly, we characterize the behavior of the knot span along the channel. We find that increasing the knot complexity increases the typical size of the knot. In the regime of low $X$, where the knot/S-loop size is large, the conformational behavior is independent of polymer topology. In addition, the scaling properties of the free energy and knot span are in agreement with predictions from a theoretical model constructed using known properties of interacting polymers in the Odijk regime. We also examine the variation of $F$ with position of a knot in conical channels for various values of the cone angle $\alpha$. The free energy decreases as the knot moves in a direction where the cone widens, and it also decreases with increasing $\alpha$ and with increasing knot complexity. The behavior is in agreement with predictions from a theoretical model in which the dominant contribution to the change in $F$ is the change in the size of the hairpins as the knot moves to the wider region of the channel., Comment: 15 pages, 11 figures, supplemental information

We consider a large class of q-series that have the structure of Nahm sums, or equivalently motivic generating series for quivers. First, we initiate a systematic analysis and classification of classical and quantum A-polynomials associated to such q-series. These quantum quiver A-polynomials encode recursion relations satisfied by the above series, while classical A-polynomials encode asymptotic expansion of those series. Second, we postulate that those series, as well as their quantum quiver A-polynomials, can be reconstructed by means of the topological recursion. There is a large class of interesting quiver A-polynomials of genus zero, and for a number of them we confirm the above conjecture by explicit calculations. In view of recently found dualities, for an appropriate choice of quivers, these results have a direct interpretation in topological string theory, knot theory, counting of lattice paths, and related topics. In particular it follows, that various quantities characterizing those systems, such as motivic Donaldson-Thomas invariants, various knot invariants, etc., have the structure compatible with the topological recursion and can be reconstructed by its means.

We argue that the usual Bloch sphere is insufficient in various aspects for the representation of qubits in quantum information theory. For example, spin flip operations with the quaternions I J K = e 2 &pi, i 2 = &minus, 1 and J I K = + 1 cannot be distinguished on the Bloch sphere. We show that a simple knot theoretic extension of the Bloch sphere representation is sufficient to track all unitary operations for single qubits. Next, we extend the Bloch sphere representation to entangled states using knot theory. As applications, we first discuss contextuality in quantum physics&mdash, in particular the Kochen-Specker theorem. Finally, we discuss some arguments against many-worlds theories within our knot theoretic model of entanglement. The key ingredients of our approach are symmetries and geometric properties of the unitary group.

Letting $C$ be a compact $C^\omega$-curve embedded in $\boldsymbol R^3$ ($C^\omega$ means real analyticity), we consider a $C^\omega$-cuspidal edge $f$ along $C$. When $C$ is non-closed, in the authors' previous works, the local existence of three distinct cuspidal edges along $C$ whose first fundamental forms coincide with that of $f$ was shown, under a certain reasonable assumption on $f$. In this paper, if $C$ is closed, that is, $C$ is a knot, we show that there exist infinitely many cuspidal edges along $C$ having the same first fundamental form as that of $f$ such that their images are non-congruent to each other, in general., Comment: 12 pages, 2 figures

Given a knot in the three-sphere, is it possible to unknot it by performing a single twist, and if so, what are the possible linking numbers of such a twist? We develop obstructions to unknotting using a twist of a specified linking number. The obstructions we describe are built using classical knot invariants, Casson-Gordon invariants, and Heegaard Floer theory., 26 pages, 4 figures

We study random knotting by considering knot and link diagrams as decorated, (rooted) topological maps on spheres and sampling them with the counting measure on from sets of a fixed number of vertices n. We prove that random rooted knot diagrams are highly composite and hence almost surely knotted (this is the analogue of the Frisch-Wasserman-Delbruck conjecture) and extend this to unrooted knot diagrams by showing that almost all knot diagrams are asymmetric. The model is similar to one of Dunfield, et al.

