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We represent in the universal form restricted one-instanton partition function of supersymmetric Yang-Mills theory. It is based on the derivation of universal expressions for quantum dimensions (universal characters) of Cartan powers of adjoint and some other series of irreps of simple Lie algebras. These formulae also provide a proof of formulae for universal quantum dimensions for low-dimensional representations, needed in derivation of universal knot polynomials (i.e. colored Wilson averages of Chern-Simons theory on 3d sphere). As a check of the (complicated) formulae for universal quantum dimensions we prove numerically Deligne's hypothesis on universal characters for symmetric cube of adjoint representation., Comment: 11 pages, Wording improved, Table 4 simplified

The affirmation of the rights in the 1776 and 1789 Declarations favoured the emergence of two important issues, which fuelled and animated the public and legal debate of the following years and became, in turn, claims of capital importance for the construction of the upcoming societies and political communities: the abolition of slavery and the end of women’s upheaval. In both cases, the central knot was the recognition of the fundamental rights’ ownership (starting with those of liberty) for both slaves and women. Nevertheless, although born together, the two claims of liberty were ‘separated at birth’ for ‘gender reasons’.

In this paper, I explain why I have chosen the expression “metaphysical anti-Semitism” to characterize Heidegger’s position in the Black Notebooks. In this context, the strong connection between the question of being and the “Jewish question” is important. My thesis is that Heidegger ties Judaism to metaphysics with a Gordian knot. His ontological, theological, and political accusations against the Jews do not derive from common racism, but from this knot. After 1945, Heidegger does not change his position and does not recognize Germany’s guilt. Yet, the Black Notebooks open a new perspective on his political thought.

The aim of this article is to study the existence of certain reducible, metabelian representations of knot groups into $\mathrm{SL}(n,\mathbf{C})$ which generalize the representations studied previously by G. Burde and G. de Rham. Under specific hypotheses we prove the existence of irreducible deformations of such representations of knot groups into $\mathrm{SL}(n,\mathbf{C})$.

In this short article we investigate the topology of the moduli space of two-convex embedded tori $S^{n-1}\times S^1\subset \mathbb{R}^{n+1}$. We prove that for $n \geq 3$ this moduli space is path-connected, and that for $n = 2$ the connected components of the moduli space are in bijective correspondence with the knot classes associated to the embeddings. Our proof uses a variant of mean curvature flow with surgery developed in our earlier article (arXiv:1607.05604) where neck regions are deformed to tiny strings instead of being cut out completely, an approach which preserves the global topology, embeddedness, as well as two-convexity., Comment: 12 pages

The conormal Lagrangian LK of a knotK in R3 is the submanifold of the cotangent bundle T ∗R3 consisting of covectors along K that annihilate tangent vectors to K. By intersecting with the unit cotangent bundle S∗R3, one obtains the unit conormal ΛK , and the Legendrian contact homology of ΛK is a knot invariant of K, known as knot contact homology. We define a version of string topology for strings in R3 ∪LK and prove that this is isomorphic in degree 0 to knot contact homology. The string topology perspective gives a topological derivation of the cord algebra (also isomorphic to degree 0 knot contact homology) and relates it to the knot group. Together with the isomorphism this gives a new proof that knot contact homology detects the unknot. Our techniques involve a detailed analysis of certain moduli spaces of holomorphic disks in T ∗R3 with boundary on R3 ∪ LK .

We consider a reduction of a knot in a bridge position along two disjoint bridge disks D 1 and D 2 . Suppose that a reduction of the knot along any subset of { D 1 , D 2 } results in a bridge position, where we get two distinct new bridges after the reduction along D 1 ∪ D 2 . We show that there are two disjoint bridge disks E 1 and E 2 such that ( D 1 , E 1 ) and ( D 2 , E 2 ) are cancelling pairs and ( D 1 ∪ E 1 ) ∩ ( D 2 ∪ E 2 ) = ∅ .

The primary cause for the emerging triple axis including China, Russia, and Pakistan in South Asia has been to curtail the Indo-US extended political, economic, and military connections. India in the post-Cold War era tilted significantly toward the West, the move which has been equally ostracized by the triumvirate. Hence, in reprisal, Russia’s recent rapprochement with the duo further solidified the Sino-Pak geostrategic bond. India’s wide-ranging collaboration with the US, primarily in the post-civil nuclear deal, led to the budding fusion of three atomic powers. Under such circumstances, the region has been enticing the major global powers and latterly various extra-regional players exhibited profound interests in the entire South Asia. Therefore, under the formation of power blocks, a new geopolitical great game has been emerging in the region. India, the leading South Asian player, therefore, has been facing an extremely problematic situation while making a balancing choice amongst the two hostile powers, China and the US. Against this backdrop, the study will primarily focus on the rise of South Asian Triple Axis and its possible consequences upon the rising Indo-US strategic leverage.

In the course of 20th-century European history Jews and Arabs, as well as Jews and Muslims, were put in the position of a ‘civilizational’ conflict that is not only political but also quasi-metaphysical. This article examines an impact of the conflict on the attitudes towards anti-Semitism and Islamophobia and considers Islamophobic implications of the ‘new anti-Semitism’ discourse. A thesis of the text is that both the struggle against anti-Semitism and Islamophobia and the one against the mechanism creating, in certain circumstances, a kind of negative feedback loop between them requires not only opposing the anti-Jewish and anti-Muslim prejudices, but also a deep, critical reconsideration of the concepts of Europeanness that lie at their foundation. The author suggests that a good starting point for this reconsideration might be the postcolonial reading of the Jewish intellectual tradition, especially the one focusing on the figure of the Mizrahi Jew.

In this paper, a numerical meshless method for solving the Gilson–Pickering equation is considered. The method is based on thin-plate radial basis function using collocation points. The scheme proposed works in a similar fashion as finite-difference method and a predictor–corrector scheme is proposed to avoid solving the nonlinear system. In addition, we use the super not-a-knot method for improving the accuracy at the boundaries. The results of numerical experiments are compared with the existing results in illustrative examples to confirm the accuracy and efficiency of the presented scheme and the norm of the error functions is obtained to show the convergence of the method.

Jun O’Hara invented a family of knot energies $$E^{j,p}$$ , $$j,p \in (0, \infty )$$ , O’Hara in Topology Hawaii (Honolulu, HI, 1990). World Science Publication, River Edge 1992. We study the negative gradient flow of the sum of one of the energies $$E^\alpha = E^{\alpha ,1}$$ , $$\alpha \in (2,3)$$ , and a positive multiple of the length. Showing that the gradients of these knot energies can be written as the normal part of a quasilinear operator, we derive short time existence results for these flows. We then prove long time existence and convergence to critical points.

Starting with the observation that there exist contradictory claims in the literature about the relationship between vitalism and emergentism—be it one of inclusion or, on the contrary, exclusion–, this paper aims at disentangling the vitalism–emergentism knot. To this purpose, after having described a particular form of emergentism, namely Lloyd Morgan’s emergent evolutionism, I develop a conceptual analysis on the basis of a distinction between varieties of monism and pluralism. This analysis allows me to identify and characterize several forms of vitalism and emergentism, and a subsequent comparison between these forms constitutes the occasion for a clarification of the relationship between both doctrines.

Defining species boundaries is important not only for the appropriate attribution of life history and ecological traits but also for sustainable fishery management and for the conservation of biodiversity. Problems arise from taxonomic uncertainty and incorrect species delineation leading to historical misidentification. This is the case of Pacific guitarfishes in the genus Zapteryx. We use a molecular phylogenetic approach combining mitochondrial and nuclear loci to investigate genetic variation in fish along the Mexican Pacific coast. Our analyses reveal a lack of nuclear and mitochondrial distinction between rays identified morphologically as banded guitarfish Z. exasperata and as southern banded guitarfish Z. xyster, casting doubts on the validity of their current systematics. However, we detected two mitochondrial lineages in accordance with the number of species described for the Pacific: a “northern” lineage corresponding to Z. exasperata and a “southern” lineage possibly attributable to Z. xyster. The poorly understood phenotypic plasticity in coloration and size of the evolutionary lineage of Z. exasperata and its apparently wider than currently thought geographic distribution (at least to Oaxaca) are the major sources of confusion regarding the taxonomic and geographic delineation of these nominal species. In light of our findings, eastern Pacific guitarfishes in the genus Zapteryx require a thorough taxonomic revision using morphological and genetic data to unveil what appears to be a complex pattern of diversification.