In this paper, we obtain the necessary and sufficient condition that two knot projections are related by a finite sequence of the first and second flat Reidemeister moves (Theorem 1). We also consider an equivalence relation that is called weak (1, 3) homotopy. This equivalence relation occurs by the first flat Reidemeister move and one of the third flat Reidemeister moves. We introduce a map sending weak (1, 3) homotopy classes to knot isotopy classes (Sec. 3). Using the map, we determine which knot projections are trivialized under weak (1, 3) homotopy (Corollary 3)., 13 pages, 25 figures

A quandle is an algebra with two binary operations satisfying three conditions which are related to Reidemeister moves in knot theory. In this paper we introduce the notion of the (canonical) tensor product of a quandle. The tensor product of the knot quandle or the knot symmetric quandle of a surface-link in 4-space can be used to classify or construct invariants of 1-handles attaching to the surface-link. We also compute the tensor products for dihedral quandles and their symmetric doubles.

We employ a recently developed method for constructing rational electromagnetic field configurations in Minkowski space to investigate several properties of these source-free finite-action Maxwell ("knot") solutions. The construction takes place on the Penrose diagram but uses features of de Sitter space, in particular its isometry group. This admits a classification of all knot solutions in terms of $S^3$ harmonics, labelled by a spin $2j\in{\mathbb N}_0$, which in fact provides a complete "knot basis" of finite-action Maxwell fields. We display a $j{=}1$ example, compute the energy for arbitrary spin-$j$ configurations, derive a linear relation between spin and helicity and characterize the subspace of null fields. Finally, we present an expression for the electromagnetic flux at null infinity and demonstrate its equality with the total energy., 1+14 pages LaTeX, 4 figures in 6 parts; v2: additional j=1 knot solution, discussion and illustration of energy densitites and field lines, 3 more refs., published in PLA

We present a new conjectural symmetry of the colored Alexander polynomial, that is the specialization of the quantum $$\mathfrak {sl}_N$$ invariant widely known as the colored HOMFLY-PT polynomial. We provide arguments in support of the existence of the symmetry by studying the loop expansion and the character expansion of the colored HOMFLY-PT polynomial. We study the constraints this symmetry imposes on the group theoretic structure of the loop expansion and provide solutions to those constraints. The symmetry is a powerful tool for research on polynomial knot invariants and in the end we suggest several possible applications of the symmetry.

Spór Cypryjski jest jednym z najważniejszych zagadnień w tureckiej polityce zagranicznej od lat pięćdziesiątych. Jest on przeważnie postrzegany jako sprawa ponad podziałami politycznymi, i prawie wszystkie tureckie partie polityczne popierają zaangażowanie państwa tureckiego na Cyprze od lat sześćdziesiątych i od Cypryjskiej Operacji Pokojowej w 1974 roku. Jednakże, po tym jak Partia AK (Partia Sprawiedliwości i Rozwoju) doszła do władzy w 2002 roku, z głównym motywem zapobieżenia świeckiego narodowego zamachu stanu, jak również mając na celu osiągnięcie pełnego członkostwa w Unii Europejskiej, partia ta przyjęła pro-aktywną politykę zagraniczną sprzyjającą rozładowaniu sytuacji na tej wyspie. Właśnie dlatego Turcja i tureccy Cypryjczycy aktywnie poparli referendum w ramach planu Annana w 2004 roku. Jednakże, po odrzuceniu planu ugody przez greckich Cypryjczyków, i po decyzji Unii Europejskiej o zaakceptowaniu rządu grecko-cypryjskiego jako członka UE i jedynego reprezentanta Republiki Cypru w tej wspólnocie, Spór Cypryjski stał się problemem, psującym stosunki nie tylko turecko-cypryjskie i grecko-cypryjskie, ale również te pomiędzy Turcją a Unią Europejską. W 2010 roku, wraz z odkryciem złóż gazu ziemnego i porozumieniami zawartymi przez administrację grecko-cypryjską, Spór Cypryjski nabrał nowego wymiaru. Jak dotąd polityka energetyczna nie mogła być użyta jako instrument w promowaniu rozwiązania na wyspie, tymczasem spór przekształcił się w o wiele bardziej skomplikowany problem, z wieloma wymiarami. Cyprus Dispute is one of the fundamental foreign policy issues in Turkish foreign policy since the 1950s. Cyprus Dispute has often been perceived as an issue above petty politics in Turkey, and almost all Turkish political parties supported the Turkish State’s involvement in Cyprus since the 1960s and Cyprus Peace Operation in 1974. However, after AK Party came to power in 2002, with the main motive of preventing a secular nationalist military coup, as well as with the aim of becoming a full member of the European Union (EU), the party adopted a proactive foreign policy favoring the solution in the island. That is why Turkey and Turkish Cypriots actively supported the Annan Plan referendum in 2004. However, upon the rejection of the settlement plan by Greek Cypriots and EU’s decision to accept Greek Cypriot government as an EU member and the only representative of the Cyprus Republic, Cyprus Dispute has transformed into a problem spoiling not only Turkish-Greek and Turkish-Cypriot relations but also Turkish-EU relations. In the 2010s, the Cyprus Dispute gained a new dimension with the gas discoveries and agreements made by the Greek Cypriot administration. So far, energy politics could not be used as a leverage to promote the solution on the island, and the dispute has transformed into a more complex problem with many layers.