The Great War is considered nationally foundational in both Australia and New Zealand. Yet, as critics of this view point out, British subjecthood remained important and sometimes central to identity at this time. This article pulls two threads from this tangled knot of belonging at a time when identifying and regulating loyal populations was critical. Looking at evidence of those Australians and New Zealanders who served in imperial forces and organisations, and the implications of passport control from 1915, I suggest that the relationship between British subjecthood and national identification was not always easily managed, and was often cut across by gender. Indeed, there is evidence that one's identification as a British subject or an Australasian citizen was not always a matter of choice or positive, and sometimes these identities were antagonists. The significant tensions between British subjecthood and being an “Australian” or a “New Zealander” were especially heightened by the increasingly intimate relationship between governments and their people during the First World War.

A killer of a group$G$is an element that normally generates$G$. We show that the group of a cable knot contains infinitely many killers such that no two lie in the same automorphic orbit.

We study $$\mathrm {U}(N|M)$$ character expectation value with the supermatrix Chern–Simons theory, known as the ABJM matrix model, with emphasis on its connection to the knot invariant. This average just gives the half-BPS circular Wilson loop expectation value in ABJM theory, which shall correspond to the unknot invariant. We derive the determinantal formula, which gives $$\mathrm {U}(N|M)$$ character expectation values in terms of $$\mathrm {U}(1|1)$$ averages for a particular type of character representations. This means that the $$\mathrm {U}(1|1)$$ character expectation value is a building block for the $$\mathrm {U}(N|M)$$ averages and also, by an appropriate limit, for the $$\mathrm {U}(N)$$ invariants. In addition to the original model, we introduce another supermatrix model obtained through the symplectic transform, which is motivated by the torus knot Chern–Simons matrix model. We obtain the Rosso–Jones-type formula and the spectral curve for this case.

We consider the question of which Dehn surgeries along a given knot bound rational homology balls. We use Ozsv\'ath and Szab\'o's correction terms in Heegaard Floer homology to obtain general constraints on the surgery coefficients. We then turn our attention to the case of integral surgeries, with particular emphasis on positive torus knots. Finally, combining these results with a lattice-theoretic obstruction based on Donaldon's theorem, we classify which integral surgeries along torus knots of the form $T_{kq\pm 1,q}$ bound rational homology balls., Comment: 32 pages, many figures. Several minor improvements and corrections. Comments are welcome!

A labelled oriented graph (LOG) group is a group given by a presentation constructed in a certain way from a labelled oriented graph: examples include Wirtinger presentations of knot groups. We show how to obtain generators for the Schur Multiplier $$H_2(G)$$ of a LOG group from the underlying LOG, and by exhibiting the n-string braid group $$B_n$$ as a LOG group, we compute $$H_2(B_n)$$ .

These notes provide an introduction to recent work by Kevin Costello in which integrable lattice models of classical statistical mechanics in two dimensions are understood in terms of quantum gauge theory in four dimensions. This construction will be compared to the more familiar relationship between quantum knot invariants in three dimensions and Chern-Simons gauge theory. (Based on a Whittaker Colloquium at the University of Edinburgh and a lecture at Strings 2016 in Beijing.), 20 pp

In this theoretical study we discuss a novel method for sorting ring polymers according to their topological, knotted state. The proposed approach harnesses the rich dynamical behaviour of polymers confined inside spatially-modulated nanochannels. The longitudinal mobility of the rings is shown to have two key properties that are ideally suited for knot sorting. First, at fixed topology, the mobility has an intriguing oscillatory dependence on chain length. Second, the mobility ranking of different knot types is inverted upon increasing the chain length. We show that this complex interplay of channel geometry, chain length and topology can be rationalised within a simple theoretical framework based on Fick-Jacobs's diffusive theory. The results and the interpretative scheme ought to be useful for designing microfluidic devices with optimal topological sorting capabilities.

I study the properties of a preon model for the substructure of the standard model quarks and leptons. The goal is to establish both local and global group representations for the particles of the model. Knot theory algebra SLq(2) is shown to be applicable to the model. Teleparallel gravity is discussed with an interesting result to hadronic physics. A tentative glimpse on quantum gravity is indicated.