In this paper we present new approximation schemes based on both quasi-interpolation and multilevel methods by using bivariate quadratic B-spline functions, defined on simple and multiple knot type-2 triangulations, improving the classical quasi-interpolating spline results. We also prove polynomial reproduction, optimal approximation order and propose some numerical results and applications.

The AJ Conjecture relates a quantum invariant, a minimal order recursion for the colored Jones polynomial of a knot (known as the $\hat{A}$ polynomial), with a classical invariant, namely the defining polynomial $A$ of the $\psl$ character variety of a knot. More precisely, the AJ Conjecture asserts that the set of irreducible factors of the $\hat{A}$-polynomial (after we set $q=1$, and excluding those of $L$-degree zero) coincides with those of the $A$-polynomial. In this paper, we introduce a version of the $\hat{A}$-polynomial that depends on a planar diagram of a knot (that conjecturally agrees with the $\hat{A}$-polynomial) and we prove that it satisfies one direction of the AJ Conjecture. Our proof uses the octahedral decomposition of a knot complement obtained from a planar projection of a knot, the $R$-matrix state sum formula for the colored Jones polynomial, and its certificate., Comment: 34 pages, 12 figures

International audience; Fossil deposits are a tangle of multiple signals that make understanding the functioning of past ecosystems a complicated and fraught process. The main difficulty is whether differences between fossil sites show an evolutionary or ecological signal, or are influenced by fossil preservation. These processes are not independent, as anatomical or behavioral differences can alter preservational pathways. It is particularly important to untangle these interacting processes when examining the animal communities of the Cambrian Explosion and Ordovician Radiation, where exceptional preservation of soft tissues provides relatively complete assemblage data. A novel method of data partitioning based on probabilistic modelling is used to examine these factors with respect to The Walcott Quarry, Burgess Shale, Canada (510Ma) and the Fezouata Shale, Morocco (c. 475Ma). As the prototypical Burgess Shale-type locality, the Walcott Quarry, is usually used as a basis for understanding Cambrian community structure and early ecosystem evolution. The result of probabilistic modelling shows that the Walcott Quarry biota best preserves the endobenthic community whilst systematically under-representing the nekton/plankton. The reverse is true for the Fezouata biota, with under-representation of the endobenthos. Taken in concert with data from a bioturbation index for these sites, a new model of comparative taphonomy is developed based on sedimentary input timing with respect to organism mortality. These results suggest that during the Cambrian Explosion and Ordovician Radiation the most exceptional fossils sites must still be calibrated against each other to understand the unfolding evolutionary events and ecosystem structures.

This article is a response to Peter Dahlgren’s review of The discursive-material knot: Cyprus in conflict and community media participation. Dahlgren’s engagement with the DMK book consisted of four questions, with an invitation to respond to them. These questions were not so much critiques, but more like invitations to clarify, and – more importantly – to expand into a few territories that were insufficiently addressed in the DMK book. This article starts with explaining the platform structure of the DMK book and the strategy that was used to write it. This then allows to focus on the first platform, explaining the basics of the DMK, the supporting role of the structure/agency dimension, and the difference between the concepts of ideology and discourse. This is also a good opportunity to think through the opportunities for (hegemonic) discourse critique. In the next part, the issues related to high theory, ontology and metaphysics are addressed. The last part returns to the DMK book’s case study and the interdependence of the different platforms, arguing that empirical research can also feed into non-essentialist ontological reflections, while these reflections also provide support for the research itself.

Let $S$ be a compact oriented finite dimensional manifold and $M$ a finite dimensional Riemannian manifold, let ${\rm Imm}_f(S,M)$ the space of all free immersions $\varphi:S \to M$ and let $B^+_{i,f}(S,M)$ the quotient space ${\rm Imm}_f(S,M)/{\rm Diff}^+(S)$, where ${\rm Diff}^+(S)$ denotes the group of orientation preserving diffeomorphisms of $S$. In this paper we prove that if $M$ admits a parallel $r$-fold vector cross product $\varphi \in \Omega ^r(M, TM)$ and $\dim S = r-1$ then $B^+_{i,f}(S,M)$ is a formally K\"ahler manifold. This generalizes Brylinski's, LeBrun's and Verbitsky's results for the case that $S$ is a codimension 2 submanifold in $M$, and $S = S^1$ or $M$ is a torsion-free $G_2$-manifold respectively., Comment: 18p version 2: 18p. final version, accepted for Journal of Symplectic Geometry

Recently, the first named author defined a 2-parametric family of groups [Formula: see text] [V. O. Manturov, Non–reidemeister knot theory and its applications in dynamical systems, geometry and topology, preprint (2015), arXiv:1501.05208]. Those groups may be regarded as analogues of braid groups. Study of the connection between the groups [Formula: see text] and dynamical systems led to the discovery of the following fundamental principle: “If dynamical systems describing the motion of [Formula: see text] particles possess a nice codimension one property governed by exactly [Formula: see text] particles, then these dynamical systems admit a topological invariant valued in [Formula: see text]”. The [Formula: see text] groups have connections to different algebraic structures, Coxeter groups, Kirillov-Fomin algebras, and cluster algebras, to name three. Study of the [Formula: see text] groups led to, in particular, the construction of invariants, valued in free products of cyclic groups. All generators of the [Formula: see text] groups are reflections which make them similar to Coxeter groups and not to braid groups. Nevertheless, there are many ways to enhance [Formula: see text] groups to get rid of this [Formula: see text]-torsion. Later the first and the fourth named authors introduced and studied the second family of groups, denoted by [Formula: see text], which are closely related to triangulations of manifolds. The spaces of triangulations of a given manifolds have been widely studied. The celebrated theorem of Pachner [P.L. homeomorphic manifolds are equivalent by elementary shellings, Europ. J. Combin. 12(2) (1991) 129–145] says that any two triangulations of a given manifold can be connected by a sequence of bistellar moves or Pachner moves. See also [I. M. Gelfand, M. M. Kapranov and A. V. Zelevinsky, Discriminants, Resultants, and Multidimensional Determinants (Birkhäuser, Boston, 1994); A. Nabutovsky, Fundamental group and contractible closed geodesics, Comm. Pure Appl. Math. 49(12) (1996) 1257–1270]; the [Formula: see text] naturally appear when considering the set of triangulations with the fixed number of points. There are two ways of introducing the groups [Formula: see text]: the geometrical one, which depends on the metric, and the topological one. The second one can be thought of as a “braid group” of the manifold and, by definition, is an invariant of the topological type of manifold; in a similar way, one can construct the smooth version. In this paper, we give a survey of the ideas lying in the foundation of the [Formula: see text] and [Formula: see text] theories and give an overview of recent results in the study of those groups, manifolds, dynamical systems, knot and braid theories.