We define a deformation of our earlier link homologies for fundamental representations of sl_m. The deformed homology of a link is isomorphic to the deformed homology of the disjoint union of its components. Moreover, there exists a spectral sequence starting with the old homology and converging to this deformed homology., Comment: 19 pages

For a 4-manifold represented by a framed knot in $S^3$, it has been well known that the 4-manifold admits a Stein structure if the framing is less than the maximal Thurston-Bennequin number of the knot. In this paper, we prove either the converse of this fact is false or there exists a compact contractible oriented smooth 4-manifold (with Stein fillable boundary) admitting no Stein structure. Note that an exotic smooth structure on $S^4$ exists if and only if there exists a compact contractible oriented smooth 4-manifold with $S^3$ boundary admitting no Stein structure.

Natality uncovers remnants of Hagar and Sarai’s voices in the news, video-game culture, pre-Christian folklore, medieval, Renaissance and contemporary art, etc.. Hagar and Sarai’s voices coalesce, come undone, lay side by side, stain, mar, beautify, knot, and unknot. And three more voices emerge: Malak, Envy, and the Moon.

This paper considers a set of twisted line segments in 3d such that they form a knot (a closed curve) or a link of two closed curves. Such line segments appear on the boundary of a family of 3d indecomposable polyhedra (like the Schonhardt polyhedron) whose interior cannot be tetrahedralised without additional vertices added. On the other hand, a 3d (non-convex) polyhedron whose boundary contains such line segments may still be decomposable as long as the twist is not too large. It is therefore interesting to consider the question: when there exists a tetrahedralisation contains a given set of knotted or linked line segments? In this paper, we studied a simplified question with the assumption that all vertices of the line segments are in convex position. It is straightforward to show that no tetrahedralisation of 6 vertices (the three-line-segments case) can contain a trefoil knot. Things become interesting when the number of line segments increases. Since it is necessary to create new interior edges to form a tetrahedralisation. We provided a detailed analysis for the case of a set of 4 line segments. This leads to a crucial condition on the orientation of pairs of new interior edges which determines whether this set is decomposable or not. We then prove a new theorem about the decomposability for a set of n ( n ≥ 3) knotted or linked line segments. This theorem implies that the family of polyhedra generalised from the Schonhardt polyhedron by Rambau [1] are all indecomposable.

Furoshiki is an environmentally friendly, Japanese technique for wrapping gifts which will give children the opportunity to test their creative skills and learn about why conventional wrapping paper is bad for the planet.

Silver Jubilee: As Chemistry-A European Journal celebrates its 25th anniversary, Peter Gölitz looks back on the events that led to the founding of the journal. From initial concept through to successful launch, collaborations and co-operations were required to cut the Gordian Knot and make a dream of Jean-Marie Lehn and others come true.

In this issue of Chem, Fujita and co-workers investigate the self-assembly of peptide-based ligands with silver ions. Through selective crystallization they were able to isolate a molecular septafoil knot and a quadruply braided [2]catenane (821 link)—entangled molecules that had, until now, evaded realization.

This study analyzes instrument motion for segments of a defined intra-corporeal suturing task in a laparoscopic simulator. We describe a system providing real-time velocity and acceleration assessment in the performance of this task. Analysis of the deconstructed task segments allows targeted assessment and teaching. A traditional box trainer was fitted with a custom-built motion-tracking system. Participants were stratified into novice, intermediate and expert groups. They performed a defined intra-corporeal suturing task. Real-time data were collected in four degrees of freedom (DOFs) (Roll, Surge, Pitch, Yaw). The task was then deconstructed into four segments: loading needle/pull-through, double-throw knot, first single-throw knot, and second single-throw knot. Motion analysis parameters (MAPs) were studied for each DOF. Sixty-four participants were tested (14 novices, 19 intermediates, 31 experts). The largest difference in MAPs was seen in the ‘double-throw knot’ segment. MAPs for the ‘loading needle/pull-through’ segment revealed differences between novices and experts in Roll and Pitch DOFs only. For the ‘first single knot’ segment, similar MAP trends were noted across all DOFs, with significant differences between novices versus experts and intermediates versus experts. For the ‘second single knot’ segment, the difference in MAPs was preserved only for novices versus experts. By analyzing motion for a defined suturing task in a laparoscopic simulator, we can gain insight into the specific hand motions distinguishing experts from non-experts. Such information may allow teaching in a more focused, effective and efficient manner.

We study 2-adjacency between a 3-strand pretzel link with two components and the trivial link, and whether the trivial knot is 2-adjacent to a pretzel knot. By investigating mainly the coefficients of their Conway polynomials, Jones polynomials and etc., we show that any nontrivial pretzel link with two-components is not 2-adjacent to the trivial link, and vice versa. Moreover, we also show that the trivial knot is not 2-adjacent to any nontrivial pretzel knot.

Stefania Pandolfo’s book, Knot of the Soul, traces a theological cartography of contemporary Morocco. Drawing on decades of ethnographic work, Pandolfo follows the torments and cures of the soul (n...

With the 2017 remaking of the legendary musical, King Kong (1959), and the mainstream media attention it has received, the history of music and theater as “cultural texts” under colonial-apartheid ...

An important conjecture in knot theory relates the large-$N$, double scaling limit of the colored Jones polynomial $J_{K,N}(q)$ of a knot $K$ to the hyperbolic volume of the knot complement, $\text{Vol}(K)$. A less studied question is whether $\text{Vol}(K)$ can be recovered directly from the original Jones polynomial ($N = 2$). In this report we use a deep neural network to approximate $\text{Vol}(K)$ from the Jones polynomial. Our network is robust and correctly predicts the volume with $97.6\%$ accuracy when training on $10\%$ of the data. This points to the existence of a more direct connection between the hyperbolic volume and the Jones polynomial., 18 pages, 9 figures, updated figures

Analogs of Kelvin's “vortex atoms” are realized at microscopic scale in chiral liquid crystals

We show that Ozsv\'ath-Szab\'o's bordered algebra used to efficiently compute knot Floer homology is a graded flat deformation of the regular block of a $\mathfrak{q}$-presentable quotient of parabolic category $\mathcal{O}$. We identify the endomorphism algebra of a minimal projective generator for this block with an explicit quotient of the Ozsv\'ath-Szab\'o algebra using Sartori's diagrammatic formulation of the endomorphism algebra. Both of these algebras give rise to categorifications of tensor products of the vector representation $V^{\otimes n}$ for $U_q(\mathfrak{gl}(1|1))$. Our isomorphism allows us to transport a number of constructions between these two algebras, leading to a new (fully) diagrammatic reinterpretation of Sartori's algebra, new modules over Ozsv\'ath-Szab\'o's algebra lifting various bases of $V^{\otimes n}$, and bimodules over Ozsv\'ath-Szab\'o's algebra categorifying the action of the quantum group element $F$ and its dual on $V^{\otimes n}$., Comment: 36 pages, tikz diagrams

Using region crossing changes, we define a new invariant called the multi-region index of a knot. We prove that the multi-region index of a knot is bounded from above by twice the crossing number of the knot. In addition, we show that the minimum number of generators of the first homology of the double branched cover of $S^3$ over the knot is strictly less than the multi-region index. Our proof of this lower bound uses Goeritz matrices., 13 pages, 12 figures. Added Theorems 4.6 and 4.8. Added computations of multi-region index of ten new knots to the tables at the end of the paper as a result of Theorem 4.8

We formulate and prove a profinite rigidity theorem for the twisted Alexander polynomials up to several types of finite ambiguity. We also establish torsion growth formulas of the twisted homology groups in a $\mathbb{Z}$-cover of a 3-manifold with use of Mahler measures. We examine several examples associated to Riley's parabolic representations of two-bridge knot groups and give a remark on hyperbolic volumes., 19pages; several remarks are inserted (v3), several minor errors are corrected (v4) +3pages; "Erratum" is added at the end (v6)

This article negotiates philosophical and epistemological aspects of technology and its teaching. After identifying the nature of technological knowledge, we unveil a number of constrains that raise demands on epistemologies used to describe its production, transfer and sharing, even without taking into account personal or discipline preferences. Difficulties in teaching the subject of technology, that result both from the multiplicity of forms of technological knowledge and the aforementioned constrains, are identified. Some limitations of existing teaching technologies and their incompatibility with the demands and constrains on using them to impart technological knowledge are investigated. The need for multiple epistemologies is identified, along with the possible spectrum they occupy. Then, the possibility of developing an integrating technology that facilitates designing the teaching of technology by using teaching technologies - as in using the modalities that ICTs offer for teaching - at the same time conforming with subject-appropriate and knowledge-type-appropriate methodologies and, in the end, epistemologies is hinted upon, thus creating a three-level technological problem. Finally, some implications for curricula and instruction are identified and the complexity of the resulting system is pointed out, along with the applicability of systems thinking for handling it.